Page Comparison

...

Source includes a number of optimisation techniques and statistical measures for automated model calibration and to assist modellers with the evaluation of the quality of calibration.   These are mainly intended for application when calibrating catchment rainfall-runoff models in Source, but are also applicable when calibrating river system models (e.g. see Lerat et al., 2013).   Optimisation techniques available The available automatic optimisation algorithms are:

• Shuffled complex evolution
• Genetic algorithms
• Uniform random sampling
• Rosenbrock method

...

Automated calibration requires the use of an objective function to direct the optimisation process. The Source calibration tool implements single objective function optimisation, which reduces the comparison between the observed and modelled data during the calibration period to a single number to be optimised (Multiple multiple objective optimisation is also available: , see Multi-objective optimisation /trade - off analysis - Insight - SRG for information).  The following nine forms

Source implements five different basic types of objective function are available in Source:

1. Match to Nash Sutcliffe Coefficient of Efficiency (NSE) of Daily Flows
2. Minimise Absolute Bias between Observed and Modelled Flows (calculated using daily flows)
3. Match to NSE of Daily Flows but Penalise Biased Solutions
4. Match to NSE of Monthly Flows
5. Match to NSE of Monthly Flows but Penalise Biased Solutions
6. Combined Match to NSE and Match to Flow Duration Curve (Daily)
7. Combined Match to NSE and Match to Logarithm of Flow Duration Curve (Daily)
8. Combined Match to NSE of Logarithms of Daily Flows with Bias Penalty
9. Combined Bias, Daily Flows and Daily Exceedance (Flow Duration) Curve (SDEB)

Further information on the first seven of these objective functions is available in Vaze et al (2011), Section 6.  Guidance on model calibration is available in many publications, including various eWater Best Modelling Practice Guidelines (Black et al, 2011; Vaze et al, 2011; Black and Podger, 2012; and Lerat 2012).

Scale

...

1.  
2. Flow duration (specifically, the NSE of the flow duration)
3. Bias penalty
4. Absolute bias
5. Square-root daily, exceedance and bias
   

The NSE can be applied to daily or monthly data, and the NSE and flow duration objectives can be applied to data that has been transformed by taking the logarithm. Source also allows the user to create composite objective functions, of which there are two types:

1. Combinations of the individual objective functions listed above. For example, the objective for calibrating streamflow at a gauging site could be a combination of the NSE and bias penalty.
2. Combinations of the objectives for different model outputs. For example, a model could be calibrated using a weighted combination of the objective functions for two or more different gauging sites.

Scale

Typically, the optimisation techniques and statistical measures are used to compare observed and estimated data at a point, such as streamflow data at a gauging station.  Both the optimisation techniques and statistical measures can be applied on a daily or monthly basis.

...

The statistical measures used in Source are well established.  They are described in statistics textbooks, hydrology textbooks and papers such as Aitken (1973) and Nash and Sutcliffe (1970).

Overview information on the four optimisation techniques in Source is available in Vaze et al (2011).  Further information is in textbooks and papers, particularly for the genetic algorithm and uniform random sampling[DB1] .  Publications on the shuffled complex evolution method include papers by Duan et al (1992) and Sorooshian et al (1993).  Publications on the Rosenbrock method include the paper by Rosenbrock (1960).

Version

Source version 3.8.8.

Dependencies

Requires observed data suitable for comparison of results from model calibration runs.

Availability

Provided with Sourcetextbooks and papers such as Aitken (1973) and Nash and Sutcliffe (1970).

Overview information on the four optimisation techniques in Source is available in Vaze et al. (2011).  Further information is in textbooks and papers, particularly for the genetic algorithm and uniform random sampling[DB1] .  Publications on the shuffled complex evolution method include papers by Duan et al. (1992) and Sorooshian et al. (1993).  Publications on the Rosenbrock method include the paper by Rosenbrock (1960).

Version

Source version 3.8.8.

Dependencies

Requires observed data suitable for comparison of results from model calibration runs.

