Koichi Unami

Case Study: Hydraulic Modeling of Runoff Processes in Ghanaian Inland Valleys

The inland valleys of West Africa are strategic in terms of food security and poverty alleviation, but scientific studies on hydrologic processes happening in these environments have not been well documented. Modeling approaches presented in this paper are an attempt to better comprehend hydraulic phenomena occurring in inland valleys. An inland valley situated in the Northern Region of Ghana is set as the study site. The inland valley comprises well-drained uplands and hydromorphic valley bottoms. There are several earthen dams across the valley bottoms, which are at the same time seasonal wetlands cultivated to rice during the rainy season. A finite volume model for the shallow water equations is developed to numerically simulate surface runoff flows in the valley bottoms during flood events. Innovation is necessitated to handle a series of different hydraulic phenomena. Flux-splitting and data reconstruction techniques are used to achieve stable computation in the complex topography of the valley bottoms. Standard problems of oblique hydraulic jump and dam break flows are used to test the accuracy of the numerical model. The Mannings roughness coefficient is determined from calibration in another Ghanaian watershed located in the Eastern Region. Using actually observed time series data of rainfall intensity, surface flows during the rainfall events are simulated in the computational domain representing the valley bottoms of the study area. Observed data of water levels in the dams are compared to predictions, and discrepancies between them are examined from the hydrological point of view. In the case of a hypothetical flood event, cascading collapses of the dams and flooding of cultivated fields are reproduced.

Optimal hydraulic design of earth dam cross section using saturated-unsaturated seepage flow model

Abstract An optimal hydraulic design problem regarding an earth dam cross section is formulated as an inverse problem for the steady model of saturated–unsaturated seepage flows in porous media. In the problem formulation, the choice of soil material to be used in each point of the dam cross sectional domain is considered as the control variable to be identified. The performance index used to evaluate the appropriateness of the design is defined as the sum of two square integral norms, which represent reducing the saturated zone and minimizing material costs. It is also shown that the first norm bounds the total seepage discharge through the earth dam. Since the governing variational boundary value problem as well as the adjoint problem is well-posed, a deterministic approach is taken. A numerical scheme including pseudo-unsteady terms is developed to calculate the optimal solution in an ideal earth dam cross section to be designed utilizing two different types of soil material. The results show that an inclined clay core of less hydraulic conductivity should be located on the upstream side of the cross section. The unsaturated zone turns out to play an important role in the flow field and the optimal design.

A distributed hydro-environmental watershed model with three-zoned cell profiling

A cell-based distributed watershed model is developed which enables us to simulate the hydrological and hydraulic aspects of the watershed in a refined fashion. With three-zoned cell profiling, the model is composed of three sub-models; tank model for a surface water zone, soil moisture model for a surface soil zone, and unconfined shallow groundwater flow model for a subsurface zone. Inclusion of the soil moisture sub-model modified to reroute the infiltration, routed from the tank sub-model, into the return flow and the groundwater recharge features the model. The groundwater flow sub-model, numerically approximated by use of the finite volume method and the implicit time-marching scheme, considers a network of on-farm drainage canals as internal boundaries, which is an essential need for modeling the watershed including farmlands. Cascade-linking of the three sub-models in a cell and assembling of all the cells over the entire watershed domain provides the global equations system to be solved. Applicability of the model is demonstrated with its practical application to a real watershed in that paddy and upland crop fields take great part of the land-use practice. It is then indicated in a quantified manner that rice farming significantly contribute as a major groundwater recharger in an irrigation period to fostering and conservation of regional water resources. Along with appropriately profiling a cell, the model is so versatile and tough that it can be applied without difficulty to a watershed of diverse terrains and land-uses and the computations can stably be carried out. It is thus concluded that the model presently developed could be a powerful “watershed simulator” to investigate and assess the time-varying hydro-environmental properties of a watershed while separating and integrating the hydrological and hydraulic components of particular importance.

An optimal management strategy for stochastic population dynamics of released Plecoglossus altivelis in rivers

Excessive predation pressure from the waterfowl Phalacrocorax carbo (Great Cormorant) on Plecoglossus altivelis (Ayu) has recently been a severe problem of river environment in Japan. Local fishery cooperatives are currently suffering from economic difficulties due to decrease of the fish catch of P. altivelis. Local fishery cooperatives and municipalities have been enthusiastically trying to develop countermeasures that can effectively reduce the predation pressure; however, their effectiveness and efficiency have not been systematically quantified well. This aim can be achieved with the help of an appropriate mathematical model. In this paper, based on a pure death process, a practical stochastic control model for population dynamics of released P. altivelis in river environment under predation pressure from P. carbo, harvesting by human, and environmental fluctuations is proposed. Finding an optimal management strategy ultimately reduces to solving a 2D Hamilton–Jacobi–Bellman equation, which is performed with a finite element scheme. Its application to a Japanese river environment successfully computes the optimal management strategy that is consistent with the reality. Numerical sensitivity analysis of the presented mathematical model is also performed for comprehension of dependence of the optimal strategy on the model parameters.

