Framework for Understanding Structural Errors (FUSE, R package)

Implementation of the framework for hydrological modelling FUSE described in Clark et al. (2008) and based on the Fortran code provided by M. Clark in 2011. The package consists of two modules: Soil Moisture Accounting module (fusesma.sim) and Gamma routing module (fuserouting.sim). It also contains default parameter ranges (fusesma.ranges and fuserouting.ranges) and three data objects: DATA (sample input dataset), parameters (sample parameters) and modlist (list of FUSE model structures).

To cite this software:
Vitolo C., Wells P., Dobias M. and Buytaert W., fuse: Framework for Understanding Structural Errors, (2012), GitHub repository, https://github.com/ICHydro/r_fuse, doi: http://dx.doi.org/10.5281/zenodo.14005

Basics

Check if dependencies are installed. If not, install them. Then load them.

list.of.packages <- c("zoo", "tgp", "devtools")
new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)

Install and load the FUSE package

library(devtools)
install_github("cvitolo/r_fuse", subdir = "fuse")
library(fuse)

Load sample data (daily time step)

data(DATA)
myDELTIM <- 1

Define parameter ranges

DefaultRanges <- data.frame(t(data.frame(c(fusesma.ranges(),
                                           fuserouting.ranges()))))
names(DefaultRanges) <- c("Min","Max")

Sample parameter set using Latin Hypercube method

numberOfRuns <- 100
parameters <- lhs( numberOfRuns, as.matrix(DefaultRanges) )
parameters <- data.frame(parameters)
names(parameters) <- row.names(DefaultRanges)

Alternatively, sample parameter set using built-in function

parameters <- generateParameters(100)

Example usage with 1 model structure

Define the model to use, e.g. TOPMODEL (MID = 60)

myMID <- 60

Use the built-in function to run FUSE for the 1st sampled parameter set

x <- fuse(DATA, myMID, myDELTIM, parameters[1,])

plot(x,xlab="",ylab="Streamflow [mm/day]")

Run FUSE for all the sampled parameter sets

plot(DATA$Q,type="l",xlab="",ylab="Streamflow [mm/day]")
allQ <- data.frame(matrix(NA,ncol=numberOfRuns,nrow=dim(DATA)[1]))
for (i in 1:numberOfRuns){
  allQ[,i] <- fuse(DATA, myMID, myDELTIM, parameters[i,])
  lines(zoo(allQ[,i],order.by=index(DATA)),col="gray",lwd=0.1)
}
lines(DATA$Q,col="black")

Ensemble example usage

Define a group of model structures to use

mids <- c(60, 230, 342, 426)

Run a multi-model calibration using the Nash-Sutcliffe efficiency as objective function

library(qualV)
indices <- rep(NA,4*numberOfRuns)
discharges <- matrix(NA,ncol=4*numberOfRuns,nrow=dim(DATA)[1])
kCounter <- 0

for (m in 1:4){

  myMID <- mids[m]

  for (pid in 1:numberOfRuns){

    kCounter <- kCounter + 1
    ParameterSet <- as.list(parameters[pid,])
    
    Qrout <- fuse(DATA, myMID, myDELTIM, parameters[pid,])
 
    indices[kCounter] <- EF(DATA$Q,Qrout)  
    discharges[,kCounter] <- Qrout
    
    }
}

Compare results

bestRun <- which(indices == max(indices))
 
bestModel <- function(runNumber){
 if (runNumber<(numberOfRuns+1)) myBestModel <- "TOPMODEL"
 if (runNumber>(numberOfRuns+1) & runNumber<(2*numberOfRuns+1)) myBestModel <- "ARNOXVIC"
 if (runNumber>(2*numberOfRuns+1) & runNumber<(3*numberOfRuns+1)) myBestModel <- "PRMS"
 if (runNumber>(3*numberOfRuns+1) & runNumber<(4*numberOfRuns+1)) myBestModel <- "SACRAMENTO"
 return(myBestModel)
}
bestModel(bestRun)
 
plot(coredata(DATA$Q),type="l",xlab="",ylab="Streamflow [mm/day]", lwd=0.5)
 
for(pid in 1:(4*numberOfRuns)){
 lines(discharges[,pid], col="gray", lwd=3)
}
 
lines(coredata(DATA$Q),col="black", lwd=1)
lines(discharges[,bestRun],col="red", lwd=1)

How the best simulation of each model structure compare to each other?

bestRun0060 <- which(indices[1:numberOfRuns] == max(indices[1:numberOfRuns]))
bestRun0230 <- numberOfRuns + which(indices[(numberOfRuns+1):(2*numberOfRuns)] == max(indices[(numberOfRuns+1):(2*numberOfRuns)]))
bestRun0342 <- 2*numberOfRuns + which(indices[(2*numberOfRuns+1):(3*numberOfRuns)] == max(indices[(2*numberOfRuns+1):(3*numberOfRuns)]))
bestRun0426 <- 3*numberOfRuns + which(indices[(3*numberOfRuns+1):(4*numberOfRuns)] == max(indices[(3*numberOfRuns+1):(4*numberOfRuns)]))
 
plot(coredata(DATA$Q),type="l",xlab="",ylab="Streamflow [mm/day]", lwd=1)
lines(discharges[,bestRun0060], col="green", lwd=1)
lines(discharges[,bestRun0230], col="blue", lwd=1)
lines(discharges[,bestRun0342], col="pink", lwd=1)
lines(discharges[,bestRun0426], col="orange", lwd=1)
 
legend("top", 
        c("TOPMODEL", "ARNOXVIC", "PRMS","SACRAMENTO"), 
        col = c("green", "blue", "pink", "orange"),
        lty = c(1, 1, 1, 1))

Use fuse with hydromad

Hydromad is an excellent framework for hydrological modelling, optimization, sensitivity analysis and assessment of results. It contains a large set of soil moisture accounting modules and routing functions. Thanks to Joseph Guillaume (hydromad’s maintainer), fuse is now compatible with hydromad and below are some examples Joseph provided to use fuse within the hydromad environment.

# Install and load hydromad
install.packages(c("zoo", "latticeExtra", "polynom", "car", 
                   "Hmisc", "reshape", "DEoptim", "coda"))
install.packages("dream", repos="http://hydromad.catchment.org")
install.packages("hydromad", repos="http://hydromad.catchment.org")
library(hydromad) 

# Load fuse and an example dataset
library(fuse)
data(DATA)

# Set the parameter ranges using hydromad.options
hydromad.options(fusesma = fusesma.ranges(),
                 fuserouting = fuserouting.ranges())

# Set up the model
modspec <- hydromad(DATA,
                    sma = "fusesma", 
                    routing = "fuserouting", 
                    mid = 1:1248, 
                    deltim = 1)

# Randomly generate 1 parameter set
myNewParameterSet <- parameterSets(coef(modspec, warn=FALSE),1,method="random")

# Run a single simulation using the parameter set generated above
modx <- update(modspec, newpars = myNewParameterSet)

# Generate a summary of the result
summary(modx)

# The instantaneous runoff is
U <- modx$U

# The routed discharge is
Qrout <- modx$fitted.values

# Plot the Observed vs Simulated value
hydromad:::xyplot.hydromad(modx)

# Add the precipitation to the above plot
hydromad:::xyplot.hydromad(modx, with.P=TRUE)

# Calibrate FUSE using hydromad's fitBy method and the Shuffled Complex Evolution algorithm
modfit <- fitBySCE(modspec)

# Get a summary of the result
summary(modfit)

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