1. Introduction
A variable and changing climate presents significant challenges to
the functioning and/or performance of both natural and engineered
systems. Managed systems—both engineered and managed natural
systems—traditionally have been designed under the assumption that
future climate conditions will mirror those experienced in the past. Yet
with the continuing advance of climate change, there is a need to
understand how systems might perform under a range of plausible future
climate conditions or, conversely, what system interventions might be
required so that systems continue to achieve desired levels of
performance. Given the complexity of most climate-sensitive systems,
formalised approaches are required to understand likely climate impacts
and evaluate the viability of adaptive measures to minimise climate
vulnerability.
To this end, scenario-neutral (or ‘bottom-up’) approaches (Prudhomme
et al. 2010, Brown 2011, Culley et al. 2016) are advocated as a means of
rigorously stress testing a system under a range of plausible future
climate conditions. These approaches treat the system’s behaviour and
performance as the central concerns of the analysis, and enable better
understanding of the complex climate-system relationships to support
adaptation decision making. These approaches can be combined with
‘top-down’ climate impact assessment methods through the integration of
projections from climate models and/or other lines of evidence. The
foreSIGHT package contains functions that support both
‘bottom-up’ system stress testing, and the analysis of the implication
of ‘top-down’ climate projections on system performance.
This vignette demonstrates the options available for climate
‘stress-testing’ a system using foreSIGHT by applying the
inverse approach (Guo et al. 2018) to optimise the parameters of one or
more stochastic weather generators. The examples in this vignette both
collate—and provide context to—information scattered in the function
help files to discuss the considerations for application of
foreSIGHT to more complex case studies and systems. It is
assumed that the reader is familiar with the basic work flow of the
package functions as has been demonstrated in the Quick Start
Guide vignette.
1.1. Objectives and application areas of foreSIGHT
The objectives of foreSIGHT are to support climate impact
and vulnerability assessments and the assessment of adaptation options
by:
- stress testing climate-sensitive systems, including both ‘current’
system configurations, as well as potential alternative system
configurations that may be considered as part of the development of
adaptation strategies;
- comparing the climate sensitivity of multiple alternative system
configurations to inform adaptation decision making; and
- comparing stress-testing outcomes with the results from ‘top-down’
climate impact assessments to better understand future risk for each
system configuration.
The foreSIGHT modelling software adopts a rigorous
quantitative approach to stress testing that has been designed with
several core assumptions in mind:
- that the system dynamics (either ‘current’ or alternative system
configurations) can be represented and adequately described by a
numerical system model that provides a mapping between weather/climate
variables and relevant system performance metrics; and
- that the system model is forced by hydroclimatic time series
data.
Indeed, it is this latter feature that gives the software its name
(the SIGHT in foreSIGHT stands for System Insights from the
Generation of Hydroclimatic Timeseries). In particular,
foreSIGHT has been designed specifically for the quantitative
analysis of systems that exhibit dynamics in time, with examples of such
systems including:
- environmental systems (either natural or managed) that may be
resilient to individual natural hazards but become vulnerable to
multiple sequential hazards or long-term structural shifts in the
climate;
- water resource systems with natural (e.g. soil moisture,
groundwater) and/or human-constructed (e.g. reservoirs, managed aquifer
recharge) storages, for which past weather can affect current system
performance;
- agricultural systems where crop outcomes (e.g. yield and various
quality measures) are influenced by the weather throughout a growing
season and even between seasons;
- renewable energy systems such as solar, wind and hydroelectricity
and/or coupled storage solutions (e.g. pumped hydroelectricity or
lithium battery systems); and
- systems that depend on one or several of the above systems, such as
mining (often dependent on groundwater and/or surface water reserves),
transportation (often sensitive to flooding and various other natural
hazards), tourism (often highly dependent on ecosystem health) and so
forth.
The focus on detailed numerical modelling and system ‘stress testing’
highlights that foreSIGHT is particularly suited to situations
where the consequences of system performance degradation and/or failure
as a result of climate change are likely to be significant, as well as
for quantitative decision making and/or engineering design. It is
assumed that a high-level (qualitative) risk assessment would have
already been conducted and the outcome of that assessment is that a
detailed quantitative analysis is required.
1.2. foreSIGHT workflow for climate stress-testing
The foreSIGHT workflow is shown the diagram below, and
comprises five distinct steps that collectively address the three
objectives outlined above. A core aspect of the foreSIGHT
functionality is to evaluate how the system performs under a range of
plausible climate scenarios created by perturbing statistical properties
of observed climate time series. The workflow involves the steps shown
in the following diagram, each of which are discussed in the case study
presented in Section 2. As highlighted in the previous section, at this
point it is assumed that a detailed quantitative analysis of a system is
required (based, for example, on the outcomes of a qualitative risk
assessment) and that a numerical system model is available or can be
developed as part of the analysis.
Each of the modelling steps are elaborated upon below.
Step A. The process of system stress testing
involves assessing how a system’s behaviour (including its ‘function’ or
‘performance’) varies as a result of plausible climatic changes. These
changes are described by means of climate attributes, which we
define as statistical measures of weather variables. Examples of
attributes are annual total rainfall, annual number of wet days, and
annual average temperature. In this step, the attributes that are deemed
to be most relevant for a particular system are identified. These
attributes are generally selected based on a priori
understanding of system dynamics and likely system vulnerability. The
minimum-maximum bounds of the perturbations in the selected attribute,
and the type of sampling within this range, are also decided. The
attributes and perturbations are used to create an ‘exposure space’. The
outcome of this step is a set of sampled points within an exposure
space, that provide the ‘targets’ for time series generation algorithms
in Step B.
Step B. This step involves generation of perturbed
time series corresponding to the sampled points of target perturbations
created in Step A. A reference (typically observed) time series of the
relevant hydro-climate variables is required to create the perturbed
time series using a selected method of perturbation. The supported
perturbation methods in foreSIGHT include the application of
scaling factors to the supplied time series, or the use of the ‘inverse
method’ of Guo et al (2018) to optimise the parameters of stochastic
weather generator type models to generate time series with desired
perturbed attributes. If stochastic models are used for time series
generation, multiple replicates of time series that correspond to the
same target can be generated to better represent stochastic (‘natural’)
variability. The outcome of this step is a set of perturbed time series
that correspond as closely as possible to each point in the exposure
space.
Step C. The perturbed time series generated in Step
B are used to drive the system model and simulate system ‘performance’.
The performance metrics should represent measures that are most relevant
to the system under consideration, and can include a variety of
economic, social and/or environmental measures. It is assumed that the
performance metrics are calculated within the system model and thus
represent the outputs from that model (i.e. the foreSIGHT
package does not calculate the performance metrics itself). The outcome
of this step is a quantitative representation of how system performance
varies across the exposure space.
Step D. This step visualises the system performance
metrics calculated in Step C to understand the system responses to the
perturbations in the selected climate attributes. If minimum or maximum
threshold criteria of the performance metrics are defined, these
thresholds can be used to identify instances of unsatisfactory system
performance/system failure. In this step, the performance metrics are
visualised in the perturbation space of the climate attributes; in other
words, the axes used for visualisation are the perturbed climate
attributes. Such figures are henceforth named ‘performance spaces’—these
visualisations enable identification of combinations of perturbations
that result in changes to system performance. In cases where the
‘stress-test’ includes multiple perturbed attributes and performance
metrics, multiple visualisations of performance spaces are used to
represent all combinations of attributes/metrics. If alternate climate
information is available from other sources of evidence (for example,
from ‘top-down’ approaches), they can be superimposed on the
visualisations generated in this step. Inclusion of this additional
climate data may provide information about the plausibility of the
perturbations in the attributes. The outcome of this step are plots of
the system performance spaces/thresholds and understanding of the system
responses to the climate perturbations.
Step E. This step involves analysis of alternate
system configurations/policies in order to support decision making.
Visualisations are created for the alternate system choices to compare
their performance. The outcomes of this step are plots of the
performance spaces/thresholds for all system choices and understanding
of the preferred choices under climate perturbations.
These five steps complete the framework of climate impact assessment
using foreSIGHT, and are discussed at length in the following
sections.
1.3. What’s covered in this tutorial?
This tutorial will provide a detailed description of the core
functionality of the foreSIGHT software, broken down into each
of the five steps described in the previous section. The basic structure
of each section is as follows:
- Each section will commence with a brief overview of the purpose of
the Step and key learning outcomes.
- Following the overview, there will be a series of subsections that
focus on key decisions that need to be made in implementing the step.
These subsections commence with a box providing basic theory and key
considerations that should be taken into account in making these
decisions, followed by a description of software functionality needed to
implement each decision.
- These elements are then combined to describe a series of ‘use
cases’, in which the basic foreSIGHT workflow is implemented
against a set of hypothetical anticipated applications of the
software.
In addition to learning about core foreSIGHT functionality,
you’ll also learn about a number of advanced usages foreSIGHT
including:
- specifying exposure space perturbations on irregular grids
- using stochastic models to generate perturbed series and modifying
the default settings for stochastic models/parameters
- modifying default optimisation settings and specifying penalty
attributes and weights
- assessing the fitness of stochastic time series relative to the
desired target attributes
- defining custom wrapper functions for system models in R
- using system models external to R
- exercising finer control on plotting performance spaces
- parallelising computationally intensive functions in the
package
The implementation of the foreSIGHT methodology, and the
bottom-up framework more generally, requires the use of a consistent set
of terminology to describe key concepts. This terminology is summarised
in a glossary section, and we use bold font when making
reference to key terms defined in the glossary.
Finally, we have developed a Frequently Asked Questions
section which we’ll be expanding on over time, and included references
to a small number of key scientific papers.
3. Step A: Identify attributes for perturbation and create an
exposure space (createExpSpace)
In this step you’ll learn…
- What’s meant by the terms exposure space,
climate attributes and exposure space
targets, as well as the difference between
perturbed and held attributes
- How to select attributes for stress testing
- How to select reasonable bounds for each attribute
- How to determine the appropriate sampling strategy for the exposure
space
- How to decide which attributes to hold at historical levels
In this step, we’ll take you through the basic process of creating an
exposure space. The term exposure space refers to the
set of future climate conditions to which a system might be exposed.
This is a multidimensional space that in principle could represent any
feature of the climate that might impact a given system, such as the
averages, variability, seasonality, intermittency, extremes, interannual
variability of a range of weather variables including rainfall,
temperature, wind, solar radiation, and so forth. We henceforth refer to
these features as attributes, which are formally
defined as statistical measures of weather time series.
While stress testing a system against the full set of plausible
changes in all relevant attributes might sound good in theory, this
would lead to an infinite number of future climate states and thus is
not feasible in practice. Rather, it will be necessary to:
- Select the attributes that are likely to be the most important for
the system in question;
- Select reasonable bounds for each attribute, to capture a
plausible set of climatic changes;
- Provide an appropriate sampling strategy to generate the exposure
space; and
- Select the attributes to ‘hold’ at historical levels
The following subsections will guide you through each of
decisions.
3.1. Step A1: Selecting Attributes for Stress Testing
Key Considerations: Step A1
The purpose of climate stress testing is to understand system
sensitivity to a range of plausible future climates, as a core
foundation for making informed adaptation decisions. In
foreSIGHT this is achieved by perturbing a number of
climate attributes, and seeing how the system responds
to those perturbations.
The first part of the stress test is to choose the relevant
attributes to perturb. This creates a dilemma: without having yet having
evaluated system sensitivity, how should one go about choosing the
attributes to use for stress testing? We suggest that the following
considerations be taken into account:
- Consider any a priori knowledge of likely system
sensitivity and vulnerability. This can come from expert understanding
of system dynamics (e.g. dominant processes and key timescales over
which the system operates), knowledge of historical system sensitivity
and/or evidence associated with any previous system ‘failures’, or any
other information that could give insight into the most important
climate attributes
- Consider likely climatic changes in the region based on available
lines of evidence (e.g. climate projections and other relevant
information). If there is reasonable confidence that an attribute is not
likely to change in the future, then there is less value for including
it in a stress test.
- If in doubt, then it is generally worth erring on the side of
caution and including the attribute in question in the analysis, rather
than risking the possibility of missing a major area of system
vulnerability.
Beyond these high-level considerations, there are also several
further practical considerations:
- Is it possible to perturb the attributes using the available
perturbation method? This is relevant as part of the choice between
‘simple/seasonal scaling’ and stochastic methods, and also as part of
the choice of specific stochastic weather generator to use (discussed
further in Step B).
- Is there enough marginal value of including an attribute
given others that have already been included? For example, if a stress
test has already been conducted on the 95 percentile of daily rainfall,
then perhaps stress testing it against the 96 percentile is unlikely to
deliver much additional insight.
- Can the system model take the relevant perturbed weather generator
values as inputs? For example if a system model runs at a daily
timescale, then its capacity to account for sub-daily inputs is limited.
Note that in this case, if a priori knowledge suggests that
variability at the sub-daily scale is very important, then it may be a
case of developing a better system model!
The outcome of attribute selection could be a large number of
attributes identified for perturbation, which may then need to be
reduced in subsequent steps. This was discussed at length by Culley et
al (2020) and will likely also dictate the sampling strategy discussed
in Step A3.
foreSIGHT has the relative unique capability to perturb a
large number of climate attributes, either jointly or in isolation. In
foreSIGHT attribute names are defined using the format
“var_strat_ funcPars_op”, where
- “var” is the variable name,
- “strat” is temporal stratification,
- “func” is function name (with “Pars” denoting additional optional
parameters), and
- “op” is an optional operation.
For example, “P_ann_tot_m” is the mean of the total rainfall
calculated over each year (i.e. mean annual rainfall) and “P_ann_P99” is
99th percentile of rainfall calculated over all days.
Variable names include
- “P”: rainfall
- “T”: temperature
- “PET”: Potential evapotranspiration
- “R”: radiation
Temporal stratifications are
- “ann”: data from entire year
- “JJA”, “SON”, etc: seasons
- “Jan”, “Feb”, etc: months
Function names (and optional parameters) include
- “tot”: total
- “P99”: 99th percentile
- “maxDSDT1”: maximum dry-spell duration (with threshold above
1mm)
A full list of attribute functions supported in foreSIGHT
can be viewed using the helper functions
viewAttributeFuncs().
foreSIGHT also allows users to define their own custom
functions. The names of these functions must have the format
“func_customName”, where “customName” is the custom attribute function.
These functions must have the argument “data”, which represents the time
series of climate data. For example,
func_happyDays = function(data){
return(length(which((data>25)&(data<30))))
}
can be used in the attribute “T_ann_happyDays_m” for calculating the
average number of days each year with temperatures between
25oC and 30oC.
Operator name is optional, and currently is limited
to
- “m”: mean value of metric calculated over all years
- Often “m” will be left empty.
The use of the operator “m” is a subtle, but important, choice. It
determines whether the metric is calculated once using all the data
(when operator is not specified), or whether the metric is calculated
for each year, and then averaged over all years (when operator specified
as “m”). For example, “P_ann_P99” refers to the 99th percentile of daily
rainfall calculated over all days, while “P_ann_P99_m” would be the mean
value of the 99th percentile of daily rainfall from each year.
The definition of each climate attribute supported by foreSIGHT
can be viewed using the helper function viewAttributeDef()
available in the package.
viewAttributeDef("P_ann_tot_m")
#> [1] "Mean annual total rainfall"
It is noted that attributes are specified either as a fractional
change relative to historical levels (and thus do not have units), or
they are specified using the metric system. For situations where the
units are not consistent with those adopted by the preferred system
model, then unit conversions will need to be included as part of the
system model wrapper function. This is covered further as part of Step
C.
The large number of supported attributes in foreSIGHT does
not mean that all attributes can be used in all situations. In
particular, foreSIGHT has two key perturbation methods –
scaling (“simple” or “seasonal”) and stochastic generation (with an
ever-increasing library of stochastic generators).
In the case of simple scaling, the only attributes that can be
perturbed are annual averages, while for with other attributes changing
in a proportional manner. For seasonal scaling, annual averages and
“seasonality ratio” can be perturbed in conjunction.
In contrast, when using stochastic generation, then the attributes
that can be perturbed will depend on the stochastic generator. For
example, stochastic generators with seasonal variations in parameters
can be used to perturb seasonally stratified attributes, whereas annual
models (with no parameter variation) cannot. In general, annual
parameter variation should not be used for perturbing attributes with
seasonal or monthly temporal stratification (e.g. “P_JJA_tot_m” and
“T_Jan_ave_m”) or seasonality ratios (e.g. “P_ann_seasRatio”). Seasonal
parameter variation should not be used for perturbing attributes with
monthly temporal stratification (e.g. “T_Jan_ave_m”).
Once the attributes are selected, we need to include these as a
vector into the function createExpSpace via the argument
attPerturb. For example if we are interested in the total
annual rainfall, the mean annual number of wet days, the total JJA
rainfall, we define the argument attPerturb as:
attPerturb <- c("P_ann_tot_m", "P_ann_nWet_m", "P_JJA_tot_m")
3.2. Step A2: Selecting reasonable bounds for each attribute
Key Considerations: Step A2
The purpose of the stress test is to evaluate system model
performance against a range of plausible future changes. Thus far we
have been vague about what we mean by the word
plausible, but it’s an absolutely fundamental element
of the stress test.
One of the primary objectives of stress testing is we want to
minimise the likelihood of surprises and unexpected system failures.
These are often called ‘Black Swan’ events and represent situations that
were not foreseen when the system was originally designed.
To minimise the risk of not capturing future changes, we first need
to make sure we capture the right types of changes, which are
defined by the attribute selection step (Step A1). But we also need to
ensure that we get the right magnitudes of overall changes.
