Uwe Ehret

A decade of Predictions in Ungauged Basins (PUB)—a review

Abstract The Prediction in Ungauged Basins (PUB) initiative of the International Association of Hydrological Sciences (IAHS), launched in 2003 and concluded by the PUB Symposium 2012 held in Delft (23–25 October 2012), set out to shift the scientific culture of hydrology towards improved scientific understanding of hydrological processes, as well as associated uncertainties and the development of models with increasing realism and predictive power. This paper reviews the work that has been done under the six science themes of the PUB Decade and outlines the challenges ahead for the hydrological sciences community. Editor D. Koutsoyiannis Citation Hrachowitz, M., Savenije, H.H.G., Blöschl, G., McDonnell, J.J., Sivapalan, M., Pomeroy, J.W., Arheimer, B., Blume, T., Clark, M.P., Ehret, U., Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V., Hughes, D.A., Hut, R.W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P.A., Uhlenbrook, S., Wagener, T., Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec, C., 2013. A decade of Predictions in Ungauged Basins (PUB)—a review. Hydrological Sciences Journal, 58 (6), 1198–1255.

Radar-based flood forecasting in small catchments, exemplified by the Goldersbach catchment, Germany

Abstract Although draining an area of only 75 km2, the Goldersbach caused several times severe flooding in the city of Tubingen, Germany. To cope with this, a flood management was set up based on flood forecasting, partial retention in reservoirs and local flood protection. Due to the small catchment size, the anticipated flood‐forecast lead time of three hours could only be achieved by using local, weather‐radar based rainfall forecasts for the next 1.5 hours. In short‐term rainfall forecasting, knowledge of the current rainfield advection is crucial. Therefore, two advection estimation techniques were applied: one based on the Doppler effect the other on covariance maximization. To combine the advantages of the available sources of rainfall observation, namely radar and rain gauges, a method for ‘geostatistical merging’ was developed. It preserves both the relatively reliable mean rainfall measurements from the rain gauges and the high spatial resolution of the radar image. Based on the advection estimates, a short‐term, auto‐regressive forecast model (SCM, or Spectrum‐Corrected Markov chain model) was developed. It follows a two‐step hierarchical approach. A bivariate, auto‐regressive process forecasts the large‐scale development of rainfall in a radar image. The individual development of each gridcell in the image is forecasted by a Markov chain approach. Finally, two rainfall‐runoff models are used for short‐term flood forecasting. The first, Fgmod, is an event‐based model, the second, HBV‐IWS, is a continuous water balance model. Both rainfall‐runoff models, in combination with the rainfall forecast, allow reasonable discharge estimates for up to three hours.

Comparing expert judgement and numerical criteria for hydrograph evaluation

Abstract This paper investigates the relationship between expert judgement and numerical criteria when evaluating hydrological model performance by comparing simulated and observed hydrographs. Using a web-based survey, we collected the visual evaluations of 150 experts on a set of high- and low-flow hydrographs. We then compared these answers with results from 60 numerical criteria. Agreement between experts was found to be more frequent in absolute terms (when rating models) than in relative terms (when comparing models), and better for high flows than for low flows. When comparing the set of 150 expert judgements with numerical criteria, we found that most expert judgements were loosely correlated with a numerical criterion, and that the criterion that best reflects expert judgement varies from expert to expert. Overall, we identified two groups of 10 criteria yielding an equivalent match with the expertise of the 150 participants in low and high flows, respectively. A single criterion common to both groups (the Hydrograph Matching Algorithm with mean absolute error) may represent a good indicator for the overall evaluation of models based on hydrographs. We conclude that none of the numerical criteria examined here can fully replace expert judgement when rating hydrographs, and that both relative and absolute evaluations should be based on the judgement of multiple experts. Editor D. Koutsoyiannis

Forecast Uncertainties in the Operational Flood Forecasting of the Bavarian Danube Catchment

Hydrological forecasts have become an important part of the flood information service, since they are calculated for all river catchments in the Bavarian Danube Catchment. Experiences with published forecasts during former flood events have shown the need for communicating the uncertainties associated with these forecasts to the civil protection authorities and the public. Therefore, methods for quantifying and representing these uncertainties have been developed and incorporated in the flood warning routine. A newly developed approach varies the dominant factors of uncertainty like the meteorological forecast in headwaters by including forecast ensembles. The remaining factors are represented by a static uncertainty measure derived from offline analysis and combined with the former. The total uncertainty is represented by the 10 and 90% exceedance probabilities published together with a single deterministic forecast via the internet.

