Statistic Calculations

The statistics contained in the HTML document and the shape file are calcu­lated using the same methods used to calculate statistics for the detailed time series output.

The standard calibration statistics calculated based on the differences between the measured observations and the calculated values at the same location and time. Thus, the error, or residual, for an calculation - observation pair is

(14.1)   Flow_Model_Editor00094.jpg

where Ei,t is the difference between the observed and calculated values at location i and time t.

Mean (ME)

The mean error at location i where n observations exist is

(14.2)   Flow_Model_Editor00097.jpg

Mean Absolute Error (MAE)

The mean of the absolute errors at location i where n observations exist is

(14.3)   Flow_Model_Editor00100.jpg

Root Mean Square Error (RMSE)

The root mean square error at location i where n observations exist is

(14.4)   Flow_Model_Editor00103.jpg

Standard Deviation of the Residuals (STDres)

The standard deviation of the residuals at location i where n observations exist is

(14.5)   Flow_Model_Editor00106.jpg

The standard deviation is a good measure to evaluate how well the dynamics of a certain observation are simulated.

Correlation Coefficient (R)

The correlation coefficient is a measure of the linear dependency between simulated and measured values. The closer the value is to 1.0, the better the match. The correlation coefficient at location i is

(14.6)   Flow_Model_Editor00109.jpg

where Flow_Model_Editor00112.jpg  and Flow_Model_Editor00115.jpg are the means of the observations and calcula­tions at location i respectively.

Nash Sutcliffe Correlation Coefficient (R2)

The Nash-Sutcliffe coefficient at location i where n observations exist is

(14.7)   Flow_Model_Editor00118.jpg

where Flow_Model_Editor00121.jpg is the mean of the observations at location i. R2 will be 1.0 if there is a perfect match.