Thus, by plausible, we mean that the changes are
deemed to be physically possible, albeit not necessarily likely in all
cases. For this reason, our guidance generally has been to select
attribute ranges (minimum and maximum values) that roughly represent the
‘worst case’ of what is possible based on current understanding. In
practice this could mean selecting bounds that are slightly wider than
the range identified by climate models (recognising that climate models
may not capture all plausible future changes), or consideration of
various other lines of evidence.
Yet we want to emphasise the word ‘slightly’ here. We know the world
is not going to warm by 100oC, so let’s not get carried away
imagining worse case scenarios that are almost certainly not going to
occur in reality! This not only would represent a waste of computational
resources, but also would direct analytical attention away from the
sorts of changes that are more likely to occur in practice.
A final note. foreSIGHT—as well as every other application
of ‘bottom-up’ or ‘scenario-neutral’ analysis we have seen thus
far—defines the bounds of the exposure space by the bounds in individual
attributes. In other words, the exposure space becomes a (hyper) cube
defined by the univariate bounds. Yet certain combinations of
changes may be more or less likely, and indeed some combinations may not
be physically possible. This is a current limitation of bottom-up
methods, and is addressed somewhat by the subsequent superposition of
‘top-down’ projections onto the exposure space to highlight parts of the
space that are more or less probable.
As highlighted in the above box, there are a lot of factors to
consider in setting the bounds of the exposure space. However, much of
this analysis needs to happen before starting to use foreSIGHT,
based on a combination of expert knowledge, and potentially the
interrogation of climate model output. To assist with this,
foreSIGHT contains a function, named
calculateAttributes, to calculate the values of attributes
from climate data. By using this function with multiple climate model
output time series (potentially in combination with some form of
downscaling and/or bias correction), the function may be used to
estimate the range of the attribute projections, which can be used as
one of the information sources to determine attribute bounds. The usage
of the function is illustrated below.
# load example climate data
data("tankDat")
# select attributes
attSel <- c("P_ann_tot_m", "P_ann_nWet_m", "P_ann_R10_m", "Temp_ann_rng_m", "Temp_ann_avg_m")
# calculate attributes
tank_obs_atts <- calculateAttributes(tank_obs, attSel = attSel)
tank_obs_atts
#> P_ann_tot_m P_ann_nWet_m P_ann_R10_m Temp_ann_rng_m Temp_ann_avg_m
#> 449.93000 132.20000 11.50000 18.55000 17.43714
Once we’ve decided upon the bounds, we put the minima and maxima in
as vectors, corresponding to the entries into the
attPerturb argument. So if we are planning on perturbing
the three attributes described in the previous section, we would define
the bounds as:
attPerturbMin = c(0.7, 0.8, 0.6)
attPerturbMax = c(1.1, 1.2, 1.1)
3.3. Step A3: Determining the appropriate sampling strategy for the
exposure space
Key Considerations: Step A3
For climate stress testing the system, we analyse the changes in
system performances over an exposure space defined by
the selected perturbed attributes (Step A1) and their
respective minimum-maximum bounds (Step A2). To do that, we need to
sample the exposure space, to obtain a set of target
attribute values for subsequent perturbation in Step B.
The method of sampling to create the target attribute values within
the exposure space is what is referred to as the sampling strategy.
Imagine an exposure space, the axes of which are the perturbed
attributes. When there are multiple perturbed attributes, the exposure
space targets can have perturbations in one perturbed attribute (while
others are held at historical levels), a subset of the perturbed
attributes (while the remaining are held at historical levels), or all
of them.
Ideally, we want to have many samples within the minimum-maximum
bounds of all perturbed attributes for comprehensive analysis of the
system performances over the entire exposure space. However, we may end
up with too many exposure space targets than it is possible to analyse
using the computational resources available. Hence we need sampling
strategies to reduce the number of exposure space targets, while
sampling the space adequately.
Thus, the primary concerns in selecting a sampling strategy is the
desired resolution of the exposure space and the computational
resources available to conduct the stress-test. Generating the perturbed
time series (Step C), and running the system model using the perturbed
time series (Step D) are typically computationally intensive, and
influence this decision.
The number of exposure space targets increase exponentially if there
are multiple attributes that need to be perturbed simultaneously.
Practically, if computational constrains exists, we perform a
preliminary assessment using one-at-a-time sampling of
attPerturb to select the most relevant attributes for the
stress-test.
Three arguments—attPerturbType,
attPerturbSamp, and attPerturbBy—determine the
sampling strategy input to createExpSpace. The type of
sampling is specified using the attPerturbType argument.
The function currently supports two types of sampling - ‘one-at-a-time’
('OAT'), and regular grid ('regGrid'). In the
case of an ‘OAT’ sampling, each attribute is perturbed one-at-a-time
while holding all other attributes constant. In contrast, in a ‘regGrid’
sampling the attributes are perturbed simultaneously to evenly sample an
exposure space encompassing all combination of perturbations in the
selected attributes. The number of samples or the increment of
perturbation is prescribed using the arguments
attPerturbSamp or attPerturbBy, respectively,
for each perturbed attribute.
Once the sampling strategy for the perturbing the three attributes
selected in the previous section has been decided, we specify these
arguments as shown below.
attPerturbType <- "OAT"
attPerturbSamp <- NULL
attPerturbBy <- c(0.1, 0.2, 0.1)
# Or equivalently, by specifying the number of samples as attPerturbSamp
attPerturbType <- "OAT"
attPerturbSamp <- c(5, 3, 5)
attPerturbBy <- NULL
In addition to OAT and regGrid sampling
methods, it is also possible to put customised target combinations as
inputs, and this option can provide flexibility to include a much wider
range of sampling methods (such as Latin hypercube sampling or other
sparse sampling approaches). In these cases, the targets are provided in
a matrix to attTargetsFile, with other arguments
(attPerturbType, attPerturbSamp,
attPerturbBy, attPerturbMin and
attPerturbMax) set to NULL. This usage is illustrated in
one of the ‘irregular perturbations’ Use Case provided later in this
chapter
3.4. Step A4: Deciding which attributes to hold at historical
levels
Key Considerations: Step A4
So, we’ve identified the attributes, identified the plausible ranges
and even identified a carefully developed strategy for sampling the
exposure space. Done, right? Wrong.
There is a significant downside in the flexibility achieved by using
stochastic generators to perturb climate, and if we’re not careful we
can easily get weather sequences that are simply not physically
realistic.
Let’s illustrate this using a simple example. Suppose we know that a
system is primarily influenced by the annual average temperature. Thus,
we have a very nice one-attribute problem, and we simply select this
attribute in foreSIGHT, identify a plausible range, and in this
case we’d just select a one-at-a-time sampling strategy.
Now let’s assume that in Step B we choose a sophisticated weather
generator that can simulate daily temperature, and we apply the ‘inverse
method’ (more on what this means in the discussion of Step B) to
simulate any possible temperature time series that achieves the target
annual temperature series.
Wait. Any possible time series? Yes - without providing more
information, it might simulate a 1oC rise in average
temperature in such a way that the day-to-day variability of the
temperature can blow up (for example one day could be +100oC
and the next -100oC), or the seasonality could reverse
(winter hotter than summer), or indeed the time series could reflect any
other change consistent with the specified target.
The way around this is tell the computer to perturb the temperature
time series to achieve the target, subject to keeping all other
attributes as close to the historical (or baseline) levels as possible.
Thus could mean asking for a 1oC rise in temperature while
keeping day-to-day variability and seasonality roughly constant. There’s
lots of theory developed on this, and if you’re interested in learning
more refer to Culley et al (2019).
As described in the Box above, holding some attributes at constant
levels (and commonly at the level of the reference time
series can be important to generate realistic weather time
series. This is where the attHold argument comes in, and
represents a list of all attributes to keep at historical levels.
Something like:
attHold <- c("P_ann_P99", "P_ann_maxWSD_m", "P_ann_seasRatio")
In this case, these three attributes are held at reference levels.
The attributes 99th percentile rainfall, maximum length of the wet
spells are held at reference levels so that the perturbations do not
result in unrealistic extreme rainfall events. In addition, the
attribute “P_ann_seasRatio” is held at reference levels so that the
seasonal cycle of the generated data is realistic. If you’re still not
convinced why this is important, go to Step B where we provide an
example of not holding some attributes at constant values. There are
also mechanisms to ensure to preferentially matching the desired values
of some attributes during time series generation, by prescribing
attribute penalty. More on this in Step B.
Now that we’ve discussed the theoretical considerations and core
functionality associated with Step A, we now bring all the pieces
together to show some realistic ‘use cases’ for the
createExpSpace function.
3.5. Use Case A1: An ‘OAT’ exposure space
Consider the starting phase of a case study, where a number climate
attributes have been identified for perturbation based on a
priori knowledge of the system dynamics. If the identified
attributes are large in number, simultaneously perturbing them would
result in an exposure space with too many target points for the stress
test. However, it could be viable to create an “OAT” exposure space
containing one-at-a-time perturbations in the identified attributes to
perform a preliminary assessment. The assessment can help identify if
there a subset of attributes to which the system performance is most
sensitive to that can be used for the analysis, noting the important
caveat that this form of assessment is not capable of analysing possible
higher-order sensitivities due to interactions between
attributes.
Suppose that an understanding of the dynamics of the system under
consideration suggests that the system is sensitive to changes in annual
and JJA rainfall totals. In addition, changes in the number of wet days
are also expected to affect the system performance. So these attributes
are selected for perturbation to create an “OAT” exposure space for the
preliminary stress-test. Regional climate projections for the region
indicate that the annual and JJA total rainfalls are expected to
decrease. The range of the projected decreases in annual total rainfall
is -20% to 0%, the range of projected decreases in JJA total is -30% to
-0%, and the projected changes in the number of wet days is -10% to +10%
for the future time-slice of interest. The minimum and maximum
perturbation bounds encompassing these projected changes are selected
for the stress-test, to cover the range of expected changes in the
region. The generated exposure space is selected to be larger than the
expected changes from climate projections by 10%. Thus the min-max
bounds selected are: (0.7 to 1.1) for “P_ann_tot_m”, (0.6 to 1.1) for
“P_JJA_tot_m”, and (0.8 to 1.2) for “P_ann_nWet_m”. Based on
computational resources required to generate the data and run the system
model we decide to perform the analysis using a total of 15 target
locations in the exposure space. This information is used to select the
perturbation increment of the perturbed attributes.
To maintain the realism of the perturbed time series, some attributes
have to be held at reference levels. The attributes “P_ann_P99”,
“P_ann_maxWSD_m” are selected to be held at reference levels so that the
generated time series have realistic wet extremes, with decreasing
annual and JJA totals. The hypothetical climate projections also
indicate that there are no changes in the extremes, so these are assumed
to stay the same as the reference series. In addition, the seasonal
rainfall ratio is held at existing levels so that the seasonal cycle
represented in the generated time series are realistic. It is noted that
as part of the “OAT” sampling strategy, each of the “perturbed”
attributes are being changed individually with the remaining perturbed
attributes staying at the levels of the reference time series, and so
effectively become “held” attributes as part of the perturbation.
The following example code illustrates the creation of an ‘OAT’
exposure space using the createExpSpace function.
# specify attributes
attPerturb <- c("P_ann_tot_m", "P_ann_nWet_m", "P_JJA_tot_m")
attHold <- c("P_ann_P99", "P_ann_maxWSD_m", "P_ann_seasRatio")
# ***** OAT Exposure Space ******
# specify perturbation type and minimum-maximum ranges of the perturbed attributes
attPerturbType <- "OAT"
attPerturbBy <- c(0.1, 0.1, 0.1)
attPerturbMin = c(0.7, 0.8, 0.6)
attPerturbMax = c(1.1, 1.2, 1.1)
# create the exposure space
expSpace_OAT <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = NULL,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attPerturbBy = attPerturbBy,
attHold = attHold)
# plot the exposure space
plotExpSpace(expSpace_OAT, y = attPerturb[1], x = attPerturb[2])
plotExpSpace(expSpace_OAT, y = attPerturb[2], x = attPerturb[3])
3.6. Use Case A2: A ‘regGrid’ exposure space
For most practical applications of the scenario-neutral method
published to-date, the mode of presentation involves plotting system
performance as a set of changing contours on a (usually but not
necessarily two-dimensional) exposure space. In foreSIGHT this
mode of presentation is facilitated through the ‘regGrid’ sampling of
the exposure space, enabling the presentation of joint variations of a
range of perturbed attributes. Although this method is
not limited to two dimensions, there is a clear trade-off in number of
attributes, grid resolution and runtimes; for example having 10
attributes with 10 samples each between the minimum and maximum bounds,
would lead to the requirement of 1010 separate time series to
be generated and run through a system model. Therefore in practice this
approach is best done once a critical set of attributes are identified,
either through the one-at-a-time method described in Use Case A1, or
more sophisticated methods described in Culley et al (2020).
In terms of implementation, after identifying the attributes and
deciding on the bounds and perturbation increments (or number of
samples), a ‘regGrid’ exposure space is created, which consists of
target points with simultaneous perturbations in the selected perturbed
attributes. The createExpSpace function can be used as
follows.
# ***** regGrid Exposure Space *****
attPerturbType <- "regGrid"
expSpace_regGrid <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = NULL,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attPerturbBy = attPerturbBy,
attHold = attHold)
# plot the exposure space
plotExpSpace(expSpace_regGrid, y = attPerturb[1], x = attPerturb[2])
plotExpSpace(expSpace_regGrid, y = attPerturb[2], x = attPerturb[3])
3.7. Use Case A3: Exposure space with irregular perturbations
Sometimes when multiple attributes are selected for perturbation, it
may not be feasible to use a ‘regGrid’ exposure space for the stress
test because the higher dimensions of the exposure space result in an
infeasibly large number of target points. As an alternative to the
one-at-a-time method described in Use Case A1, the user may wish to
input custom target combinations, which potentially could be obtained
from a sampling method such as Latin hypercube sampling (see Culley et
al, 2020).
To this end, the createExpSpace function offers the
functionality to input target points created externally to
foreSIGHT through the function argument
attTargetsFile. The argument is intended for users who want
to sample target locations using alternate sampling techniques not
currently available in createExpSpace.
The target locations are created by the user outside
foreSIGHT, saved in a CSV file and provided as an input to
createExpSpace. In this case, the arguments
attPerturbSamp, attPerturbMin,
attPerturbMax, attPerturbType, and
attPerturbBy should be set to NULL. It is to
be noted that createExpSpace does not perform checks on the
user input target locations read in from the CSV file. The user must
therefore ensure that the perturbations specified in this file are
feasible. The CSV file should contain column headers that
correspond to all attributes specified as attPerturb and
attHold. The rows of the file should correspond to the
target locations in the exposure space.
The below code provides an example of this usage.
attPerturb <- c("P_ann_tot_m", "P_ann_nWet_m", "P_JJA_tot_m")
attHold <- c("P_ann_P99", "P_ann_maxWSD_m", "P_ann_seasRatio")
# creating example target locations and saving it in a CSV file for illustration
# note that the user would create these target locations using a sampling method of their choice
# the file should contain all perturbed and held attributes
tempFile <- paste0(tempdir(), "\\targetsFile.csv")
attTargets <- rbind(c(1, 1, 1, 1, 1, 1),
c(0.7, 1, 0.6, 1, 1, 1),
c(0.8, 1, 0.7, 1, 1, 1),
c(0.9, 1, 0.8, 1, 1, 1),
c(1.1, 1, 1, 1, 1, 1),
c(0.7, 1.2, 0.6, 1, 1, 1),
c(0.8, 1.2, 1, 1, 1, 1),
c(0.9, 1.2, 1.1, 1, 1, 1),
c(1, 0.8, 1, 1.1, 0.7, 1),
c(1.1, 0.8, 1.1, 0.8, 1, 1))
colnames(attTargets) <- c(attPerturb, attHold)
write.table(attTargets, file = tempFile, sep = ",")
# creating exposure space using targets from csv file
expSpace_Irreg <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = NULL,
attPerturbMin = NULL,
attPerturbMax = NULL,
attPerturbType = NULL,
attPerturbBy = NULL,
attHold = attHold,
attTargetsFile = tempFile)
#> [1] "READING ATTRIBUTE TARGETS FROM FILE"
# plot the exposure space
plotExpSpace(expSpace_Irreg, y = attPerturb[1], x = attPerturb[2])
plotExpSpace(expSpace_Irreg, y = attPerturb[2], x = attPerturb[3])
4. Step B: Generate perturbed climate time series
(generateScenarios)
In this step you’ll learn…
- What’s meant by the terms reference period,
simple and seasonal scaling, stochastic
generation, stochastic weather generator,
attribute penalty, realisation and
random seed
- How to select an appropriate reference period for subsequent
analysis
- How to select the time series perturbation method
- How to select the stochastic generator
- Whether and how to select attribute penalties
- How to select length of the perturbed time series, the number of
replicates and how to control the random seed
Now that we have identified the specific points in the exposure space
to analyse, we turn to the challenge of generating time series that
correspond to those attribute values. In this step, we create perturbed
hydro-climate time series with attributes corresponding to the
target attribute values. The function
generateScenarios can be used to create the perturbed time
series. The mandatory arguments required are a reference (typically
observed) time series (argument obs) and the exposure space
created in Step A (argument expSpace).
Before doing this, the user needs to make a number of decisions:
- What is the reference period for analysis, which determines the
baseline for subsequent perturbations?
- What is the time series perturbation method?
If the time series perturbation method is a stochastic one (i.e. one
that uses stochastic weather generators), there are several other
decisions that need to be made:
- Which stochastic weather generator to use;
- How to weight the different perturbed and
held attributes to balance trade-offs and achieve the
desired time series; and
- Other considerations such as length of each stochastic realisation,
number of realisations and control of the random seed.