Convergence Index: a new performance measure for the temporal stability of operational rainfall forecasts

In this study, a new performance measure is presented which evaluates to what extent a sequence of forecasts converges, with decreasing lead time, towards the observation without oscillation. Convergence and non-oscillation are important quality criteria when actions requiring time-consistency such as flood management or reservoir operation during floods have to be based on the forecasts. The underlying theory of the Convergence Index is presented as well its application during a seven-month series of three forecast models (COSMO-EU, NOAA GFS and Persistence) in the alpine catchment of the Iller, Germany. The expressiveness of the Convergence Index is critically evaluated and compared to a standard measure (Root Mean Square Error). In summary, the Convergence Index can, in combination with other measures that express forecast quality in absolute rather than relative terms, contribute to a more comprehensive evaluation of forecasts.

A Maximum-Entropy Method to Estimate Discrete Distributions from Samples Ensuring Nonzero Probabilities

When constructing discrete (binned) distributions from samples of a data set, applications exist where it is desirable to assure that all bins of the sample distribution have nonzero probability. For example, if the sample distribution is part of a predictive model for which we require returning a response for the entire codomain, or if we use Kullback–Leibler divergence to measure the (dis-)agreement of the sample distribution and the original distribution of the variable, which, in the described case, is inconveniently infinite. Several sample-based distribution estimators exist which assure nonzero bin probability, such as adding one counter to each zero-probability bin of the sample histogram, adding a small probability to the sample pdf, smoothing methods such as Kernel-density smoothing, or Bayesian approaches based on the Dirichlet and Multinomial distribution. Here, we suggest and test an approach based on the Clopper–Pearson method, which makes use of the binominal distribution. Based on the sample distribution, confidence intervals for bin-occupation probability are calculated. The mean of each confidence interval is a strictly positive estimator of the true bin-occupation probability and is convergent with increasing sample size. For small samples, it converges towards a uniform distribution, i.e., the method effectively applies a maximum entropy approach. We apply this nonzero method and four alternative sample-based distribution estimators to a range of typical distributions (uniform, Dirac, normal, multimodal, and irregular) and measure the effect with Kullback–Leibler divergence. While the performance of each method strongly depends on the distribution type it is applied to, on average, and especially for small sample sizes, the nonzero, the simple “add one counter”, and the Bayesian Dirichlet-multinomial model show very similar behavior and perform best. We conclude that, when estimating distributions without an a priori idea of their shape, applying one of these methods is favorable.

Earth system dynamics as the consequence of the second law: Maximum power limits, dissipative structures, and planetary interactions

Planet Earth is a thermodynamic system far from equilibrium and its functioning—obviously—obeys the second law of thermodynamics, at the detailed level of processes, but also at the planetary scale of the whole system. Here, we describe the dynamics of the Earth system as the consequence of sequences of energy conversions that are constrained by thermodynamics. We first describe the well-established Carnot limit and show how it results in a maximum power limit when interactions with the boundary conditions are being allowed for. To understand how the dynamics within a system can achieve this limit, we then explore with a simple model how different configurations of flow structures are associated with different intensities of dissipation. When the generation of power and these different configuration of flow structures are combined, one can associate the dynamics towards the maximum power limit with a fast, positive and a slow, negative feedback that compensate each other at the maximum power state. We close with a discussion of the importance of a planetary, thermodynamic view of the whole Earth system, in which thermodynamics limits the intensity of the dynamics, interactions strongly shape these limits, and the spatial organization of flow represents the means to reach these limits.