# NSE: Several metrics to evaluate the accuracy of hydrological... In VICmodel: The Variable Infiltration Capacity (VIC) Model

## Description

Calculate several metrics for the evaluating of hydrological modeling accuracy, including the Nash-Sutcliffe coefficient of efficiency (NSE), Logarithmic NSE (log-NSE), relative NSE (rNSE), and relative bias (RB).

## Usage

 ```1 2 3 4 5 6 7``` ```NSE(sim, obs) logNSE(sim, obs) rNSE(sim, obs) RB(sim, obs) ```

## Arguments

 `sim` Data series to be evaluated, usually are the simulated streamflow of hydrological model. `obs` Data series as benchmark to evaluate `sim`, usually are the observed streamflow.

## Details

The Nash-Sutcliffe coefficient of efficiency (NSE) (Nash and Sutcliffe, 1970) is a widely used indicator of the accuracy of model simulations, or other estimation method with reference to a benchmark series (usually the observations), especially the hydrological modeling.

NSE is equal to one minus the normalized mean square error (ratio between the mean square error and the variation of observations):

NSE=1-∑(sim-obs)**2/∑(obs-mean(obs))**2

1 is the perfect value of NSE, and NSE < 0 indicates that the simulation results are unusable.

The conventional NSE is ususlly affected by the accuracy of high values, and would impact the low flow simulation when be taken as the objective function in hydrological model calibration. Therefore, some revised NSE were proposed.

Oudin et al. (2006) proposed the log-NSE to increase the sensitivity to the accuracy of low flow simulations:

log-NSE=1-∑(log(sim)-log(obs))**2/∑(log(obs)-log(mean(obs)))**2

Krause et al. (2005) proposed the relative NSE to reduce the impact of the magnitude of data:

rNSE=1-∑((sim-obs)obs)**2/∑((obs-mean(obs))/mean(obs))**2

Relative bias (RB) is used to quantify the relative systematic bias of the simulation results:

RB=sum(sim)/sum(obs)-1

Positive or negative value of RB indicate the positive or negative bias of simulations respectively. Perfect value of RB is 0.

## Value

The value of NSE, log-NSE, rNSE and RB.

## References

Krause, P., Boyle, D. P., and Base, F., 2005, Comparison of different efficiency criteria for hydrological model assessment, Advances in Geoscience, 5, 89-97. doi: 10.5194/adgeo-5-89-2005

Nash, J. E., Sutcliffe, J. V., 1970. River flow forecasting through conceptual models part I - A discussion of principles. Journal of Hydrology. 10(3): 282-290. doi:10.1016/0022-1694(70)90255-6

Oudin, L., Andreassian, V., Mathevet, T., Perrin, C., Michel, C., 2006. Dynamic averaging of rainfall-runoff model simulations from complementary model parameterizations. Water Resources Research, 42(7). doi: 10.1029/2005WR004636

`Lohmann_UH`, `Lohmann_conv`