Performance measures

Introduction

Here is a selection of measures you can use for assessing the performance of your model.

Nash-Sutcliffe efficiency

The Nash-Sutcliffe efficiency is a widely used performance measure based on the error variance. It is implemented as NSeff() in the topmodel package. It takes two vectors, containing the simulated (Qsim) and observed (Qobs) discharge:

  Eff <- NSeff(Qobs,Qsim)

The underlying code is very simple:

  NSeff <- function (Qobs, Qsim){
     Qsim <- Qsim[!is.na(Qobs)]
     Qobs <- Qobs[!is.na(Qobs)]
     Qobs <- Qobs[!is.na(Qsim)]
     Qsim <- Qsim[!is.na(Qsim)]
     NS <- 1 - (sum((Qobs - Qsim)^2)/sum((Qobs - mean(Qobs))^2))
     return(NS)
  }

Coefficient of determination

The coefficient of determination is the square of the Pearson's product-moment correlation coefficient. Note that the COD only evaluates linear relations between variables!

  COD <- cor(Qobs, Qsim, use="complete.obs")^2

Root mean squared error

As the name suggests, the root mean squared error is the square root of the mean squared error:

  RMSE <- (mean((Qobs - Qsim)^2))^0.5