Get mean translation time between hydrographs with
get_lag()
For the identification of AEs, the translation time between
neighboring hydrographs and the event amplitude have to be considered.
For the first criterion, the mean translation time (LAG)
between hydrographs has to be estimated and the cumulative values
appended to the relation data for further processing, if
not available yet.
Function get_lag_file() uses:
Q_file A path to a file that contains the
Q data from several stations or a data frame that contains
this information.relation_file A path to a relation file.
The IDs of the stations must be in Q.
If the argument save is TRUE, the
relation data with appended LAG column is
written to a file specified in outfile. If a
LAG column already exists, argument overwrite
has to be set to TRUE to overwrite the existing column. The
function can be applied to several relation files by
iterating over file paths or if a single Q data file is
available, get_lag_dir() can be used. relation
files can be selected from a directory using regular expressions
(argument relation_pattern).
The following code shows this for single file names:
Q_file <- system.file("testdata", "Q.csv", package = "hydroroute")
relation <- system.file("testdata", "relation.csv", package = "hydroroute")
(get_lag_file(Q_file, relation, inputsep = ",", format = "%Y-%m-%d %H:%M",
save = FALSE, overwrite = TRUE))
#> ID Type Station fkm LAG
#> 1 100000 Gauge S1 0.01 00:00
#> 2 200000 Gauge S2 9.16 01:15
#> 3 300000 Gauge S3 17.02 02:45
#> 4 400000 Gauge S4 29.27 04:00
This code indicates the use with get_lag_dir() where the
directory is specified:
Q_file <- system.file("testdata", "Q.csv", package = "hydroroute")
relations_path <- file.path(tempdir(), "testdata")
dir.create(relations_path)
file.copy(list.files(system.file("testdata", package = "hydroroute"),
full.name = TRUE),
relations_path, recursive = FALSE, copy.mode = TRUE)
#> [1] FALSE FALSE TRUE TRUE TRUE TRUE TRUE
(get_lag_dir(Q_file, relations_path, inputsep = ",",
inputdec = ".", format = "%Y-%m-%d %H:%M", overwrite = TRUE))
#> [[1]]
#> ID Type Station fkm LAG
#> 1 100000 Gauge S1 0.01 00:00
#> 2 200000 Gauge S2 9.16 01:15
#> 3 300000 Gauge S3 17.02 02:45
#> 4 400000 Gauge S4 29.27 04:00
Estimate settings with estimate_AE()
Greimel et al. (2022) propose the following algorithm to identify
AEs:
“For every event x at the upstream hydrograph, the mean
translation time between the neighboring hydrographs (calculated by an
autocorrelation analysis) is subtracted from the downstream hydrograph.
This then captures several events from the downstream hydrograph within
a time slot +/- the translation time. Among those matches only those
events are retained where the relative difference in amplitude is +/-
one. In the following, a potential AE is the event y
detected with the smallest time difference to x after
accounting for the mean translation time meeting the time and amplitude
criteria. […]
The relative difference in amplitude is then determined for these
events, and parabolas are fitted to the histograms obtained for the
relative difference data binned into intervals from -1 to 1 with a width
0.1 by fixing the vertex at the inner maximum of the histogram […]. The
width of the parabola is determined by minimizing the average squared
distances between the parabola and the histogram data along arbitrary
symmetric ranges from the inner maximum. Based on the fitted parabola,
cut points with the x-axis are determined so that only
those potential AEs whose relative difference is within these cut points
are retained. If this automatic scheme does not succeed in determining
suitable cut points, e.g., because the estimated cut points are outside
the defined intervals, a strict criterion for the relative difference in
amplitude is imposed to identify AEs considering only deviations of at
most 10%.”
estimate_AE() estimates suitable settings for the
amplitude based on the method developed in Greimel et al. (2022) based
on potential associated events identified using the specified time and
metric deviations allowed for a match.
It performs this procedure for two neighboring hydrographs, i.e., it
takes a subset of relation and the two corresponding
Event files as input. The gauging station IDs
in the subset of relation and in the Event
files must match. Suitable settings for the amplitude are estimated as
follows:
Sy$Time is shifted by the optimal mean translation
time between Sx and Sy.
Based on the specified time lags, matches between Sx
and Sy are captured.
Relative differences in AMP are computed, e.g.,
(Sy$AMP - Sx$AMP) / Sx$AMP, and only matches are retained
where these relative differences are within the range
specified.
Matched events are iteratively filtered to retain those where the
time lag is most similar leading to the potential AEs.
