Les modèles hydrologiques sont des outils indispensables pour calculer les débits a l’exutoire des bassins versants, la gestion des aménagements hydrauliques ou encore la prévision et la prévention des inondations. Les précipitations représentent la variable climatique principale à l’origine des débits des cours d’eau qui s’écoulent au sein d’un bassin versant. De ce fait, la réponse hydrologique du bassin est fortement dépendante de la représentativité des données d’entrée de précipitation.Les radars météorologiques, qui permettent aujourd’hui d’accéder a des mesures a haute résolution spatiale et temporelle des champs de précipitation, sont de plus en plus utilises dans le domaine de la prévision, pour le suivi des situations hydrométéorologiques. Cependant, la mesure des précipitations par radar est entachée d’erreurs qui peuvent affecter gravement la qualité des simulations de débit. De ce fait, l’utilisation des données de précipitations a haute résolution spatiale pour la modélisation hydrologique est souvent limitée par rapport a l’utilisation des données pluviométriques.Récemment, Météo-France a développe une réanalyse des lames d’eau au pas de temps horaire, sur une durée de 10 ans, en combinant l’ensemble des données de précipitation radar et pluviométriques : les mesures radars ont été corrigées et étalonnées avec le réseau de mesure au sol horaire et journalier. Dans cette thèse, nous proposons d’étudier l’intérêt de cette nouvelle base de données à haute résolution spatiale pour la modélisation pluie-débit.Dans un premier temps, nous avons développe et valide un modèle hydrologique semi-distribue qui a la capacité de fonctionner pour différentes résolutions spatiales, de la représentation globale jusqu’a une discrétisation spatiale très fine des bassins. Dans un deuxième temps, l’impact de la résolution spatiale des données d’entrée de précipitation sur la simulation des débits a été analysé. L’apport de l’information radar pour l’estimation des précipitations a été évalue par rapport a une utilisation exclusive des pluviomètres, par le biais de la modélisation pluie-débit en termes de précision des débits a l’exutoire des bassins. Enfin, le modèle semi-distribue TGR a été comparé avec le modèle global GRP actuellement opérationnel dans les Services de Prévision des Crues. L’originalité de notre travail réside sur l’utilisation de données d’observation sur un large échantillon de 181 bassins versants français représentant une grande diversité de tailles et conditions climatiques, ce qui nous permet d’apporter un diagnostic robuste et des éléments de réponse sur les problématiques scientifiques traitées. / Hydrologic models are essential tools to compute the catchment rainfall-runoff response required for river management and flood forecast purposes. Precipitation dominates the high frequency hydrological response, and its simulation is thus dependent on the way rainfall is represented. In this context, the sensitivity of runoff hydrographs to the spatial variability of forcing data is a major concern of researchers. However, results from the abundant literature are contrasted and it is still difficult to reach a clear consensus.Weather radar is considered to be helpful for hydrological forecasting since it provides rainfall estimates with high temporal and spatial resolution. However, it has long been shown that quantitative errors inherent to the radar rainfall estimates greatly affect rainfall-runoff simulations. As a result, the benefit from improved spatial resolution of rainfall estimates is often limited for hydrological applications compared to the use of traditional ground networks.Recently, Météo-France developed a rainfall reanalysis over France at the hourly time step over a 10-year period combining radar data and raingauge measurements: weather radar data were corrected and adjusted with both hourly and daily raingauge data. Here we propose a framework to evaluate the improvement in streamflow simulation gained by using this new high resolution product.First, a model able to cope with different spatial resolutions, from lumped to semi-distributed, was developed and validated. Second, the impact of spatial rainfall resolution input on streamflow simulation was investigated. Then, the usefulness of spatial radar data measurements for rainfall estimates was compared with an exclusive use of ground raingauge measurements and evaluated through hydrological modelling in terms of streamflow simulation improvements. Finally, semi-distributed modelling with the TGR model was performed for flood forecasting and compared with the lumped forecasting GRP model currently in use in the French flood forecast services. The originality of our work is that it is based on actual measurements from a large set of 181 French catchments representing a variety of size and climate conditions, which allows to draw reliable conclusions.

