airGR is a package that brings into the R software the hydrological modelling tools used and developed at the Catchment Hydrology Research Group at Irstea (France), including the GR rainfall-runoff models and a snowmelt and accumulation model, CemaNeige. Each model core is coded in Fortran to ensure low computational time. The other package functions (i.e. mainly the calibration algorithm and the efficiency criteria calculation) are coded in R.
The airGR package has been designed to fulfill two major requirements: to facilitate the use by non-expert users and to allow flexibility regarding the addition of external criteria, models or calibration algorithms. The names of the functions and their arguments were chosen to this end. airGR also contains basics plotting facilities.
Six hydrological models and one snowmelt and accumulation model are implemented in airGR. The snow model can be used alone or together with the daily hydrological models.
The models can be called within airGR using the following functions:
RunModel_GR4H(): four-parameter hourly lumped hydrological model [@mathevet_quels_2005]
RunModel_GR4J(): four-parameter daily lumped hydrological model [@perrin_improvement_2003]
RunModel_GR5J(): five-parameter daily lumped hydrological model [@le_moine_bassin_2008]
RunModel_GR6J(): six-parameter daily lumped hydrological model [@pushpalatha_downward_2011]
RunModel_GR2M(): two-parameter monthly lumped hydrological model [@mouelhi_vers_2003; @mouelhi_stepwise_2006]
RunModel_GR1A(): one-parameter yearly lumped hydrological model [@mouelhi_vers_2003; @mouelhi_linking_2006]
RunModel_CemaNeige(): two-parameter degree-day snowmelt and accumulation model [@valery_as_2014]
RunModel_CemaNeigeGR4J(): combined use of GR4J and CemaNeige
RunModel_CemaNeigeGR5J(): combined use of GR5J and CemaNeige
RunModel_CemaNeigeGR6J(): combined use of GR6J and CemaNeige
The GRP forecasting model and the Otamin predictive uncertainty tool are not available in airGR.
In this vignette, we show how to prepare and run a calibration and a simulation with airGR hydrological models.
In the following example, we use a data sample contained in the package. For real applications, the user has to import its data into R and to prepare it with an adequate data.frame format as described below.
First, it is necessary to load the airGR package:
Below is presented an example of a
data.frame of daily hydrometeorological observations time series for a fictional catchment included in the airGR package that contains:
## DatesR P T E ## Min. :1984-01-01 Min. : 0.000 Min. :-18.700 Min. :0.000 ## 1st Qu.:1991-04-02 1st Qu.: 0.000 1st Qu.: 4.100 1st Qu.:0.600 ## Median :1998-07-02 Median : 0.300 Median : 9.100 Median :1.400 ## Mean :1998-07-02 Mean : 2.915 Mean : 9.147 Mean :1.764 ## 3rd Qu.:2005-10-01 3rd Qu.: 3.600 3rd Qu.: 14.500 3rd Qu.:2.900 ## Max. :2012-12-31 Max. :66.800 Max. : 28.400 Max. :5.500 ## ## Qls Qmm ## Min. : 70 Min. : 0.0168 ## 1st Qu.: 1643 1st Qu.: 0.3943 ## Median : 4070 Median : 0.9768 ## Mean : 6134 Mean : 1.4720 ## 3rd Qu.: 7889 3rd Qu.: 1.8933 ## Max. :99500 Max. :23.8800 ## NA's :755 NA's :755
The usual functions (e.g.
read.table()) can be used to load real-case data sets.
To run a model, the functions of the airGR package (e.g. the models, calibration and criteria calculation functions) require data and options with specific formats.
To facilitate the use of the package, there are several functions dedicated to the creation of these objects:
CreateInputsModel(): prepares the inputs for the different hydrological models (times series of dates, precipitation, observed discharge, etc.)
CreateRunOptions(): prepares the options for the hydrological model run (warm up period, calibration period, etc.)
CreateInputsCrit(): prepares the options in order to compute the efficiency criterion (choice of the criterion, choice of the transformation on discharge: “log”, “sqrt”, etc.)
CreateCalibOptions(): prepares the options for the hydrological model calibration algorithm (choice of parameters to optimize, predefined values for uncalibrated parameters, etc.)
