Equation

The Equation tab is only visible when performing updating with weighting function.

Equations are used to specify how error correction functions derived during the update period (simulation time up to Time of Forecast) is applied during the forecast period.

New Equations are added or deleted using the Append ‘+’ or Delete ‘-’ but­tons above the overview table located in the bottom of the dialog.

Equation parameter definitions

Parameters to be used in the Equation definition are specified here.

Parameter name. Identification name of an equation parameter.

Type. Equation variables can be defined as one out of three types:

·         Constant value: the parameter is assigned a constant value.

·         Time series: the parameter is assigned a time-varying value specified in an external time series.

·         State variable: the parameter is a state variable, i.e. a computed water level or discharge at a grid point in the river network.

Depending on the type definition selection for the equation parameter, spe­cific parameters must be defined

Specific parameters for ‘Constant value’ type include:

·         Estimated. For a parameter defined as a ‘Constant’ type, an automatic parameter estimation can be performed to estimate the value from the computed time-varying error. Select this option to enable the parameter estimation.

·         Value. Value assigned to the parameter. Must be defined for Constant type parameters for which the ‘Estimated’ option is not selected.

·         Minimum value. Lower bound of the parameter when automatic param­eter estimation is applied.

·         Maximum value. Upper bound of the parameter when automatic param­eter estimation is applied.

Specific parameters for ‘Timeseries’ type include:

·         Time series file. The time series containing the values, for time-varying parameters. The button to the right may be used to either browse, cre­ate, edit or plot the time series.

·         Item. This field shows the name of the item selected in the time series.

Specific parameters for ‘State variable’ type include:

·         Branch name. The branch name where the state variable is located.

·         Chainage. The chainage at which the state variable is located.

·         Item. State variable type. Depending on the modules included in the sim­ulation (in the Modules page), it can either be water level, discharge, or AD/WQ component.

·         AD / WQ component. The component from the Advection-Dispersion module or the state variable from the Water Quality module, when the updated item is set to AD/WQ component.

Equation definitions

Equations are specified here, using the parameters below.

Equation name. Identification name of the equation. This name is shown in the drop-down list of available equations, when selecting an error forecast model in the ‘Update parameters’ tab.

Equation. The equation is defined here. The ‘Edit’ button gives access to an equation editor, from which it is possible to select the available parameters as well as a number of operators and functions.

A ‘Validate’ button evaluates whether the syntax of the equation is correct or not.

As an example, suppose the error forecast model is to be expressed as a function of the variables X1, X2 and X3 as 5 times variable X1 minus the square of variable X2 plus 2 times the natural logarithm of X3, the Equation field should be written:

5*[X1] - Power([X2], 2) + 2*Log([X3])

Where:

X1, X2 and X3 are defined equation parameters.

Another example: assuming that the error forecast model is based on a sec­ond order auto regressive model, the Equation field should be written:

[A] * E(-1)+ [B] * E(-2)

Where:

A and B are the auto regressive equation parameters.

E(L) is Error function with time lag; L (L<0). That is, E(-1) is the error function value at the previous time step.

Estimation period. For parameters defined as ‘constant values’, automatic parameter estimations can be applied based on the record of computed errors. The period of the record to be used for the parameter estimation can be specified relative to the time of forecast.

This option allows parameters of the error forecast models to be updated continuously, and hence the error forecast models to adapt from one forecast to the next to the prevailing conditions at the time of forecast. For instance, the error forecast models can be adapted to the structural differences in the model errors that are often seen for different flow regimes.

Note: If the amount of observed data available before the time of forecast is not enough to compute the error prediction, the updating location may be dis­abled. Be aware that computing the error on a long period will therefore increase the risk that the update is disabled, when only a limited set of observed data is available.