Error characteristics associated with satellite-derived precipitation products are important for atmospheric and hydrological model data assimilation, forecasting, and climate diagnostic applications. This information also aids in the refinement of physical assumptions within algorithms by identifying geographical regions and seasons where existing algorithm physics may be incorrect or incomplete. Examination of relative errors between independent estimates derived from satellite microwave data is particularly important over regions with limited surface-based equipments for measuring rain rate such as the global oceans and tropical continents. In this context, analysis of microwave based satellite datasets from the Tropical Rainfall Measuring Mission (TRMM) enables to not only provide information regarding the inherent uncertainty within the current TRMM products, but also serves as an opportunity to prototype error characterization methodologies for the TRMM follow-on program, the Global Precipitation Measurement (GPM) . Most of the TRMM uncertainty evaluation studies focus on the accuracy of rainfall accumulated over time (e.g., season/year). Evaluation of instantaneous rainfall intensities from TRMM orbital data products is relatively rare. These instantaneous products are known to potentially cause large uncertainties during real time flood forecasting studies at the watershed scale. This is more so over land regions, where the highly varying land surface emissivity offers a myriad of complications, hindering accurate rainfall estimation. The error components of orbital data products also tend to interact nonlinearly with hydrologic modeling uncertainty. Keeping these in mind, the present thesis fosters the development of uncertainty analysis using instantaneous satellite orbital data products (latest version 7 of 1B11, 2A25, 2A23, 2B31, 2A12) derived from the passive and active microwave sensors onboard TRMM satellite, namely TRMM Microwave Imager (TMI) and precipitation radar (PR). The study utilizes 11 years of orbital data from 2002 to 2012 over the Indian subcontinent and examines the influence of various error sources on the convective and stratiform precipitation types. Two approaches are taken up to examine uncertainty. While the first approach analyses independent contribution of error from these orbital data products, the second approach examines their combined effect. Based on the first approach, analysis conducted over the land regions of Mahanadi basin, India investigates three sources of uncertainty in detail. These include 1) errors due to improper delineation of rainfall signature within microwave footprint (rain/no rain classification), 2) uncertainty offered by the transfer function linking rainfall with TMI low frequency channels and 3) sampling errors owing to the narrow swath and infrequent visits of TRMM sensors. The second approach is hinged on evaluating the performance of rainfall estimates from each of these orbital data products by accumulating them within a spatial domain and using error decomposition methodologies. Microwave radiometers have taken unprecedented satellite images of earth’s weather, proving to be a valuable tool for quantitative estimation of precipitation from space. However, as mentioned earlier, with the widespread acceptance of microwave based precipitation products, it has also been recognized that they contain large uncertainties. One such source of uncertainty is contributed by improper detection of rainfall signature within radiometer footprints. To date, the most-advanced passive microwave retrieval algorithms make use of databases constructed by cloud or numerical weather model simulations that associate calculated microwave brightness temperature to physically plausible sample rain events. Delineation of rainfall signature from microwave footprints, also known as rain/norain classification (RNC) is an essential step without which the succeeding retrieval technique (using the database) gets corrupted easily. Although tremendous advances have been made to catapult RNC algorithms from simple empirical relations formulated for computational expedience to elaborate computer intensive schemes which effectively discriminate rainfall, a number of challenges remain to be addressed. Most of the algorithms that are globally developed for land, ocean and coastal regions may not perform well for regional catchments of small areal extent. Motivated by this fact, the present work develops a regional rainfall detection algorithm based on scattering index methodology for the land regions of study area. Performance evaluation of this algorithm, developed using low frequency channels (of 19 GHz, 22 GHz), are statistically tested for individual case study events during 2011 and 2012 Indian summer monsoonal months. Contingency table statistics and performance diagram show superior performance of the algorithm for land regions of the study region with accurate rain detection observed in 95% of the case studies. However, an important limitation of this approach is comparatively poor detection of low intensity stratiform rainfall. The second source of uncertainty which is addressed by the present thesis, involves prediction of overland rainfall using TMI low frequency channels. Land, being a radiometrically warm and highly variable background, offers a myriad of complications for overland rain retrieval using microwave radiometer (like TMI). Hence, land rainfall algorithms of TRMM TMI have traditionally incorporated empirical relations of microwave brightness temperature (Tb) with rain rate, rather than relying on physically based radiative transfer modeling of rainfall (as implemented in TMI ocean algorithm). In the present study, sensitivity analysis is conducted using spearman rank correlation coefficient as the indicator, to estimate the best combination