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| Titel |
Uncertainty assessment through a precipitation dependent HUP: an application to a small Southern Italy catchment |
| VerfasserIn |
D. Biondi, P. Versace, B. Sirangelo |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250027533
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| Zusammenfassung |
| The present study focuses on the application of a precipitation dependent HUP
(Hydrologic Uncertainty Processor) to assess the predictive uncertainty on water
discharge predictions for a small headwater catchment located in Calabria (South Italy)
through a complete example of the estimation procedure, modelling assumptions and
results.
The applied HUP was proposed by Krzysztofowicz in 1999, and is a component of the
Bayesian forecasting system (BFS) which provides a general methodology for probabilistic
forecasting via any deterministic hydrologic model. Within the BFS framework, the
task of the HUP is to quantify the effects of various uncertainty sources on the
forecasts, e.g. of river discharges, under the hypothesis that there is no precipitation
uncertainty.
According to the principle of Bayesian revision of a probability distribution, the general
formulation of the HUP supplies the hydrologic uncertainty in terms of a family,gÏ(-
|s,h0),
of posterior densities of discharge H, for every possible realization s of the model river
discharge process S and observation H0 = h0 of river discharge up to the forecast
time.
This result is obtained through the revision of a prior distribution g of the predictand,
which exists before the preparation of a forecast, on the basis of a likelihood function f
estimated from past evidence on model performance against observations.
The implemented HUP rests on the following assumptions:
precipitation dependent structure;
nonstationarity of both actual river stage and model river stage process with lead
time n;
meta-gaussian formulation for all the conditional distributions.
The study watershed is the test site of the Turbolo Creek catchment (29 km2), a tributary of the
Crati River, located in Southern Italy. The hydro-meteorological database used within this
study comprises rainfall, temperature, and discharge values sampled with a 20 minutes
temporal resolution.
The hydrologic response in the HUP is simulated by the RISE (Runoff by Infiltration and
Saturation Excess) rainfall-runoff model which is a process-oriented one, conceived for
applications to small and medium size catchments. It considers both conceptual and
physically-based schemes to represent the primary processes of the hydrological cycle, and
has been designed through a stepwise approach, with the aim of a realistic description of the
mechanisms that are assumed to be dominant in controlling storm runoff production and
saturated area space-temporal dynamics.
An almost continuous five-year period starting at the 2000 and ending at 2005 was
examined. Furthermore we assumed that:
precipitation forecasts are produced hourly, so that each hour marks the
beginning of a separate realization of the precipitation event and the model actual
river discharge process;
the processor has three branches and each distribution of the HUP is conditioned
on the indicator of precipitation V according to the basin average forecasted
precipitation amount R with: V = 0 - R = 0; V = 1 - 0 < R< 2 mm and V
= 2 - R-¥ 2 mm.
the hydrologic model outputs a time series of river discharges at 20 minutes
steps, but probabilistic forecasts of river discharge are prepared in 1-h steps for
times t1, -¦, tN , with N=3 (the time to peak of the unit hydrograph is about 2
hours).
The HUP processor was specified by deriving parametric expressions for the family of the prior
density and the family of the likelihood functions through a detailed statistical analysis of
available observed and simulated data following the steps laid out in Krzysztofowicz & Herr
(2001) and Maranzano & Krzysztofowicz (2004), in order to reduce the conditioning of the
likelihood functions and the prior distributions in the transformed space to the smallest
dimension that is necessary to capture the dependence structures between the model output
and the actual process.
The end result of the estimation procedure, is the evaluation of the dependence
parameters of the posterior distributions. A first order Markov process for the prior densities
and a conditional Markov process of order 1 for the likelihood function were assumed
respectively.
The analysis of the obtained posterior distributions showed that under each hypothesis
about the precipitation event, the hydrologic uncertainty increases with lead time n as one
would expect. Furthermore, hydrologic uncertainty increases with the forecasted discharge
and it’s higher when precipitation occurs, confirming the merit of assuming a precipitation
dependent HUP.
A real time simulation of 4 storm events was performed: within this application observed
discharges were compared with the median value of the 1 hour ahead prior and posterior
distributions: the prior mostly underestimates the actual discharge while forecasted
discharges are closer to the bisector and more symmetrically distributed in the posterior
distribution. Results also highlight a partial inadequacy of the linear model as a dependence
structure between observed and simulated discharge for high values and prove the
deterioration of the processor performance with increasing lead times which is mainly due to
the zero precipitation fed into the hydrologic model beyond the forecast period. |
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