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A new Maximum Likelihood Criterion (MLE) suitable for data which are recorded at unequal time intervals and contain auto-correlated errors is developed. Validation of the new MLE criterion has been carried out both on a simple two - parameter reservoir model using synthetical data and on a more complicated hillslope model using real data from the Pukeiti Catchment in New Zealand. Comparison between the new MLE criterion and the Simple Least Squares (SLS) criterion reveals the superiority of the former over the latter. Comparison made between the new MLE and the MLE for auto-correlated case proposed by Sorooshian in 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used. However, the new MLE can work on variable time interval data which provide more information than equal time interval data, and therefore produces better visual results in hydrologic simulations.

The aim of this research project was to estimate parameters for the distribution of annual maximum flood levels for the Zambezi River at Katima Mulilo. The estimation of parameters was done by using the maximum likelihood method. The study aimed to explore data of the Zambezi's annual maximum flood heights at Katima Mulilo by means of fitting the Gumbel, Weibull and the generalized extreme value distributions and evaluated their goodness of fit.

Extreme weather events have a large effect on society. As such, it is important to understand these events and to project how they may change in a future, warmer climate. The aim of this thesis is to develop a deeper understanding of two types of extreme weather events: subtropical floods and tropical cyclones (TCs). In the subtropics, the latitude is high enough that quasi-geostrophic dynamics are at least qualitatively relevant, while low enough that moisture may be abundant and convection strong. Extratropical extreme precipitation events are usually associated with large-scale flow disturbances, strong ascent, and large latent heat release. In the first part of this thesis, I examine the possible triggering of convection by the large-scale dynamics and investigate the coupling between the two. Specifically two examples of extreme precipitation events in the subtropics are analyzed, the 2010 and 2014 floods of India and Pakistan and the 2015 flood of Texas and Oklahoma. I invert the quasi-geostrophic omega equation to decompose the large-scale vertical motion profile to components due to synoptic forcing and diabatic heating. Additionally, I present model results from within the Column Quasi-Geostrophic framework. A single column model and cloud-revolving model are forced with the large-scale forcings (other than large-scale vertical motion) computed from the quasi-geostrophic omega equation with input data from a reanalysis data set, and the large-scale vertical motion is diagnosed interactively with the simulated convection. It is found that convection was triggered primarily by mechanically forced orographic ascent over the Himalayas during the India/Pakistan flood and by upper-level Potential Vorticity disturbances during the Texas/Oklahoma flood. Furthermore, a climate attribution analysis was conducted for the Texas/Oklahoma flood and it is found that anthropogenic climate change was responsible for a small amount of rainfall during the event but the intensity of this event may be greatly increased if it occurs in a future climate. In the second part of this thesis, I examine the ability of high-resolution global atmospheric models to simulate TCs. Specifically, I present an intercomparison of several models' ability to simulate the global characteristics of TCs in the current climate. This is a necessary first step before using these models to project future changes in TCs. Overall, the models were able to reproduce the geographic distribution of TCs reasonably well, with some of the models performing remarkably well. The intensity of TCs varied widely between the models, with some of this difference being due to model resolution.

The aim of this research project was to estimate parameters for the distribution of annual maximum flood levels for the Zambezi River at Katima Mulilo. The estimation of parameters was done by using the maximum likelihood method. The study aimed to explore data of the Zambezi's annual maximum flood heights at Katima Mulilo by means of fitting the Gumbel, Weibull and the generalized extreme value distributions and evaluated their goodness of fit.

The problem of correlating unit hydrograph features to topographic and man-made basin characteristics received attention in this report. The unit graph features considered herein were the peak discharge and the time lag of basin response. In order to facilitate the desired regression analysis, the two-parameter gamma model proposed by Edson was utilized in the investigation. The parameters of the model were obtained by the simultaneous solution of the equations for unit graph peak and lag using observed unit hydrographs for 16 basins in the Piedmont region of North Carolina and 14 basins located in Northern Virginia. In the opinion of many, these parameters are a better measure of the complex relationship which exists between the runoff from a basin and the topographic features of that basin than are the values of the unit graph peak and lag time themselves. The basin characteristics utilized in the investigation were: basin area, length of the longest streamcourse in the basin, average stream slope between points 10 percent and 85 percent downstream of the headwaters, and the percent of the impervious area contained in the basin. This last factor served as a measure of the amount of urban development present in the watershed. The investigation was hampered by a regrettable lack of sufficient data to derive regression equations of good reliability. This fact was due to the reduction of the data into groups by narrow geographical ranges. Thus, the number of stations available for analysis in anyone group was insufficient for purposes of a reliable regression analysis. From the investigation, it appears that the most significant basin characteristics affecting runoff are length, slope, and urban development. The strongest regression equations were derived using those three characteristics. It appears that the length and slope factors give better results when combined in the form (L/√S). / Master of Science