of TMI low frequency channels that are highly sensitive to near surface rainfall rate (NSR) from PR. Results indicate that, the TMI channel combinations not only contain information about rainfall wherein liquid water drops are the dominant hydrometeors, but also aids in surface noise reduction over a predominantly vegetative land surface background. Further, the variations of rainfall signature in these channel combinations were seldom assessed properly due to their inherent uncertainties and highly non linear relationship with rainfall. Copula theory is a powerful tool to characterize dependency between complex hydrological variables as well as aid in uncertainty modeling by ensemble generation. Hence, this work proposes a regional model using Archimedean copulas, to study dependency of TMI channel combinations with respect to precipitation, over the land regions of Mahanadi basin, India, using version 7 orbital data from TMI and PR. Studies conducted for different rainfall regimes over the study area show suitability of Clayton and Gumbel copula for modeling convective and stratiform rainfall types for majority of the intraseasonal months. Further, large ensembles of TMI Tb (from the highly sensitive TMI channel combination) were generated conditional on various quantiles (25th, 50th, 75th, 95th) of both convective and stratiform rainfall types. Comparatively greater ambiguity was observed in modeling extreme values of convective rain type. Finally, the efficiency of the proposed model was tested by comparing the results with traditionally employed linear and quadratic models. Results reveal superior performance of the proposed copula based technique. Another persistent source of uncertainty inherent in low earth orbiting satellites like TRMM arise due to sampling errors of non negligible proportions owing to the narrow swath of satellite sensors coupled with a lack of continuous coverage due to infrequent satellite visits. This study investigates sampling uncertainty of seasonal rainfall estimates from PR, based on 11 years of PR 2A25 data product over the Indian subcontinent. A statistical bootstrap technique is employed to estimate the relative sampling errors using the PR data themselves. Results verify power law scaling characteristics of relative sampling errors with respect to space time scale of measurement. Sampling uncertainty estimates for mean seasonal rainfall was found to exhibit seasonal variations. To give a practical demonstration of the implications of bootstrap technique, PR relative sampling errors over the sub tropical river basin of Mahanadi, India were examined. Results revealed that bootstrap technique incurred relative sampling errors of <30% (for 20 grid), <35% (for 10 grid), <40% (for 0.50 grid) and <50% (for 0.250 grid). With respect to rainfall type, overall sampling uncertainty was found to be dominated by sampling uncertainty due to stratiform rainfall over the basin. In order to study the effect of sampling type on relative sampling uncertainty, the study compares the resulting error estimates with those obtained from latin hypercube sampling. Based on this study, it may be concluded that bootstrap approach can be successfully used for ascertaining relative sampling errors offered by TRMM-like satellites over gauged or ungauged basins lacking in in-situ validation data. One of the important goals of TRMM Ground Validation Program has been to estimate the random and systematic uncertainty associated with TRMM rainfall estimates. Disentangling uncertainty in seasonal rainfall offered by independent observations of TMI and PR enables to identify errors and inconsistencies in the measurements by these instruments. Motivated by this thought, the present work examines the spatial error structure of daily precipitation derived from the version 7 TRMM instantaneous orbital data products through comparison with the APHRODITE data over a subtropical region namely Mahanadi river basin of the Indian subcontinent for the seasonal rainfall of 6 years from June 2002 to September 2007. The instantaneous products examined include TMI and PR data products of 2A12, 2A25 and 2B31 (combined data from PR and TMI). The spatial distribution of uncertainty from these data products was quantified based on the performance metrics derived from the contingency table. For the seasonal daily precipitation over 10x10 grids, the data product of 2A12 showed greater skill in detecting and quantifying the volume of rainfall when compared with 2A25 and 2B31 data products. Error characterization using various error models revealed that random errors from multiplicative error models were homoscedastic and that they better represented rainfall estimates from 2A12 algorithm. Error decomposition technique, performed to disentangle systematic and random errors, testified that the multiplicative error model representing rainfall from 2A12 algorithm, successfully estimated a greater percentage of systematic error than 2A25 or 2B31 algorithms. Results indicate that even though the radiometer derived 2A12 is known to suffer from many sources of uncertainties, spatial and temporal analysis over the case study region testifies that the 2A12 rainfall estimates are in a very good agreement with the reference estimates for the data period considered. These findings clearly document that proper characterization of error structure offered by TMI and PR has wider implications in decision making, prior to incorporating the resulting orbital products for basin scale hydrologic modeling. The current missions of GPM envision a constellation of microwave sensors that can provide instantaneous products with a relatively negligible sampling error at daily or higher time scales. This study due to its simplicity and physical approach offers the ideal basis for future improvements in uncertainty modeling in precipitation.

