Macarius Yangyuoru

Rationalization of building micro-dams equipped with fish passages in West African savannas

Micro-dams in West African savannas are investigated in conjunction with aquatic fauna and human activities at a community level. A study area is chosen in the Northern Region of Ghana. The micro-dams in the study area serve as habitats for fish, providing food and job opportunities for inhabitants, but their construction has sacrificed rice fields and fragmented migration routes of fish. A stochastic population dynamics model is developed to rigorously assess the effect of establishing fish passages between the fragmented habitats containing the micro-dams on the ichthyological fauna. Values of the model parameters are estimated from the literature and results of field surveys, in which ten fish species including cichlidae, clariidae, bagridae, schilbeidae, cyprinidae, and alistidae are reported to be present. A sustainability criterion is proposed to judge whether a set of model parameters realizes stationarity of the stochastic process representing the population dynamics. It is suggested that ichthyological fauna can be sustainable provided that the fishing activity is restricted to upstream migrating and fast growing species. More generally, building micro-dams in West African savannas will be much better justified when the dams are equipped with appropriately designed fish passages.

Application of shallow water equations to analyze runoff processes in hilly farmlands

Analysis of runoff processes in farmlands during storm events in particular is an important engineering topic. The shallow water equations describing the physical conservation laws are attractive tools for understanding motion of surface water. A numerical model is developed to reproduce surface water flows during storm events, using the finite element method and the finite volume method applied to the one-dimensional shallow water equations. The numerical model has the advantage of dealing with transcritical flows, wet, and dry processes, irregular channel bed slopes, and channel junctions involving multiply connected networks. Standard numerical tests demonstrated some of these features. Runoff processes from farmlands in a Japanese hilly area is analyzed with the numerical model coupled with another runoff model of black-box type. Parameters of the models are calibrated and validated using observed series of rainfall and runoff discharge data. Simulated results included submergence of hydraulic jumps and flood storage in farming plots, which are very informative in terms of assessing diverse functions of the farmlands.

Verifying optimality of rainfed agriculture using a stochastic model for drought occurrence

It may be paradoxical but subsistence rainfed agriculture is the predominant source of food in Sub-Saharan Africa where the production uncertainty is associated with the stochastic nature of rainfall. This paper attempts to comprehend the rationale of this situation by a mathematical approach. Considering the level of drought severity as the zero-reverting Ornstein–Uhlenbeck process, optimality of rainfed agriculture is investigated in the context of stochastic control theory. Occurrence of drought terminating growth of crops is modelled with the concept of first exit time. A stochastic control problem allowing for virtual cost of irrigation, water stress to crops, and benefits of farming is formulated with irrigation effort as the control variable. The Hamilton–Jacobi–Bellman equation governing the optimal control is studied to identify the set of cost functions optimizing rainfed agriculture in an inverse problem approach. Data and information were collected in the coastal savanna agro-ecological zone of Ghana, to identify model parameters, formulate the stochastic control problem, solve the inverse problem, and then verify optimality of rainfed agriculture. The results indicated that rainfed agriculture is not optimal when the crop is more tolerant to water stress.