Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.     

Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

Modélisation de la relation pluie-ruissellement par durée d'épisode pluvieux dans un bassin du nord de la Tunisie

Résumé

Un modèle hydrologique global a été calé sur des épisodes pluvieux de durée très variable (de un à plus de dix jours). Les épisodes pris en compte sont ceux qui sont encadrés par au moins un jour sec et ne provoquant pas de déversement du barrage. L'entrée de ce modèle comprend la pluie moyenne du bassin versant et l'indice des précipitations antérieures de Kohler & Linsley. Les expressions du modèle hydrologique du début et au cours de la saison humide, selon un seuil du cumul des pluies de la saison depuis le début de l'automne, sont de la forme non linéaire polynomiale du second ordre. Le modèle s'est montré performant dans l'évaluation de la lame ruisselée malgré le faible nombre de postes pluviométriques (un) pour la taille du bassin versant de 48 km². L'absence d'autres postes pluviométriques sur le bassin versant n'a pas permis d'étudier la précision du modèle en considérant une pluie moyenne sur le bassin versant au lieu de la pluie uniquement au site du Barrage Ghézala.

Citation Mathlouthi. M. & Lebdi, F. (2010) Modélisation de la relation pluie–ruissellement par durée d'épisode pluvieux dans un bassin du nord de la Tunisie. Hydrol. Sci. J. 55(7), 1111–1122.     

L'Amazone à Óbidos (Brésil): étude statistique des débits et bilan hydrologique

Résumé

Effectuées dans le cadre du Projet Hidrologia e geoquímica na Bacia Amazönica (HiBAm), les nouvelles mesures de débit à Obidos ont amélioré la connaissance des caractéristiques hydrologiques de l'Amazone à cette station qui contrâle les plus forts débits du monde. Une nouvelle méthode de correction détermine les débits journaliers avec une précision de ±3.0%. La reconstitution des périodes manquantes, avec les observations faites à Manaus, permet de disposer d'une chronologie de près d'un siècle. Avec cet échantillon commençant en 1902, le module interannuel de l'Amazone à Obidos est de 163 000 m³ s^?1, avec un coefficient d'irrégularité extrêmement faible (K3 = 1.28). L'étiage décennal (78 000 m³ s^?1) est de même grandeur que la crue centenaire du Congo à Brazzaville. La crue décennale est estimée à 260 000 m³ s^?1. Le Bilan hydrologique indique un déficit d'écoulement de 1193 mm, qui peut être assimilé à l'évapotranspiration réelle. En conclusion, l'Amazone est bien le fleuve le plus puissant et le plus régulier de la planète.     

Development and utilization of a national web-based chronology of hydrological events/Développement et utilisation sur internet d’une chronologie nationale d’événements hydrologiques

Abstract

Abstract The Chronology of British Hydrological Events (CBHE) has been created as an on-line information resource (http://www.dundee.ac.uk/geography/cbhe/) in order to enhance access to and use of historical facts pertaining to British hydrological phenomena. Its scope covers floods, droughts and all other notable historical phenomena of hydrological interest. This paper sets out the technical means by which the CBHE has been created, explains the benefits to hydrologists in creating such a facility, and illustrates its utility with a number of examples. Benefits include hydrological risk assessments, historical studies of individual events and objectives in environmental education. The scope for establishing comparable national chronologies for other countries is identified, along with prospects for enhancing the utility of such systems with additional functionality such as links to on-line gazetteers and maps.     

Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitations

Abstract

Abstract In the first part of this study, theoretical analyses showed that the Gumbel distribution is quite unlikely to apply to hydrological extremes and that the extreme value distribution of type II (EV2) is a more consistent choice. Based on these theoretical analyses, an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the theoretical results. In addition, it shows that the shape parameter of the EV2 distribution is constant for all examined geographical zones (Europe and North America), with value κ = 0.15. This simplifies the fitting and the general mathematical handling of the distribution, which become as simple as those of the Gumbel distribution.     

Hydrological extremes in a southwestern Ontario river basin under future climate conditions/Extrêmes hydrologiques dans un basin versant du sud-ouest de l'Ontario sous conditions climatiques futures

Abstract

The global climate change may have serious impacts on the frequency, magnitude, location and duration of hydrological extremes. Changed hydrological extremes will have important implications on the design of future hydraulic structures, flood-plain development, and water resource management. This study assesses the potential impact of a changed climate on the timing and magnitude of hydrological extremes in a densely populated and urbanized river basin in southwestern Ontario, Canada. An ensemble of future climate scenarios is developed using a weather generating algorithm, linked with GCM outputs. These climate scenarios are then transformed into basin runoff by a semi-distributed hydrological model of the study area. The results show that future maximum river flows in the study area will be less extreme and more variable in terms of magnitude, and more irregular in terms of seasonal occurrence, than they are at present. Low flows may become less extreme and variable in terms of magnitude, and more irregular in terms of seasonal occurrence. According to the evaluated scenarios, climate change may have favourable impacts on the distribution of hydrological extremes in the study area.     

Modélisation de propagation d’écoulement entre lits mineur et majeur sur les fleuves Sénégal et Niger

In the Senegal River valley and Niger Inner Delta, the annual floods inundate a wide floodplain consisting of a complex network of lakes and channels, where topographic information needed by standard hydraulic models is difficult to obtain. To represent the flood propagation between mainstream and floodplain, we use a model designed for flood propagation in river mainstreams with flat bed and large overflow and without topographic data. Depending on the water level in the riverbed, the model calibrated on the levels observed at two stations gives the level in the floodplains and propagation time between stations. Several cases are tested for various types of hydraulic connections between mainstream and floodplain. The model could correctly reproduce the flood rise and fall in the floodplain, even for a lake connected by a single channel to the riverbed or in the case of a strong attenuation of the flood between very distant stations.     

Uncertainty,entropy, scaling and hydrological stochastics. 2. Time dependence of hydrological processes and time scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 2. Dépendance temporelle des processus hydrologiques et échelle temporelle

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation and lag-one autocorrelation. In the first part of the study, the marginal distributional properties of hydrological processes and the state scaling behaviour were investigated. This second part of the study is devoted to joint distributional properties of hydrological processes. Specifically, it investigates the time dependence structure that may result from the ME principle and shows that the time scaling behaviour (or the Hurst phenomenon) may be obtained by this principle under the additional general condition that all time scales are of equal importance for the application of the ME principle. The omnipresence of the time scaling behaviour in numerous long hydrological time series examined in the literature (one of which is used here as an example), validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes.     

Relationship between precipitation phase and air temperature: comparison between the Bolivian Andes and the Swiss Alps / Relation entre phase de précipitation et température de l'air: comparaison entre les Andes Boliviennes et les Alpes Suisses

Abstract

Determining the precipitation phase—rain or snow—is an important factor in modelling discharge in mountainous basins. In a study carried out in the outer tropical Andes Cordillera of Bolivia, half-hourly determination of precipitation phase was obtained by applying a suitable expert system, taking 11 meteorological parameters into consideration that are measured over 21 months at an altitude close to 4800 m. Straightforward relationships between the determined precipitation phase and observed air temperature were analysed in histograms that contain percentage occurrences of snowfall, rainfall and mixed precipitation events for 0.5°C air temperature increments. The graph shows a nearly identical distribution of percentage occurrences of snowfall in the Andes to that on a 1600-m high site in the Swiss Alps. This result suggests that, for hydrological modelling purposes in the outer tropical Andes, the same rain/snow threshold temperature as in the compared Swiss site can be applied.