Les catastrophes naturelles comme les canicules, les tempêtes ou les précipitations extrêmes, proviennent de processus physiques et ont, par nature, une dimension spatiale ou spatiotemporelle. Le développement de modèles et de méthodes d'inférences pour ces processus est un domaine de recherche très actif. Cette thèse traite de l'inférence statistique pour les événements extrêmes dans le cadre spatial et spatio-temporel. En particulier, nous nous intéressons à deux classes de processus stochastique: les processus spatiaux max-mélange et les processus max-stable spatio-temporels. Nous illustrons les résultats obtenus sur des données de précipitations dans l'Est de l'Australie et dans une région de la Floride aux Etats-Unis. Dans la partie spatiale, nous proposons deux tests sur le paramètre de mélange a d'un processus spatial max-mélange: le test statistique Za et le rapport de vraisemblance par paire LRa. Nous comparons les performances de ces tests sur simulations. Nous utilisons la vraisemblance par paire pour l'estimation. Dans l'ensemble, les performances des deux tests sont satisfaisantes. Toutefois, les tests rencontrent des difficultés lorsque le paramètre a se situe à la frontière de l'espace des paramètres, i.e., a ∈ {0,1}, dues à la présence de paramètre de “nuisance” qui ne sont pas identifiés sous l'hypothèse nulle. Nous appliquons ces tests dans le cadre d'une analyse d'excès au delà d'un grand seuil pour des données de précipitations dans l'Est de l'Australie. Nous proposons aussi une nouvelle procédure d'estimation pour ajuster des processus spatiaux max-mélanges lorsqu'on ne connait pas la classe de dépendance extrêmal. La nouveauté de cette procédure est qu'elle permet de faire de l'inférence sans spécifier au préalable la famille de distributions, laissant ainsi parle les données et guider l'estimation. En particulier, la procédure d'estimation utilise un ajustement par la méthode des moindres carrés sur l'expression du Fλ-madogramme d'un modèle max-mélange qui contient les paramètres d'intérêt. Nous montrons la convergence de l'estimateur du paramètre de mélange a. Une indication sur la normalité asymptotique est donnée numériquement. Une étude sur simulation montrent que la méthode proposée améliore les coefficients empiriques pour la classe de modèles max-mélange. Nous implémentons notre procédure d'estimations sur des données de maximas mensuels de précipitations en Australie dans un but exploratoire et confirmatoire. Dans la partie spatio-temporelle, nous proposons une méthode d'estimation semi-paramétrique pour les processus max-stables spatio-temporels en nous basant sur une expression explicite du F-madogramme spatio-temporel. Cette partie permet de faire le pont entre la géostatistique et la théorie des valeurs extrêmes. En particulier, pour des observations sur grille régulière, nous estimons le F-madogramme spatio-temporel par sa version empirique et nous appliquons une procédure basée sur les moments pour obtenir les estimations des paramètres d'intérêt. Nous illustrons les performances de cette procédure par une étude sur simulations. Ensuite, nous appliquons cette méthode pour quantifier le comportement extrêmal de maximum de données radar de précipitations dans l'Etat de Floride. Cette méthode peut être une alternative ou une première étape pour la vraisemblance composite. En effet, les estimations semi-paramétriques pourrait être utilisées comme point de départ pour les algorithmes d'optimisation utilisés dans la méthode de vraisemblance par paire, afin de réduire le temps de calcul mais aussi d'améliorer l'efficacité de la méthode / Natural hazards such as heat waves, extreme wind speeds, and heavy rainfall, arise due to physical processes and are spatial or spatio-temporal in extent. The development of models and inference methods for these processes is a very active area of research. This thesis deals with the statistical inference of extreme and rare events in both spatial and spatio-temporal settings. Specifically, our contributions are dedicated to two classes of stochastic processes: spatial max-mixture processes and space-time max-stable processes. The proposed methodologies are illustrated by applications to rainfall data collected from the East of Australia and from a region in the State of Florida, USA. In the spatial part, we consider hypothesis testing for the mixture parameter a of a spatial maxmixture model using two classical statistics: the Z-test statistic Za and the pairwise likelihood ratio statistic LRa. We compare their performance through an extensive simulation study. The pairwise likelihood is employed for estimation purposes. Overall, the performance of the two statistics is satisfactory. Nevertheless, hypothesis testing presents some difficulties when a lies on the boundary of the parameter space, i.e., a ∈ {0,1}, due to the presence of additional nuisance parameters which are not identified under the null hypotheses. We apply this testing framework in an analysis of exceedances over a large threshold of daily rainfall data from the East of Australia. We also propose a novel estimation procedure to fit spatial max-mixture processes with unknown extremal dependence class. The novelty of this procedure is to provide a way to make inference without specifying the distribution family prior to fitting the data. Hence, letting the data speak for themselves. In particular, the estimation procedure uses nonlinear least squares fit based on a closed form expression of the so-called Fλ-madogram of max-mixture models which contains the parameters of interest. We establish