A multi-state Markov chain model for rainfall to be used in optimal operation of rainwater harvesting systems

Nop, Channpisey; Fadhil, Rasha M.; Unami, Koichi

doi:10.1016/j.jclepro.2020.124912

Cited by 12 publications

(7 citation statements)

References 37 publications

(39 reference statements)

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“…The authors of paper [18] present a survey of financial applications under a specific semimartingale result of Markov chains and two of the described strategies apply DP approach. Besides, other recent studies apply DP in the field of genomics and bioinformatics [15], for developing modern rainwater harvesting systems [17], for optimizing the synchronization and reducing gear-shifting time in mechanical transmissions [13], and even for solving the School Bus Routing Problem [19].…”

Section: Literature Reviewmentioning

confidence: 99%

DP-solver: automating dynamic programming

Kátai

Elekes

2021

Acta Universitatis Sapientiae, Informatica

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Dynamic programming (DP) is a widely used optimization method with several applications in various fields of science. The DP problem solving process can be divided in two phases: mathematical part and programming part. There are a number of researchers for whom the mathematical part is available, but they are not familiar with computer programming. In this paper we present a software tool that automates the programming part of DP and allows users to solve problems based only on their mathematical approach. The application builds up the “d-graph model” of the problem to be solved and applies the “d-variant” of the corresponding single source shortest path algorithm. In addition, we report experimental results regarding the e ciency of the tool relative to the Matlab implementation.

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Section: Literature Reviewmentioning

confidence: 99%

DP-solver: automating dynamic programming

Kátai

Elekes

2021

Acta Universitatis Sapientiae, Informatica

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“…Stochastic dynamic programming (SDP) theory is the general framework to establish reservoir operation policies, as explored decades ago (Heidari et al 1971;Tejada-Guibert et al 1993, 1995Yakowitz 1982). The SDP typically provides optimal operation policies with thresholds of opening valves or switching pumps (Nop et al 2021;Unami, Mohawesh 2018;Unami et al 2019b). However, reservoir operators generally do not accept such theoretically generated policies but instead rely on their empirical knowledge to make decisions when unexpected risks are involved (El-Shafie et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Identification of nominal release policies implemented in a multi-purpose water reservoir

Fadhil¹,

Unami²,

Rowshon³

et al. 2022

Meteorol. Hydrol. Water Manage.

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A water reservoir's operation should follow a rational policy to ensure adequate water provision for different purposes without adverse effects. However, it is not well-studied how to identify operational policies currently being implemented. This study establishes a new approach to identifying nominal release policies as implemented in a multi-purpose water reservoir. We chose Bukit Merah Reservoir (BMR), located in Perak State, Malaysia, as a study site to examine its release policies for meeting irrigation, municipal, and industrial water demands and for mitigating floods and environmental hazards. The operator of BMR releases the reservoir's water into two primary irrigation canals, the Main Canal and the Selinsing Canal. Generalized additive models (GAMs) are applied to time series data observed at BMR to identify the annual dynamics of its water management. Operational policies for the release discharges into the two primary irrigation canals are assumed to be based on information on the time-of-year and the reservoir water level. First, a backfitting algorithm identifies each contributing function of the GAMs representing the release policies. Then, spurious oscillations in the functions are removed by total variation (TV) regularization (TVR) to obtain nominal release policies, which are quite reasonable in the sense of conventional reservoir management practice. Finally, the identified nominal release policies are utilized to examine shifts in the operation of BMR during the period from 2000 through 2011. The decomposition of release policies illustrates the two aspects of the irrigation demand's annual patterns and the hydraulic structures' functions. The spurious oscillations removed by TVR are considered to represent indecision by the reservoir operator.

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“…Coupling a fitted gamma distribution of positive rainfall depths to the first-order Markov chain with the multiple states of DSL results in a multi-state Markov chain model, which can be applied to drought risk assessment. This multi-state Markov chain model is essentially different from any of the earlier models by the authors, including Sharifi et al (2016), Unami and Mohawesh (2018), and Nop et al (2021). Sharifi et al (2016) used a time-continuous Markov process with the continuous states of soil moisture.…”

Section: Introductionmentioning

confidence: 99%

“…Unami and Mohawesh (2018) developed a time-continuous Markov process with the continuous states of a water flow index. Nop et al (2021) considered a multi-state Markov chain with the states of discretized rainfall depth ranges. The overwhelming advantages of this multi-state Markov chain model are the first-order Markovian properties and the ability to capture the memory effect of sequential dry days.…”

Section: Introductionmentioning

confidence: 99%

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

Fadhil

Unami

2021

Stoch Environ Res Risk Assess

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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

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A multi-state Markov chain model for rainfall to be used in optimal operation of rainwater harvesting systems

Cited by 12 publications

References 37 publications

DP-solver: automating dynamic programming

DP-solver: automating dynamic programming

Identification of nominal release policies implemented in a multi-purpose water reservoir

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

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