Level-set methods applied to the kinematic wave equation governing surface water flows.

Critical issues arising from the governing nonlinear equations in surface water hydrodynamic include discontinuities in water surface levels, blow-up of water surface gradient, and treatment of dry beds or zero water depths, involving mathematical problems related to functional regularities of unknown variables such as the water depth. The level-set method is a powerful approach to relax requirements for functional regularities of unknowns in nonlinear partial differential equations of first order. In this study, the level-set method is applied to the one-dimensional kinematic wave equation, resulting in a linear level-set equation of the first order in a two-dimensional space to tackle dry beds. The zeros of the level-set function represent the water depths. Hypothesizing that the level-set function is continuous in the domain, it is numerically computed with a characteristic method. The development of overturning is regulated with singular viscosity regularization (SVR), whose effect is to relocate the zeros of the level-set function close to the exact positions of the shock fronts in dam-break problems. The method is firstly verified with the explicitly known exact solutions of primitive dam-break problems, optimizing a parameter of SVR. Then, abrupt water release from Chan Thnal Reservoir, Kampong Speu Province, Cambodia into an initially dry bed of its irrigation canal system is simulated as a practical demonstrative example. In contrast to most of the available software tools using either the shallow water equations with some artificial viscosity or the diffusion wave approximation, the proposed method turns out to be free from spurious diffusive deformation of water surfaces even if relatively coarse computational mesh is used.

A singular stochastic control model for sustainable population management of the fish-eating waterfowl Phalacrocorax carbo.

Using a tractable singular stochastic control model, this study seeks a sustainable population management policy for the fish-eating waterfowl Phalacrocorax carbo (Great Cormorant), a major predator of riverine fish in Japan. The bird population dynamics around a habitat lake are described by a stochastic differential equation with a singular control variable representing human interventions to suppress the predation. The optimal population management policy maximizes a performance index that covers the cost of countermeasures, the loss of riverine fish, and the ecosystem services provided by the bird. The dynamic programming principle obtains an exactly-solvable variational inequality that governs a sustainable, threshold-type optimal management policy. In this policy, countermeasures are taken when the population reaches a certain level. The model is applied to management of P. carbo population around Lake Biwa, Japan, where predation of riverine fish is the most severe in the country. The current management policy around the lake is analyzed and verified in the context of the proposed model, focusing on the population-control threshold and the average population reduction per unit time.

Holistic water quality dynamics in rural artificial shallow water bodies.

The water environment in diversely used rural artificial water bodies is generally varied with seasonal and diurnal changes, stability of which is significant in water resources management. Understanding of interaction among different water quality parameters that depend on their diurnal variations is the concern of this study. A rural homestead pond used for aquaculture in Bangladesh and a micro-dam used as an irrigation tank for paddy farming in Japan are chosen for contrasting the analysis of data. The observed data series of four typical water quality parameters exhibits the diurnal variations, which are primarily inferred to be driven by solar radiation and complex bio-chemical interactions. The study proposes a stochastic differential equation model to represent holistic water quality dynamics based on continuous measurements. The water quality parameters are considered as temporally continuous Markov process, where their individual effects on each parameter are evaluated in a specific time step and immediately reflected to the next observation. The model parameters are calibrated and the stability is discussed based on the eigenvalues of model parameters. The result mostly shows the mean reverting properties for dissolved oxygen and water temperature, while pH and oxidation reduction potential are rather depend on other parameters or external disturbance.