the consistency of the estimator of the mixing parameter a. An indication for asymptotic normality is given numerically. A simulation study shows that the proposed procedure improves empirical coefficients for the class of max-mixture models. In an analysis of monthly maxima of Australian daily rainfall data, we implement the proposed estimation procedure for diagnostic and confirmatory purposes. In the spatio-temporal part, based on a closed form expression of the spatio-temporal Fmadogram, we suggest a semi-parametric estimation methodology for space-time max-stable processes. This part provides a bridge between geostatistics and extreme value theory. In particular, for regular grid observations, the spatio-temporal F-madogram is estimated nonparametrically by its empirical version and a moment-based procedure is applied to obtain parameter estimates. The performance of the method is investigated through an extensive simulation study. Afterward, we apply this method to quantify the extremal behavior of radar daily rainfall maxima data from a region in the State of Florida. This approach could serve as an alternative or a prerequisite to pairwise likelihood estimation. Indeed, the semi-parametric estimates could be used as starting values for the optimization algorithm used to maximize the pairwise log-likelihood function in order to reduce the computational burden and also to improve the statistical efficiency

The field of urban hydrology is in need of high temporal resolution data series in order to effectively model and analyse existing and future trends in extreme precipitation. When high resolution data sets are, for any number of reasons, not available for a given location, the technique of disaggregation using a random cascade model can be applied. Previous studies have demonstrated the relevance of random cascades in the context of rainfall data disaggregation with temporal resolutions usually down to 1 hour. In this study, an attempt at disaggregation to a resolution of 1 minute was made. Using newly disaggregated rainfall data for different regions in Sweden, the possibility of clustering rain events into separate regional hyetographs was investigated. The random cascade model was calibrated using existing municipal rainfall data with a temporal resolution of 1 minute, in order to disaggregate continuous 15 minutes data series provided by the Swedish Meteorological and Hydrological Institute (SMHI). The disaggregation process was then performed in multiple stochastic realisations, in order to correct the uncertainties inherent to the random cascade model. The disaggregation results were assessed by comparing them with calibration data: two main rainfall parameters, EV and ED, were analysed by determining their behaviours and distribution. The possibility of transfering calibration parameters from one station to another was also assessed in a similar manner, again by studying EV &amp; ED for different scenarios. Finally, hyetographs were clustered, compared and contrasted, in order to ascertain previously theorized differences between regions. This research showed the feasibility of applying a random cascade model to very high temporal resolutions in Sweden, while replicating rainfall characteristics from the calibration data quite well. The analysis of the spatial transferability of calibration parameters yielded inconclusive results, as rainfall characteristics were preserved in some cases but failed in others. Lastly, distinct regional differences in hyetographs were noted, but no clear conclusions could be drawn owing to the delimitations of this study. / Inom småskalig hydrologisk modellering finns det idag ett behov av dataserier med hög tidsupplösning för att effektivt kunna modellera och analysera både aktuella och kommande trender hos extrema regnhändelser. När högupplösta dataserier är otillgängliga vid en önskad mätplats kan disaggregering med hjälp av en slumpmässig kaskadmodell tillämpas. Tidigare forskning har visat att kaskadmodeller är användbara för disaggregering av regndata med en tidsupplösning av 1 timme. I denna studie disaggregerades dataserier med syftet att uppnå en tidsupplösningav av 1 minut. För att kunna analysera eventuella skillnader mellan regioner klustrades även hyetografer med de framtagna dataserierna. Den slumpmässiga kaskadmodellen kalibrerades med befintlig kommunal data med en tidsupplösning på 1 minut, för att sedan kunna disaggregera 15 minuters data från SMHIs databaser. Disaggregeringen genomfördes i ett antal olika stokastiska realisationer för att kunna ta hänsyn till, och korrigera, de inneboende osäkerheterna i den slumpmässiga kaskadmodellen. Disaggregeringsresultaten bedömdes genom en jämförelse med kalibreringsdata: två regnegenskaper, regnvaraktighet (ED) och regnvolym (EV), analyserades för att kunna bestämma derasfördelningar och beteenden. Kalibreringsparametrarnas överförbarhet analyserades också med hjälp av ED &amp; EV för olika scenarier. Slutligen klustrades hyetografer för att fastställa potentiella skillnader mellan regioner. Studien påvisade möjligheten att använda en slumpmässig kaskadmodell till höga tidsupplösningar i Sverige. Modellen lyckades återskapa regnegenskaper från kalibreringsdata vid disaggregeringen. Möjligheten att överföra kalibreringsparametrar från en station till en annan visade sig dock inte vara helt övertygande: regnegenskaper återskapades endast i vissa fall, men inte i samtliga. Slutligen konstaterades regionala skillnader i hyetografer, men tydliga slutsatser kunde inte dras på grund av underliggande begränsningar med studien.

