Objective
Context
End of summer 2018, the river La Meuse à Saint-Mihiel has reached its lowest level for several years and the rain is still awaited for on this catchment characterized by many water uses in summer. In charge of the monitoring of the streamflows in period of low-flow, you have been called by the local officials who are panicking about the drought situation and ask you to produce an estimate of the streamflows of the river for the next weeks.
Unfortunately, you have not received the weather forecast from the regional forecasting service for several weeks… You do not have any forecast of the coming precipitation, but you still have to quantify the possible streamflows on the catchment for the next weeks.
The exercise consists in using the available hydro-climatic data (at daily time step) on La Meuse à Saint-Mihiel (2543 km²), and a rainfall-runoff model to forecast the streamflows of the coming weeks by using (1) the last observed streamflow on the considered catchment, (2) the observed precipitation climatology and (3) the observed streamflow climatology. This information will provide ranges of potential streamflows for the coming weeks (see following figure).
This work will be completed in four steps:
- Statistical analysis of the streamflow climatology to obtain an order of magnitude of the streamflows historically observed during the study period, i.e. the daily streamflow regime.
- Calibration of the hydrological model on the historical period considering a criterion centered on low flows.
- Pessimistic scenario of zero precipitation: rainfall-runoff simulation over the summer studied from the last observed streamflow considering no future precipitation and a series of potential evapotranspiration (PE) constituted from the interannual average PE.
- Non-zero future precipitation scenarios: rainfall-runoff simulations for the studied summer based on the last observed discharge by hindcasting the precipitation climatology, i.e. the precipitation observed during the other summers. There will be as many simulations as there are historical years.
Instructions
This section aims to make explicit some of the expected tasks and to describe the hydrological model calibration and simulation conditions (parameter calibration period, reservoir initialization periods, calibration criteria, etc.).
Analysis of streamflow climatology
In a hydrological forecasting context, “flow climatology” refers to the streamflow regime, i.e. the series of interannual mean streamflows. If you want to forecast the streamflow of the day to come (for example on 1 September), the simplest forecast from a technical point of view consists in calculating the average of the streamflows observed on this day during the past years. This average can also be framed thanks to the calculations of quantiles of these same historical streamflows (for example the quantiles 10 and 90 %), which makes it possible to have a first “probabilistic” estimate of the future streamflows, without carrying out rainfall-runoff modelling and without using a precipitation forecast.
In this exercise, you analyze all the streamflows observed during the forecast period (from 1 September 2018 to 20 October 2018) during the previous years. 20 years are available for this analysis, which allows to constitute 20 series of historical daily streamflows for the forecast period. Once grouped in a single table, these streamflows can be summarized by calculating quantiles such as 10, 25, 50, 75 and 90 % quantiles for each day considered. These quantiles will then be used as a first estimate of future streamflows.
Rainfall-runoff model
You will use the GR6J model (Pushpalatha et al. 2011). It is a lumped rainfall-runoff model, operating on a daily time step and having six parameters. It requires continuous time series of daily precipitation and potential evapotranspiration (PE) as input.
This model is easily usable thanks to the airGRteaching package (Delaigue et al. 2024, 2023), developped for the R software by the Catchment Hydrology research group of the HYCAR research unit (INRAE, France).
The time series of observed precipitation, PE and streamflow can be
easily formatted using the PrepGR() function. A
rainfall-runoff simulation can be performed with the
SimGR() function, and a parameter calibration using the
CalGR().
Calibration (and warm-up) period
Initialization is particularly important in a context of hydrological forecasting by modelling: this warm-up consists in estimating the saturation state of the basin (i.e. the internal states of the model) which will then be used as initial conditions for all the tested scenarios. These scenarios are all based on the same state at the date of launching the forecasts.
The period to be considered to calibrate the parameters of the model on La Meuse à Saint-Mihiel catchment starts on 1 September 2000 and ends on 31 August 2018. A warm-up period of 20 months should also be considered from 1 January 1999 to 31 August 2000.
Calibration criterion
The calibration criterion to be considered in this exercise is the Nash and Sutcliffe criterion (Nash and Sutcliffe 1970) calculated on the natural logarithms of the streamflows, noted \(NSE_{ln}\) hereafter (see following equation). This criterion is widely used in hydrological modelling.