Fuzzy optimization model for integrated management of total nitrogen loads from distributed point and nonpoint sources in watershed

A fuzzy optimization model is developed to allocate allowable total nitrogen (T-N) loads to distributed nonpoint sources (NPSs) and point sources (PSs) in a watershed for river water quality management using the linear programing technique. The watershed is divided into uniform grid cells on which T-N loads issuing from NPSs such as paddy fields, upland crop fields and cities are controlled. A geographic information system integrated with the digital elevation model facilitates computation of route lengths of surface and subsurface flows from cells to a river running through the watershed. The T-N loads discharged from their sources are assumed to decay, subject to distance-related first-order kinetics. As management goals, maximizations of total allowable NPS loads, total allowable PS loads and total yield of rice are considered from environmental and economic viewpoints. A prime constraint is an effluent limitation standard for the aggregate amount of loads that arrive at the downstream end of the river. The fuzzy sets theory helps appropriately describe vague attitudes of decision-makers (i.e., stakeholders and management authorities) in terms of constraints and conflicting goals. An application of the fuzzy optimization model, developed as an improvement over our last nonfuzzy model, to a real watershed in Shiga prefecture, Japan, demonstrates that the fuzzy model embodies our last model, and is capable of creating management alternatives for T-N load allocation in a more practical and flexible manner.

Systematic assessment of flood mitigation in a tank irrigated paddy fields area

Flood mitigation in irrigation tanks and paddy fields is their favorable aspect though its practical effect is not known very well. A dynamic and systematic approach is presented to assess flood mitigation in a tank irrigated paddy fields area in the worst case where no static buffer function is expected. Based on the linear control theory, transfer function models for runoff process in catchments are identified. Hydraulic models are developed to represent flood dynamics in irrigation tanks, paddy fields, and drainage channels. These models are integrated as an ordinary differential equations system. Then, using the perturbed linear system, flood mitigation in each component of the system is examined in terms of frequency response. An application example demonstrates that a tank irrigated paddy fields area has a significant flood mitigation effect as a low-pass filter. This method has the advantage of assessing flood mitigation even in the case of an increase in the total runoff ratio.

A stochastic model for behaviour of fish ascending an agricultural drainage system

Adults of Carassius auratus grandoculis ascend from Lake Biwa, Japan, into riparian paddy fields via agricultural drainage systems for the purpose of spawning. However, land improvement works conducted in the second half of the twentieth century have brought about obstacles for passage of the fish, and several restoration projects to recover the migratory environment are being attempted. A continuous Markov process model is presented to scientifically support such a project, defining an ascending probability that quantitatively assesses the ability of an agricultural drainage system with hydraulic structures for the ascent of the fish. Computational methods are developed to numerically obtain flow fields of the agricultural drainage system and then the ascending probability in the entire spatio-temporal domain. The values of model parameters are deductively inferred, referring to results of field observations. From the computational results of the ascending probability in the agricultural drainage system, effects of hydraulic structures allowing ascent of the fish are clarified.

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.

A physically based FVM watershed model fully coupling surface and subsurface water flows.

A sophisticated modeling approach for simulating-coupled surface and subsurface flows in a watershed is presented. The watershed model developed is a spatially distributed physically based model of composite dimension, consisting of 3-D variably saturated groundwater flow submodel, 2-D overland flow submodel and 1-D river flow submodel. The 3-D subsurface flow is represented by the complete Richards equation, while the 2-D and 1-D surface flows by the diffusive approximations of their complete dynamic equations. For piecewise integration of these equations, the finite volume method (FVM) is employed assuming unknown variables such as the water depth and the pressure head to be volume-averaged state ones. Problem plane geometry is meshed with the unstructured cells of triangular shape which conforms to external as well as internal irregular boundaries such as those between 1-D and 2-D flows. A cell size controlling scheme, referred to as quasi-adaptive meshing scheme, is introduced to keep the local discretization errors caused by topographic elevation gradient even over the entire-meshed geometry. Performance of the model is tested through its practical application to a rugged intermountain watershed. Tuning the values of the three key parameters ensures successful calibration of the model. Once the model is so calibrated, it could reproduce satisfactory runoff response to any rainfall event. Expansion and shrinkage of the contributing area importantly affecting the direct runoff, caused by the vicissitude of rainfall during its total duration, are well reproduced, like what the commonly accepted runoff theory argues. It is thus concluded that the model developed could serve as a powerful watershed simulator usable for investigating and assessing the hydrological aspect of a watershed.