Objective functions available in Kalix for hydrological model calibration. All objective functions are configured for minimisation during optimisation.

NSE - Nash-Sutcliffe Efficiency

Description

The Nash-Sutcliffe Efficiency (NSE) is one of the most widely used statistics for assessing the goodness-of-fit of hydrological models. It compares the performance of the model against a simple baseline (the mean of observed values).

Formula

$\text{NSE} = 1 - \frac{\sum_{i=1}^{n} (Q_o[i] - Q_m[i])^2}{\sum_{i=1}^{n} (Q_o[i] - \overline{Q_o})^2}$

Where:

• Qo[i] = observed value at timestep i
• Qm[i] = modeled/simulated value at timestep i
• $\overline{Q_o}$ = mean of observed values
• n = number of timesteps

Optimisation

• Original range: (−∞, 1] where 1 = perfect fit
• Minimisation: NSE is negated so objective = −NSE
• Optimal value: -1.0 (corresponds to NSE = 1.0)

When to Use

• General-purpose calibration metric
• Emphasizes high flows (squared errors give more weight to large deviations)
• NSE = 1: perfect fit
• NSE = 0: model performs as well as using the mean
• NSE < 0: model performs worse than using the mean

LNSE - Log Nash-Sutcliffe Efficiency