Traditional stochastic approaches for synthetic generation of weather variables often assume a prior functional form for the stochastic process, are often not capable of reproducing the probabilistic structure present in the data, and may not be uniformly applicable across sites. In an attempt to find a general framework for stochastic generation of weather variables, this study marks a unique departure from the traditional approaches, and ushers in the use of data-driven nonparametric techniques and demonstrates their utility. Precipitation is one of the key variables that drive hydrologic systems and hence warrants more focus . In this regard, two major aspects of precipitation modeling were considered: (I) resampling traces under the assumption of stationarity in the process, or with some treatment of the seasonality, and (2) investigations into interannual and secular trends in precipitation and their likely implications. A nonparametric seasonal wet/dry spell model was developed for the generation of daily precipitation. In this the probability density functions of interest are estimated using non parametric kernel density estimators. In the course of development of this model, various nonparametric density estimators for discrete and continuous data were reviewed, tested, and documented, which resulted in the development of a nonparametric estimator for discrete probability estimation. Variations in seasonality of precipitation as a function of latitude and topographic factors were seen through the non parametric estimation of the time-varying occurrence frequency. Nonparametric spectral analysis, performed on monthly precipitation, revealed significant interannual frequencies and coherence with known atmospheric oscillations. Consequently, a non parametric, nonhomogeneous Markov chain for modeling daily precipitation was developed that obviated the need to divide the year into seasons. Multivariate nonparametric resampling technique from the nonparametrically fitted probability density functions, which can be likened to a smoothed bootstrap approach, was developed for the simulation of other weather variables (solar radiation, maximum and minimum temperature, average dew point temperature, and average wind speed). In this technique the vector of variables on a day is generated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the current day generated from the wet/dry spell model.

Firstly, this dissertation proposes a new characterization and classification method for daily sky conditions by using the daily sky clearness index (KD) and the daily probability of persistence (POP-KD) that can be derived from ground-based irradiance measurement data. Quality of daily solar irradiance is characterized by a newly proposed parameter, POP-KD. This characterized daily quality is varying and uncertain at the middle level of the quantity, but high and more certain at very high and low quantity levels. In addition, the proposed characterization method shows interesting results for KD and POP-KD: a statistical consistency for multiple years and similarity for their seasonal trends. The classification results also indicate an existence of dominant classes, and transitions between the dominant classes are significant for all locations. This dissertation also generates annual synthetic sequences of KD and POP-KD using a Markov approach. The generated sequences show statistical similarities with observed sequences. Secondly, this dissertation proposes methodologies to estimate day-ahead solar irradiance using the National Weather Service (NWS) sky cover forecast. For model development, this paper splits up a direct estimation process from the sky cover forecast to solar irradiance into two stages: forecast verification and cloud-to-irradiance conversion. Uncertainty for each stage and for the overall estimation process is quantified. NWS forecast uncertainty (about 20%) is identified as the main source of uncertainty for the overall process. In addition, verification of the sky cover forecast shows approximately 20% overestimated bias at days with a high irradiance level. Thus, the NWS sky cover forecast needs to be adjusted based on the type of day. This dissertation also proposes a conversion equation relating daily quantity of cloud information and daily quantity of solar irradiance. The proposed conversion equation achieves accuracy with simplicity. Five day-ahead solar irradiance quantity estimation methods are proposed in this dissertation. The proposed methods incorporate different schemes for dealing with the bias discovered in the cloud forecast. The observed data are regularly found within the 95% confidence intervals of the estimated values. Estimation results demonstrate the effectiveness of the conditional adjustment schemes at different irradiance levels. Lastly, this dissertation proposes a methodology to estimate day-ahead solar irradiance using fluctuation information of the NWS sky cover forecast. POP-KD was used as a parameter for the quality of daily solar irradiance. POP-KD efficiently represents the quality of daily solar irradiance. In addition, POP-KD indicates the probability that solar irradiance variability is within the ramp rates of common generators in power systems at a certain photovoltaic penetration level. This dissertation also proposes a new equation for the conversion from cloud fluctuation information to daily quality of surface solar irradiance. The proposed equation achieves accuracy. The proposed day-ahead solar irradiance quality estimation method is based on fluctuation information provided by the NWS sky cover forecast. This method uses a normalization approach to relate fluctuation of cloud forecast and fluctuation of cloud observation. The observed data are regularly found within the 95% CIs of the estimated values. / Ph. D.