The subsections below provide a guide to each of these decisions,
followed by a set of practical ‘Use Case’ examples to show how these
come together.
4.1. Step B1. Selecting the reference time series
Key Considerations: Step B1
As part of the scenario neutral methodology, all perturbations are
described against some reference attribute values,
which in turn are usually calculated from a reference weather time
series. This reference period is generally synonymous
with the notion of a climatological baseline.
There are no requirements in the foreSIGHT software for the
nature of the reference time series other than that it must conform to
certain formatting requirements described in the examples below.
However, in practice, there are a number of considerations in choosing
the reference period:
Purpose of analysis: In many cases it is
anticipated that the focus of the stress testing will be to evaluate
plausible changes in system performance either against current system
performance or system performance over some historical period of
record.
Length of reference period: The length of the
reference period must be sufficient to obtain appropriately precise
estimates of relevant climate attributes. The World Meteorological
Organisation generally suggests a minimum period of 30 years, although
the specific decision will depend on the data availability, the degree
of non-stationarity and various other considerations.
Integration with top-down climate impact
assessments. For situations where top-down projections will be
included as part of the analysis—perhaps by superimposition of top-down
projections on the scenario-neutral performance space, or by way of a
comparative analysis—it might be necessary to ensure all the approaches
are calculated relative to a consistent climatological
baseline.
Availability of (high-quality) historical weather
data. Data availability can be a major constraint to stochastic
modelling, with even relatively densely gauged regions experiencing
regular interruptions in the historical record or other data anomalies.
The quality of reference weather time series should be evaluated using
established methods where possible.
The potential non-stationarity of historical weather
data. Given that climate change is increasingly detectable in
weather time series data, system performance can be expected to be
different across different reference periods such as: (i) aggregated
over the instrumental record; (ii) aggregated over the recent record
such as the last decade or two; or (iii) estimated based on the
‘current’ climate.
The above factors highlight that it is not possible to provide
prescriptive guidance on the choice of reference period, and will
require careful tailoring to the unique circumstances of each
foreSIGHT application.
The variables available in foreSIGHT and their units can be
viewed using the function viewVariables(). It is important
to ensure that the input reference time series are specified in these
units if stochastic models are used to generate the perturbed time
series. This is because the default bounds of the stochastic model
parameters in the package are based on these units. The input
reference data should contain the variables that are
required for the system under consideration (i.e. as input to the
system model described in Step C). These
reference data need not contain all the variables that are
available in foreSIGHT, but can be a subset of them which are
to be used in the stress-test.
# Hydro-climate variables available
viewVariables()
#> shortName longName units
#> [1,] "Simple" NA NA
#> [2,] "P" "Precipitation" "mm"
#> [3,] "Temp" "Temperature" "°C"
#> [4,] "PET" "Evapotranspiration" "mm"
#> [5,] "Radn" "Radiation" "MJ/m2"
The reference data can either be a data.frame or a list.
List format is required for multi-site data. When using a data.frame,
the first three columns should contain the year,
month, and day of the data named accordingly.
Further columns of the data.frame should contain the hydro-climate
variables of interest named by their short names as listed in the
viewVariables() function. An example reference
data.frame object representing a general Adelaide (South Australia)
climate is available in the package and can be loaded using the
data command as shown below. This is intended to illustrate
the expected data.frame format of reference.
# Load example climate data
data(tankDat)
# Expected data.frame format of the input obs climate data
head(tank_obs)
#> year month day P Temp
#> 1 2007 1 1 0.0 25.50
#> 2 2007 1 2 0.0 24.50
#> 3 2007 1 3 0.0 29.75
#> 4 2007 1 4 0.0 32.25
#> 5 2007 1 5 0.0 32.50
#> 6 2007 1 6 4.5 26.50
When specifying multi-site reference data as a list, the
list should contain vectors for the year,
month, and day, and matrices for multi-site
data hydro-climate variables. An example with multi-site rainfall data
in the Barossa Valley (South Australia) is provided.
# Load example multi-site rainfall data
data("barossaDat")
# Expected format of multi-site rainfall data within reference list.
head(barossa_obs$P)
#> X23300 X23302 X23305 X23309 X23312 X23313 X23317 X23318 X23321 X23363
#> [1,] 24.6 24.4 16.8 25.4 17.3 33.8 17.2 20.5 17.3 28.8
#> [2,] 2.5 3.8 1.4 3.0 1.8 5.6 1.7 1.6 1.8 4.1
#> [3,] 0.0 0.3 0.8 0.0 0.0 0.5 0.0 0.0 0.0 0.2
#> [4,] 1.3 2.0 0.0 0.0 0.0 2.0 0.0 0.3 0.0 1.3
#> [5,] 0.0 0.0 0.0 0.0 0.0 0.8 0.0 0.0 0.0 0.4
#> [6,] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
#> X23373 X23752 X23756
#> [1,] 17.3 26.7 31.2
#> [2,] 1.8 4.4 5.1
#> [3,] 0.0 0.0 0.3
#> [4,] 0.0 1.0 1.8
#> [5,] 0.0 0.0 0.3
#> [6,] 0.0 0.0 0.0
The climate time series can be input to the
generateScenarios function using the reference
argument. For example, for using the single site tank_obs
data, we would specify
foreSIGHT also contains a function that can be used to
calculate the attributes of interest for climate data supplied by the
user: calculateAttributes(). The usage of this function is
shown below. The function is intended for use with the
reference data or additional climate data from other
sources that will be used with the plotting functions in
foreSIGHT (see Step D).
attSel <- c("P_ann_tot_m", "P_MAM_tot_m", "P_JJA_tot_m", "Temp_ann_avg_m", "Temp_ann_rng_m")
tank_obs_atts <- calculateAttributes(tank_obs, attSel)
tank_obs_atts
#> P_ann_tot_m P_MAM_tot_m P_JJA_tot_m Temp_ann_avg_m Temp_ann_rng_m
#> 449.93000 127.47000 167.99000 17.43714 18.55000
4.2. Step B2. Selecting the time series perturbation method
Key Considerations: Step B2
As highlighted in the Introduction, a key role of the
foreSIGHT software is to enable the quantitative stress testing
of climate-sensitive systems using perturbed hydroclimatic time series.
But what is the best way of achieving the perturbations?
There are two approaches supported in foreSIGHT, and these
reflect the main approaches that have been adopted in most published
scenario-neutral applications thus far.
The first approach is based on scaling the observed hydroclimatic
time series, which can be performed in foreSIGHT using either
Simple Scaling or Seasonal Scaling.
Simple Scaling scales the weather time series by specified additive or
multiplicative time-invariant factors to achieve the desired perturbed
time series. Seasonal scaling follows a similar approach, but allows the
multiplicative factors to vary throughout the year. Although the scaling
methods have the benefit of simplicity, there are a number of
disadvantages:
- some statistical properties such as the rainfall wet-dry patterns or
extremes cannot be perturbed
- many attributes cannot be perturbed in combination
- it is not possible to hold some desired attributes at historical
levels while perturbing others
- the length of the generated time series cannot be longer than the
supplied reference time series.
The second method involves the use of Stochastic Weather
Generators to generate perturbed weather time series that
correspond to the target attribute values. This approach has the
advantage of considerably more flexibility, in that it can perturb
complex combinations of changes such as the simultaneous decrease in the
averages, increase in the intermittency and increase in the extremes of
rainfall. It also has the advantage of being able to represent
stochastic variability, in the sense that it is possible to generate
multiple ‘realisations’ or Stochastic Replicates of
future weather that each share the same attribute values but evolve
differently over time, and also generate realisations of different
lengths. Yet this approach also has several disadvantages:
- The process of calibrating stochastic generators to achieve
particular attribute values is much slower and can involve considerable
runtimes
- Care is needed to identify useful Perturbed
Attributes that are physically feasible (for example it is not
possible to simulate a rainfall time series that simultaneously shows
both an increase in the annual total rainfall and number of wet days,
and yet a decrease in the amounts per wet day).
- If both the Perturbed Attributes and Held
Attributes are not carefully specified, it is possible to
generate unrealistic time series
- Care is needed to match the specific stochastic generator to the
problem requirements.
It is difficult to provide definitive advice on the most appropriate
method to select, as it will depend on the unique aspects of each
problem. However the best guide will come from the attributes that were
selected during the analysis of Step A1—if individual attributes or
attribute combinations have been selected that cannot be generated using
Simple or Seasonal Scaling, then this provides strong
indication that stochastic methods are likely to be most
appropriate.
As highlighted in the above box, care is needed to decide select the
specific perturbation method, with the decision depending significantly
on the attributes selected for stress testing as part of Step A1. Once
the method of perturbation has been selected, you need to supply this
information to the function generateScenarios via the
argument controlFile.
In particular, if simple or seasonal scaling is required, then simply
use the argument:
If a stochastic model is required, there are two options. Firstly,
one can simply use the default stochastic model and associated settings
in foreSIGHT by not specifying a controlFile
argument, or by setting the controlFile argument to
NULL.
The default assumes WGEN with a harmonic function to capture
seasonality, and will simulate all the supported WGEN weather variables
that are input as part of the reference (e.g. observed) climate time
series. It also assumes that every attribute is treated equally (i.e. no
penalty applied to different attributes). In contrast, to provide a
greater level of customisation, the argument is entered as:
# input a user created JSON file that specifies the selection of model options
controlFile = path-to-a-user-created-JSON-file
where the JSON file contains a range of advanced options including
selecting the type of stochastic model, overwriting the default model
parameter bounds, changing default optimisation arguments, and setting
penalty attributes to be used in optimisation.
If you elect to use simple or seasonal scaling you can skip straight
to Use Case 1 (Simple Scaling) or Use Case 2 (Seasonal Scaling) at the
end of this chapter. If you elect to use the default stochastic method,
you can skip straight to Use Case 3 (Using the Default Stochastic
Models). However if you would like to choose the stochastic generator or
add penalty weights to the attributes, then continue reading (for other
settings in the JSON file such as default weather generator parameter
bounds or optimisation arguments, refer to Options for Advanced Users
chapter at the end of this tutorial).
4.3. Step B3: Selecting the stochastic generator
Key Considerations: Step B3
There is a plethora of options for stochastic weather generators
described in the scientific literature, each with different features and
assumptions. This variety provides a high degree of flexibility for
perturbing weather time series in a variety of ways to comprehensively
‘stress test’ a climate-sensitive system. The foreSIGHT
software currently supports a small number of weather generators;
however the software has been developed in such a way that additional
weather generators can be added over time.
There is no single ‘correct’ weather generator for all applications,
with the choice depending on a range of considerations:
Data timestep. Most weather generators run at a
daily timestep, which is a common timestep for reporting of key weather
variables. However there are also weather generators available at
various sub-daily timesteps, as well as longer aggregated timesteps such
as monthly or annual. The key consideration here is to ensure the time
step is consistent with the likely timescales of system performance
sensitivity, which in turn need to correspond to the relevant time
scales of weather inputs that are require for the system model.
The key timescales of system sensitivity. In
addition to data timestep, it is important that the stochastic generator
is able to simulate variability in Climate Attributes
representing key timescales of system sensitivity. For example some
systems may respond at sub-seasonal and seasonal timescales, and others
at interannual timescales. It is noted that a stochastic generator may
be able to simulate variability at timescales that are equal to or
longer than its timestep, but not shorter.
Relevant weather variables. Weather generators
have the capability of simulating a range of surface variables,
including precipitation, temperature, wind, solar radiation, humidity
and so forth—as well as derived variables such as potential
evapotranspiration that are calculated through various recognised
formulations. In many cases weather generators simulate precipitation
first, followed by the other variables that are then conditioned to the
precipitation time series; however each weather generator is different
and it is necessary to review the documentation to understand the basis
for generating the weather time series.
Other key structural features that drive the
weather generator’s capacity to simulate individual or combined changes
in attributes. For example, some weather generators use ‘harmonic’
functions to simulate the seasonal cycle, which may enable capacity to
simulate key shifts in seasonality but may necessarily be capable of
simulating changes at the month-by-month level.
It is beyond the scope of this tutorial to review the structure of
each weather generator supported by foreSIGHT, and the reader
is referred to relevant references for further information. Beyond
developing a theoretical understanding of the structure (and potential
structural limitations) of individual weather generators, a pragmatic
approach to assess the appropriateness of weather generation choice is
through evaluating the relevant diagnostics in achieving specified
target attributes. Poor performance in diagnostics may be due to several
issues, including weather generator suitability. The use of weather
generator diagnostics is discussed later in this chapter.
Finally, if you have a preferred stochastic weather generator that
you’d like to have included in the overall foreSIGHT software,
then please contact the software developers.
foreSIGHT includes a few stochastic models that the user can
select to generate the scenarios. The options differ in the model
formulation and the temporal variation of the model parameters (refer to
the package description using the command
packageDescription("foreSIGHT") to view the references to
each stochastic generator). The models available in foreSIGHT
can be viewed using the function viewModels as shown below.
The defaultModel column indicates the default stochastic
model that will be used if the controlFile argument is
NULL. The usage of this function is demonstrated below. The
compatibleAtts argument can be set to TRUE to
view the attributes that are compatible with each model.
viewModels()
#> [1] "Please select a valid variable. The valid variable names are:"
#> [1] "P" "Temp" "PET" "Radn"
# View the models available for a specific climate variable
viewModels("P")
#> modelType modelParameterVariation modelTimeStep defaultModel
#> 1 wgen annual daily FALSE
#> 2 wgen seasonal daily FALSE
#> 3 wgen harmonic daily TRUE
#> 4 latent annual daily FALSE
#> 5 latent harmonic daily FALSE
# View models available for temperature
viewModels("Temp")
#> modelType modelParameterVariation modelTimeStep defaultModel
#> 1 wgen harmonic daily TRUE
#> 2 wgen-wd harmonic daily FALSE
#> 3 wgen-wdsd harmonic daily FALSE
The stochastic models used by generateScenarios can be
modified using the controlFile argument. If the
controlFile argument is not specified or set to
NULL, the default stochastic model and associated settings
will be used to generate the scenarios. To use stochastic models
different from the default models in the package, the user can input a
JSON file via the controlFile argument specifying the model
choices. The models are defined using the modelType and
modelParameterVariation fields in the
controlFile; both these fields should be specified.
The helper function writeControlFile available in
foreSIGHT can be used to create a sample JSON file that
provides a template to create control files to specify alternate models
that the user needs. The writeControlFile function can be
used without arguments as shown below. Note that the following function
call will write a JSON file named sample_controlFile.json
into your working directory.
The user can create a JSON file in the same format for input to
generateScenarios. As an example, the following text may be
used in the JSON file to select alternate models for precipitation and
temperature.
# Example text to be copied to a text JSON file
{
"modelType": {
"P": "latent",
"Temp": "wgen-wd"
},
"modelParameterVariation": {
"P": "harmonic",
"Temp": "harmonic"
}
}
Alternatively, the toJSON function from the
jsonlite package can be used to create a JSON file from an
R list as shown below. The file can be used as an input to
generateScenarios using the controlFile
argument.
# create a list containing the specifications of the selected models
modelSelection <- list()
modelSelection[["modelType"]] <- list()
modelSelection[["modelType"]][["P"]] <- "latent"
modelSelection[["modelType"]][["Temp"]] <- "wgen-wd"
modelSelection[["modelParameterVariation"]] <- list()
modelSelection[["modelParameterVariation"]][["P"]] <- "harmonic"
modelSelection[["modelParameterVariation"]][["Temp"]] <- "harmonic"
utils::str(modelSelection)
#> List of 2
#> $ modelType :List of 2
#> ..$ P : chr "latent"
#> ..$ Temp: chr "wgen-wd"
#> $ modelParameterVariation:List of 2
#> ..$ P : chr "harmonic"
#> ..$ Temp: chr "harmonic"
# write the list into a JSON file
modelSelectionJSON <- jsonlite::toJSON(modelSelection, pretty = TRUE, auto_unbox = TRUE)
write(modelSelectionJSON, file = paste0(tempdir(), "\\eg_controlFile.json"))
# input a the JSON file
controlFile = paste0(tempdir(), "\\eg_controlFile.json")
If you’ve elected to use an alternate stochastic model, refer to Use
Case ‘Choosing a different stochastic model’ for an example.
4.4. Step B4: Selecting penalised attributes and weight
Key Considerations: Step B4
As part of the ‘inverse’ approach to stochastic generation, an
optimisation algorithm is used to identify time series with attributes
that are as close as possible to the target attributes.
To understand what is going on, we need to get into a bit more
theory. Let’s imagine we have i=1,…,n different
attributes, such as mean annual rainfall and mean
annual temperature (in which case n=2). For a given attribute
target vector (indexed by j), the standard (non-penalised)
optimisation approach would seek to generate time series that minimise
the difference in target values between the attribute values of a
simulated time series \(a_{i,j}\) and
target values \(t_{i,j}\), as given by
the following equation:
\(O(\mathbf{a}_j, \mathbf{t}_j) =
\sqrt{\sum_{i=1}^{n} (a_{i,j} - t_{i,j})^2}\)
In this example, the optimiser will search for ‘solutions’
(i.e. parameter values of the stochastic generator) that minimise the
unweighted difference between \(a_{i,j}\) and \(t_{i,j}\) until ideally the difference
becomes zero (a perfect match).
However, what happens if, because of the specific configuration of
the problem, it is not possible to find a solution that reduces the
distances for each attribute to zero? In this case, the optimiser will
search to find the best possible trade-off, in order to find the minimum
distance across all the attributes.
