A geostatistical inverse method of estimating hydraulic parameters of a heterogeneous porous medium at discrete points in space, called pilot points, is presented. In this inverse method the parameter estimation problem is posed as a nonlinear optimization problem with a likelihood based objective function. The likelihood based objective function is expressed in terms of head residuals at head measurement locations in the flow domain, where head residuals are the differences between measured and model-predicted head values. Model predictions of head at each iteration of the optimization problem are obtained by solving a forward problem that is based on nonlocal conditional ensemble mean flow equations. Nonlocal moment equations make possible optimal deterministic predictions of fluid flow in randomly heterogenous porous media as well as assessment of the associated predictive uncertainty. In this work, the nonlocal moment equations are approximated to second order in the standard deviation of log-transformed hydraulic conductivity, and are solved using the finite element method. To enhance computational efficiency, computations are carried out in the complex Laplace-transform space, after which the results are inverted numerically to the real temporal domain for analysis and presentation. Whereas a forward solution can be conditioned on known values of hydraulic parameters, inversion allows further conditioning of the solution on measurements of system state variables, as well as for the estimation of unknown hydraulic parameters. The Levenberg-Marquardt algorithm is used to solve the optimization problem. The inverse method is illustrated through two numerical examples where parameter estimates and the corresponding predictions of system state are conditioned on measurements of head only, and on measurements of head and log-transformed hydraulic conductivity with prior information. An example in which predictions of system state are conditioned only on measurements of log-conductivity is also included for comparison. A fourth example is included in which the estimation of spatially constant specific storage is demonstrated. In all the examples, a superimposed mean uniform and convergent transient flow field through a bounded square domain is used. The examples show that conditioning on measurements of both head and hydraulic parameters with prior information yields more reliable (low uncertainty and good fit) predictions of system state, than when such information is not incorporated into the estimation process.

One major acknowledged challenge in daily precipitation is the inability to model extreme events in the spectrum of events. These extreme events are rare but may cause large losses. How to realistically simulate extreme behavior of daily precipitation is necessary and important. To that end, a hybrid probability distribution is developed. The logic of this distribution is to simulate the low to moderate values by an exponential distribution and extremes by a generalized Pareto distribution. Compared with alternatives, the developed hybrid distribution is capable of simulating the entire range of precipitation amount and is much easier to use. The hybrid distribution is then used to construct a bivariate discrete-continuous mixed distribution, which is used for building a daily precipitation generator. The developed generator can successfully reproduce extreme events. Compared with other widely used generators, the most important advantage of the developed generator is that it is apt at extrapolating values significantly beyond the upper range of observed data. The major challenge in monthly streamflow simulation is referred to the underrepresentation of inter-annual variability. The inter-annual variability is often related with sustained droughts or periods of high flows. Preserving inter-annual variability is thus of particular importance for the long-term management of water resources systems. To that end, variables conveying such inter-annual signals should be used as covariates. This requires models that must be flexible at incorporating as many covariates as necessary. Keeping this point in mind, a joint conditional density estimation network is developed. Therein, the joint distribution of streamflows of two adjacent months is assumed to follow a specific parametric family. Parameters of the distribution are estimated by an artificial neural network. Due to the seasonal concentration of precipitation or the joint effect of rainfall and snowmelt, monthly streamflow distribution sometimes may exhibit a bimodal shape. To reproduce bimodality, nonparametric models are often preferred. However, the simulated sequences from existing nonparametric models represent too close a resemblance to historical record. To address this issue, while retaining typical merits of nonparametric models, a multi-model regression-sampling algorithm with a few weak assumptions is developed. Collecting hydrometric data is the first step for building hydrologic models, and for planning, design, operation, and management of water resource systems. In this dissertation, an entropy-theory-based criterion, termed maximum information minimum redundancy, is proposed for hydrometric monitoring network evaluation and design. Compared with existing similar approaches, the criterion is apt at finding stations with high information content, and locating independent stations.