The relative differences of potential AEs are binned into
intervals of length 0.1 from -1 to 1. The created relative frequency
table of the binned relative differences is passed to function
get_parabola() where either suitable cut points with the
x-axis are determined or a strict criterion is returned.
The table of the relative differences is visualized in a plot
where the fitted parabola and the cut points with the x-axis are also
shown.
The estimated settings for amplitude, a data frame of “real” AEs,
i.e., associated events within the estimated cut points, and the plot
are returned.
Note that the metric flow ratio (RATIO) does not make sense for
S1 if the hydrograph is not of type Gauge. So
metric RATIO is set to NA internally in this
case.
The following code shows this procedure for two Event
files:
# file paths
Sx <- system.file("testdata", "Events", "100000_2_2014-01-01_2014-02-28.csv",
package = "hydroroute")
Sy <- system.file("testdata", "Events", "200000_2_2014-01-01_2014-02-28.csv",
package = "hydroroute")
relation <- system.file("testdata", "relation.csv", package = "hydroroute")
# read data
Sx <- utils::read.csv(Sx)
Sy <- utils::read.csv(Sy)
relation <- utils::read.csv(relation)
relation <- relation[1:2, ]
# estimate AE, exact time matches
results <- estimate_AE(Sx, Sy, relation, timeLag = c(0, 1, 0))
results$settings
#> station.x station.y bound lag metric
#> 1 S1 S2 lower 0 0.9286046
#> 2 S1 S2 inner 1 1.0500000
#> 3 S1 S2 upper 0 1.1713954
Column bound represents the lower, inner and upper
bounds that are used to subset potential AEs. lag
represents the time lag. Only exact matches are used in this examples,
which is specified by argument timeLag = c(0, 1, 0), which
refers to 0 deviation at the lower and upper bound and 1 at the inner
bound, meaning, that the mean translation time from
relation is not altered when time matches are computed.
head(results$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 2 2014-01-11 17:15:00 39.01 20.4 13.00333 3 12.177650
#> 2 100000 2 2014-01-14 12:30:00 15.00 6.0 2.50000 6 1.262238
#> 3 100000 2 2014-01-15 06:15:00 77.14 38.3 12.85667 6 27.060811
#> 4 100000 2 2014-01-15 20:15:00 10.20 5.1 2.55000 4 1.312883
#> 5 100000 2 2014-01-19 06:45:00 74.41 23.7 9.30125 8 30.883534
#> 6 100000 2 2014-01-27 15:45:00 0.10 0.1 0.10000 1 1.001391
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y dur.y
#> 1 S1 200000 2 2014-01-11 18:15:00 39.06 20.3 6.510 6
#> 2 S1 200000 2 2014-01-14 13:30:00 14.40 5.3 2.400 6
#> 3 S1 200000 2 2014-01-15 07:15:00 77.49 33.2 15.498 5
#> 4 S1 200000 2 2014-01-15 21:15:00 10.20 4.0 2.040 5
#> 5 S1 200000 2 2014-01-19 07:45:00 76.36 28.9 9.545 8
#> 6 S1 200000 2 2014-01-27 16:45:00 0.10 0.1 0.100 1
#> ratio.y station.y diff_metric
#> 1 7.804878 S2 1.281723e-03
#> 2 1.231140 S2 -4.000000e-02
#> 3 14.111675 S2 4.537205e-03
#> 4 1.280992 S2 0.000000e+00
#> 5 16.457490 S2 2.620616e-02
#> 6 1.001311 S2 1.469658e-13
Combine everything with peaktrace()
Function peaktrace combines the identification of
potential AEs and the estimation of suitable amplitude settings for a
whole river section as specified in a relation file. In
addition, the flow metrics of the AEs are pictured by scatter plots and
the translation and retention process between the hydrographs is
described by linear models.
In the following, the input arguments of function
peaktrace() are described:
relation_path: Is the path where the whole relation
file from a river section is to be read from.
events_path: Is the path of the directory where the
Event files are located. These files must correspond to the
format described earlier in the section discussing the input
data.