To run a GR hydrological model or CemaNeige, the user has to prepare the input data with the
As arguments, this function needs the function name corresponding to the model the user wants to run, a vector of dates, a vector of precipitation and a vector of potential evapotranspiration.
In the example below, we already have the potential evapotranspiration. If the user does not have these data, it is possible to compute it with the Oudin's formula with the
PEdaily_Oudin() function (this function only needs Julian days, daily average air temperature and latitude).
Missing values (
NA) of precipitation (or potential evapotranspiration) are not allowed.
InputsModel <- CreateInputsModel(FUN_MOD = RunModel_GR4J, DatesR = BasinObs$DatesR, Precip = BasinObs$P, PotEvap = BasinObs$E) str(InputsModel)
## List of 3 ## $ DatesR : POSIXlt[1:10593], format: "1984-01-01" "1984-01-02" ... ## $ Precip : num [1:10593] 4.1 15.9 0.8 0 0 0 0 0 2.9 0 ... ## $ PotEvap: num [1:10593] 0.2 0.2 0.3 0.3 0.1 0.3 0.4 0.4 0.5 0.5 ... ## - attr(*, "class")= chr [1:3] "InputsModel" "daily" "GR"
CreateRunOptions() function allows to prepare the options required to the
RunModel*() functions, which are the actual models functions.
The user must at least define the following arguments:
FUN_MOD: the name of the model function to run
InputsModel: the associated inputs data
IndPeriod_Run: the period on which the model is run
To select a period for which the user wants to run the model, select the corresponding indexes for different time periods (not the POSIXt dates), as follows:
Ind_Run <- seq(which(format(BasinObs$DatesR, format = "%d/%m/%Y %H:%M")=="01/01/1990 00:00"), which(format(BasinObs$DatesR, format = "%d/%m/%Y %H:%M")=="31/12/1999 00:00")) str(Ind_Run)
## int [1:3652] 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 ...
The initialization of hydrological models is of the utmost importance. Indeed, an inaccurate initialization causes poor quality discharge simulations during the earliest stages of the running period. For example, in the GR models, by default, the production and the routing store levels store level are respectively set to 30 % and 50 % of their capacity, which may be far from their ideal value. Two solutions are offered to accurately initialize the GR models in airGR: manually predefining the initial states (e.g. from a previous run) or running the models during a warm up period before the actual running period. It is generally advised to set up this warm up period to be equal or superior to one year.
As a consequence, it is possible to define in
CreateRunOptions() the following arguments:
IniStates: the initial states of the 2 unit hydrographs (20 + 40 = 60 units)
IniResLevels: the initial levels of the production and routing stores
IndPeriod_WarmUp: the warm up period used to run the model, to be defined in the same format as
RunOptions <- CreateRunOptions(FUN_MOD = RunModel_GR4J, InputsModel = InputsModel, IndPeriod_Run = Ind_Run, IniStates = NULL, IniResLevels = NULL, IndPeriod_WarmUp = NULL)
## Warning in CreateRunOptions(FUN_MOD = RunModel_GR4J, InputsModel = InputsModel, : Model warm up period not defined -> default configuration used ## The year preceding the run period is used
## List of 6 ## $ IndPeriod_WarmUp: int [1:365] 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 ... ## $ IndPeriod_Run : int [1:3652] 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 ... ## $ IniStates : num [1:67] 0 0 0 0 0 0 0 0 0 0 ... ## $ IniResLevels : num [1:3] 0.3 0.5 NA ## $ Outputs_Cal : chr "Qsim" ## $ Outputs_Sim : chr [1:20] "DatesR" "PotEvap" "Precip" "Prod" ... ## - attr(*, "class")= chr [1:3] "RunOptions" "GR" "daily"
CreateRunOptions() function returns warnings if the default initialization options are used:
IniResLevelsare automatically set to initialize all the model states at 0, except for the production and routing stores, which are initialized at respectively 30% and 50 % of their capacity
IndPeriod_WarmUpdefault setting ensures a one-year warm up using the time steps preceding the
IndPeriod_Run, if available
CreateInputsCrit() function allows to prepare the input in order to calculate a criterion. It is possible to define the following arguments:
FUN_CRIT: the name of the error criterion function (the available functions are introduced later on)
InputsModel: the inputs of the hydrological model previously prepared by the
RunOptions: the options of the hydrological model previously prepared by the
Qobs: the observed discharge expressed in mm/time step
Missing values (
NA) are allowed for observed discharge.
