Statistics are generated and may be analysed in many parts of Source. This page provides information on the statistical functions available in Source including what they measure and how they're interpreted. For information on how to use statistics in Source, see the relevant section of the user guide.
Types in general, how they're used,
link to optimisation
In Results Manager, statistics are User generated and auto generated
Locations
Where statistics are put in, created, may be analysed
In Results Manager, statistics are categorised as either user or auto generated.
Univariate and Bivariate Statistics
Univariate statistics provide information on single ......
Bivariate statistics .....
It is common for hydrological time series to contain missing values and to have differing start and end dates. Generally, Source 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 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
Qmod,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. It 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)
Definition
NSE Log is the standard NSE statistic (equation (1)) applied to the logarithm of flow data:
| Equation 2 |
|---|
where
c is a positive constant equal to the maximum of 1 ML and the 10th percentile of the observed flow
other terms are as defined in equation (1)
As with the standard NSE, the time step size is arbitrary. The NSE Log cannot be applied to time series with negative values, as the logarithm of a number less than or equal to zero is undefined.
Interpretation
Using the logarithm of flows has the effect of reducing the sensitivity of the statistic to high flows and increasing the sensitivity to low and mid-range flows. For this reason, NSE Log is often used where low-flow performance is important. The use of the constant c de-emphasises very small flows, which tend to be unreliable, and avoids numerical problems arising from attempting to calculate the logarithm of zero flows.
The NSE Log can range between -∞ and 1 and the interpretation is the same as for the NSE, but applied to log data.
Links
Absolute Bias
Definition
Interpretation
Links
Bias Penalty
Definition
Interpretation
Links
Pearson's Correlation
Definition
Interpretation
Links
Flow Duration and log flow duration
Definition
Interpretation
Links
Square-root Daily, Exceedance and Bias
Definition
Interpretation
Links
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.