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
The root mean squared error is the square root of the variance:

RMSE <- cov(Qobs, Qsim, use="complete.obs")^0.5