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| Titel |
Application of a normalized Nash-Sutcliffe efficiency to improve the accuracy of the Sobol' sensitivity analysis of a hydrological model |
| VerfasserIn |
J. Nossent, W. Bauwens |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250058487
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| Zusammenfassung |
| Sensitivity analysis (SA) has become a main practice in hydrological modelling, since it
allows to identify the influential and non-influential parameters of a model and can give
insights on the model processes and their relation with the system. A very robust SA
technique that is becoming popular in hydrology is the Sobol’ method (Sobol’, 1990). This
method quantifies the amount of variance that each parameter contributes to the unconditional
variance of the model output. This variance contribution is expressed with sensitivity
indices, which are assessed by means of Monte Carlo integrals. Hereto, a large
number of random points are sampled in the parameter hyperspace to evaluate the
model.
When the Sobol’ method is applied to assess the influence of the model parameters
on simulated time series, an objective function is required to transform the vector
output of the model into a scalar input for the SA. Since the accuracy of the variance
estimation with the numerical integrals may decrease when the mean value of the scalar
inputs for the SA is large (Sobol’, 2001), the Nash-Sutcliffe efficiency (NSE) is
assumed to yield more accurate results than e.g. the also commonly used Sum of
Squared Residuals (SSR). In our application on a SWAT model of the Kleine Nete
catchment (Belgium) (Nossent et al., 2011), this is indeed valid for flow predictions,
as the mean NSE for all model evaluations is -0.73. However, for water quality
simulations with the same model, the mean NSE values become highly negative
(even an extreme value of -4E6 is obtained for nitrate concentration simulations). In
such cases, the Nash-Sutcliffe efficiency is not suitable for the Sobol’ sensitivity
analysis.
We therefore introduce a normalized version of the Nash-Sutcliffe efficiency (NNSE) that
yields values between 0 and 1, but preserves the main characteristics of the regular
NSE:
- (oi - o)2
N NSE = –-1––= -––i–––––––
2- N SE (oi - si)2 + (oi - o)2
i
where si is the simulated value on day i, oi is the observed value on day i and o is the
average of the observations. As for the regular NSE, 1 is the optimal value for the NNSE. On
the other hand, a value of 0.5 for the NNSE corresponds with a 0 value for the NSE,
whereas the worst NNSE value is 0. As a consequence, the mean value of the scalar
inputs for the SA is for the different variables in our SWAT model smaller than
0.5 and mostly even less than 0.05, which increases the accuracy of the variance
estimates.
Besides the introduction of this normalized Nash-Sutcliffe efficiency, our presentation
will furthermore provide evidence on the influence of the applied objective function on the
outcome of the sensitivity analysis.
Nossent, J., Elsen, P., Bauwens, W. (2011): Sobol’ sensitivity analysis of a complex
environmental model. Environmental Modelling & Software. 26 (2011), 1515-1525.
Sobol’, I.M. (2001): Global sensitivity indices for nonlinear mathematical models and
their Monte Carlo estimates. Mathematics and Computers in Simulation. 55 (1-3),
271-280.
Sobol’, I.M. (1990): On sensitivity estimation for nonlinear mathematical models.
Matematicheskoe Modelirovanie. 112-118. |
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