Within the frame work of the International Water Research Alliance Saxony (IWAS), project “Middle East” a complex integrated water management system is developed and tested in the project region of Middle East (Oman and Saudi-Arabia). Hence, new solutions for a sustainable management of the scarce water resources in (semi-) arid regions are explored within IWAS in the sultanate of Oman on which this study work is carried out. Rainfall runoff models are established to estimate the “water yield” of the catchments in the project region. Modeling is a very important tool that enables hydrologists to make more comprehensive use of rainfall time series. Rainfall-runoff modeling is also useful for water resources assessment as these models can generate a long representative time series of stream flow volumes from which water supply schemes can be designed (D.A. Hughes, 1995). Therefore, this study project mainly focuses on the following main tasks such as data analysis, data processing and statistical evaluation; Model selection and model setup; Model adaptation test and verification. As part of the common modeling protocol, sensitivity analysis of a Rainfall-Runoff Modeling Toolbox (RRMT) is carried out in this study with the aim to identify sensitive model parameters. RRMT has been developed in order to produce parsimonious, lumped model structures with a high level of parameter identifiability. Such identifiability is crucial if relationships between the model parameters representing the system and catchment characteristics are to be established. RRMT is a modular framework that allows its user to implement different model structures to find a suitable balance between model performance and parameter identifiability. The study is carried out in the upper catchment part of Wadi Ma’wil (gauge near to Afi’), Batinah Region of the Sultanate of Oman. Arid and semi-arid zones are characterized by rainfall which is highly variable in space, time, quantity and duration (Noy-Meir, 1973). The Sultanate of Oman is characterized by hyper-arid (<100 mm rainfall), through the arid (100–250 mm rainfall) and semi-arid (250–500 mm rainfall) environments that are experienced in different parts of the country. Furthermore, arid areas have distinctive hydrological features substantially different from those of humid areas. The high temporal and spatial distribution of the rainfall, flash floods, absence of base flow, sparsity of plant cover, high transmission losses, high amounts of evaporation and evapotranspiration and the general climatologies are examples of such differences.:Acknowledgments i Abstract ii List of Figures and Photos v List of Tables and Plots v 1. Description of Study Area 1 1.1 General characteristics of arid regions 1 1.2 Study area (Batinah Region and Ma’awil catchment of gauge ‘Afi’) 2 1.2.1 Overview of Study area 2 1.2.2 Wadi Ma’awil and Gauge near to Afi’ 3 2. Data Processing and Evaluation 6 2.1 Rainfall data 6 2.1.1 Monthly and Annual Mean Rainfall Analyses 6 2.1.2 Estimation of Missing Precipitation Data 6 2.1.3 Annual and monthly average rainfall 6 2.2 Runoff data 9 2.2.1Rainfall-Runoff events – Processing and Analysis 9 2.2.2 Wadi Ma’awil Runoff Analysis 9 2.3 Areal Precipitation 11 2.3.1 Area 11 2.3.2 Summary of Calculated Results of Mean Annual Areal Precipitation 12 2.4 Evapotranspiration 13 2.4.1 Evaporation and Potential Evapotranspiration 13 2.4.2 Calculation of Evapotranspiration by FAO Penman-Monteith Equation 13 2.4.3 Sample Calculation for Daily ET using FAO Penman-Monteith Equation 14 2.4.4 Comparisons of Evapotranspiration Calculation Results 16 3. Rainfall-Runoff Modeling 16 3.1 Modeling approach – selection of modules 16 3.1.1 Basic Principle 16 3.1.2 Classification of models 16 3.1.3 Modeling Process 17 3.2 Rainfall-Runoff Modeling Toolbox 19 3.2.1 Introduction 19 3.2.2 Data Needs and Model Structure 20 3.3 Provision of input data 20 3.4 Calibration and Validation 20 3.4.1 Model Calibration and Validation 21 3.5 Sensitivity Analysis 22 3.6 Discussions of Results 23 3.6.1 