initial_values_path: Is the path where initial
values for predicting the metric at the neighboring stations are to be
read from. It should not contain missing values. But missing values can
be imputed with a method specified in argument
impute_method, which is by default max. An
example for such a file is:
initial_values_path <- system.file("testdata", "initial_value_routing.csv",
package = "hydroroute")
initials <- read.csv(initial_values_path)
initials
#> Station Metric Value Name
#> 1 S1 AMP 93.00000 Q_max
#> 2 S1 AMP 69.75000 Q_0.75
#> 3 S1 AMP 46.50000 Q_0.5
#> 4 S1 AMP 23.25000 Q_0.25
#> 5 S1 MAFR 93.00000 Q_max
#> 6 S1 MAFR 69.75000 Q_0.75
#> 7 S1 MAFR 46.50000 Q_0.5
#> 8 S1 MAFR 23.25000 Q_0.25
#> 9 S1 MEFR 93.00000 Q_max
#> 10 S1 MEFR 69.75000 Q_0.75
#> 11 S1 MEFR 46.50000 Q_0.5
#> 12 S1 MEFR 23.25000 Q_0.25
#> 13 S1 DUR 1.00000 N
#> 14 S2 RATIO 19.90099 Max
The columns must be identical to this example. The content may vary.
The initial values used for prediction must not contain any missing
values.
Station refers to the gauging station of the
hydrograph. Here, all initial values correspond to gauging station
S1 except for metric RATIO, which starts at
gauging station S2.
Metric corresponds to the metric. This is used to
pick the corresponding fitted predictive model.
Value can be chosen arbitrarily or estimated with a
data-driven approach. A unique Name is assigned which can
be used to characterize the curve obtained from this initial value used
to predict the metrics in downstream direction. E.g., for this example
the initial values are set to certain quantiles of the metrics at
station S1.
The return value of function peaktrace() is structured
as follows:
relation_path <- system.file("testdata", "relation.csv", package = "hydroroute")
events_path <- system.file("testdata", "Events", package = "hydroroute")
initial_values_path <- system.file("testdata", "initial_value_routing.csv",
package = "hydroroute")
res <- peaktrace(relation_path, events_path, initial_values_path)
The first list object refers to event type 2 (IC event).
res$`2`$settings
#> station.x station.y bound lag metric
#> 1 S1 S2 lower 1 0.7388856
#> 2 S1 S2 inner 1 0.9500000
#> 3 S1 S2 upper 1 1.1611144
#> 4 S2 S3 lower 1 0.8818457
#> 5 S2 S3 inner 1 1.0500000
#> 6 S2 S3 upper 1 1.2181543
#> 7 S3 S4 lower 1 0.8267117
#> 8 S3 S4 inner 1 0.9500000
#> 9 S3 S4 upper 1 1.0732883
The settings data frame contains the estimated time lag
and metric settings computed with estimate_AE(). In this
example with 4 stations, it contains nine rows where three rows describe
the relation between two neighboring stations. Since only exact time
matches were allowed, the lag values are 0 for
lower and upper bound and 1 for
inner. metric contains the range of relative
values of the amplitude allowed.
Events, where the relative difference in amplitude and the relative
difference in time are within these settings, are considered as “real”
AE and therefore events caused by disruptive factors are excluded as far
as possible.
The following plot shows the histograms obtained for the relative
differences in amplitude for each pair of neighboring gauging stations
binned into intervals from -1 to 1 of width 0.1. The dashed line shows
the fitted parabola and the cut points of the parabola with the x-axis
are indicated. Potential AEs where the relative difference is within
these cut points are considered as “real” AEs.
grid::grid.draw(res$`2`$plot_threshold)
The “real” AEs can be inspected using:
head(res$`2`$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 2 2014-01-01 01:00:00 27.07 12.2 6.767500 4 10.565371
#> 2 100000 2 2014-01-01 10:15:00 29.38 15.5 7.345000 4 11.801471
#> 3 100000 2 2014-01-01 17:30:00 30.91 16.9 7.727500 4 12.490706
#> 4 100000 2 2014-01-02 17:30:00 26.88 14.1 4.480000 6 8.636364
#> 5 100000 2 2014-01-03 05:00:00 27.34 12.9 9.113333 3 10.559441
#> 6 100000 2 2014-01-03 16:00:00 27.16 14.8 3.017778 9 10.912409
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y dur.y
#> 1 S1 200000 2 2014-01-01 02:15:00 25.83 13.11 5.166000 5
#> 2 S1 200000 2 2014-01-01 11:30:00 28.49 14.54 5.698000 5
#> 3 S1 200000 2 2014-01-01 18:45:00 29.15 14.98 7.287500 4
#> 4 S1 200000 2 2014-01-02 19:00:00 26.43 11.49 3.303750 8
#> 5 S1 200000 2 2014-01-03 06:15:00 26.69 13.70 5.338000 5
#> 6 S1 200000 2 2014-01-03 17:30:00 27.03 12.20 3.861429 7
#> ratio.y station.y diff_metric
#> 1 7.506297 S2 -0.045807167
#> 2 8.679245 S2 -0.030292716
#> 3 8.379747 S2 -0.056939502
#> 4 6.427105 S2 -0.016741071
#> 5 7.655860 S2 -0.023774689
#> 6 7.808564 S2 -0.004786451
The scatter plots of the metrics at the neighboring gauging stations
for the “real” AEs are contained in plot_scatter. The
scatter plots are arranged in a grid where each row contains scatter
plots for a specific metric and each colums contains a different pair of
neighboring gauging stations. The x-axis is the upstream hydrograph
Sx, the y-axis is the downstream hydrograph
Sy. A linear regression line and the corresponding \(R^2\) value are added to each plot. By
default the aspect ratio is fixed and the axis limits are equal within
each plot.
