Partial Differential Equation Model for Spatially Distributed Statistics of Contaminant Particles in Localy One-Dimensional Open Channel Networks

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Time periodic optimal policy for operation of a water storage tank using the dynamic programming approach

Operation of a water storage tank in a specific environment motivates mathematical studies on a discrete-time deterministic dynamic programming problem. The operator decides whether or not to open the valve releasing the water in the tank to a drip irrigation system, based on the information on the storage volume of the tank. Two cases of functional regularity, which are Lipschitz continuous and of bounded variations, are considered for the reward defining the performance index to be maximized. Firstly, it is shown that the value function inherits the Lipschitz continuity of the reward in the infinite time horizon problem with discounting. Then, time periodic value functions are discussed in terms of the fixed-point theorem. Discrete approximation of value functions is discussed as well, to conduct numerical experiments with a-posteriori error estimation applied to the real-world problem where the discount rate approaches to unity. It is found that a Skiba point appears as a threshold of valve opening for each day in an optimal policy for operation. Practically, setting a constant threshold throughout the period is quite reasonable and acceptable for the operator of the water storage tank to irrigate the farmland

A thorough description of one-dimensional steady open channel flows using the notion of viscosity solution

Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ordinary differential equations, which are of mathematical interest. We show that the notion of viscosity solution is useful in thoroughly describing the characteristics of possibly non-smooth and discontinuous solutions to such problems, achieving the conservation of momentum and the entropy condition. Those viscosity solutions are the generalized solutions in the space of bounded measurable functions. Generalized solutions to some Dirichlet problems are not always unique, and a necessary condition for the non-uniqueness is derived. A concrete example illustrates the non-uniqueness of discontinuous viscosity solutions in a channel of a particular cross-sectional shape

Rainfall-runoff models with fractional derivatives applied to kurau river basin, Perak, Malaysia

The 5th International Conference on Agricultural and Food Engineering (CAFEi) 2021Kurau River Basin (KRB), which covers an area of 322 km² and is the main drainage artery pouring into Bukit Merah Reservoir (BMR), is located in Perak State of Malaysia. The study of rainfall-runoff processes in KRB is important because BMR plays a vital role in rice production, flood control, ecosystems, and tourism in the region. This study proposes a new approach to rainfall-runoff modeling based on the fractional calculus. A dataset of daily rainfall and streamflow has been acquired. Then, the standard linear autoregressive with exogenous input (ARX) model is identified from the dataset in the sense of least square error. We consider the ARX model as a discretized differential equation with fractional orders. Such a model with fractional derivatives is versatile to represent hysteresis, which is intrinsically linked to the real runoff processes in tropical catchment basins like KRB

水輸送/貯留系の最適化と制御

京都大学0048新制・論文博士博士(農学)乙第10044号論農博第2214号新制||農||774(附属図書館)学位論文||H11||N3230(農学部図書室)UT51-99-D248(主査)教授 河地 利彦, 教授 青山 咸康, 教授 三野 徹学位規則第4条第2項該当Doctor of Agricultural ScienceKyoto UniversityDFA

A dual finite volume method scheme for catastrophic flash floods in channel networks

This paper develops a new numerical scheme for flash floods based on the one-dimensional shallow water equations in channel networks, referred to as the dual finite volume method (DFVM) scheme. The scheme uses an upwind spatial discretization based on staggered meshes so that the flows in multiply connected channel networks are consistently handled without complicated treatment at junctions. The scheme is firstly examined with a series of test cases including idealized and experimental dam break problems to demonstrate its accuracy and versatility. The scheme is then applied to numerical simulation of a flash flood resulting from an earthquake-induced complete dam failure in Japan. Channels from a reservoir to the downstream rivers are modelled as a multiply connected channel network with non-prismatic cross-sections, steep slopes, and bends. The computational results agree well with the field observations and eyewitness reports. Numerical simulation of alternative scenarios as possible cases is also performed to analyze potential risks of the downstream area

A unique value function for an optimal control problem of irrigation water intake from a reservoir harvesting flash floods

砂漠の洪水を灌漑用水に変える --ヨルダンの乾燥地で数理的最適戦略によるプロトタイプを運用--. 京都大学プレスリリース. 2018-03-08.Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton–Jacobi–Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB equation. The optimal control strategy derived from the approximate value function is summarized in terms of rule curves to be presented to the operator of the irrigation scheme

A multi-state Markov chain model to assess drought risks in rainfed agriculture: a case study in the Nineveh Plains of Northern Iraq

連続干天日数に関する数学モデルを構築し、旱魃の回避に役立つ方法論を提案 --イラク北部のニネベ平原における事例研究--. 京都大学プレスリリース. 2021-04-06.Counting the dry days to avert drought --Case study in the Nineveh Plains of Northern Iraq--. 京都大学プレスリリース. 2021-04-06.The occurrence of prolonged dry spells and the shortage of precipitation are two different hazardous factors affecting rainfed agriculture. This study investigates a multi-state Markov chain model with the states of dry spell length coupled with a probability distribution of positive rainfall depths. The Nineveh Plains of Northern Iraq is chosen as the study site, where the rainfed farmers are inevitably exposed to drought risks, for demonstration of applicability to real-time drought risk assessment. The model is operated on historical data of daily rainfall depths observed at the city Mosul bordering the Nineveh Plains during the period 1975–2018. The methodology is developed in the context of contemporary probability theory. Firstly, the Kolmogorov–Smirnov tests are applied to extracting two sub-periods where the positive rainfall depths obey to respective distinct gamma distributions. Then, empirical estimation of transition probabilities determining a multi-state Markov chain results in spurious oscillations, which are regularized in the minimizing total variation flow solving a singular diffusion equation with a degenerating coefficient that controls extreme values of 0 and 1. Finally, the model yields the statistical moments of the dry spell length in the future and the total rainfall depth until a specified terminal day. Those statistical moments, termed hazard futures, can quantify drought risks based on the information of the dry spell length up to the current day. The newly defined hazard futures are utilized to explore measures to avert drought risks intensifying these decades, aiming to establish sustainable rainfed agriculture in the Nineveh Plains