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Bivariate statistics .....
It is common for hydrological time series to contain missing values and to have differing start and end dates. Generally, calculates bivariate statistics using only data from those time steps for which there are complete data pairs. *TODO: where is this not true? Bivariate statis in charting??
See Calibration analysis - SRG, /wiki/spaces/TIME/pages/56721988,
Nash-Sutcliffe
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Efficiency (NSE)
Definition
The NSE is a normalised statistic that measures the relative magnitude of the model error variance compared to the measured data variance (Nash and Sutcliffe, 1970). It is commonly used to evaluate the fit of modelled to observed streamflow data, and the definition and discussion below assume that it is being applied in this context. However, the NSE can be used to evaluate the fit between time series of any type.
The NSE defined as:
| Equation 1 |
|---|
where
Qobs,i is the observed flow for time step i
Qsim,i is the modelled flow for time step i
N is the number of time steps
The time step size is arbitrary.
Interpretation
The NSE can range between -∞ and 1.
- NSE = 1 corresponds to a perfect match between modelled and observed data
- NSE = 0 indicates that the model predictions are as accurate as the mean of the observed data
- NSE < 0 indicates that the mean of the observed data is a better predictor than the model
The NSE is sensitive to the timing of flow events. .
Log Daily, Daily, Monthly,
What it measures
How it's interpreted
Relevant equations
Links to selected locationsIt is often applied on a daily time step. Applying it on a longer time step, such as monthly, can be used to evaluate the fit to the monthly pattern of flows without being influenced by the timing of individual runoff events.
Sensitive to extreme values and insensitive to small values. For example, the NSE is generally not suitable for evaluating the fit to low flows as the value will be dominated by the fit to high flows
Links
NSE of Log Data
NSE Log
sNSE-Bias penalty (Nash-Sutcliffe coefficient of efficiency with penalised bias solutions), daily and monthly variants
What it measures
How it's interpreted
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Square-root Daily, Exceedance and Bias
References
Nash, J.E. and J.V. Sutcliffe (1970), River flow forecasting through conceptual models part I — A discussion of principles, Journal of Hydrology, 10 (3), 282–290.