grid::grid.draw(res$`2`$plot_scatter)
The fitted regression models may also be inspected:
res$`2`$models
#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.5542922 1.0194716 164 0.99658281
#> 2 S1 S2 dur lm y ~ x 1.6520198 0.8453943 164 0.64266715
#> 3 S1 S2 mafr lm y ~ x -0.3694711 1.0066784 164 0.91454377
#> 4 S1 S2 mefr lm y ~ x 0.4813008 0.7150873 164 0.70223571
#> 5 S2 S3 amp lm y ~ x 0.7597112 0.9782935 100 0.99765823
#> 6 S2 S3 dur lm y ~ x 0.7959971 0.7868426 100 0.70537848
#> 7 S2 S3 mafr lm y ~ x -1.0932362 1.5764049 100 0.94356887
#> 8 S2 S3 mefr lm y ~ x 0.5505522 1.0358693 100 0.76774263
#> 9 S2 S3 ratio lm y ~ x 0.5890385 0.6172956 100 0.97341252
#> 10 S3 S4 amp lm y ~ x -0.1251017 0.9485448 30 0.98810523
#> 11 S3 S4 dur lm y ~ x 3.0299519 0.4642539 30 0.09809454
#> 12 S3 S4 mafr lm y ~ x 3.0964565 0.5820430 30 0.87656463
#> 13 S3 S4 mefr lm y ~ x 2.2653366 0.7352544 30 0.56098791
#> 14 S3 S4 ratio lm y ~ x 1.2112368 0.3257644 30 0.44545302
The models data frame contains the fitted (linear)
models for each pair of neighboring stations and each metric.
station.x is the upstream hydrograph
Sx.station.y is the downstream hydrograph
Sy.metric is the name of the corresponding metric.type is the model class, by default
lm.formula is the expression that is used to fit the
model.(Intercept), x are the extracted
coefficients (called with coef).n is the number of events used to fit the model.r2 is the extracted or computed \(R^2\) for each model.
Finally the fitted regression models are used to predict the values
of the metrics along the longitudinal flow path given the initial
values:
gridExtra::grid.arrange(grobs = res$`2`$plot_predict$grobs, nrow = 3, ncol = 2)
If a file with initial values is passed to peaktrace(),
predictions along the longitudinal flow path are made and visualized in
a plot. Each line in the plot represents a different scenario, e.g., the
uppermost solid lines for AMP, MAFR and MEFR represent the values of
Q_max in the initial file. Starting from these initial
values, predictions are made with the corresponding models, e.g., the
first value of the initial valus file is passed to the model that
describes the relationship of AMP between S1 and
S2 to predict the value at S2.
The initial value and the first fitted model are:
initials[1, ]
#> Station Metric Value Name
#> 1 S1 AMP 93 Q_max
res$`2`$models[1, ]
#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.5542922 1.019472 164 0.9965828
The resulting predicted value is then passed to the next model along
the flow path, i.e., the model of S2 and S3 to
predict the value at S3.
res$`2`$models[6, ]
#> station.x station.y metric type formula (Intercept) x n r2
#> 6 S2 S3 dur lm y ~ x 0.7959971 0.7868426 100 0.7053785
Finally, this predicted value is passed to the last model along this
river section: the model between S3 and S4 to
predict the value at S4.
res$`2`$models[11, ]
#> station.x station.y metric type formula (Intercept) x n r2
#> 11 S3 S4 dur lm y ~ x 3.029952 0.4642539 30 0.09809454
This procedure is repeated for all metrics according to the initial
values file. Note that in this initial values file metric RATIO starts
at station S2. Therefore the first value of RATIO to
predict is at station S3.