Optimization Modules 23 3.6.2 Soil Moisture Accounting (SMA) Modules 24 3.6.3 Routing (R) Modules 25 3.6.4 The objective functions 26 3.6.5 Visualization Modules Results 27 3.7 Conclusions and Recommendations 35 3.7.1 Conclusions 35 3.7.2 Limitations and Recommendations 35 References 37 Appendix 38 Appendix A: Daily extraterrestrial radiation (Ra) for different latitudes for the 15th day of the month 38 Appendix B: Mean daylight hours (N) for different latitudes for the 15th of the month 38 Annexes 39 Annex - A: Mean Rainfall for the Gauge Afi’ from 1995 – 2005 39 Annex A-1: Annual Mean Rainfall for Gauge Afi’ for the time period 1995-2005 39 Annex A-2: Monthly Mean Rainfall for Gauge Afi’ for the time period 1995-2005 39 Annex A-3: Monthly Mean Rainfall for each Rain Gauge within the Wadi Ma’awil Catchment area for the time period 1995-2005 40 Annex - B: Rainfall - Runoff events for the Gauge Afi’ 41 Annex B-1: Annual Rainfall Vs Runoff events for the Gauge Afi’ from 1995 – 2005 42 Annex B-2: Monthly Rainfall Vs Runoff events for the Gauge Afi’ from 1995 – 2005 44 Annex B-3: Daily Rainfall Vs Runoff events for the Gauge Afi’ sample graphs with the time period from 1995to 2005 46

further development of the simple and promising analytical probabilistic approach / Urban stormwater management aims at mitigating the adverse impacts of urbanization. Hydrological models are used in support of stormwater management planning and design. There are three main approaches that can be applied for this modeling purpose: (1) continuous simulation approach which is accurate but time-consuming; (2) design storm approach, which is widely used and its accuracy highly depends on the selected antecedent moisture conditions and temporal distribution of design storms; and (3) the analytical probabilistic approach which is recently developed and still not used in practice. Although it is time-effective and it can produce results as accurate as the other two approaches; the analytical probabilistic approach requires further developments in order to make it more reliable and accurate. For this purpose, three subtopics are investigated in this thesis. (1) Rainfall data analysis as required by the analytical probabilistic approach with emphasis on testing the exponentiality of rainfall event duration, volume and interevent time (i.e., time separating it from its preceding rainfall event). A goodness-of-fit testing procedure that is suitable for this kind of data analysis was proposed. (2) Derivation of new analytical probabilistic models for peak discharge rate incorporating trapezoidal and triangular hydrograph shapes in order to include all possible catchment’s responses. And (3) the infiltration process is assumed to continue until the end of the rainfall event; however, the soil may get saturated earlier and the excess amount would contribute to the runoff volume which may have adverse impact if not taken into consideration. Thus, in addition to the infiltration process, the saturation excess runoff is also included and new models for flood frequencies are developed. All the models developed in this thesis are tested and compared to methods used in practice, reasonable results were obtained. / Thesis / Doctor of Philosophy (PhD) / Urban stormwater management aims at mitigating the adverse impacts of urbanization. Hydrological models are used in support of stormwater management planning and design. The analytical probabilistic stormwater management model (APSWM) is a promising tool for planning and design analysis. The purpose of this thesis is to further develop APSWM in order to make it more reliable and accurate. First, a clear procedure for rainfall data analysis as required by APSWM is provided. Second, a new APSWM is derived incorporating other runoff temporal-distribution patterns. Finally, the possibility of soil layer saturation while it is still raining is added to the model. All the models developed in this thesis are tested and compared to methods used in engineering practice, reasonable results were obtained.