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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 11 |
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where:
α is a weighting factor whose value can be set by the modeller (0 ≤ α ≤ 1).set to 0.1
λ is an exponent set to 0.5
RQobsk is the k’th ranked observed flow of a total of N ranked flows,
RQsimk is the k’th ranked modelled flow of a total of N ranked flows, and
Other terms are as defined previously.
As explained by discussed in Lerat et al. (2013), this function combines three terms: (i)
- the sum of
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- errors on power
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- transformed flow,
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- the same sum on sorted flow values
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- and
- the relative simulation bias.
The coefficient α and the power transform λ are used to balance the three terms within the objective function. The weighting factor α is used to reduce the impact of the timing errors on the objective function. This type of error can have a significant effect on the first term in the equation (11), where a slight misalignment of observed and simulated peak flow timing can result in large amplitude errors. Conversely, the The second term is based on sorted flow values, which remain unaffected by timing errors. By way of example, Lerat et al. (2013) in in their study of the Flinders and Gilbert Rivers in Northern Australia used , Lerat et al. (2013) used values of α of 0.1 for the Flinders calibration and 1.0 for the Gilbert calibration.
Using values of power transform of λ of less than 1 has the effect of reducing the weight of the errors in high flows, where the flow data are known to be less accurate. Lerat et al. (2013) found that a power transform of ½ led to the best compromise between high and low flow performance in their project. This value has been adopted in Source.
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