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Definition
Interpretation
Links
Flow Duration
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Definition
Interpretation
Links
Square-root Daily, Exceedance and Bias
Definition
Interpretation
Links
References
Definition
The Flow Duration statistic is calculated by sorting the observed and modelled data values in increasing order and then calculating the NSE (equation (1)) of the sorted data.
It can be applied for any time step size.
Interpretation
The Flow Duration is insensitive to the timing of flows and instead measures the fit to the overall distribution of flow magnitudes. It is sensitive to high flows and less sensitive to low flows.
Links
Flow Duration of Log Data (Log Flow Duration)
Definition
The Log Flow Duration statistic is calculated applying the Flow Duration to log transformed data:
| Equation X |
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Interpretation
The Log Flow Duration measures the fit to the overall distribution of flow magnitudes and it is sensitive to low and mid-range flows.
Links
Combined Bias, Daily Flows and Daily Exceedance (Flow Duration) Curve (SDEB)
Definition
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 X |
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where:
α is a weighting factor set to 0.1
λ is an exponent set to 0.5
RQobs,k is the k’th ranked observed flow of a total of N ranked flows
RQsim,k is the k’th ranked modelled flow of a total of N ranked flows
Other terms are as defined previously.
Interpretation
As discussed in Lerat et al. (2013), this function combines three terms:
the sum of errors on power transformed flow,
the same sum on sorted flow values 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 equation (11), where a slight misalignment of observed and simulated peak flow timing can result in large amplitude errors. The second term is based on sorted flow values, which remain unaffected by timing errors. By way of example, in their study of the Flinders and Gilbert Rivers in Northern Australia, 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 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.
Links
References
Coron, L., V. Andrassian, P. Perrin, J. Lerat, J. Vaze, M. Bourqui and F. Hendrickx (2012) Crash testing hydrological models in contrasted climate conditions: an experiment on 216 Australian catchments. Water Resources Research, 48, W05552, doi:10.1029/ 2011WR011721.
Lerat, J., C.A. Egan, S. Kim, M. Gooda, A. Loy, Q. Shao and C. Petheram (2013) Calibration of river models for the Flinders and Gilbert catchments. A technical report to the Australian Government from the CSIRO Flinders and Gilbert Agricultural Resource Assessment, part of the North Queensland Irrigated Agriculture Strategy. CSIRO Water for a Healthy Country and Sustainable Agriculture flagships, Australia.
Nash, J.E. and J.V. Sutcliffe (1970) , River flow forecasting through conceptual models part I — A discussion of principles, . Journal of Hydrology, 10 (3), 282–290.