To view statistics for a time series output, first create time series output by double-clicking on a catchment, river, or reservoir segment with the GUI in Output Mode. Click on a parameter in the list on the left side of the dialog. Then click on Statistics. The following dialog will appear:
The spreadsheet gives statistical values for each scenario’s simulation results and observed data for the location and parameter shown in the dialog’s caption. The units are those shown in the caption. Following are explanations of each of the statistics.
The first three statistics describe each scenario’s simulation results and observed data without respect to each other.
Mean is the arithmetic average of all values over the entire time period of simulation as plotted in the time series output from which the output statistics are generated.
Minimum is the least of all values over the entire time period of simulation as plotted in the time series output from which the output statistics are generated.
Maximum is the greatest of all values over the entire time period of simulation as plotted in the time series output from which the output statistics are generated.
The remaining statistics evaluate a comparison between each scenario’s simulation results and observed data. In each case “error” is the simulation result minus the observed data value and can be calculated only for timesteps when both exist. All of these are blank if there is no observed data. None of these measures account for the possibility that errors are in timing and not in magnitude.
# Compare Pts is the number of points used in the comparison between simulated results and observed data for the remaining statistical functions. It is the number of timesteps when there are both simulation results for the applicable scenario and observed data.
Relative Error is the average of all errors over all timesteps for which it can be calculated. Overpredictions can cancel out underpredictions. It is a measure of model accuracy.
relative error = Sum of (x – c) where x is the simulated value, c is the observed value and n is number of observations
Absolute Error is the average of the absolute value of all errors over all timesteps for which it can be calculated. Overpredictions and underpredictions do not cancel each other out. It is a measure of model precision.
absolute error = (Sum of |(x – c)|)/n, where x is the simulated value, c is the observed value and n is number of observations
RMS Error is the “Root-Mean-Square” error, which is the square root of the average of the squares of all errors over all timesteps for which it can be calculated. This magnifies the effect of larger than average errors.
RMS error = [(Sum of (x-c)^2) / n]^0.5 where x is the simulated value, c is the observed value and n is number of observations
R-Squared is the square of the correlation coefficient between simulated results and observed data over all time steps for which both exist. It is a measure of the model’s ability to predict trends in the data, but is often not very useful when there is a large amount of scatter in observed data. A perfect correlation has a value of 1.
Three different types of plots can be shown depending on which option is selected. None of these plots show anything if there is no observed data. In each case, a perfect match between simulation results and observed data would show the plot for simulation results coincident with the black line for observed data.
Scatter Plot shows the errors between simulated and observed data for timesteps when both exist.
Frequency Distribution shows the spread in values within simulation results and within observed data when sorted from lowest to highest for timesteps when both exist. It is used to evalute if a scenario’s simulations show similar variation in its values to observed data without respect to timing.
Cumulative Quantity shows the accumulation of flow over the course of the simulation. It is a measure of how well a scenario predicts seasonal and annual flow. This type of plot can only be viewed for flow.
Output may be viewed for several output statistics summaries and time series plots simultaneously. Leave the output statistics dialog open and then create other plots from the same location or view output from elsewhere on the Map. To move the output statistics dialog, click the mouse button down on the caption of the dialog, hold the button down, and drag the mouse. Let the mouse button up to drop the dialog. To close the dialog, click on the 
in the upper right corner.