Difference between revisions of "GLUE analysis"

Latest revision as of 18:13, 12 August 2009

Since I am now at Imperial College London, this page has moved and can now be found on the wiki page of the R-project.

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 [[Category:Hydrology in R]]
+Since I am now at Imperial College London, this page has moved and can now be found on [http://wiki.r-project.org/rwiki/doku.php?id=guides:tutorials:hydrological_data_analysis the wiki page of the R-project].
-===Introduction===
-This is an example of R code to perform a Generalised Likelihood Uncertainty Estimation (GLUE) on a hydrological model. In the example we use [[topmodel]] (implemented as ''topmodel()'') on a catchment in the Ecuadorian Andes (Huagrahuma). Other models can be used as long as they are implemented as an R function.
-===Libraries needed===
-Library Hmisc ([http://cran.r-project.org/web/packages/Hmisc/index.html CRAN]) is needed for the ''wgt.quantile()'' function. See ?wgt.quantile for details.
-   > library(Hmisc)
-   > library(topmodel)
-   > data(Huagrahuma)
-===Procedure===
-Sample a parameter set from a prior parameter distribution. This example uses the uniform distribution, which can be sampled between 0 and 1 with ''runif()''. We then scale to the appropriate range and offset.
-   qs0   <- runif(1)*0.00012+0.00012
-   lnTe  <- runif(1)*5-2
-   m     <- runif(1)*0.1
-   Sr0   <- runif(1)*0.2
-   Srmax <- runif(1)*0.1
-   td    <- runif(1)*3
-   vch   <- 1000
-   vr    <- 100+runif(1)*2500
-   k0    <- runif(1)*10
-   psi   <- 1
-   dtheta<- runif(1)*5
-   dt    <- 0.25
-   parameters<-c(qs0,lnTe,m,Sr0,Srmax,td,vch,vr,k0,psi,dtheta,dt)
-(TODO: explain the parameters and the chosen ranges)
-Run the model for the calibration period with the generated parameter set to obtain the simulated discharge
-   Qsim <- topmodel(parameters,topidx,delay,rain,ET0)
-Calculate the likelihood of this parameter set using the simulated and observed discharge. The choice of the likelihood function is up to the user, but the Nash - Sutcliffe efficiency is given here as an example:
-   eff <- 1 - sum((Qobs - Qsim)^2) / sum((Qobs-mean(Qobs))^2)
-NOTE: calculation of the Nash-Sutcliffe efficiency is also implimented in NSeff() of the [[topmodel]]-package.
-Decide whether the parameter set is behavioural or not and retain the parameter set if behavioural
-NOTE: this decision is again subjective. For a more scientifically sound determination of the behavioural limit, see Beven (2006). Here we will use an efficiency of 0.6 as a threshold.
-The efficiency, parameter set and simulated discharge of a behavioural run are stored in resp. the objects total.eff, total.param.set and total.qsim
-   if(eff > 0.6) {
-      total.eff <- c(total.eff,eff)
-      behavioural.parameters <- cbind(behavioural.parameters,parameters)
-   }
-The above procedure should be repeated until enough behavioural runs are obtained (e.g. using a while()-loop)
-In the next section it is assumed that each column of behavioural.parameters contains a behavioural parameter set and that the corresponding efficiency is found at the same location in the total.eff vector
-Rerun the model for the prediction period, using each of the behavioural parameter sets. The simulated discharges are stored in the columns of a matrix called predicted.qsim
-   predicted.qsim <- model(behavioural.parameters[,1], rain, ...)
-   for(i in 2:dim(param.set)[2]) {
-      qsim <- model(behavioural.parameters[,i], rain, ...)
-      predicted.qsim <- cbind(predicted.obs,qobs)
-   }
-Normalise the efficiencies so that they sum up to 1:
-   eff <- eff - 0.6
-   eff <- eff/sum(eff)
-Define a quantile for the prediction bounds. Here we take the 0.05 and 0.95 quantiles resulting in 90% prediction limits.
-   lower <- 0.05
-   upper <- 0.95
-Create the objects in which we will store the prediction limits:
-   Ulimit <- 0
-   Llimit <- 0
-Now we calculate the quantiles for each timestep (this can also be done with apply() function)
-   for(i in 1:dim(predicted.qsim)[1]) {
-      Llimit[i] <- wtd.quantile(predicted.qsim[i,],weights = eff, probs = lower, normwt=T)
-      Ulimit[i] <- wtd.quantile(predicted.qsim[i,],weights = eff, probs = upper, normwt=T)
-   }
-If everything went well, the final prediciton limits are in Llimit and Ulimit.
-===Final notes===
-* If topmodel is used, some loops can be avoided because topmodel() can work on entire parameter set matrices. It can also return the Nash-Sutcliffe efficiency directly (see the topmodel page)
-* The procedure can be very memory intensive because all simulated discharges for all parameter sets are stored in memory (the matrix predicted.qsim). If the model can give output per timestep, the above procedure can be repeated for each timestep separately to reduce memory usage
-===References===
-* Beven, K., and Binley, A. The future of distributed models: Model calibration and uncertainty prediction. Hydrological Processes 6 (1992), 279-298.
-* Beven, K. A manifesto for the equifinality thesis. Journal of Hydrology 320 (2006), 18-36.

Difference between revisions of "GLUE analysis"

Latest revision as of 18:13, 12 August 2009

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