<p>Topography, vegetation, nutrient dynamics, soil features and hydroclimatic forcing are inherently coupled, with feedbacks occurring over a wide range of temporal and spatial scales. Vegetation growth may be limited by soil moisture, nutrient or solar radiation availability, and in turn influences both soil moisture and nutrient balances at a point. These dynamics are further complicated in a complex terrain, through a series of spatial interactions. A number of experiments has characterized the feedbacks between soil moisture and vegetation dynamics, but a theoretical framework linking short-term leaf-level to interannual plot-scale dynamics has not been fully developed yet. Such theory is needed for optimal management of water resources in natural ecosystems and for agricultural, municipal and industrial uses. Also, it complements the current knowledge on ecosystem response to the predicted climate change.</p><p>In this dissertation, the response of vegetation dynamics to unpredictable environmental fluctuations at multiple space-time scales is explored in a modeling framework from sub-daily to interannual time scales. At the hourly time scale, a simultaneous analysis of photosynthesis, transpiration and soil moisture dynamics is carried out to explore the impact of water stress on different photosynthesis processes at the leaf level, and the overall plant activity. Daily soil moisture and vegetation dynamics are then scaled up to the growing season using a stochastic model accounting for daily to interannual hydroclimatic variability. Such stochastic framework is employed to explore the impact of rainfall patterns and different irrigation schemes on crop productivity, along with their implications in terms of sustainability and profitability. To scale up from point to landscape, a probabilistic representation of local landscape features (i.e., slope and aspect) is developed, and applied to assess the effects of topography on solar radiation. Finally, a minimalistic ecosystem model, including soil moisture, vegetation and nutrient dynamics at the year time scale, is outlined; when coupled to the proposed probabilistic topographic description, the latter model can serve to assess the relevance of spatial interactions and to single out the main biophysical controls responsible for ecohydrological variability at the landscape scale.</p> / Dissertation

Dans cette thèse je travaille sur la relation entre la pluviosité et l’érosion fluviatile en utilisant une approche probabiliste. Je développe une méthodologie indépendante de la moyenne pour caractériser la variabilité de la pluviosité journalière.L’indépendance vis-à-vis de la moyenne permet une comparaison simpleetobjectivedelavariabilitédelapluviosité sous différents régimes climatiques. Elle semontre également utile pour intégrer le concept de variabilité de la pluviosité dans lathéorie que je développe ensuite. J’applique cette approche à la chaine de montagnesHimalayenne en utilisant des données de pluviosité de hautes résolutions spatiale ettemporelle et trouve qu’il existe des variations significatives de la variabilité de la pluviositédans l’Himalaya. En prenant en compte la variabilité de la pluviosité en plusde la pluviosité moyenne, je trouve un lien entre pluviosité et érosion qui, d’un pointde vue géomorphologique, diffère, de façon significative, de celui déduit de la seulepluviosité moyenne.Ensuite, je développe une théorie d’érosion fluviatile du type ’puissance de flux‘ quicomprend une paramétrisation réaliste de la pluviosité et de l’hydrologie. Ceci estréalisé en intégrant un modèle hydrologique stochastique-mécaniste bien établi dansune formulation stochastique de la puissance de flux comprenant un seuil. La théoriehydrologique conduit à des expressions mathématiques pour la distribution et la variabilitédu débit journalier en fonction des conditions climatiques qui sont valablespour la majorité des régimes de débit observés à la surface de la Terre. Les nouveauxparamètres qui en découlent ont une signification bien ancrée dans des théories climatiqueet hydrologique établies et se mesurent facilement. Cette approche nous permetde prédire comment le taux d’érosion fluviatile répond à des changements du forçageclimatique. Je trouve ainsi que les processus hydrologiques peuvent avoir une influencesignificative sur l’efficacité érosive d’un forçage climatique donné. Cette approchepeut également être utilisée comme fondement de nouveaux modèles d’évolution desreliefs qui prennent en compte des conditions aux limites climatique et hydrologique.Une des principales conséquences d’intégrer l’hydrologie dans le modèle de puissancede flux est de révéler le double effet de la moyenne et de la variabilité du forçage climatiquesur la réponse écohydrologique. Une corrélation négative existe entre la moyenneet la variabilité qui restreint grandement les réponses possibles d’un bassin versant àdes changements climatiques. L’approche théorique que j’ai développée décrit égalementles relations qui relient la variabilité journalière à plusieurs paramètres écohydroclimatiques.Je trouve ainsi que l’index d’aridité, le temps de réponse du bassin versant,et l’épaisseur effective de sol sont les contrôles les plus importants sur la variabilité dudébit. Ceci a d’importantes conséquences pour le rôle que jouent l’hydrologie et lavégétation sur l’évolution des reliefs.Finalement, je démontre que l’influence de la variabilité journalière du forçage climatiquesur le taux d’érosion des rivières est principalement déterminée par l’existence et la valeur de seuils d’érosion. Je démontre