This is where the problem becomes troublesome. In this case, we have
two different attributes that measure two different variables (rainfall
and temperature), that are measured on different scales (fraction
relative to historical for rainfall, or degrees Celsius for
temperature). So for example a 0.1oC temperature difference
would be ‘weighted’ the same as a 0.1 fraction (or 10%) difference in
precipitation relative to the reference series. Moreover, in some cases
one might want the flexibility to focus the optimiser on particular
attributes (usually the Perturbed Attributes) at the
expense of other attributes (usually the Held
Attributes).
The proposed response to this, as described in further detail by
Culley et al (2019), is to change the weights of error terms in the
objective function to increase (or decrease) the focus on individual
attributes. This involves adjusting the objective function to the
following:
\(O(\mathbf{a}_j, \mathbf{t}_j) =
\sqrt{\sum_{i=1}^{n} [\lambda_i(a_{i,j} - t_{i,j})]^2}\)
where \(\lambda_i\) represents a
user-specified penalty parameter for each attribute \(i\). Larger values for \(\lambda_i\) emphasises those attributes in
the calibration. The precise value of \(\lambda_i\) depends on the overall
objectives of the problem and will often be adjusted after assessing the
diagnostics of the stochastically generated time series (discussed later
in this section). The likely usage of this is to provide a means of
instructing the optimiser to: ‘generate stochastic realisations that
reflect the perturbed attributes, while keeping other relevant features
of the time series described by the held attributes as close to the
reference time series as possible’— by placing greater priority on the
perturbed attributes.
If the user needs to specify penalty attributes and penalty weights,
they should be specified in the JSON file input to the
controlFile argument of generateScenarios. The
penalty attributes should be a subset of the perturbed/held attributes
selected during the creation of the exposure space used to generate the
scenarios. Note that if you want to specify both alternate model choices
(Step B3), and penalty attributes to generate scenarios, the JSON
controlFile should contain both the settings.
Consider an exposure space containing the following attributes.
attPerturb <- c("P_ann_tot_m", "P_ann_nWet_m", "Temp_ann_avg_m")
attHold <- c("P_Feb_tot_m", "P_SON_dyWet_m", "Temp_ann_rng_m", "P_DJF_avgDSD_m")
The default objective function used in optimization assigns equal
weights (weight=1) to each attribute. Penalty attributes and weights can
be used to increase (or even decrease) the weight assigned to each
attribute.
To apply penalties to a few selected attributes, the
penaltyAttributes and penaltyWeights fields of
the JSON controlFile can be specified using the text shown
below. The text has to be used in the JSON file.
# Example text to be copied to a JSON text file
"penaltyAttributes": ["P_ann_tot_m", "Temp_ann_avg_m", "P_Feb_tot_m", "Temp_ann_rng_m"],
"penaltyWeights": [3, 1.5, 2, 2]
Alternatively, the toJSON function from the
jsonlite package can be used to create a json file from an
R list as shown below. The file can be used as an input to
generateScenarios using the controlFile
argument.
# create a list containing the specifications of the selected models
penaltySelection <- list()
penaltySelection[["penaltyAttributes"]] <- c("P_ann_tot_m", "Temp_ann_avg_m",
"P_Feb_tot_m", "Temp_ann_rng_m")
penaltySelection[["penaltyWeights"]] <-c(3, 1.5, 2, 2)
utils::str(penaltySelection)
#> List of 2
#> $ penaltyAttributes: chr [1:4] "P_ann_tot_m" "Temp_ann_avg_m" "P_Feb_tot_m" "Temp_ann_rng_m"
#> $ penaltyWeights : num [1:4] 3 1.5 2 2
# write the list into a JSON file
penaltySelectionJSON <- jsonlite::toJSON(penaltySelection, pretty = TRUE, auto_unbox = TRUE)
write(penaltySelectionJSON, file = paste0(tempdir(), "\\eg_controlFile.json"))
# input a the JSON file
controlFile = paste0(tempdir(), "\\eg_controlFile.json")
If you have elected to use penalty attributes to generate scenarios,
refer to Use Case ‘Specifying penalty attributes’ for an example.
4.5. Step B5. Length of the perturbed time series, the number of
replicates and controlling the random seed
Key Considerations: Step B5
The issues in this section only pertain to stochastically generated
series; for simple/seasonal scaling, the length of Perturbed
Time Series is equivalent to the Reference Time
Series, and given there is no random element to the
perturbation, issues such as number of replicates and randomisation
process are not relevant.
For the stochastic generation algorithm, it is possible to generate
time series of any arbitrary length, which can be significantly longer
than the reference time series. For example, one may have a 30 year
historical weather time series as the reference, yet each stochastic
replicate (including, if desired, for the ‘no change’ situation) can be
much longer, such as 100s or 1000s of years of length. Advantages for
long replicates are that this can often result in a smoother
Performance Space, by improving the signal-to-noise
ratio (the signal being the climatic changes represented by the
Perturbed Attributes, and the noise being the
stochastic Weather Noise). Disadvantages are largely
linked to run-time, both for optimisation of the stochastic generator
(i.e. as done during Step B), and for running the system model (see Step
C).
A similar but subtly different approach to addressing stochastic
variability is to alter the number of replicates (or Stochastic
Realisations). In this case, for each attribute target one
might wish to generate multiple realisations (often but not necessarily
of the same length as the Reference Time Series), which
provide alternative versions of the weather that correspond to
the same attribute values. This can be used for statistical analysis
purposes, and also can provide a useful indicator of whether the system
model is sensitive to elements of the weather that are not included as
part of the Attribute Targets.
Finally, although stochastic sequences are generally viewed as
‘random’, they can better be described as Pseudo Random
Numbers, in which the stochastic sequences have the appearance
of random but are in fact completely determined by the initial
conditions provided to the random number generator. To create the
appearance of randomness, the initial conditions are usually based on a
varying number such as the system clock; however it is also possible to
set the initial value of the generator (called a random
seed) to achieve reproducibility in the code (e.g. by enabling
a peer reviewer or other interested party to completely replicate a set
of results).
The argument simLengthNyrs can be used to specify the
desired length of the stochastically generated perturbed time series in
years using generateScenarios
# simulation length of 100 years
simLengthNyrs = 100
By default, generateScenarios will generate a single
replicate (or stochastic realisation) of the perturbed time series. More
replicates can be generated by specifying the numReplicates
argument of generateScenarios.
The random seed used for stochastic generation of the first replicate
is selected by generateScenarios by randomly sampling a
number between 0 and 10,000. The random seeds for the subsequent
replicates are incremented by 1. Thus, the perturbed stochastic data
generated using generateScenarios for the same function
arguments would typically be different. The function saves the value of
the random seed used for each replicate in the output list containing
the perturbed time series.
Sometimes, it may be of interest to the user to reproduce a previous
stochastic simulation. It is possible to achieve this by specifying the
seedID argument of the generateScenarios
function to that of the first replicate of the previous simulation. The
function would use the specified seedID as the random seed.
Note that it is recommended to specify seedID only to
reproduce a prior result.
# the seed of the first replicate from a previous result is set as seedID
seedID = 1234
Use Case B1: Simple Scaling
Consider a simple system that is affected only by changes in annual
totals or means of one or more hydroclimate variables. Simple scaling
can be used to generate perturbed time series in this case. The below
code provides an example of the usage.
# specify perturbed attributes
attPerturb <- c("Temp_ann_avg_m", "P_ann_tot_m")
# specify perturbation type and minimum-maximum ranges of the perturbed attributes
attPerturbType <- "regGrid"
attPerturbSamp <- c(9, 13)
attPerturbMin = c(-1, 0.80)
attPerturbMax = c(1, 1.2)
# create the exposure space
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = NULL) # no attributes held at historical levels
#> Note: There are no attributes held at historical levels
# Load example obs climate data
data(tankDat)
# generate perturbed time series using simple scaling
sim <- generateScenarios(reference = tank_obs, # input observed data
expSpace = expSpace, # exposure space created by the user
controlFile = "scaling") # using scaling
#> Generating replicate number 1 out of 1 replicates...
#> Simulation completed
Simple scaling can also be applied to multi-site climate data. See
the help file for generateScenarios for details and a
working example.
Use Case B2: Seasonal Scaling
Seasonal scaling can be used to perturb the seasonal pattern in a
hydroclimate variable, in addition to perturbing annual totals/means.
The following code provides an example where the “seasRatio” – defined
as the ratio of total wet season rainfall to dry season rainfall – is
perturbed.
# specify perturbed attributes
attPerturb <- c("P_ann_tot_m","P_ann_seasRatio")
# specify perturbation type and minimum-maximum ranges of the perturbed attributes
attPerturbType <- "regGrid"
attPerturbSamp <- c(9, 9)
attPerturbMin = c(0.8, 0.9)
attPerturbMax = c(1.2, 1.3)
# create the exposure space
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = NULL) # no attributes held at historical levels
#> Note: There are no attributes held at historical levels
# Load example obs climate data
data(tankDat)
# generate perturbed time series using simple scaling
sim <- generateScenarios(reference = tank_obs, # input observed data
expSpace = expSpace, # exposure space created by the user
controlFile = "scaling") # using scaling
#> Generating replicate number 1 out of 1 replicates...
#> Simulation completed
Use Case B3: Using the default stochastic models
The default stochastic models in foreSIGHT can be used to
generate data in most cases. These models are compatible with all the
hydro-climate attributes in foreSIGHT. This use case
illustrates stochastic generation using the default models.
To use generateScenarios with the defaults, and without
penalty attributes, only two input arguments are mandatory: the
target attribute values and the reference time
series. Optional additional arguments comprising the length of
the generated perturbed time series (simLengthNyrs) and the
number of replicates (numReplicates) may be specified as
desired.
Consider the following exposure space of precipitation and
temperature attributes. After deciding the attributes, perturbed bounds,
and sampling strategy as described in Step A, the target attribute
values that sample the exposure space is created using the
createExpSpace function. The total annual precipitation and
mean annual temperature are perturbed while holding the attributes
"P_ann_R10_m", "P_DJF_tot_m","Temp_ann_rng_m", "Temp_DJF_avg_m"
at existing levels (Use viewAttributeDef() for definitions
of these attributes). The createExpSpace function call
returns the exposure space in an R list. The targetMat
(named after “target matrix”) element of the list contains the locations
of the four selected target locations in the exposure space with
perturbations in annual total precipitation and annual mean temperature.
Each row of this matrix is a target location. In this exposure space,
target 1 corresponds to perturbation of 0.8 in “P_ann_tot_m”, and -0.5
in “Temp_ann_avg_m”, while the other attributes are held at existing
levels and so on. Remember that the perturbations in precipitation are
multiplicative while that in temperature is additive.
# Selected attributes
attPerturb <- c("P_ann_tot_m", "Temp_ann_avg_m")
attHold <- c("P_ann_R10_m", "P_DJF_tot_m","Temp_ann_rng_m", "Temp_DJF_avg_m")
# Sampling bounds and strategy
attPerturbType = "regGrid"
attPerturbSamp = c(2, 2)
attPerturbMin = c(0.8,-0.5)
attPerturbMax = c(1.2,0.5)
# Creating the exposure space
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
utils::str(expSpace)
#> List of 8
#> $ targetMat :'data.frame': 4 obs. of 6 variables:
#> ..$ P_ann_tot_m : num [1:4] 0.8 1.2 0.8 1.2
#> ..$ Temp_ann_avg_m: num [1:4] -0.5 -0.5 0.5 0.5
#> ..$ P_ann_R10_m : num [1:4] 1 1 1 1
#> ..$ P_DJF_tot_m : num [1:4] 1 1 1 1
#> ..$ Temp_ann_rng_m: num [1:4] 0 0 0 0
#> ..$ Temp_DJF_avg_m: num [1:4] 0 0 0 0
#> $ attRot : NULL
#> $ attPerturb : chr [1:2] "P_ann_tot_m" "Temp_ann_avg_m"
#> $ attHold : chr [1:4] "P_ann_R10_m" "P_DJF_tot_m" "Temp_ann_rng_m" "Temp_DJF_avg_m"
#> $ attPerturbSamp: num [1:2] 2 2
#> $ attPerturbMin : num [1:2] 0.8 -0.5
#> $ attPerturbMax : num [1:2] 1.2 0.5
#> $ attPerturbType: chr "regGrid"
# Four target locations in the exposure space
expSpace$targetMat
#> P_ann_tot_m Temp_ann_avg_m P_ann_R10_m P_DJF_tot_m Temp_ann_rng_m Temp_DJF_avg_m
#> 1 0.8 -0.5 1 1 0 0
#> 2 1.2 -0.5 1 1 0 0
#> 3 0.8 0.5 1 1 0 0
#> 4 1.2 0.5 1 1 0 0
Having generated the exposure space, we progress to Step B of the
work flow. The example climate time series, tank_obs,
available in the package is used as the reference to create perturbed
time series. The default stochastic models in foreSIGHT are
used by not specifying a controlFile argument in the
generateScenarios function call. Note that the following
function call takes about 10 minutes to execute.
# ******************************** NOTE ****************************
# The following generateScenarios call takes ~10 mins to complete
# ******************************************************************
data("tankDat")
sim <- generateScenarios(reference = tank_obs, # reference time series
expSpace = expSpace, # exposure space
numReplicates = 3) # number of replicates
The biases in the simulated attributes with respect to the specified
target values of the attributes for each target are examined using the
plotScenarios function. The following function call creates
heatmap plots of the biases.
The plot of the mean of absolute biases of the simulated values
relative to the target values in this simulation is shown below. Note
that the above generateScenarios function call has been set
to generate three stochastic replicates. If you are running the code in
this tutorial, you won’t necessarily reproduce the figure below as
generateScenarios randomly selects a seedID
for each simulation. If you wish to reproduce the simulation in this use
case set the seedID argument to 2407.
The mean of the absolute biases in each simulated attribute (both
perturbed and held) for each target across the three replicates are
plotted. The biases in the scenarios are typically low as indicated by
the green shades in the plot. In other words, the attributes of the
generated perturbed time series correspond well to the desired target
values of the attributes. This means we may proceed with analysing other
characteristics of the perturbed time series, and simulating system
performance.
In this example the use of default stochastic models without penalty
attributes yields satisfactory results for the target values of the
specified attributes.
Use Case B4: Why holding attributes at reference levels are
necessary
When using stochastic models to generate the perturbed time series,
it is necessary to hold some attributes at reference levels to ensure
the realism of the simulated climate data. This use case provides an
example to illustrate why.
Consider an exposure space with perturbations only in mean annual
total rainfall (“P_ann_tot_m”). First, let’s create an exposure space
that contains only a single perturbed target of this attribute, with no
other attributes held at reference levels. The below code generates data
corresponding to the single target location.
attPerturb <- c("P_ann_tot_m")
attHold <- NULL
attPerturbType = "regGrid"
attPerturbSamp = c(1)
attPerturbMin = c(1.3)
attPerturbMax = c(1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
#> Note: There are no attributes held at historical levels
expSpace$targetMat # exposure space containing a single target
#> P_ann_tot_m
#> 1 1.3
data(tankDat) # reference data
sim <- generateScenarios(reference = tank_obs[, 1:4], expSpace = expSpace) # simulation
#> Generating replicate number 1 out of 1 replicates...
#> Warning: No attributes held at historical levels
#>
#> Simulation completed
We can use the calculateAttributes function to calculate
the values of various attributes of both the reference and simulated
time series as shown below. The percentage differences in various
attributes of the simulated data with respect to the reference is also
calculated. The perturbations in the attribute “P_ann_tot_m” is close to
the desired increase of 30%. However, the other attributes show large
differences from the reference. This is because we created the exposure
space to generate perturbations in “P_ann_tot_m”, without any
constraints in other attributes, rendering the simulation
unrealistic.
# calculate selected attributes from reference
attSel <- c("P_ann_tot_m", "P_ann_seasRatio", "P_ann_nWet_m", "P_ann_maxDSD_m", "P_ann_maxWSD_m",
"P_ann_R10_m", "P_ann_dyWet_m", "P_ann_P99")
obsAtts <- calculateAttributes(tank_obs, attSel)
# get the simulated precipitation and dates from sim & calculate the same attributes
P <- sim[["Rep1"]][["Target1"]][["P"]][["sim"]]
simData <- cbind(as.data.frame(sim[["simDates"]]), P)
simAtts <- calculateAttributes(simData, attSel)
# calculate the % differences between simulated attributes and reference
percAttDiff <- (simAtts - obsAtts)/obsAtts*100
percAttDiff
#> P_ann_tot_m P_ann_seasRatio P_ann_nWet_m P_ann_maxDSD_m P_ann_maxWSD_m P_ann_R10_m
#> 30.00000 10.38539 97.88200 -72.72727 1270.00000 32.17391
#> P_ann_dyWet_m P_ann_P99
#> -33.96602 28.23517
Thus, we need to select some other attributes to hold at existing
levels to make sure that the simulated data is physically realistic.
Consider the other precipitation attributes calculated above. Some of
them are related to number and sequence of wet precipitation days
(number of wet days, wet & dry spell lengths), while others are
related to the intensity of precipitation (mean wet day rainfall,
99th percentile rainfall). “P_ann_R10_m” is actually a
combined measure of frequency and intensity, and “P_ann_seasRatio” is a
measure of wet to dry seasonal rainfall (Note: use
viewAttributeDef for attribute definitions). If we select
all these attributes to be held at existing levels, it would become
almost impossible to perturb the annual precipitation as desired since a
30% increase in “P_ann_tot_m” warrants changes in atleast some of these
rainfall characteristics. So, we need to select a viable subset of these
other attributes to hold at reference levels.
