An empirical method is developed for constructing likelihood functions required in a Bayesian probabilistic flash flood forecasting model using data on objective quantitative precipitation forecasts and their verification. Likelihoods based on categorical and probabilistic forecast information for several forecast periods, seasons, and locations are shown and compared. Data record length, forecast information type and magnitude, grid area, and discretized interval size are shown to affect probabilistic differentiation of amounts of potential rainfall. Use of these likelihoods in Bayes' Theorem to update prior probability distributions of potential rainfall, based on preliminary data, to posterior probability distributions, reflecting the latest forecast information, demonstrates that an abbreviated version of the flash flood forecasting methodology is currently practicable. For this application, likelihoods based on the categorical forecast are indicated. Apart from flash flood forecasting, it is shown that likelihoods can provide detailed insight into the value of information contained in particular forecast products.

Report to Hydrology Laboratory, Office of Hydrology, National Weather Service, NOAH, Dept. of Commerce, Contract 6 -35229 / The value of a forecast system in preventing urban property damage depends on the accuracy of the forecasts, the time at which they are received, the response by the floodplain dweller and the êfficacy of that response. A systems model of the overall flood forecast -response system is developed. Evaluation of the system is accomplished by a decision theoretic methodology. A case study is done for Milton, Pennsylvania, which evaluates the present system and potential changes to it. It is concluded that the sequential nature of the forecast sequence must be considered in modeling the flood forecast -response system if a meaningful evaluation of the economic value of the system is to be obtained. Methodology for obtaining the parameterization of the model from the available data is given. Computer programs have been written to handle a good portion of the calculations. While more work is needed on obtaining accurate parameterization of certain parts of the model, such as the actual response to forecasts; use of the procedures and programs as they now stand produces reasonable evaluations.

Many techniques have been developed over the years in first world countries for the estimation of flood hydrographs from small catchments for application in design, management and operations of water related issues. However, relatively little attention has been directed towards the transfer and adaptation of such techniques to developing countries in which major hydrological decisions are crucially needed, but in which a scarcity of quality hydrological data often occurs. As a result, hydrologists and engineers in developing countries are frequently unable to alleviate the problems that extreme rainfall events can create through destructive flood flows or, alternatively, they do not possess the appropriate tools with which to design economically viable hydraulic structures. Eritrea is a typical example of a developing country which faces difficulties in regard to the adaptation of an appropriate design flood estimation technique for application on small catchments. As a result, the need has arisen to adapt a relatively simple and robust design flood model that can aid hydrologists and engineers in making economic and safe designs of hydraulic structures in small catchments. One objective of this study was, therefore, to review approaches to hydrological modelling and design flood estimation techniques on small catchments, in order to identify the barriers regarding their adaptation, as well as to assist in the selection of an appropriate technique for application, in Eritrea. The southern African adaptation of the SCS (i.e. Soil Conservation Service) design hydrograph technique, which has become a standard method for design flood estimation from small catchments in that region, was selected for application on small catchments in Eritrea for several reasons. It relies on the determination of a simple catchment response index in the form of an initial Curve Number (CN), which reflects both the abstraction characteristics and the non-linear stormflow responses of the catchment from a discrete rainfall event. Many studies on the use of SCS-based hydrological models have identified that adjustment of the initial CN to a catchment's antecedent soil moisture (ASM) to be crucial, as the ASM has been found to be one of the most sensitive parameters for accurate estimates of design flood volumes and peak discharges. In hydrologically heterogeneous regions like Eritrea, the hypothesis was postulated that simulations using a suitable soil water budgeting procedure for CN adjustment would lead to improved estimates of design flood volumes and peak discharges when compared with adjustments using the conventional SCS antecedent moisture conditions (SCS-AMC) method. The primary objective of this dissertation was to develop a surrogate methodology for the soil water budgeting procedure of CN adjustment, because any direct applications of soil water budgeting techniques are impractical in most parts of Eritrea owing to a scarcity of adequate and quality controlled hydrological information. It was furthermore hypothesised that within reasonably similar climatic regions, median changes in soil moisture storage from the socalled "initial" catchment soil moisture conditions, i.e. LIS, were likely to be similar, while between different climatic regions median LISs were likely to be different. Additionally, it was postulated that climatic regions may be represented by a standard climate classification system. Based on the above hypotheses, the Koppen climate classification, which can be derived from mean monthly rainfall and temperature information, was first applied to the 712 relatively homogeneous hydrological response zones which had previously been identified in southern Africa. A high degree of homogeneity of median values of LIS, derived by the daily time step ACRU soil moisture budgeting model, was observed for zones occurring within each individual Koppen climate class (KCC) - this after a homogeneity test had been performed to check if zones falling in a specific KCC had similar values of median LIS. Further assessment within each KCC found in southern Africa then showed that a strong relationship existed between LIS and Mean Annual Precipitation (MAP). This relationship was, however, different between KCCs. By developing regression equations, good simulations of median LIS from MAP were observed in each KCC, illustrating the potential application of the Koppen climate classification system as an indicator of regional median LIS, when only very basic monthly climatological information is available. The next critical task undertaken was to test whether the estimate of median LIS from MAP by regression equation for a specific Koppen climate class identified in southern Africa would remain similar for an identical Koppen climatic region in Eritrea. As already mentioned, LIS may be determined from daily time step hydrological soil moisture budget models such as ACRU model. The performance of the ACRU stormflow modelling approach was, therefore, first verified on an Eritrean gauged research catchment, viz. the Afdeyu, in order to have confidence in the use of values of LIS generated by it. A SCS-ACRU stormflow modelling approach was then tested on the same catchment by using the new approach of CN adjustment, termed the ACRU-Koppen method, and results were compared against stormflow volumes obtained using the SCS-AMC classes and the Hawkins' soil water budgeting procedures for CN adjustment, as well as when CNs remain unadjusted. Despite the relatively limited level of information on climate, soils and land use for the Afdeyu research catchment, the ACRU model simulated both daily and monthly flows well. By comparing the outputs generated from the SCS model when using the different methods of CN adjustment, the ACRU-Koppen method displayed better levels of performances than either of the other two SCS-based methods. A further statistical comparison was made among the ACRU, the SCS adjusted by ACRU-Koppen, the SCS adjusted by AMC classes and the unadjusted SCS models for the five highest stormflows produced from the five highest daily rainfall amounts of each year on the Afdeyu catchment. The ACRU model produced highly acceptable statistics from stormflow simulations on the Afdeyu catchment when compared to the SCS-based estimates. In comparing results from the ACRU-Koppen method to those from the SCS-AMC and unadjusted CN methods it was found that, statistically, the ACRU-Koppen performed much better than either of the other two SCS based methods. On the strength of these results the following conclusions were drawn: • Changes in soil moisture storage from so-called "initial" catchment soil moisture conditions, i.e. L1S, are similar in similar climatic regions; and • Using the ACRU-Koppen method ofCN adjustment, the SCS-SA model can, therefore, be adapted for application in Eritrea, for which Koppen climates can be produced from monthly rainfall and temperature maps. Finally, future research needs for improvements in the SCS-ACRU-Koppen (SAK) approach in light of data availability and the estimation ofL1S were identified. From the findings of this research and South African experiences, a first version of a "SCSEritrea" user manual based on the SAK modelling approach has been produced to facilitate its use throughout Eritrea. This user manual, although not an integral part of this dissertation, is presented in its entirety as an Appendix. A first Version of the SCS-Eritrea software is also included. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2004.