The second list object refers to event type 4 (DC event). The nested
objects of this event type are shown below.
res$`4`$settings
#> station.x station.y bound lag metric
#> 1 S1 S2 lower 1 0.8168386
#> 2 S1 S2 inner 1 0.9500000
#> 3 S1 S2 upper 1 1.0831614
#> 4 S2 S3 lower 1 0.9202873
#> 5 S2 S3 inner 1 1.0500000
#> 6 S2 S3 upper 1 1.1797127
#> 7 S3 S4 lower 1 0.5814461
#> 8 S3 S4 inner 1 0.8500000
#> 9 S3 S4 upper 1 1.1185539
head(res$`4`$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 4 2014-01-01 02:00:00 27.07 13.40 3.867143 7 10.565371
#> 2 100000 4 2014-01-01 11:15:00 29.47 13.90 3.274444 9 12.205323
#> 3 100000 4 2014-01-01 18:30:00 31.04 16.00 3.448889 9 13.125000
#> 4 100000 4 2014-01-02 07:45:00 27.44 13.98 6.860000 4 12.154472
#> 5 100000 4 2014-01-02 20:15:00 27.37 14.20 3.421250 8 10.033003
#> 6 100000 4 2014-01-03 18:15:00 26.87 13.90 5.374000 5 9.867987
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y
#> 1 S1 200000 4 2014-01-01 03:30:00 26.09 6.5 0.8153125
#> 2 S1 200000 4 2014-01-01 12:45:00 28.09 6.5 1.7556250
#> 3 S1 200000 4 2014-01-01 19:45:00 29.50 7.1 1.2826087
#> 4 S1 200000 4 2014-01-02 08:45:00 26.37 6.2 1.6481250
#> 5 S1 200000 4 2014-01-02 21:00:00 27.26 6.5 0.8793548
#> 6 S1 200000 4 2014-01-03 19:15:00 25.84 6.4 1.9876923
#> dur.y ratio.y station.y diff_metric
#> 1 32 8.032345 S2 -0.036202438
#> 2 16 7.834550 S2 -0.046827282
#> 3 23 9.194444 S2 -0.049613402
#> 4 16 8.069705 S2 -0.038994169
#> 5 31 7.747525 S2 -0.004018999
#> 6 13 6.007752 S2 -0.038332713
grid::grid.draw(res$`4`$plot_threshold)
grid::grid.draw(res$`4`$plot_scatter)
res$`4`$models
#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.6331382 1.0230064 159 0.9976993
#> 2 S1 S2 dur lm y ~ x 3.4889475 1.1941344 159 0.5660323
#> 3 S1 S2 mafr lm y ~ x 0.3670848 0.6093259 159 0.8288550
#> 4 S1 S2 mefr lm y ~ x 0.3152232 0.5218025 159 0.6858269
#> 5 S2 S3 amp lm y ~ x 0.8889574 0.9860819 89 0.9960296
#> 6 S2 S3 dur lm y ~ x 2.5702522 0.6747927 89 0.8660458
#> 7 S2 S3 mafr lm y ~ x 0.8424465 0.8700683 89 0.9305420
#> 8 S2 S3 mefr lm y ~ x 0.9748893 0.6441977 89 0.7688562
#> 9 S2 S3 ratio lm y ~ x 0.6994949 0.5659408 89 0.9776473
#> 10 S3 S4 amp lm y ~ x -0.4977512 0.8877421 50 0.9569848
#> 11 S3 S4 dur lm y ~ x 1.6421232 0.6351157 50 0.7096118
#> 12 S3 S4 mafr lm y ~ x -0.2972899 0.8213848 50 0.5844032
#> 13 S3 S4 mefr lm y ~ x 0.2811406 1.1317973 50 0.2960442
#> 14 S3 S4 ratio lm y ~ x 0.8553193 0.3178922 50 0.7922559
gridExtra::grid.arrange(grobs = res$`4`$plot_predict$grobs, nrow = 3, ncol = 2)
References
Greimel F, Zeiringer B, Höller N, Grün B, Godina R, Schmutz S (2016).
“A Method to Detect and Characterize Sub-Daily Flow Fluctuations.”
Hydrological Processes, 30(13), 2063-2078. doi: 10.1002/hyp.10773
Greimel F, Grün B, Hayes DS, Höller N, Haider J, Zeiringer B,
Holzapfel P, Hauer C, Schmutz S (2022). “PeakTrace: Routing of
Hydropower Plant-Specific Hydropeaking Waves Using Multiple Hydrographs
- A Novel Approach.” River Research and Applications, 1-14. doi:
10.1002/rra.3978
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.