Suppose a priori knowledge suggests that an increase in
rainfall intensity is the typical driving mechanism behind increases in
annual rainfall in the region, and that a change in seasonal ratio is
unrealistic. We can decide to hold the wet day frequency, spell length,
and seasonal ratio related attributes at reference levels, while
allowing changes in the intensity attributes. An updated exposure space
and simulation are generated as shown below.
attPerturb <- c("P_ann_tot_m")
attHold <- c("P_ann_seasRatio", "P_ann_nWet_m", "P_ann_maxDSD_m", "P_ann_maxWSD_m")
attPerturbType = "regGrid"
attPerturbSamp = c(1)
attPerturbMin = c(1.3)
attPerturbMax = c(1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
expSpace$targetMat # exposure space containing a single target
#> P_ann_tot_m P_ann_seasRatio P_ann_nWet_m P_ann_maxDSD_m P_ann_maxWSD_m
#> 1 1.3 1 1 1 1
data(tankDat) # reference data
simHold <- generateScenarios(reference = tank_obs[ ,1:4], expSpace = expSpace) # simulation
#> Generating replicate number 1 out of 1 replicates...
#> Simulation completed
The updated simulated shows much lower differences in most attributes
from the reference series. As expected, the attributes related to the
intensity of the rainfall show large differences - generating the
desired perturbation in mean annual rainfall.
P <- simHold[["Rep1"]][["Target1"]][["P"]][["sim"]]
simHoldData <- cbind(as.data.frame(simHold[["simDates"]]), P)
simHoldAtts <- calculateAttributes(simHoldData, attSel)
percDiff <- (simHoldAtts - obsAtts)/obsAtts*100
percDiff
#> P_ann_tot_m P_ann_seasRatio P_ann_nWet_m P_ann_maxDSD_m P_ann_maxWSD_m P_ann_R10_m
#> 3.000000e+01 -2.704248e-08 4.538578e-01 -7.905138e-01 1.000000e+00 5.130435e+01
#> P_ann_dyWet_m P_ann_P99
#> 2.977900e+01 5.264020e+01
Typically, we would also look at other characteristics of the
simulation, to ensure that the perturbed series are suitable for the
specific stress test. For example, let us consider the monthly rainfall
climatology of the reference and simulated data. The mean monthly
rainfall (in mm/day) is calculated and plotted below. We find that the
simulation with held attributes are more similar to the reference
series.
# calculate mean monthly rainfall in mm/day
tank_obs_monClim <- aggregate(tank_obs[,4], by = list(tank_obs[,2]), FUN = mean)$x
sim_monClim <- aggregate(simData[,4], by = list(simData[,2]), FUN = mean)$x
simHold_monClim <- aggregate(simHoldData[,4], by = list(simHoldData[,2]), FUN = mean)$x
# plot monthly climatology
yMax <- max(tank_obs_monClim, sim_monClim, simHold_monClim)
colSel <- c("black", "red", "forestgreen")
lwdSel <- 2
plot(tank_obs_monClim, type = "l", ylim = c(0,yMax), lwd = lwdSel, ylab = "Monthly P (mm/day)", xlab = "months", col = colSel[1])
lines(sim_monClim, col = colSel[2], lwd = lwdSel)
lines(simHold_monClim, col = colSel[3], lwd = lwdSel)
legend("topright", legend = c("reference", "sim", "simHold"), col = colSel, lwd = lwdSel)
We can conduct further analyses of the characteristics of the
simulation to decide if other attributes need to be included in
attHold. We leave it to the reader to build on this use
case to explore what adding other attributes does. In some cases, it may
become difficult to obtain the desired target values (perturbations or
existing levels), due to intrinsic dependencies between the attributes
(eg: totals are related to intensity & frequency). In these
instances, the functionality to prescribe penalty attributes and weights
can be used to set preferences for lower biases in some attributes over
others to obtain desired target values. More on penalty attributes in
further use cases.
Use Case B5: Specifying penalty attributes
In some cases, the attributes of the generated perturbed time series
can show large biases in the target values of some attributes.
Specifying penalties for biases in these attributes can reduce the
biases. However, the reduction is often at the expense of increased
biases in other attributes. Therefore, you may need a few trials to
identify appropriate penalty settings that provide desired results for
specific scenarios. This use case provides such an example.
Consider the following exposure space of precipitation attributes.
The annual total precipitation and number of wet days are perturbed
while holding the attributes
"P_ann_P99", "P_Feb_tot_m", "P_SON_dyWet_m", "P_JJA_avgWSD_m", "P_MAM_tot_m", "P_ann_seasRatio"
at existing levels (use viewAttributeDef() to view the
definitions of these attributes). After deciding the perturbation bounds
of the relevant attributes and the sampling strategy, the
createExpSpace function is used to create the exposure
space. The function call returns an R list containing the exposure
space. The targetMat (named after “target matrix”) element
of the list contains the locations of the four selected target locations
in the exposure space. Each row of this matrix is a target location. In
this exposure space, target 1 corresponds to perturbations of 0.8 each
in “P_ann_tot_m” and “P_ann_nWet_m”, while the other attributes are held
at existing levels, and so on.
# Selected attributes
attPerturb <- c("P_ann_tot_m","P_ann_nWet_m")
attHold <- c("P_ann_P99","P_Feb_tot_m", "P_SON_dyWet_m", "P_JJA_avgWSD_m",
"P_MAM_tot_m","P_ann_seasRatio")
# Sampling bounds and strategy
attPerturbType = "regGrid"
attPerturbSamp = c(2,2)
attPerturbMin = c(0.8,0.8)
attPerturbMax = c(1.1,1.1)
# Creating the exposure space
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
utils::str(expSpace)
#> List of 8
#> $ targetMat :'data.frame': 4 obs. of 8 variables:
#> ..$ P_ann_tot_m : num [1:4] 0.8 1.1 0.8 1.1
#> ..$ P_ann_nWet_m : num [1:4] 0.8 0.8 1.1 1.1
#> ..$ P_ann_P99 : num [1:4] 1 1 1 1
#> ..$ P_Feb_tot_m : num [1:4] 1 1 1 1
#> ..$ P_SON_dyWet_m : num [1:4] 1 1 1 1
#> ..$ P_JJA_avgWSD_m : num [1:4] 1 1 1 1
#> ..$ P_MAM_tot_m : num [1:4] 1 1 1 1
#> ..$ P_ann_seasRatio: num [1:4] 1 1 1 1
#> $ attRot : NULL
#> $ attPerturb : chr [1:2] "P_ann_tot_m" "P_ann_nWet_m"
#> $ attHold : chr [1:6] "P_ann_P99" "P_Feb_tot_m" "P_SON_dyWet_m" "P_JJA_avgWSD_m" ...
#> $ attPerturbSamp: num [1:2] 2 2
#> $ attPerturbMin : num [1:2] 0.8 0.8
#> $ attPerturbMax : num [1:2] 1.1 1.1
#> $ attPerturbType: chr "regGrid"
# Four target locations in the exposure space
expSpace$targetMat
#> P_ann_tot_m P_ann_nWet_m P_ann_P99 P_Feb_tot_m P_SON_dyWet_m P_JJA_avgWSD_m P_MAM_tot_m
#> 1 0.8 0.8 1 1 1 1 1
#> 2 1.1 0.8 1 1 1 1 1
#> 3 0.8 1.1 1 1 1 1 1
#> 4 1.1 1.1 1 1 1 1 1
#> P_ann_seasRatio
#> 1 1
#> 2 1
#> 3 1
#> 4 1
Having generated the exposure space, we progress to Step B of the
work flow. The example climate time series, tank_obs,
available in the package is used as the reference to create perturbed
time series. Consider the case where the default stochastic models in
foreSIGHT without penalty attributes are used to generate the
time series for the target locations in the exposure space, similar to
use case B2. The function call is set up without specifying the
controlFile argument of generateScenarios. The
below code generates the perturbed time series and heatmap plots to
evaluate the ‘fitness’. Note that the generateScenarios
function call takes about 5 minutes to execute. The ‘fitness’ of the
scenarios in terms of the biases in simulated attributes relative to the
targets values of the attributes generated using the
plotScenarios function is shown in the subsequent
figure.
# ******************************** NOTE ****************************
# The following generateScenarios call takes ~5 mins to complete
# ******************************************************************
data("tankDat")
sim <- generateScenarios(reference = tank_obs, # reference time series
expSpace = expSpace, # exposure space
numReplicates = 1, # number of replicates
simLengthNyrs = 10, # length of simulated time series
seedID = 2) # random seed
plotScenarios(sim)
Note that the above generateScenarios function call is
set to generate a single stochastic replicate.
There are large biases (>10%) in the perturbed attribute annual
total rainfall of the second and third targets. To lower this bias, we
can add a penalty for biases in this attribute while using
generateScenarios via a JSON controlFile.
Consider the case where the penalty weight of this attribute to 10, as a
first guess. The below code shows the function call with this penalty
setting. Note that we have specified the seedID as 1 -
which is the random seed selected by the function for the simulation
shown in the previous figure. Thus, this new simulation starts from the
same seed as the previous one, but has an additional penalty attribute
and weight. More on the seed towards the end of this use case. Thus, in
the new simulation we specify penalties for biases in “P_ann_tot_m” with
weight set to 10. The fitness of the generated perturbed series is
assessed using the heatmaps created using the plotScenarios
function.
# specify the penalty settings in a list
penaltySelection <- list()
penaltySelection[["penaltyAttributes"]] <- c("P_ann_tot_m","P_ann_nWet_m")
penaltySelection[["penaltyWeights"]] <- c(10,10)
# write the list into a JSON file
penaltySelectionJSON <- jsonlite::toJSON(penaltySelection, pretty = TRUE, auto_unbox = TRUE)
write(penaltySelectionJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios with penalty setting
sim_wPenalty <- generateScenarios(reference = tank_obs, expSpace = expSpace, numReplicates = 1,
simLengthNyrs = 10, seedID = 2,
controlFile = paste0(tempdir(), "controlFile.json"))
plotScenarios(sim_wPenalty)
The figure shows that the biases in the attribute for which penalty
is applied, “P_ann_tot_m”, is close to zero. However, the biases in the
attributes that are held at historical levels are too high. Thus, it
appears that the application of this penalty setting is geared towards
lower biases in “P_ann_tot_m” too strongly in these scenarios. To
balance the errors, suppose we lower the weight of the penalty attribute
to 2 instead of 10. The below code shows the corresponding function
calls.
# specify the penalty settings in a list
penaltySelection <- list()
penaltySelection[["penaltyAttributes"]] <- c("P_ann_tot_m","P_ann_nWet_m")
penaltySelection[["penaltyWeights"]] <- c(2,2)
# write the list into a JSON file
penaltySelectionJSON <- jsonlite::toJSON(penaltySelection, pretty = TRUE, auto_unbox = TRUE)
write(penaltySelectionJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios with penalty setting
sim_wPenalty2 <- generateScenarios(reference = tank_obs, expSpace = expSpace, numReplicates = 1,
simLengthNyrs = 10, seedID = 2,
controlFile = paste0(tempdir(), "controlFile.json"))
plotScenarios(sim_wPenalty2)
The figure shows that the biases in the attributes of the simulated
time series are more evenly distributed among the attributes in the
latest simulation. The biases in all the attributes are about 5% or
lower, and the generated perturbed time series correspond well to the
desired target values of the attributes. We may proceed with analysing
other characteristics of the perturbed time series, and simulating
system performances.
A note about the use of seedID in these examples: The
seedID of the simulations using penalty settings are set to
that of the first simulation without using penalty attributes to
highlight the differences in simulation fitness with the addition of the
penalty setting. If sufficient replicates are generated for the
scenarios, the difference would be apparent in the mean fitness without
setting the seedID. Three replicates are generated in this
use case so that the simulations can be performed without much
computational effort. We leave it to the reader to try performing
similar simulations with more replicates and a longer time series length
to assess the differences.
The examples presented in this use case are relatively simple, but
illustrates the use of penalty attribute functionality and the
trade-offs in fitness involved. We expect that the users would need to
apply penalty attributes and weights in most of their stress-tests to
obtain the desired perturbed time series. The application becomes more
complex in cases where a penalty has to be applied to multiple
attributes, and one needs to decide the penalty weights for all of them.
A few trial simulations may be necessary to decide the penalty settings
to be used for the final stress-test in real world applications.
Use Case B6: Choosing a different stochastic model
In some cases, one might want to select an alternate stochastic model
different from the default models in foreSIGHT. Note that the
viewModels() function can be used to view the details of
all the stochastic models available in the package. A different model
may be selected based on prior knowledge about the ability of the
stochastic model to represent characteristics of the climate data that
are relevant for the specific case study. This use case provides an
example to show how to select a different stochastic generator using the
controlFile argument.
Consider the the following exposure space that consists of attributes
pertaining to annual statistics of rainfall. After deciding the
perturbation bounds and the sampling strategy, the
createExpSpace function is used to create the exposure
space. The function call returns an R list containing the exposure
space. The default precipitation stochastic model in foreSIGHT
can be used to generate the perturbed time series as shown below.
# create the exposure space
attPerturb <- c("P_ann_tot_m", "P_ann_P99")
attHold <- c("P_ann_maxWSD_m", "P_ann_nWet_m")
attPerturbType = "regGrid"
attPerturbSamp = c(2, 2)
attPerturbMin = c(0.9, 0.9)
attPerturbMax = c(1.3, 1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
# specify the penalty settings in a list
controlFileList <- list()
controlFileList[["penaltyAttributes"]] <- c("P_ann_tot_m")
controlFileList[["penaltyWeights"]] <- c(0.5)
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
sim <- generateScenarios(reference = tank_obs, expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
Now, suppose you want to select an alternate stochastic generator to
generate the perturbed time series, the “wgen” model that has an annual
variation in the parameters (modelType = "wgen", and
modelParameterVariation = "annual"). These changes can be
specified along with the penalty attribute settings in the
controlFile as shown below.
# specify the penalty settings in a list
controlFileList <- list()
controlFileList[["penaltyAttributes"]] <- c("P_ann_tot_m")
controlFileList[["penaltyWeights"]] <- c(0.5)
controlFileList[["modelType"]] <- list()
controlFileList[["modelType"]][["P"]] <- "wgen"
controlFileList[["modelParameterVariation"]] <- list()
controlFileList[["modelParameterVariation"]][["P"]] <- "annual"
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
sim <- generateScenarios(reference = tank_obs, expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
foreSIGHT also has the capability to perform multisite
stochastic rainfall simulations, where changes can be specified in the
attributes at each site, as well as in the spatial correlation between
sites. See the help file for generateScenarios() for
details and a working example.
6. Step D: Visualise system performances
(plotPerformanceSpace, plotPerformanceOAT,
plotPerformanceSpaceMulti)
In this step you’ll learn…
- The different types of performance space visualisations that are
available in foreSIGHT
- How to add Performance Thresholds to plotting
elements
- How to combine Bottom-up and
Top-down frameworks by integrating climate model
projections into the plotting
- How to plot performance spaces for systems with multiple performance
metrics
Now that we’ve generated samples of a Performance
Space as part of Step C, we now turn to the challenge of
visualisation. On the surface this might seem like a relatively trivial
problem relative to the difficulties of generating the exposure space in
the first place, however there are various issues to consider:
- How to plot performance spaces for different numbers of
attributes
- Alternative visualisations of system performance, including for
situations where there are clearly defined performance thresholds
- How to overlay climate projections and other ‘lines of evidence’
onto the performance space
- Troubleshooting when the performance spaces do not look the way they
should
Key considerations associated with plotting are discussed next,
followed by various example ‘Use Cases’ of the plotting
functionality.
Key Considerations: Step D
As highlighted in various other parts of this tutorial, most
climate-sensitive systems can be extremely complex, and this complexity
means that the system can be sensitive to a large number of climate
features (or Climate Attributes, using the preferred
foreSIGHT terminology). One of the primary objectives of
climate stress tests is to uncover how systems might respond to
plausible future changes, including the identification of possible modes
of system failure. The plotting functions in foreSIGHT are
designed with this purpose in mind.
However, before delving into the mechanics of plotting, it’s worth
stressing an extremely important caveat. We know that climate
change can alter a broad range of statistical features (including
changes to the averages, seasonality, intermittency, interannual
variability, and extremes) of a broad range of hydroclimate variables
(rainfall, humidity, wind, evapotranspiration, etc). We also
know that systems can respond to climatic stressors in complex
and unexpected ways. Yet traditional bottom-up stress tests tend to
focus on only a small number of attributes, given limitations in both
computational power (both in generating the perturbed time series and
running it through the system model, as discussed in Steps B and C) and
visualisation (we have difficulty looking at plots in more than two
dimensions). This latter point in particular means that, if we are not
careful, we could miss major modes of variability just because of the
method we’ve chosen to visualise the results.
This brings us to an important point: each visualisation contains
(often very strong) ceteris paribus assumptions; or in plain
English, the conventional plotting approaches assume that the elements
not included in the plot will remain constant and usually at
the levels of the reference (e.g. historical) climate.
To minimise the risk of this issue, we make the following
recommendations:
- Experiment with multiple plotting options, always being aware of the
ceteris paribus assumptions that are implicit in any decision
not to plot a certain attribute
- Compare the results from high-dimensional plots (that generally
contain greater information content and fewer assumptions, but are also
harder to interpret) with low-dimensional plots of key attributes
- Always compare the results from top-down assessments with
those from bottom-up assessments. This latter point is a particularly
important one, and generally not discussed in most of the
scenario-neutral literature. A top-down analysis involves running a set
of (often downscaled) climate projections through a system model and
plotting the system performance. These performance values can be
superimposed on the results of a bottom-up analysis using plotting
features that are available in foreSIGHT, to see whether these
yield similar results. If they produce different results, it must be
because the system is somehow sensitive to features (or attributes) that
are not the ones being plotted on the performance space; or, in
other words, the discrepancy suggests that the ceteris paribus
assumption is not being met. Hopefully you don’t have this difficulty,
but if you do we’ll cover possible approaches to address this
discrepancy in the next update for this vignette.
