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The choice of an appropriate objective function for calibration depends on the intended application of the model. Different objective functions are designed with the intention of emphasizing the fit of modelled flow to different aspects of the observed hydrograph (Vaze et al., 2011). The objective functions available in the Source Calibration Wizard are listed in Table 1, including useful references for further information. Refer to the Bivariate Statistics User Guide entry for the objective function equations and further information on their interpretation.
Table 1. List of Source calibration objective functions.Anchor Table 1 Table 1
| Objective Function Name | Description | Reference |
|---|---|---|
| NSE Daily | Maximise the NSE of daily flows | Vaze et al. (2011), Section 6 |
| NSE Monthly | Maximise the NSE of monthly flows | Vaze et al. (2011), Section 6 |
| NSE Log Daily | Maximise the NSE of the logarithm of daily flows | |
| Absolute Bias | Minimise the Absolute value of the relative bias | Vaze et al. (2011), Section 6 |
| NSE Daily & Bias Penalty | Maximise the NSE of daily flows and bias penalty | Vaze et al. (2011), Section 6 |
| NSE Log Daily & Bias Penalty | Maximise the NSE of the logarithm of daily flows and bias penalty | |
| NSE Monthly & Bias Penalty | Maximise the NSE of monthly flows and bias penalty | Vaze et al. (2011), Section 6 |
| NSE Daily & Flow Duration | Maximise the NSE of daily flows and the NSE of the flow duration | Vaze et al. (2011), Section 6 |
| NSE Daily & Log Flow Duration | Maximise the NSE of daily flows and the NSE of the flow duration of log flows | Vaze et al. (2011), Section 6 |
| Square-root Daily, Exceedance and Bias | Minimise a combination of the bias, daily Flows and daily exceedance (flow duration) curve | Lerat et al., 2013 |
Implementation Details
The Bivariate Statistics SRG User Guide entry provides general information on the objective function equations and their interpretation. Implementation details that are specific to the Source Calibration Wizard are described below.
Missing Data
It is common for observed time series of hydrological processes to contain missing values. Also, the observed and modelled time series may have different start and end dates. The Source calibration tool calculates the objective function values using only data from those time steps for which both observed and modelled data is available. In other words, the calibration objective function are calculated using observed and modelled data has been filtered to include only:
- data from within the calibration period, and
- data for time steps with complete data pairs.
Monthly Flows
The NSE Monthly objective function uses monthly streamflow values. These are calculated as follows:
- If the model is run on a daily time step, monthly flows are calculated by summing the observed and modelled daily flow values. The NSE calculation ignores observed and modelled data for all months where there are one or more days of missing data in the observed flow series.
- If the model is run on a monthly time step, then the monthly values are unchanged.
Data
Input data
Details on data to be input by the modeller are provided in the Source User Guide. Requirements for data series inputs to the various objective functions are included in the descriptions of each objective function, above.
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Modellers have the option of selecting one optimisation technique, two optimisation techniques (in series), or manual optimisation. Modellers can also select which objective function they wish to use. The other parameters the modeller can input are described in the following table:in Table 2.
Table 2. Objective function parameters. Refer to the Bivariate Statistics SRG User Guide entry for further information on their implementation.Anchor Table 2 Table 2
Objective Function | Parameter | Parameter Description | Units | Default | Range |
|---|---|---|---|---|---|
| NSE Daily & Flow Duration | a | Weight on NSE in the combined objective | Dimensionless | 0.5 | 0 ≤ α ≤ 1 |
| NSE Daily & Log Flow Duration | a | Weight on NSE in the combined objective | Dimensionless | 0.5 | 0 ≤ α ≤ 1 |
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