InputsCrit <- CreateInputsCrit(FUN_CRIT = ErrorCrit_NSE, InputsModel = InputsModel, RunOptions = RunOptions, Qobs = BasinObs$Qmm[Ind_Run]) str(InputsCrit)
## List of 5 ## $ BoolCrit : logi [1:3652] TRUE TRUE TRUE TRUE TRUE TRUE ... ## $ Qobs : num [1:3652] 1.99 1.8 2.86 2.4 3.31 ... ## $ transfo : chr "" ## $ Ind_zeroes: NULL ## $ epsilon : NULL ## - attr(*, "class")= chr "InputsCrit"
Before using the automatic calibration tool, the user needs to prepare the calibration options with the
CreateCalibOptions() function. For that, it is necessary to define the following arguments:
FUN_MOD: the name of the model function
FUN_CALIB: the name of the calibration algorithm
CalibOptions <- CreateCalibOptions(FUN_MOD = RunModel_GR4J, FUN_CALIB = Calibration_Michel) str(CalibOptions)
## List of 3 ## $ FixedParam : logi [1:4] NA NA NA NA ## $ SearchRanges : num [1:2, 1:4] 4.59e-05 2.18e+04 -1.09e+04 1.09e+04 4.59e-05 ... ## $ StartParamDistrib: num [1:3, 1:4] 169.017 247.151 432.681 -2.376 -0.649 ... ## - attr(*, "class")= chr [1:3] "CalibOptions" "GR4J" "HBAN"
The evaluation of the quality of a simulation is estimated through the calculation of criteria. These criteria can be used both as objective-functions during the calibration of the model, or as a measure for evaluating its performance on a control period.
The package offers the possibility to use different criteria:
ErrorCrit_RMSE(): Root mean square error (RMSE)
ErrorCrit_NSE(): Nash-Sutcliffe model efficiency coefficient (NSE)
ErrorCrit_KGE(): Kling-Gupta efficiency criterion (KGE)
ErrorCrit_KGE2(): modified Kling-Gupta efficiency criterion (KGE')
It is also possible to create user-defined criteria. For doing that, it is only necessary to define the function in R following the same syntax as the criteria functions included in airGR.
The objective of the calibration algorithm is to identify the model parameters: by comparing the model outputs with observed data, this algorithm determines the combination of parameters that represents the best the behavior of the watershed.
In the airGR package, a function called
Calibration_Michel() is implemented. This functions allows running a calibration with the package models.
The calibration algorithm optimizes the error criterion selected as objective-function. This algorithm works in two steps:
OutputsCalib <- Calibration_Michel(InputsModel = InputsModel, RunOptions = RunOptions, InputsCrit = InputsCrit, CalibOptions = CalibOptions, FUN_MOD = RunModel_GR4J, FUN_CRIT = ErrorCrit_NSE)
## Grid-Screening in progress (0% 20% 40% 60% 80% 100%) ## Screening completed (81 runs) ## Param = 247.151 , -0.020 , 83.096 , 2.384 ## Crit NSE[Q] = 0.7685 ## Steepest-descent local search in progress ## Calibration completed (20 iterations, 226 runs) ## Param = 257.238 , 1.012 , 88.235 , 2.208 ## Crit NSE[Q] = 0.7985
Param <- OutputsCalib$ParamFinalR Param
##  257.237556 1.012237 88.234673 2.207958
Calibration_Michel() function is the only one implemented in the airGR package to calibrate the model, but the user can implement its own calibration function. Two vignettes explain how it can be done (2.1 Plugging in new calibration and 2.2 MCMC parameter estimation).
Calibration_Michel() function returns a vector with the parameters of the chosen model, which means that the number of values can differ depending on the model that is used. It is possible to use the
Calibration_Michel() function with user-implemented hydrological models.
This step assesses the predictive capacity of the model. Control is defined as the estimation of the accuracy of the model on data sets that are not used in its construction, and in particular its calibration. The classical way to perform a control is to keep data from a period separated from the calibration period. If possible, this control period should correspond to climatic situations that differ from those of the calibration period in order to better point out the qualities and weaknesses of the model. This exercise is necessary for assessing the robustness of the model, that is to say its ability to keep stable performances outside of the calibration conditions.