The NSE criterion, bounded between \(-\infty\) and \(1\), allows to quantify the performance of a model in a relative way, by comparing a series of simulated streamflows with a so-called “naive” model, here the average of the observed streamflows (i.e. a series of streamflows constituted in each time step by the average of the observed streamflows). Thus, a NSE value equal to 1 indicates a perfect agreement between the series of observed and simulated streamflows (which is never the case), whereas a NSE value lower than 0 means that the simulation considered is less efficient than the simulation of the “naive” model. The calculation of \(NSE_{ln}\) is detailed in the following equation, where \(Q_{obs,t}\) is the observed streamflow at time step \(t\), \(Q_{sim,t}\) is the simulated streamflow at time step \(t\), \(\overline{Q_{obs}}\) is the average of the observed streamflows, \(\epsilon\) is a constant defined below, and \(n\) is the number of observations:
\[\begin{equation} NSE_{ln} = 1-\frac{\sum_{t=1}^{n}(ln(Q_{obs,t}+\epsilon)-ln(Q_{sim,t}+\epsilon))^{2}}{\sum_{t=1}^{n}(ln(Q_{obs,t}+\epsilon)-\overline{ln(Q_{obs}+\epsilon)})^{2}} \end{equation}\]
The calculation of the \(\epsilon\) value is detailed in the following equation. The addition of this \(\epsilon\) is necessary when zero streamflows are present in the observed streamflow series.
\[\begin{equation} \epsilon=\frac{\overline{Q_{obs}}}{100} \end{equation}\]
The logarithmic transformation allows to give more weight to the lowest streamflows, and thus to limit the errors made on the simulation of low flows (Ludovic Oudin et al. 2006). Considering a series constituted by the inverse of the streamflows during the calibration is also recommended to obtain a good performance during the simulation of very low flows (Pushpalatha et al. 2012).
The elements necessary for the calculation of the calibration
criterion have to be set as arguments of the CalGR()
function, which allows to specify if the criterion must be calculated on
“transformed” streamflows with the transfo argument (here
equal to "log").
Automatic calibration of the model parameters
Automatic parameter estimation aims at using a search algorithm in the parameter space. This algorithm will automatically generate sets of parameters, test them, and generate others according to the performance of those already tested, until converging to an optimum. The algorithm developed by Michel (1991) will be used in this exercise.
Simulation period
The simulation period, which can also be called the forecast period in this exercise, runs from 1 September 2018 to 20 October 2018. The set of time steps preceding this calibration period can be used as the warm-up period.
Pessimistic scenario of zero precipitation
Having a rainfall-runoff model calibrated on the studied catchment allows to use future precipitation scenarios and to transform them into streamflow scenarios. The simplest scenario to test (and the most pessimistic one) is the so-called “zero precipitation” scenario: no precipitation will be observed over the time steps of the forecast period. This will be the lower bound of the rainfall-runoff modelling forecast.
To implement this scenario in the airGRteaching environment, it is necessary to create a “dummy” data table containing a time series of precipitation equal to 0 over the forecast period. For PE, a realistic assumption is to use the interannual regime of this variable. Thus, for each forecast day, the interannual average value of observed PE will be used: the PE of 1 September for this scenario will be equal to the average of observed PE values for all past 1 September.
Non-zero future precipitationscenario
This last step aims at performing several rainfall-runoff simulations considering non-zero future precipitation scenarios. These precipitation scenarios will be constructed from historical precipitation data. 20 years of past precipitation are available for this analysis, which allows to build 20 scenarios of historical daily precipitation and PE for the forecast period. A rainfall-runoff simulation will be performed for each of these past years, starting the simulation with the same warm-up period. Once grouped in a single table, the simulated streamflows can be summarized by calculating quantiles such as 10, 25, 50, 75 and 90 % quantiles for each day considered. These quantiles will then be used as an indication of possible future streamflows.
Data available
The data set available to the rainfall-runoff modelling consists of:
- a time series of daily total precipitation (liquid + solid) [mm/d]
(
Ptot); - a time series of daily potential evapotranspiration calculated with
the L. Oudin et al. (2005) formula [mm/d]
(
Evap); - a time series of daily streamflows expressed as a specific discharge
[mm/d] (
Qmmd).
