The purpose of this study was to develop a stochastic model of the snowfall, snow accumulation and ablation process. Snow storms occurring in a fixed interval were assumed to be a homogeneous Poisson process with intensity X. The snow storm magnitudes were assumed to be independent and identically distributed random variables. The magnitudes were independent of the number of storms and concentrated at the storm termination epochs. The snow water equivalent from all storms was a compound Poisson process. In the model, storms then occurred as positive jumps whose magnitudes equaled the storm amounts. Between storms, the snowpack ablated at a constant rate. Random variables characterizing this process were defined. The time to the occurrence of the first snowpack, generated by the first storm, was a random variable, the first snow-free period. The snowpack lasted for a random duration, the first snowpack duration. The alternating sequence of snow-free periods followed by snowpacks of random duration continued throughout the fixed interval. The snow-free periods were independent and identically distributed random variables as were the snowpack durations. The sum of each snow-free period and the immediately following snowpack duration formed another sequence of independent and identically distributed random variables, the snow-free, snow cycles. The snow-free, snow cycles represented the interarrival times between epochs of complete ablation, and thus defined a secondary renewal process. This process, called the snow renewal process, gave the number of times the snowpacks ablated in the interval. Distribution functions of the random variables were derived. The snow-free periods were exponentially distributed. The distribution function of the snowpack durations was obtained using some results from queueing theory. The distribution function of the first snow-free, snow cycle was derived by convoluting the density function of the first snowfree period and the first snowpack duration. The distribution of the sum of n snow-free, snow cycles was then the n-fold convolution of the first snow-free, snow cycle with itself. The probability mass function of the snow renewal process was evaluated numerically, from a known relationship with the sum of snow-free, snow cycles. The snowpack ablation rate was considered to be a random variable, constant within a season, but varying between seasons. The snowpack durations and snow-free, snow cycles were conditioned on the ablation rate, then unconditional distributions derived. An application of the model was made in the case where snow storm magnitudes were exponentially distributed. Specific expressions for the distribution functions of the random variables were obtained. These distributions were functions of the Poisson parameter X, the exponential parameter of storm magnitudes, Ne l, and the snowpack ablation rate. The snow model was compared with data from the climatological station at Flagstaff, Arizona. Snow storms were defined as sequences of days receiving 0.01 inch or more of snow water equivalent separated from other storms by one or more dry days. Snow storms occurred approximately as a homogeneous Poisson process. Storm magnitudes were exponentially distributed. Empirical distributions of snowpack ablation rates were obtained as the coefficients of a regression analysis of snowpack ablation. Two methods of estimating the Poisson parameter were used. The theoretical distribution functions were compared with the observed. The method of moments estimate generally gave more satisfactory results than the second estimate.

Note: / The purpose of this study was to develop and evaluate a numerical model for simulating the influence of seasonal snow cover on the ground thermal regime.The physical processes occurring within the snow pack and underlying ground, as well as at the surface, are reviewed from the viewpoint of their eventual inclusion in a practical numerical model. A finite difference heat conduction model suitable for long-term studies of the snow-ground thermal interaction is presented. This model incorporates a numerical prediction of density and temperature profiles within an evolving snow cover. Phase change within the ground is treated by a new numerical method which has important computational advantages over older methods.[...] / Cette etude avait pour but Ie developpement et l'evaluation d'un modele numerique pour la simulation de l'influence du manteau neigeux saisonier sur Ie regime thermique du sol.Les processus physiques rencontres dans Ie manteau neigeux et Ie sol sous-jacent ainsi quIa l'interface air-surface sont discutes et passes en revue dans l'optique restreinte de leur eventuelle inclusion dans un modele numerique. On presente ensuite un modele a conduction en differences finies qui convient pour les etudes de l'interaction thermique neige-sol a long terme. Le modele inclut un calcul numerique de l'evolution temporelle des profiles de densite et de temperature du manteau neigeux. Les changements de phase dans Ie sol sont traites par une nouvelle technique numerique avantageuse pour Ie calcul.[...]

This thesis is a combination of two separate studies which examine hydrologic data assimilation techniques: 1) to determine the applicability of assimilation of remotely sensed data in operational models and 2) to compare the effectiveness of assimilation and other calibration techniques. The first study examines the ability of Data Assimilation of remotely sensed microwave radiance data to improve snow water equivalent prediction, and ultimately operational streamflow forecasts. Operational streamflow forecasts in the National Weather Service River Forecast Center are produced with a coupled SNOW17 (snow model) and SACramento Soil Moisture Accounting (SAC-SMA) model. A comparison of two assimilation techniques, the Ensemble Kalman Filter (EnKF) and the Particle Filter (PF), is made using a coupled SNOW17 and the Microwave Emission Model for Layered Snowpack model to assimilate microwave radiance data. Microwave radiance data, in the form of brightness temperature (TB), is gathered from the Advanced Microwave Scanning Radiometer-Earth Observing System at the 36.5GHz channel. SWE prediction is validated in a synthetic experiment. The distribution of snowmelt from an experiment with real data is then used to run the SAC-SMA model. Several scenarios on state or joint state-parameter updating with TB data assimilation to SNOW-17 and SAC-SMA models were analyzed, and the results show potential benefit for operational streamflow forecasting. The second study compares the effectiveness of different calibration techniques in hydrologic modeling. Currently, the most commonly used methods for hydrologic model calibration are global optimization techniques. While these techniques have become very efficient and effective in optimizing the complicated parameter space of hydrologic models, the uncertainty with respect to parameters is ignored. This has led to recent research looking into Bayesian Inference through Monte Carlo methods to analyze the ability to calibrate models and represent the uncertainty in relation to the parameters. Research has recently been performed in filtering and Markov Chain Monte Carlo (MCMC) techniques for optimization of hydrologic models. At this point, a comparison of the effectiveness of global optimization, filtering and MCMC techniques has yet to be reported in the hydrologic modeling community. This study compares global optimization, MCMC, the PF, the Particle Smoother, the EnKF and the Ensemble Kalman Smoother for the purpose of parameter estimation in both the HyMod and SAC-SMA hydrologic models.

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