Performing a model control with airGR is similar to running a simulation (see below), followed by the computation of one or several performance criteria.
To run a model, the user has to use the
RunModel*() functions (
RunOptions and parameters).
All the data needed have already been prepared in the previous steps defined in this guide.
OutputsModel <- RunModel_GR4J(InputsModel = InputsModel, RunOptions = RunOptions, Param = Param) str(OutputsModel)
## List of 20 ## $ DatesR : POSIXlt[1:3652], format: "1990-01-01" "1990-01-02" ... ## $ PotEvap : num [1:3652] 0.3 0.4 0.4 0.3 0.1 0.1 0.1 0.2 0.2 0.3 ... ## $ Precip : num [1:3652] 0 9.3 3.2 7.3 0 0 0 0 0.1 0.2 ... ## $ Prod : num [1:3652] 196 199 199 201 200 ... ## $ Pn : num [1:3652] 0 8.9 2.8 7 0 0 0 0 0 0 ... ## $ Ps : num [1:3652] 0 3.65 1.12 2.75 0 ... ## $ AE : num [1:3652] 0.2833 0.4 0.4 0.3 0.0952 ... ## $ Perc : num [1:3652] 0.645 0.696 0.703 0.74 0.725 ... ## $ PR : num [1:3652] 0.645 5.946 2.383 4.992 0.725 ... ## $ Q9 : num [1:3652] 1.78 1.52 3.86 3.17 3.45 ... ## $ Q1 : num [1:3652] 0.2 0.195 0.271 0.387 0.365 ... ## $ Rout : num [1:3652] 53.9 53.6 55.3 56.1 56.9 ... ## $ Exch : num [1:3652] 0.181 0.18 0.177 0.197 0.207 ... ## $ AExch1 : num [1:3652] 0.181 0.18 0.177 0.197 0.207 ... ## $ AExch2 : num [1:3652] 0.181 0.18 0.177 0.197 0.207 ... ## $ AExch : num [1:3652] 0.362 0.36 0.353 0.393 0.414 ... ## $ QR : num [1:3652] 2.05 1.99 2.36 2.55 2.78 ... ## $ QD : num [1:3652] 0.381 0.375 0.447 0.584 0.572 ... ## $ Qsim : num [1:3652] 2.43 2.37 2.8 3.14 3.35 ... ## $ StateEnd:List of 3 ## ..$ Store :List of 3 ## .. ..$ Prod: num 189 ## .. ..$ Rout: num 48.9 ## .. ..$ Exp : num NA ## ..$ UH :List of 2 ## .. ..$ UH1: num [1:20] 0.514 0.54 0.148 0 0 ... ## .. ..$ UH2: num [1:40] 0.056306 0.057176 0.042253 0.012187 0.000578 ... ## ..$ CemaNeigeLayers:List of 2 ## .. ..$ G : num NA ## .. ..$ eTG: num NA ## ..- attr(*, "class")= chr [1:3] "IniStates" "GR" "daily" ## - attr(*, "class")= chr [1:3] "OutputsModel" "daily" "GR"
Although it is possible for the user to design its own graphics from the outputs of the
RunModel*() functions, the airGR package offers the possibility to make use of the
plot.OutputsModel() function (or
plot() with an
OutputsModel object). This function returns a dashboard of results including various graphs (depending on the model used):
plot(OutputsModel, Qobs = BasinObs$Qmm[Ind_Run])
Moreover, if the CemaNeige model is used, the air temperature and the simulated snowpack water equivalent time series are plotted.
To evaluate the efficiency of the model, it is possible to use the same criterion as defined at the calibration step or to use another criterion.
OutputsCrit <- ErrorCrit_NSE(InputsCrit = InputsCrit, OutputsModel = OutputsModel)
## Crit. NSE[Q] = 0.7985
OutputsCrit <- ErrorCrit_KGE(InputsCrit = InputsCrit, OutputsModel = OutputsModel)
## Crit. KGE[Q] = 0.7855
## SubCrit. KGE[Q] cor(sim, obs, "pearson") = 0.8983 ## SubCrit. KGE[Q] sd(sim)/sd(obs) = 0.8163 ## SubCrit. KGE[Q] mean(sim)/mean(obs) = 1.0439