Availability

Provided with Source.

Some of these objective functions can be combined to create composite objective functions. For composite objective functions, the user is often able to enter a weight that determines the relative contribution of each objective function component to the 

The following nine forms of objective function are available in Source:

1. Match to Nash Sutcliffe Coefficient of Efficiency (NSE) of Daily Flows
2. Minimise Absolute Bias between Observed and Modelled Flows (calculated using daily flows)
3. Match to NSE of Daily Flows but Penalise Biased Solutions
4. Match to NSE of Monthly Flows
5. Match to NSE of Monthly Flows but Penalise Biased Solutions
6. Combined Match to NSE and Match to Flow Duration Curve (Daily)
7. Combined Match to NSE and Match to Logarithm of Flow Duration Curve (Daily)
8. Combined Match to NSE of Logarithms of Daily Flows with Bias Penalty
9. Combined Bias, Daily Flows and Daily Exceedance (Flow Duration) Curve (SDEB)

Further information on the first seven of these objective functions is available in Vaze et al. (2011), Section 6. Guidance on model calibration is available in many publications, including various eWater Best Modelling Practice Guidelines (Black et al., 2011; Vaze et al., 2011; Black and Podger, 2012; and Lerat, 2012).

Structure & processes

As the optimisation techniques and statistical measures of calibration performance used in Source are well established, they are not re-described here.   However, as the objective functions used in the optimisation techniques have been customised for Source, further information on these follows and as many of them rely on the Nash Sutcliffe Coefficient of Efficiency (NSE), its formulation is restated below.

The traditional formula for NSE is:

where:

Qobs_i    is the observed flow on day i,

...

N           is the number of days

Alternatively,

This formulation obviates the necessity to calculate the average of the observed flows before evaluating the denominator in the traditional version.

...

This objective function will produce a match on the overall volume of flow generated but often will produce a poor fit to the timing of flows (Vaze et al, 2011). It has the following form:

Equation 3	Image Modified

The evaluation of this objective function uses observed and modelled daily flow data for all days within the calibration period for which observed daily flow data, including zero flow values, is available.

...

This objective function is a weighted combination of the daily NSE and a logarithmic function of bias based on Viney et al (2009), and the aim is to find its maximum value. 

Equation 4	Image Modified

where:

B is the bias; and

Equation 5	Image Modified

The evaluation of this objective function uses observed and modelled daily flow data for all days within the calibration period for which observed daily flow data, including zero flow values, is available.

...

For this case the aim is to maximise the objective function, where:

where:

A is a weighting factor whose value can be set by the modeller (0 ≤ A ≤ 1); and

...

For this case the aim is to maximise the objective function, where:

where:

Ais a weighting factor whose value can be set by the modeller (0 ≤ A ≤ 1);

...

This objective function is given by:

NSE(logarithms of daily flows) is calculated using value pairs of  ln(Qobs_i+c) and ln(Qsim_i+c), where B and v are defined in the same way as above.  The Bias Penalty is based on Viney et al (2009) and is: 

Equation 9	Image Modified

This objective function captures the model’s ability to fit the shape of the observed daily flow hydrograph, with an emphasis on mid-range to low flows (in contrast to the arithmetic form of the NSE which tends to put an emphasis on medium to high flows), while ensuring a low bias in the total streamflow.

...

This objective function is based on the function introduced by Coron et al (2012) and has been successfully applied in a number of projects (e.g. Lerat et al, 2013).  It has the following equation:

Equation 10	Image Modified

where:

α is a weighting factor whose value can be set by the modeller (0 ≤ α ≤ 1).

...

Modellers have the option of selecting one optimisation technique, multiple optimisation techniques (in parallel), or combinations two optimisation techniques (in series), or not using 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:

Output data

Outputs include results of the evaluation of the selected objective function and other calibration performance statistics. 

...

Rosenbrock, H.H. (1960). An automated method of finding the greatest of least value of a function.   The Computer Journal, 3, 303-307.

...