Finally, we note that just as every system is different, so too are
the needs of each stress test. We’ve tried to make the plotting
functions flexible to a range of visualisation options to enable high
levels of customisation, and new options are regularly being added so
make sure to check the plotting function help files for the latest
information.
foreSIGHT contains three functions to visualise the system
performances - plotPerformanceOAT,
plotPerformanceSpace, and
plotPerformanceSpaceMulti.The performance plotting
functions use the system performance and the simulation summary as input
arguments. There are three functions available in foreSIGHT to
plot performance metrics. Brief descriptions of these functions are
provided below and detailed usages are illustrated in the use cases
presented in the following sub-sections.
plotPerformanceOAT: The function creates line plots
(with shading to show the range from replicates) to show the variations
in a system performance metric with one-at-a-time (OAT) perturbations in
attributes. This function is intended for use with an “OAT” exposure
space, assuming all other attributes are held constant (usually at their
historical levels). However, if “OAT” perturbations exist in a “regGrid”
exposure space, the function will subset these targets to create the
plots. This subset can be thought of as a slice through the exposure
space when the other attributes are kept at historical levels. If the
exposure space does not contain attribute values at historical levels,
the “OAT” plots cannot be created. plotPerformanceOAT will
print an error to inform that there are no “OAT” perturbations in the
exposure space in such an instance.
plotPerformanceSpace: The function plots
two-dimensional heatmaps and contours of the selected system performance
metric at multiple target locations in the exposure space. The
performance metric outputs created from a ‘regGrid’ exposure space is
termed the “performance space” as it contains the system
performance at multiple target locations in the exposure space, that can
be visualised using two-dimensional plots. If the exposure space
contains more than two dimensions, the function can be used to create a
plot using two dimensions selected by the user. To analyse
higher-dimensional performance spaces, the plots can be placed in panels
to asses the impact of simultaneous perturbations in multiple
attributes. In some cases, there may be a clear performance ‘threshold’,
above or below which the system performance becomes undesirable and/or
triggers a system ‘failure’ (for example, an agreed minimum specified
level of system reliability). In this case, the user may specify the
threshold value of the performance metric as an input argument,
resulting in the addition of a thick contour line to the plot in order
to mark this threshold in the performance space.
It is possible to add various lines of evidence to provide guidance
on which parts of the exposure space are more or less plausible in a
future climate. For example it is possible to superimpose projections
from climate models to the performance space plotted using
plotPerformanceSpace. This climate data should contain
values of projected changes in attributes that are used as the axes of
the performance space, and which need to be developed separately from
the foreSIGHT work flow. For example, one might extract
relevant attribute values from a 30 year future timeslice from the
relevant climate model output, potentially after downscaling, bias
correction or other processing.
One may also elect to use the climate model simulations (potentially
after downscaling, bias correction or other processing) as inputs to the
system model to generate new performance values corresponding to each
projection time series, and in this case it is possible to plot the
performance values corresponding to the climate model simulations as
coloured data points in plots created using
plotPerformanceSpace, using the same colour scale.
plotPerformanceSpaceMulti: The third function
available in foreSIGHT for plotting system performance is the
joint presentation of multiple system performance metrics to facilitate
decision making. The function plots contours showing the number of
performance metric thresholds exceeded in the performance space. The
user should specify the minimum or maximum thresholds of each
performance metric as input arguments for calculation.
If the exposure space contains many target locations and the
perturbed time series contains multiple replicates, the simulation
(sim) can be quite large in size, . The
getSimSummary function in foreSIGHT can be used to
get the summary metadata (exposure space, controlFile, simulation seed
etc.) of a simulation, which is easy to store and use with the plotting
functions in foreSIGHT.
simSummary <- getSimSummary(sim)
The mandatory arguments to the these plotting functions are the
simulation (or simulation summary, see below) of the perturbed scenarios
generated in Step B (sim), and the performance metric
calculated by the system model in Step C (performance) to
be plotted.
plotPerformanceOAT(performance, sim)
plotPerformanceSpace(performance, sim)
plotPerformanceSpaceMulti(performance, sim)
The functions contain other arguments to subset the data and control
the appearance of the plots. We present some use cases to illustrate
these capabilities in the following sub-sections.
Use Case D1: Plotting performance metrics of OAT perturbations
A climate stress-test typically starts with a preliminary assessment
using ‘OAT’ perturbations in the climate attributes selected based on an
understanding of the system dynamics. Such an assessment provides
guidance for the selection of attributes for a more rigorous
stress-test, with the caveat that system vulnerabilities arising from
simultaneous perturbations in the attributes will not be considered.
Suppose that you have selected the preliminary attributes, created an
‘OAT’ performance space, generated perturbed time series and run the
system model to simulate system performance metrics employing all the
key considerations outlined in this tutorial. As the next step, you
would need to visualise the performance metrics to understand the system
responses to ‘OAT’ perturbations in the selected climate attributes. The
function plotPerformanceOAT can be used for this
purpose.
Fine resolution perturbations of the selected attributes, and
multiple replicates are necessary to obtain a smoother picture of the
changes in performance metric. Since it is not feasible to generate such
perturbed time series quickly, we use example datasets available in the
foreSIGHT package for illustration here. The data are the
summary of an ‘OAT’ perturbed simulation (egSimOATSummary)
and the performance metrics of one configuration of the rain water tank
system model created using the simulation
(egSimOATPerformance). The daily operation of the rain
water tank is simulated using precipitation and temperature time series
as input, and these metrics quantify the performance of the tank (see
section on inbuilt system models) First lets understand the structure of
the simulation and system performance metrics.
# load data
data("egSimOATSummary")
data("egSimOATPerformance")
egSimOATSummary$expSpace$attPerturb # the perturbed attributes
#> [1] "P_ann_tot_m" "P_ann_seasRatio_m" "P_ann_nWet_m" "P_ann_R10_m"
utils::str(egSimOATSummary$expSpace) # targets in the exposure space
#> List of 8
#> $ targetMat :'data.frame': 88 obs. of 11 variables:
#> ..$ P_ann_tot_m : num [1:88] 0.8 0.816 0.832 0.847 0.863 ...
#> ..$ P_ann_seasRatio_m: num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_ann_nWet_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_ann_R10_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_Feb_tot_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_SON_dyWet_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_JJA_avgWSD_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_MAM_tot_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_DJF_avgDSD_m : num [1:88] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ Temp_ann_rng_m : num [1:88] 0 0 0 0 0 0 0 0 0 0 ...
#> ..$ Temp_ann_avg_m : num [1:88] 0 0 0 0 0 0 0 0 0 0 ...
#> $ attRot : chr [1:88] "P_ann_tot_m" "P_ann_tot_m" "P_ann_tot_m" "P_ann_tot_m" ...
#> $ attPerturb : chr [1:4] "P_ann_tot_m" "P_ann_seasRatio_m" "P_ann_nWet_m" "P_ann_R10_m"
#> $ attHold : chr [1:7] "P_Feb_tot_m" "P_SON_dyWet_m" "P_JJA_avgWSD_m" "P_MAM_tot_m" ...
#> $ attPerturbSamp: num [1:4] 20 32 14 22
#> $ attPerturbMin : num [1:4] 0.8 0.8 0.85 0.9
#> $ attPerturbMax : num [1:4] 1.1 1.3 1.05 1.25
#> $ attPerturbType: chr "OAT"
utils::str(egSimOATSummary, max.level = 1)
#> List of 13
#> $ Rep1 :List of 88
#> $ Rep2 :List of 88
#> $ Rep3 :List of 88
#> $ Rep4 :List of 88
#> $ Rep5 :List of 88
#> $ Rep6 :List of 88
#> $ Rep7 :List of 88
#> $ Rep8 :List of 88
#> $ Rep9 :List of 88
#> $ Rep10 :List of 88
#> $ simDates :'data.frame': 109572 obs. of 3 variables:
#> $ expSpace :List of 8
#> $ controlFile:List of 6
utils::str(egSimOATPerformance) # system performance metrics from simulations of the tank model
#> List of 2
#> $ Avg. Deficit (L): num [1:88, 1:10] 26.3 25.9 26.7 27 26.6 ...
#> $ Reliability (-) : num [1:88, 1:10] 0.813 0.816 0.813 0.811 0.812 ...
The simulation contains four perturbed precipitation attributes and a
total of 88 target locations in the exposure space, generated using an
‘OAT’ perturbation method. The minimum-maximum bounds and the number of
samples show that the perturbations have a resolution of 0.015 to 0.017.
There are twenty replicates in the simulation to incorporate random
variability into the generated data. The system performance data
contains two performance metrics of the rain water tank model - the
average daily deficit of water in litres, and the reliability of the
tank in meeting the water demand as a fraction. The performance metrics
can be plotted using the function plotPerformanceOAT. The
function contains arguments to specify the metric to be plotted
(metric), the colour of the plots (col), the
number of top replicates (in terms of fitness) to be used for the plots
(topReps), and the the y-axis limit (ylim).
The topReps argument sorts the replicates by closeness of
fit in terms of the objective function used for optimisation, and uses
the specified topReps number replicates to create the
plots. In the example code below, the top 8 replicates out of the total
10 are used. The function creates paneled plots showing the variations
in the performance metric with changes in each perturbed attribute.
p1 <- plotPerformanceOAT(performance = egSimOATPerformance, # list of performance metrics
sim = egSimOATSummary, # simulation metadata
metric = "Reliability (-)", # the metric to be plotted
col ="orange", # colour of the plot
topReps = 8, # number of top replicates to be used
ylim = c(0.7, 0.9)) # y-axis limits
The figure shows the variation in the performance metric “Reliability
(-)” with changes in the four perturbed attributes. The performance
metric is most sensitive to two attributes - mean annual total rainfall,
and the mean annual seasonal ratio. The results indicate that the
attributes may be selected for a more rigorous stress-test using a
‘regGrid’ exposure space of multiple target locations involving
simultaneous perturbations in these attributes.
Use Case D2: Plotting performance spaces
Comprehensive climate stress-test of a system typically involves the
use of an exposure space with ‘regGrid’ perturbations in two or more
attributes (i.e. a multi-dimensional exposure space). The performance
metric values corresponding to all target locations in the exposure
space is referred to as the performance space. Visualisation of
performance spaces using multiple performance metrics are necessary to
identify the most vulnerable areas in an exposure space.
Suppose you’ve conducted the first three steps of a stress-test using
a ‘regGrid’ exposure space - creation of the exposure space, generation
of perturbed time series, and simulations using the system model to
calculate the system performance metrics. In the next step, you need to
visualise the performance space using the functions
plotPerformanceSpace and
plotPerformanceSpaceMulti to draw conclusions about system
vulnerability and system failure from the stress-test. Smooth
performance spaces are often necessary to draw inferences from the data.
Practically, finer resolutions of the exposure space and multiple
stochastic replicates are required to obtain smooth performance spaces.
We use example data available in foreSIGHT to illustrate.
Consider the following example data - a stochastic simulation summary
(egSimSummary), and corresponding performance metrics
calculated using a configuration of the tank system model
(egSimPerformance). The tank model simulated the daily
operation of a rain water tank using precipitation and temperature time
series as input and the calculated metrics quantify the performance of
the tank (see section on inbuilt system models).
# load data
data("egSimSummary")
data("egSimPerformance")
egSimSummary$expSpace$attPerturb # the perturbed attributes
#> [1] "P_ann_tot_m" "P_ann_seasRatio"
utils::str(egSimSummary$expSpace) # target locations in the exposure space
#> List of 8
#> $ targetMat :'data.frame': 160 obs. of 11 variables:
#> ..$ P_ann_tot_m : num [1:160] 0.8 0.833 0.867 0.9 0.933 ...
#> ..$ P_ann_seasRatio: num [1:160] 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 ...
#> ..$ P_ann_nWet_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_ann_R10_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_Feb_tot_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_SON_dyWet_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_JJA_avgWSD_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_MAM_tot_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_DJF_avgDSD_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ Temp_ann_rng_m : num [1:160] 0 0 0 0 0 0 0 0 0 0 ...
#> ..$ Temp_ann_avg_m : num [1:160] 0 0 0 0 0 0 0 0 0 0 ...
#> $ attRot : NULL
#> $ attPerturb : chr [1:2] "P_ann_tot_m" "P_ann_seasRatio"
#> $ attHold : chr [1:9] "P_ann_nWet_m" "P_ann_R10_m" "P_Feb_tot_m" "P_SON_dyWet_m" ...
#> $ attPerturbSamp: num [1:2] 10 16
#> $ attPerturbMin : num [1:2] 0.8 0.8
#> $ attPerturbMax : num [1:2] 1.1 1.3
#> $ attPerturbType: chr "regGrid"
utils::str(egSimSummary, max.level = 1)
#> List of 13
#> $ Rep1 :List of 160
#> $ Rep2 :List of 160
#> $ Rep3 :List of 160
#> $ Rep4 :List of 160
#> $ Rep5 :List of 160
#> $ Rep6 :List of 160
#> $ Rep7 :List of 160
#> $ Rep8 :List of 160
#> $ Rep9 :List of 160
#> $ Rep10 :List of 160
#> $ simDates :'data.frame': 109572 obs. of 3 variables:
#> $ expSpace :List of 8
#> $ controlFile:List of 6
utils::str(egSimPerformance) # system performance metrics from simulations of the tank model
#> List of 2
#> $ Avg. Deficit (L): num [1:160, 1:10] 25.3 22.9 21 22.5 21.3 ...
#> $ Reliability (-) : num [1:160, 1:10] 0.818 0.836 0.85 0.84 0.845 ...
The example simulation contains two perturbed precipitation
attributes and a total of 160 target locations in a ‘regGrid’ exposure
space. Considering the minimum-maximum bounds and the number of samples
we see that the perturbations have a resolution of about 0.03. There are
twenty replicates in the simulation to incorporate random variability in
the generated data. The system performance data contains two performance
metrics of the rain water tank model - the average daily deficit of
water in litres, and the reliability of the tank in meeting the water
demand as a fraction. These performance metrics can be visualised using
the function plotPerformanceSpace. Consider the performance
space of the metric - Avg. Deficit (L) can be plotted using the code
shown below, which shows the variation in this metric with perturbations
in the two perturbed attributes.
p2 <- plotPerformanceSpace(performance = egSimPerformance, # list of performance metrics
sim = egSimSummary, # simulation metadata
metric = "Avg. Deficit (L)", # the metric to be plotted
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to be used
colMap = viridisLite::plasma(20), # colour map to use
colLim = c(18, 34)) # colour limits
The plotPerformanceSpace function creates 2-dimensional
heatmaps and contours showing the performance space. The function
arguments are used to specify the metric to be plotted
(metric), the perturbed attributes to use on the x- and
y-axes (attX, attY), the colour map and colour
limits of the plot (colMap, colLim), the
number of top replicates (in terms of fitness) to be used for the plots
(topReps), and the the y-axis limit (ylim).
The attX and attY arguments become especially
relevant for performance spaces that contain more than two perturbed
attributes - these arguments specify the slice of the performance space
to be plotted. The topReps argument sorts the replicates by
closeness of fit in terms of the objective function used for
optimisation, and uses the specified topReps number
replicates to create the plots. In the example code above, the top 8
replicates out of the total 10 are used.
From the figure (below), we see that the most vulnerable areas
(higher values of average daily deficit) of the performance space occur
with simultaneous decreases in mean annual total rainfall, and increases
in seasonal ratio - the upper left portion of the performance space. To
understand the system performance better, we need to superimpose
additional information on the performance space to understand (a) which
areas of the performance space violate threshold criteria (if they
exist) of the performance metric? (b) how plausible are the perturbed
values of the attributes from alternate climate data like
projections?
Consider that the maximum threshold value of the average daily
deficit beyond which the tank system becomes economically non-viable is
29 litres. This maximum threshold is one of the design criteria used
while designing the rain water tank to operate under the current climate
conditions and corresponds to about 10% of the water use of a single
person house hold. We need to know which areas of the performance space
exceed this maximum threshold under perturbations in climate. We can add
this threshold as a thick contour line to the performance space plotted
above using the perfThreshold and
perfThreshLabel arguments of the
plotPerformanceSpace function. In addition, suppose we have
alternate climate information from climate projections for the region
corresponding to a future time slice centered on the year 2050. We want
to superimpose these top-down projections on the performance space to
understand how plausible the perturbations simulated in the bottom-up
climate impact assessment are. Here we use example climate data
available in the package for demonstration. We can add additional
information to the performance space as demonstrated below.
data("egClimData")
p3 <- plotPerformanceSpace(performance = egSimPerformance, # list of performance metrics
sim = egSimSummary, # simulation metadata
metric = "Avg. Deficit (L)", # the metric to be plotted
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to be used
colMap = viridisLite::plasma(20), # colour map to use
colLim = c(18, 34), # colour limits
perfThresh = 29, # thershold value
perfThreshLabel = "Max. Deficit (29L)", # thershold label
climData = egClimData # other climate data
)
The above figure of the performance space shows that perturbations
roughly higher than 1.2 in the seasonal rainfall ratio, combined with a
reduction in annual total rainfall (perturbation values lower than 1)
would breach the maximum average deficit threshold criteria of the tank
model. Alternately, if the reduction if annual rainfall is higher
(perturbation values lower than 0.9) combined with perturbations higher
than about 1.1 in the seasonal ratio would also cause the maximum
deficit threshold criteria to be breached. But looking at the super
imposed climate projections, we see that 5 of the 6 data points fall in
areas well below the threshold. One of the points is close to the
threshold line, but has not breached the threshold. Thus, the climate
perturbations that result in performance metric values higher than the
maximum threshold do not appear to be very plausible based on these
alternate lines of evidence.