que, quelques soient les détails du processus d’érosion considéré, c’est le rapport entre la valeur du seuil et la valeur moyenne du forçage climatique qui détermine si la variabilité compte ou pas, et dans quel sens.Parmi de nombreuses autres applications, ces découvertes contribuent à l’élaborationd’un nouveau cadre permettant de comprendre et prédire la réponse de la surface dela Terre à des changements de la moyenne et de la variabilité de la pluviosité et du débit des rivières. La généralité de ces découvertes a d’importantes implications pour le reste des travaux présentés dans la thèse, ainsi que pour les travaux antécédents sur le rôle de la variabilité de la pluviosité et du débit sur l’efficacité érosive des rivières. / In this thesis, we address the problem of how climate drives landscape evolution. Specifically, we work on the relationship between rainfall and fluvial erosion using a probabilistic approach. First we develop a mean-independent methodology to characterize the variability of daily rainfall. The mean-independent nature allows for simple, objective comparison of rainfall variability in climatically different regions. It also proves useful for integrating the concept of rainfall variability into theory. We apply this method over the Himalayan orogen using high spatial and temporal resolution rainfall data sets and find significant variations in rainfall variability over the Himalayan orogen. By taking into account variability of rainfall in addition to mean rainfall rate, we find a pattern of rainfall that, from a geomorphological perspective, is significantly different from mean rainfall rate alone. Next we develop of theory of stream power fluvial erosion that allows for realistically parameterized rainfall and hydrology. This is accomplished by integrating an established stochastic-mechanistic model of hydrology into a threshold-stochastic formulation of stream power. The hydrological theory provides equations for the daily streamflow distribution and variability as a function of climatic boundary conditions that are applicable across most of the observed range of streamflow regimes on Earth. The new parameters introduced are rooted firmly in established climatic and hydrological theory and are easily measured. This framework allows us to predict how fluvial erosion rates respond to changes in realistic rainfall forcing. We find that hydrological processes can have a significant influence on how erosive a particular climatic forcing will be. This framework can be used as a foundation for landscape evolution models that have realistic climatic and hydrological boundary conditions. One of the main strengths of integrating hydrology into the stream power model is to reveal the dependence of both streamflow mean and variability on the climatic forcing and ecohydrological response. This negative correlation of the mean and variability vastly restricts the likely responses of a river basin to changing climate. Our theoretical framework also describes the scaling daily variability with several other ecohydroclimatic parameters. We find that the aridity index, the basin response time, and the effective soil depth are the most important controls on discharge variability. This has important implications for the role of hydrology and vegetation in landscape evolution. Finally, we demonstrate that the way the Earth's surface responds to short-term climatic forcing variability is primarily determined by the existence and magnitude of erosional thresholds. We show that, irrespective of the nature of the erosional process, it is the ratio between the threshold magnitude and the mean magnitude of climatic forcing that determines whether variability matters or not and in which way. Among many other implications, our findings help provide a general framework to understand and predict the response of the Earth's surface to changes in mean and variability of rainfall and river discharge. The generality of this finding has important implications for the other work in this thesis, as well as previous work on role of rainfall and discharge variability on fluvial erosion.

abstract: The Phoenix Metropolitan region is subject to intense summer monsoon thunderstorms that cause highly localized flooding. Due to the challenges in predicting these meteorological phenomena and modeling rainfall-runoff transformations in urban areas, the ability of the current operational forecasting system to predict the exact occurrence in space and time of floods in the urban region is still very limited. This thesis contributes to addressing this limitation in two ways. First, the existing 4-km, 1-h Stage IV and the new 1-km, 2-min Multi-Radar Multi-Sensor (MRMS) radar products are compared using a network of 365 gages as reference. It is found that MRMS products consistently overestimate rainfall during both monsoonal and tropical storms compared to Stage IV and local rain gauge measurements, although once bias-corrected offer a reasonable estimate for true rainfall at a higher spatial and temporal resolution than rain gauges can offer. Second, a model that quantifies the uncertainty of the radar products is applied and used to assess the propagation of rainfall errors through a hydrologic-hydraulic model of a small urban catchment in Downtown Phoenix using a Monte Carlo simulation. The results of these simulations suggest that for this catchment, the magnitude of variability in the distribution of runoff values is proportional to that of the input rainfall values. / Dissertation/Thesis / Masters Thesis Civil, Environmental and Sustainable Engineering 2020