Suppose we use the precipitation and temperature time series from
climate projections to run the system model (in this case the tank
model) and obtain performance metrics in a future climate from a
top-down assessment. Such performance metric estimates can be input to
the plotPerformanceSpace function as a column in the
data.frame input to the climData argument. In this case,
the superimposed climate data points will be coloured using the same
colour scale as the performance space to enable comparison of the
performance metric estimates from bottom-up and top-down assessments.
The column name should match the name of the metric plotted in the
performance space. The sixth column of the data egClimData
in the package contains values of average deficit, the column name of
which is slightly different. The reader may rename this column and
re-plot the above performance space for an example of how this
works.
data("egClimData")
names(egClimData)[6] <- "Avg. Deficit (L)"
p4 <- plotPerformanceSpace(performance = egSimPerformance, # list of performance metrics
sim = egSimSummary, # simulation metadata
metric = "Avg. Deficit (L)", # the metric to be plotted
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to use
colMap = viridisLite::plasma(20), # colour map to use
colLim = c(18, 34), # colour limits
perfThresh = 29, # thershold value
perfThreshLabel = "Max. Deficit (29L)", # thershold label
climData = egClimData # other climate data
)
Imagine a case when you have more than two attributes that are
perturbed using ‘regGrid’ sampling - resulting in a multi-dimensional
performance space. You can specify attX and
attY in the plotPerformanceSpace function call
to select which slice of the performance space is to be plotted. The
figures representing multiple slices can be placed together in panels to
visualise the multiple dimensions of the performance space. The
dimensions of the performance space that are not displayed (i.e., the
perturbed attributes that are not attX or
attY) are averaged in the figure. For example, imagine that
the example data above has another perturbed attribute “P_ann_R10_m”
with perturbations ranging from 0.8 to 1.2. In this case, the
performance spaces displayed above would be averaged across the
perturbations in this attribute. Now suppose you wish to subset the
range of this hidden dimension before plotting - maybe you are
interested in the performance spaces for only the perturbations that
reduce or maintain the current levels of “P_ann_R10_m”. The argument
attSlices of plotPerformanceSpace is intended
for use in such a scenario. To specify the hypothetical slice described
above, the attSlices argument would be specified as
shown.
attSlices <- list()
attSlices[["P_ann_R10_m"]] <- c(0.8, 1) # the minimum & maximum bounds for subsetting
This functionality is not demonstrated in this use case since the
example contains only two perturbed attributes. We leave it to the
reader to perform an experiment using a multi-dimensional performance
space that uses the attSlices argument.
From the above figures and discussion we understand the patterns in
the performance space of the metric “Avg. Deficit (L)” in the example
data. It is common to use more than one metric to assess multiple
performance criteria for the same system. The example performance data
used in this section contains two performance metrics—the average
deficit and tank reliability. The maximum threshold value for the
average deficit is 29 litres. Suppose, in addition, we also desire a
rain water tank reliability of at least 0.82. In other words, we want to
specify a minimum threshold of 0.82 for the metric “Reliability (-)” and
a maximum threshold of 29 litres for the metric “Avg. Deficit (L)” and
assess the vulnerability of the performance space using both these
criteria. The function plotPerformanceSpaceMulti can be
used for this purpose to create plots using multiple performance
metrics. The function plots filled contours to show the number of
performance thresholds exceeded in the performance space.
# plot number of performance thresholds exceeded
p5 <- plotPerformanceSpaceMulti(egSimPerformance, # 2 performance metrics
egSimSummary, # simulation summary
perfThreshMin = c(NA, 0.82), # min thresholds for each metric
# use NA if not applicable
perfThreshMax = c(29, NA), # max thresholds for each metric
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to use
climData = egClimData, # other climate data
col = viridisLite::inferno(7, direction = -1) # colours to use
)
When both the performance metrics are assessed together, at least one
performance threshold is exceeded in larger areas of the performance
space. Two out of six climate model projections are located in areas
where one performance threshold is exceeded indicating that there is
some plausibility that this rain water tank would not be viable in a
future climate.
7. Step E: Analyse system performances and facilitate decision
making (plotOptions)
In this step you’ll learn…
- Compare the performance spaces from multiple system configurations
or operating policies
The process of climate ‘stress-testing’ is often undertaken to
facilitate decisions involving choices between multiple system
configurations or operating policies. Step E of the process involves
comparison of the results from these alternate choices under climate
perturbations.
Current foreSIGHT functionality for comparing multiple
options involves interrogating each option as described in Step D, and
creating difference plots of performance metrics for two alternate
system options using a function plotOptions. It is intended
that future versions of foreSIGHT will significantly expand the
comparative capability including under a range of decision-theoretic
frameworks.
Key Considerations: Step E
The comparison of multiple alternative options can be a valuable tool
for adaptation decision making, with the core element of the comparison
being an analysis of how different options impact on the
Performance Spaces. This can provide a range of useful
information including:
- The overall sensitivity of alternative options to plausible climate
changes
- The climate conditions over which alternative system configurations
are ‘acceptable’ or result in a ‘failure’ (for situations where there
are clearly defined performance thresholds)
- The extent to which alternative options improve overall system
performance relative to climate projections, by incorporating climate
model output and/or other lines of evidence.
By superimposing climate projections for different future time
horizons, it may also be possible to use these analyses to inform
adaptation triggers, by identifying conditions when the system
performance is expected to become unacceptable.
foreSIGHT contains a function named plotOptions
that can be used to create plots of the differences in performance
metrics calculated using two system options. The function uses the
performance metrics calculated by running two alternate system model
configurations using the same perturbed time series, and the perturbed
simulation summary as inputs. The function call using the three
mandatory function arguments is shown below.
plotOptions(performanceOpt1, # performance metrics of system option 1
performanceOpt2, # performance metrics of system option 2
sim) # summary of the perturbed simulation
The use case below demonstrates the usage of this function.
Use Case E1: Plotting system options
Climate stress-tests often involves comparison of the performance of
two or more alternate configurations of the system to identify the best
option. In this use case, we’ll compare the performance of two
configurations of a rain water tank (for details of this system model
see section on inbuilt system models).
Consider the proposal to install a rain water tank in a house. Two
alternate configurations are proposed for the tank. The cost of these
alternate configurations are the same - the choice of the tank thus
depends only on the differences in the performances of the two systems.
The two configurations are described below.
Based on the layout of the house, it is possible to harvest rain
water from a total of 205 sq.m of roof area (including house and garage)
to direct water to a rain water tank of volume 2400 litres. This tank
requires 2 mm/m2 of the initial water collected from each
storm (first flush) to be removed for water quality reasons. Let us name
this system “Tank 1”.
As an alternative, it is possible to install a rainwater tank to
collect water only from the roof area of the house (155 sq.m) without
including the garage. The location of the proposed installation in this
case allows for a larger tank volume of 2750 litres. This tank requires
1mm/m2 of the first flush to be removed from each storm.
Let’s name this system “Tank 2”.
Steps A to C of the bottom-up climate impact assessment work flow
detailed in this document are applied to the two systems, and the
generated performance metrics are available as example data sets in the
package. The structure of the data are shown below.
# load data
data("egSimSummary") # summary of the stochastic simulation
data("egSimPerformance") # performance metrics of "Tank 1"
data("egSimPerformance_systemB") # performance metrics of "Tank 2"
egSimSummary$expSpace$attPerturb # the perturbed attributes
#> [1] "P_ann_tot_m" "P_ann_seasRatio"
utils::str(egSimSummary$expSpace) # target locations in the exposure space
#> List of 8
#> $ targetMat :'data.frame': 160 obs. of 11 variables:
#> ..$ P_ann_tot_m : num [1:160] 0.8 0.833 0.867 0.9 0.933 ...
#> ..$ P_ann_seasRatio: num [1:160] 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 ...
#> ..$ P_ann_nWet_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_ann_R10_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_Feb_tot_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_SON_dyWet_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_JJA_avgWSD_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_MAM_tot_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ P_DJF_avgDSD_m : num [1:160] 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ Temp_ann_rng_m : num [1:160] 0 0 0 0 0 0 0 0 0 0 ...
#> ..$ Temp_ann_avg_m : num [1:160] 0 0 0 0 0 0 0 0 0 0 ...
#> $ attRot : NULL
#> $ attPerturb : chr [1:2] "P_ann_tot_m" "P_ann_seasRatio"
#> $ attHold : chr [1:9] "P_ann_nWet_m" "P_ann_R10_m" "P_Feb_tot_m" "P_SON_dyWet_m" ...
#> $ attPerturbSamp: num [1:2] 10 16
#> $ attPerturbMin : num [1:2] 0.8 0.8
#> $ attPerturbMax : num [1:2] 1.1 1.3
#> $ attPerturbType: chr "regGrid"
utils::str(egSimPerformance) # system performance metrics
#> List of 2
#> $ Avg. Deficit (L): num [1:160, 1:10] 25.3 22.9 21 22.5 21.3 ...
#> $ Reliability (-) : num [1:160, 1:10] 0.818 0.836 0.85 0.84 0.845 ...
utils::str(egSimPerformance_systemB) # system performance metrics
#> List of 2
#> $ Avg. Deficit (L): num [1:160, 1:10] 23.5 21.4 19.1 20.7 19.2 ...
#> $ Reliability (-) : num [1:160, 1:10] 0.832 0.847 0.864 0.854 0.861 ...
The simulation contains two perturbed precipitation attributes and a
total of 160 target locations in a ‘regGrid’ exposure space. Considering
the minimum-maximum bounds and the number of samples we see that the
perturbations have a resolution of about 0.03. The system performance
data of both the system configurations contain two performance metrics
of the rain water tank model - the average daily deficit of water in
litres (“Avg. Deficit (L)”), and the reliability of the tank in meeting
the water demand as a fraction (“Reliability (-)”).
If you interrogate egSimSummary, you will see that the
stochastic simulation contains twenty replicates to account for random
variability in the generated data. The desired system performance
criteria based on the requirements of the household are: (1) the maximum
average daily deficit of water from the tank should not be higher than
29 litres, and (2) the reliability of the system should be at least
0.82. The performances of the two system configurations have to be
assessed using these threshold criteria. The performance of the
individual systems (“Tank 1”, “Tank 2”) can be assessed using
performance spaces like the ones shown in Use Case D2. Such figures
provide insight into the performance metrics and number of thresholds
exceeded for each individual system configuration. After understanding
the patterns in the performance spaces of the individual systems, we use
the plotOptions function to create plots of the differences
in performance metrics of “Tank 1” and “Tank 2”, and the shift in the
performance threshold contour as a part of Step E of the work flow. This
functionality is demonstrated in this use case.
Similar to the performance spaces shown in Step D, these difference
plots can also be superimposed with thick contour lines of the
thresholds of the performance metric for each system, and climate data
from alternate sources (eg: climate projections). The figure below shows
the differences between “Tank 1” and “Tank 2” for both the performance
metrics. Similar to plotPerformanceSpace, the
plotOptions function contains arguments to control the
appearance/labels of the plot (colMap, colLim,
opt1Label, opt2Label, titletext),
the axes and slices of the space (attX, attY,
attSlices), and the number of replicates to use
(topReps).
data("egClimData") # load climate projections data
p6 <- plotOptions(performanceOpt1 = egSimPerformance, # performance metrics of option 1
performanceOpt2 = egSimPerformance_systemB, # performance metrics of option 2
sim = egSimSummary, # simulation metadata
metric = "Avg. Deficit (L)", # the metric to be plotted
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to be used
opt1Label = "Tank 1", # label of option 1
opt2Label = "Tank 2", # label of option 2
titleText = "Avg Deficit: Tank 2 - Tank 1", # plot title
perfThresh = 29, # threshold value of the metric
perfThreshLabel = "Max. Deficit (29L)", # label of the threshold contour
climData = egClimData, # other climate data
colMap = RColorBrewer::brewer.pal(9, "Blues"), # colour map to use
colLim = c(-2, -1.4)) # colour limits
The performance metric reliability can be plotted using the code
below.
data("egClimData") # load climate projections data # colour limits
p7 <- plotOptions(performanceOpt1 = egSimPerformance, # performance metrics of option 1
performanceOpt2 = egSimPerformance_systemB, # performance metrics of option 2
sim = egSimSummary, # simulation metadata
metric = "Reliability (-)", # the metric to be plotted
attX = "P_ann_tot_m", # x-axis perturbed attribute
attY = "P_ann_seasRatio", # y-axis perturbed attribute
topReps = 8, # number of top replicates to be used
opt1Label = "Tank 1", # label of option 1
opt2Label = "Tank 2", # label of option 2
titleText = "Reliability: Tank 2 - Tank 1", # plot title
perfThresh = 0.82, # threshold value of the metric
perfThreshLabel = "Min. Reliability (0.82)", # label of the threshold contour
climData = egClimData, # other climate data
colMap = viridisLite::plasma(50), # colour map to use
colLim = c(0.01, 0.015)) # colour limits
The figure shows the differences in one performance metric for the
two system options. In the case of the metric average deficit , “Tank 2”
shows lower values than “Tank 1” in all areas of the performance space.
Consequently, the threshold contour of “Tank 2” shows a small area of
the performance space that is vulnerable to perturbations in the
selected climate attributes, compared to “Tank 1”. The inference is the
same for the performance metric “reliability”. Hence, in this use case
the results of the stress-test indicate that “Tank 2” is preferable as
it should operate satisfactorily across a wider range of conditions,
including the drier climate projected by the alternate climate data.
8.1. Rainwater Tank Model
The rainwater tank model is a representation of a domestic rainwater
tank system, which has been designed to meet both indoor (grey water)
and outdoor (garden irrigation) water demands. Although this system
model example is simpler than anticipated real-world usages of the
foreSIGHT model, it nevertheless provides important insights
associated with system sensitivities, the role of temporal dynamics and
the behaviour of storages, the interaction between supply and demand,
and the identification and comparison of multiple system configurations.
The core functionality of this model is now described.
A schematic representation of the rainwater tank system model is
shown in the figure below. Rain falling on the roof of a house is
captured and directed towards the rainwater tank. Before the rainwater
is able to enter the tank, a depth of water (called the first flush) is
removed from the start of each storm for water quality reasons. The
water remaining after the first flush extraction flows into the
rainwater tank. The amount of water supplied by the tank is calculated
based on the water level in the tank. The indoor and outdoor water
demands deplete the water stored in the tank. The indoor water demand is
assumed to be constant throughout the year, and the outdoor water demand
varies seasonally. The outdoor seasonal demand pattern is also dependent
upon the daily temperature. For example, on hot days (say above
28oC), the gardener is assumed to apply more than the
seasonal average and vice versa. The operation of the rain water tank
system model is thus dependent upon the climate variables rainfall and
temperature.
The tank model simulates rainwater capture and water use processes at
a daily time step using rainfall and temperature time series as input.
The parameters of the model that the user should specify are: the area
of the roof used for rain water harvesting, the volume of the tank, the
number of people using the water and the depth of water removed as the
first flush. These parameters can be varied for alternate system
designs.
The system model estimates the performance of the rainwater tank
using five metrics:
- Average Daily Deficit - the volume of average deficit in water
supplied by the tank in litres
- Reliability - the fraction of days on which the full demand could be
supplied
- Volumetric reliability - the total water supplied as a fraction of
the total demand
- System efficiency - the amount of water used as a percentage of the
water captured by the roof
- Storage efficiency - the amount of water spilled as a percentage of
the water captured by the rainwater tank
- Average tank storage - the volume of average daily storage in the
tank in litres
This example system model provides sufficient scope for climate
stress testing using foreSIGHT. This is because the tank
responds to multiple climate drivers (i.e. rainfall and temperature),
and the removal of the first flush at the start of the storm means that
the wet-dry pattern of the rainfall and the seasonality of the demand
pattern may become important in the functioning of the tank. The system
model is available as the tankWrapper() function in
foreSIGHT. The performance metrics available in the tank model
can be viewed using the viewTankMetrics() function.
Daily observed precipitation and temperature over the period from
2007 to 2016 obtained by combining data from multiple station locations
to represent the general climate of Adelaide, South Australia is
included in the demonstration, and may be be loaded using the data
command.
A typical function call to the rainwater tank system model
(tankWrapper) is shown below. The call returns the system
performance metrics specified by the user.
# Load example climate data
data(tankDat)
# View the metrics available for use
tankMetrics <- viewTankMetrics()
#> [1] "volumetric reliability (fraction)" "reliability (fraction)"
#> [3] "system efficiency (%)" "storage efficiency (%)"
#> [5] "average tank storage (L)" "average daily deficit (L)"
# User input: system model parameters
systemArgs <- list(roofArea = 50, # roof area in m2
nPeople = 1, # number of people using water
tankVol = 3000, # tank volume in L
firstFlush = 1, # depth of water removed each event in mm
write.file = FALSE, # write output tank timeseries to file T/F?
fnam = "tankperformance.csv") # name of file
# performance metric chosen for reporting
metrics <- c("average daily deficit (L)", "reliability (fraction)")
performanceOut <- tankWrapper(data = tank_obs, systemArgs = systemArgs, metrics = metrics)
performanceOut
#> $`average daily deficit (L)`
#> [1] 40.93813
#>
#> $`reliability (fraction)`
#> [1] 0.6884752
# Now try a different metric e.g. volumetric reliability
performanceOut <- tankWrapper(data = tank_obs, systemArgs = systemArgs, metrics = tankMetrics[1])
performanceOut
#> $`volumetric reliability (fraction)`
#> [1] 0.4380711
9. Options for advanced users
In this section you’ll learn about advanced functionality of some of
the functions in foreSIGHT…
- What’s meant by the terms optimisation arguments, stochastic model
parameters
- How to modify the default optimisation arguments in
foreSIGHT
- How to check the default bounds of stochastic model parameters and
modify them
- How to use the computationally intensive functions in
foreSIGHT in a parallel computing environment
9.1. The default optimisation arguments and how to modify them
The inverse method in foreSIGHT uses numerical optimization
to find optimal parameter values that generate time series with target
perturbations in selected climate attributes. The choice of numerical
optimization routine and settings plays a large role in how well the
simulated attributes match the desired targets.
The default optimization routine used in foreSIGHT is the
Robust Gauss Newton (RGN) algorithm (Qin et al, 2018). Default values
for optimization arguments in foreSIGHT can be viewed using the
viewDefaultOptimArgs() helper function in the package.
viewDefaultOptimArgs()
#> $optimizer
#> [1] "RGN"
#>
#> $obj.func
#> [1] "WSS"
#>
#> $seed
#> NULL
#>
#> $nMultiStart
#> [1] 5
#>
#> $OFtol
#> [1] 0
#>
#> $seed
#> NULL
#>
#> $RGN.control
#> $RGN.control$iterMax
#> [1] 100
This shows that RGN is the default optimizer, and that optimization
will be performed using 5 different initial parameter sets
(multi-starts) to improve optimization. It also shows control settings
used in the RGN algorithm.
foreSIGHT has the capability to use alternate optimization
routines, including a genetic algorithm (‘GA’), the shuffled complex
evolution algorithm (‘SCE’), and the Nelder-Mead method (‘NM’). Default
settings for ‘GA’ are shown using
viewDefaultOptimArgs('GA')
#> $optimizer
#> [1] "GA"
#>
#> $obj.func
#> [1] "WSS"
#>
#> $seed
#> NULL
#>
#> $nMultiStart
#> [1] 5
#>
#> $OFtol
#> [1] 0
#>
#> $seed
#> NULL
#>
#> $GA.args
#> $GA.args$pcrossover
#> [1] 0.8
#>
#> $GA.args$pmutation
#> [1] 0.1
#>
#> $GA.args$maxiter
#> [1] 50
#>
#> $GA.args$maxFitness
#> [1] -0.001
#>
#> $GA.args$popSize
#> [1] 500
#>
#> $GA.args$run
#> [1] 20
#>
#> $GA.args$parallel
#> [1] FALSE
#>
#> $GA.args$keepBest
#> [1] TRUE
The controlFile argument of
generateScenarios can be used to modify the default values
of the optimisation arguments. The writeControlFile()
helper function can be used to write a sample JSON file to obtain a
template of the controlFile including the advanced option
by setting the basic argument to FALSE. Note that the
following function call would write a JSON file (named
‘sample_controlFile.json’) into your working directory
writeControlFile(basic = FALSE)
The code below demonstrates how user-specified optimisation arguments
can be used in the controlFile input to
generateScenarios.
This first example shows how the number of multi-starts can be
changed to 1 (from the default value of 5)
# load data
data("tankDat")
# create the exposure space
attPerturb <- c("P_ann_tot_m", "P_ann_P99")
attHold <- c("P_ann_maxWSD_m", "P_ann_nWet_m")
attPerturbType = "regGrid"
attPerturbSamp = c(2, 2)
attPerturbMin = c(0.9, 0.9)
attPerturbMax = c(1.3, 1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
controlFileList <- list()
# add user-specified values for optimisation arguments
controlFileList[["optimisationArguments"]] <- list()
controlFileList[["optimisationArguments"]][["nMultiStart"]] <- 1
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
sim_RGN_ms1 <- generateScenarios(reference = tank_obs[,1:4], expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
This second example shows how we can change the optimizer to ‘GA’,
and specify GA::ga() arguments for maximum iterations (‘maxiter’) and
stopping criteria (‘run’)
# add user-specified values for optimisation arguments
controlFileList[["optimisationArguments"]] <- list()
controlFileList[["optimisationArguments"]][["optimizer"]] <- 'GA'
controlFileList[["optimisationArguments"]][["nMultiStart"]] <- 1
controlFileList[["optimisationArguments"]][["GA.args"]] <- list(maxiter=100,run=40)
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
sim_GA_ms1 <- generateScenarios(reference = tank_obs[,1:4], expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
The controlFile field in the output sim
list will show the specified optimisation arguments have been used to
generate the scenarios.
9.2. The default bounds of stochastic model parameters and how to
modify them
The generateScenarios function uses stochastic
generators to create perturbed time series by optimising the parameters
of stochastic models to obtain the specified target perturbations in
climate attributes. Each stochastic model typically contains different
number and type of parameters based on the structure of the model. The
reader may refer to the publications detailing the model structure
listed in the package description for details about the structure of the
stochastic models (see
utils::packageDescription("foreSIGHT"))
foreSIGHT contains default settings for the bounds of each
stochastic model parameter. These bounds are necessary to (1) ensure
that the optimisation algorithm does not assign parameter bounds outside
the feasible range during its iterations, and (2) provide a narrower
search space so that optimisation algorithm can converge to the
parameter values required to generate the target perturbations. So how
are the bounds of the stochastic model parameters decided?
The model structure definition and nature of the climate variables
that the model simulates provide a feasibility range for each parameter.
For example, model parameters that represent autocorrelation of a time
series is bound to the range [-1, 1]. Similarly, model parameters that
represent the angle of seasonal variation in the harmonic function of a
parameter has to adhere to the range [0, 6.28], the parameters that
represent probabilities has to fall in the range [0, 1], the parameters
that represent mean or standard deviation of a precipitation or
evapotranspiration time series has to be positive, and so forth.
But these bounds that stem from the very nature of the parameters are
often too wide with respect to the optimisation algorithm. As a result,
a large number of iterations may be necessary for the algorithm to
converge to a solution (if it does converge at all!), or the algorithm
may start from a initial guess that would not converge to the global
optimum solution. These problems can be reduced by specifying closer
bounds for the parameters of the stochastic models that reduces the
search space for optimisation. The model parameter estimates available
from forward calibration of the models to data can be used to inform the
parameter bounds. Indeed, the default parameter bounds of the stochastic
models in foreSIGHT are based on expert knowledge of historical
conditions in Australia. If the user has existing knowledge about the
bounds of the model parameters of the selected stochastic model in their
region of interest, we recommend that they modify the bounds of the
stochastic models for their application. However, it is not recommended
to randomly modify the parameter bounds in the package as it can have
unintended consequences.
The model parameters and their default bounds in foreSIGHT
can be viewed using the helper function
viewModelParameters(). The function requires the short name
of the variable, the modelType and
modelParameterVariation of the stochastic model as the
input arguments. As you know modelType and
modelParameterVariation uniquely define the stochastic
models for each variable. Remember that the viewModels()
helper function can be used to view the stochastic models available in
foreSIGHT. The usage of the viewModelParameters()
function is shown below.
viewModelParameters(variable = "P",
modelType = "wgen", modelParameterVariation = "harmonic")
#> parameter min_bound max_bound
#> 1 pdd_m 0.476 0.950
#> 2 pdd_amp 0.006 0.557
#> 3 pdd_ang 0.000 6.280
#> 4 pwd_m 0.093 0.728
#> 5 pwd_amp 0.004 0.519
#> 6 pwd_ang 0.000 6.280
#> 7 alpha_m 0.330 0.950
#> 8 alpha_amp 0.002 0.600
#> 9 alpha_ang 0.000 6.280
#> 10 beta_m 0.085 15.000
#> 11 beta_amp 0.028 10.000
#> 12 beta_ang 0.000 6.280
viewModelParameters(variable = "Temp",
modelType = "wgen", modelParameterVariation = "harmonic")
#> parameter min_bound max_bound
#> 1 cor0 0.45 0.90
#> 2 WD-mCycle-m 7.00 28.00
#> 3 WD-mCycle-amp 1.00 9.00
#> 4 WD-mCycle-ang -0.05 0.81
#> 5 WD-sCycle-m 0.90 4.90
#> 6 WD-sCycle-amp 0.10 1.40
#> 7 WD-sCycle-ang -1.60 3.15
To modify the default bounds of the stochastic model parameters
user-specified bounds may be input via the JSON file input to the
controlFile argument of generateScenarios. To
obtain a template JSON file containing parameter bounds that the user
may modify, use the helper function writeControlFile()
specifying the basic argument as FALSE.
writeControlFile(basic = FALSE)
The below code provides an examples to show how the the user can
create JSON control files with parameter bounds for input to
generateScenarios, for the default precipitation stochastic
model in foreSIGHT.
# create the exposure space
attPerturb <- c("P_ann_tot_m", "P_ann_P99")
attHold <- c("P_ann_maxWSD_m", "P_ann_nWet_m")
attPerturbType = "regGrid"
attPerturbSamp = c(2, 2)
attPerturbMin = c(0.9, 0.9)
attPerturbMax = c(1.3, 1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
# specify the penalty settings in a list
controlFileList <- list()
controlFileList[["penaltyAttributes"]] <- c("P_ann_tot_m")
controlFileList[["penaltyWeights"]] <- c(0.5)
# add user-specified bounds for model parameters
controlFileList[["modelParameterBounds"]] <- list()
controlFileList[["modelParameterBounds"]][["P"]] <- list()
controlFileList[["modelParameterBounds"]][["P"]][["pdd_m"]] <- c(0.35, 1)
controlFileList[["modelParameterBounds"]][["P"]][["pwd_m"]] <- c(0.05, 0.65)
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
data("tankDat")
sim <- generateScenarios(reference = tank_obs[,1:4], expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
The output sim list stores the parameter values that
were used for the simulation inside the field controlFile.
The parameter bounds saved in sim should now contain the
values input by the user used for the simulation.
If you wish to use an alternate stochastic model and modify the
default bounds of the parameters of that model, the JSON control file
input should contain specifications of the selected model and the new
bounds. The below code provides such an example.
# create the exposure space
attPerturb <- c("P_ann_tot_m", "P_ann_P99")
attHold <- c("P_ann_maxWSD_m", "P_ann_nWet_m")
attPerturbType = "regGrid"
attPerturbSamp = c(2, 2)
attPerturbMin = c(0.9, 0.9)
attPerturbMax = c(1.3, 1.3)
expSpace <- createExpSpace(attPerturb = attPerturb,
attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin,
attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType,
attHold = attHold)
# specify the penalty settings in a list
controlFileList <- list()
controlFileList[["penaltyAttributes"]] <- c("P_ann_tot_m")
controlFileList[["penaltyWeights"]] <- c(0.5)
# specify the alternate model selections
controlFileList[["modelType"]] <- list()
controlFileList[["modelType"]][["P"]] <- "latent"
controlFileList[["modelParameterVariation"]] <- list()
controlFileList[["modelParameterVariation"]][["P"]] <- "harmonic"
# add user-specified bounds for model parameters
controlFileList[["modelParameterBounds"]] <- list()
controlFileList[["modelParameterBounds"]][["P"]] <- list()
controlFileList[["modelParameterBounds"]][["P"]][["mu_m"]] <- c(-5, 0)
controlFileList[["modelParameterBounds"]][["P"]][["alpha_m"]] <- c(0.35, 0.95)
# write the list into a JSON file
controlFileJSON <- jsonlite::toJSON(controlFileList, pretty = TRUE, auto_unbox = TRUE)
write(controlFileJSON, file = paste0(tempdir(), "controlFile.json"))
# generate scenarios
sim <- generateScenarios(reference = tank_obs[, 1:4], expSpace = expSpace,
controlFile = paste0(tempdir(), "controlFile.json"))
Again, the controlFile field saved in the output
sim list should reflect the user-specified changes to the
JSON control file that was used for the simulation.
9.3. Parallelising computationally intensive functions in
foreSIGHT
Consider an exposure space containing many climate attributes and
several target locations in the exposure space. The computational
resources and time required to generate perturbed time series
corresponding to the target locations are often non-trivial, and
increases manifold when multiple replicates of the time series are
required to be generated. Thus, generateScenarios is one of
the computationally intensive functions in foreSIGHT.
Another potential computationally intensive function is
runSystemModel(). The computational resources required for
this function depends on the run-time of the system model under
consideration, which can easily be non-trivial for complex system
models. Remember that for a climate stress-test the system model would
need to be run at least as many times as the number of perturbed time
series. Most stress-tests also involve the assessment of multiple system
options, resulting in the system model (with different system
configurations) being run multiple times for each perturbed scenario.
Thus in some cases runSystemModel() can be the
computational bottle neck in the stress testing work flow.
Thus, to generate comprehensive scenarios to stress-test complex
system models parallelisation of these key functions are inevitable.
Here we provide a template code to use the core functionality of
generateScenarios in a parallel environment.
The generateScenarios function calls the function
generateScenario under its hood for each target location in
the exposure space for each stochastic replicate. The function
generateScenario is an exported function in
foreSIGHT intended for use by the advanced users of the package
to implement the core functionality of generateScenarios on
parallel processors. Consider the code of the
generateScenarios() function (you can view the R code of
any function by simply typing the function name, here
generateScenarios). This function intentionally does not
use call any internal functions in package so that the code can easily
be adapted for use in a script that can run in parallel on multiple
CPUs. The equivalent parallel code implemented using the
doParallel and foreach packages in R is shown
below.
# import packages
library(foreach)
library(doParallel)
library(foreSIGHT)
# set paths
setwd(<path-to-working-directory>)
controlFile <- <path-and-name-of-controlFile>
# create exposure Space
attPerturb <- c("P_ann_tot_m","P_ann_seasRatio")
attHold <- c("P_ann_nWet_m", "P_ann_R10_m", "P_Feb_tot_m", "P_SON_dyWet_m", "P_JJA_avgWSD_m",
"P_MAM_tot_m", "P_DJF_avgDSD_m", "Temp_ann_rng_m","Temp_ann_avg_m")
attPerturbType = "regGrid"
attPerturbSamp = c(10, 16)
attPerturbMin = c(0.8, 0.80)
attPerturbMax = c(1.1, 1.3)
expSpace <- createExpSpace(attPerturb = attPerturb, attPerturbSamp = attPerturbSamp,
attPerturbMin = attPerturbMin, attPerturbMax = attPerturbMax,
attPerturbType = attPerturbType, attHold = attHold, attTargetsFile = NULL)
# load reference data
data("tankDat")
# assign generateScenarios inputs
reference <- tank_obs
simLengthNyrs <- 300
numReplicates <- 20
seedID <- NULL
# Number of targets
nTarget <- dim(expSpace$targetMat)[1]
# Replicates and seed don't go with scaling
if (!is.null(controlFile)) {
if (controlFile == "scaling") {
if (numReplicates > 1) stop("Simple scaling cannot generate replicates.
Please set numReplicates to 1.")
if (!is.null(seedID)) stop("Simple scaling cannot use a seed.
Please set seedID to NULL.")
}
}
# Create random seedID
if (is.null(seedID)) {
seedID <- round(stats::runif(1)*10000)
}
# Create seedID vector for all replicates
if (numReplicates>0 & numReplicates%%1==0) {
seedIDs <- seedID + seq(0, numReplicates-1)
nRep <- length(seedIDs)
} else {
stop("numReplicates should be a positive integer")
}
# parallel tasks
#================================================
#************************* NOTE *************************
# This part of the script to determine the number of cores depends upon
# the settings of your parallel computing environment & job scheduler
#*********************************************************
slurm_ntasks <- as.numeric(Sys.getenv("SLURM_NTASKS")) # Obtain environment variable SLURM_NTASKS
if (is.numeric(slurm_ntasks)) {
cores = slurm_ntasks # if slurm_ntasks is numerical, then assign it to cores
} else {
stop("Cores not found")
}
c1 <- makeCluster(cores)
registerDoParallel(c1)
allSim <- foreach (iRep=1:nRep) %:%
foreach (iTarg=1:nTarget) %dopar% {
library(foreSIGHT)
# Get the target location in the exposure space
expTarg <- expSpace
expTarg$targetMat <- expSpace$targetMat[iTarg, ]
if(!is.null(expSpace$attRot)) {
expTarg$attRot <- expSpace$attRot[iTarg]
}
cat(paste0("=============================================================\n",
"Commencing Replicate No. ", iRep, " Target No. ", iTarg,
"\n=============================================================\n"),
file = "fSrun_log.txt", append = TRUE)
# Call generateScenario for the target
to.allSim <- foreSIGHT::generateScenario(reference = reference,
expTarg = expTarg,
simLengthNyrs = simLengthNyrs,
seedID = seedIDs[iRep],
fSNamelist = fSNamelist)
}
stopCluster(c1)
# End parallel tasks
#=================================================
save(allSim, file = "allSim_prelim.Rdata")
names(allSim) <- paste0("Rep", 1:nRep)
allSim[["simDates"]] <- allSim[[1]][[1]]$simDates
allSim[["expSpace"]] <- expSpace
allSim[["controlFile"]] <- allSim[[1]][[1]]$nml
for (i in 1:nRep) {
for (j in 1:nTarget) {
allSim[[i]][[j]]$simDates <- NULL
allSim[[i]][[j]]$nml <- NULL
names(allSim[[i]]) <- paste0("Target", 1:nTarget)
}
}
save(allSim, file = "allSim.Rdata")
Similarly, the runSystemModel is also coded to not use
any internal functions in foreSIGHT for ease of use in a script
and parallelisation of the core functionality. The function contains a
loop across all target locations and replicates that may be run in
parallel, similar to the code shown above. This section of the vignette
will be updated with a code template for runSystemModel
ease of the user in the next revision.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
