TROPICAL DAILY RAINFALL AMOUNT MODELLING USING MARKOV CHAIN-MIXED EXPONENTIAL (MCME)

2015 ◽  
Vol 74 (11) ◽  
Author(s):  
Fadhilah Yusof ◽  
Lee Mee Yung ◽  
Zulkifli Yusop
Keyword(s):  
Markov Chain ◽  
Daily Rainfall ◽  
Predictive Ability ◽  
First Order ◽  
Rainfall Occurrence ◽  
Rainfall Process ◽  
Proposed Model ◽  
Rainfall Model ◽  
Rainfall Occurrences ◽  
Mixed Exponential Distribution

This study is concerned with the development of a stochastic rainfall model that can generate many sequences of synthetic daily rainfall series with the similar properties as those of the observed. The proposed model is Markov chain-mixed exponential (MCME). This model is based on a combination of rainfall occurrence (represented by the first-order two-state Markov chain) and the distribution of rainfall amounts on wet days (described by the mixed exponential distribution). The feasibility of the MCME model is assessed using daily rainfall data from four rainfall stations (station S02, S05, S07 and S11) in Johor, Malaysia. For all the rainfall stations, it was found that the proposed MCME model was able to describe adequately rainfall occurrences and amounts. Various statistical and physical properties of the daily rainfall processes also considered. However, the validation results show that the models’ predictive ability was not as accurate as their descriptive ability. The model was found to have fairly well ability in predicting the daily rainfall process at station S02, S05 and S07. Nonetheless, it was able to predict the daily rainfall process at station S11 accurately. 

On Stochastic Characterization of Temporal Storm Patterns

1984 ◽  
Vol 16 (8-9) ◽  
pp. 147-153 ◽  
Author(s):  
Van-Thanh-Van Nguyen
Keyword(s):  
Markov Chain ◽  
Probability Distributions ◽  
First Order ◽  
Stochastic Characterization ◽  
Order Markov Chain ◽  
Hourly Rainfall ◽  
General Stochastic Model ◽  
Storm Rainfall ◽  
Rainfall Occurrences

The present study, a continuation of a previous work by the author, suggests a new theoretical approach to the characterization of the temporal pattern of storms. A storm is defined as a continuous run of non-zero one-hour rainfall depths. A general stochastic model is developed to determine the probability distributions of cumulative storm rainfall amounts at successive time intervals after the storm began. The previous model for characterizing storm temporal patterns was based on the assumption that hourly rainfall depths were independent and identically exponentially distributed random variables, while sequences of wet hours were modeled by a first-order stationary Markov chain. Hence, the model did only introduce dependence of wet hour occurences into the rainfall process through the first-order Markov chain. The present paper proposes a more general model that can take into account both the persistence in hourly rainfall occurrences and the dependence between successive hourly rainfall depths. Results of an illustrative example show that by accounting for the correlation structure of consecutive rainfall depths the present model gives a better fit to the observations than the previous one.

scholarly journals Development and evaluation of a stochastic daily rainfall model with long-term variability

2017 ◽  
Vol 21 (12) ◽  
pp. 6541-6558 ◽  
Author(s):  
A. F. M. Kamal Chowdhury ◽  
Natalie Lockart ◽  
Garry Willgoose ◽  
George Kuczera ◽  
Anthony S. Kiem ◽  
...  
Keyword(s):  
Gamma Distribution ◽  
Transition Probabilities ◽  
Daily Rainfall ◽  
Primary Objective ◽  
Generation Model ◽  
Gamma Model ◽  
Rainfall Occurrence ◽  
Rainfall Model ◽  
Two Parameters

Abstract. The primary objective of this study is to develop a stochastic rainfall generation model that can match not only the short resolution (daily) variability but also the longer resolution (monthly to multiyear) variability of observed rainfall. This study has developed a Markov chain (MC) model, which uses a two-state MC process with two parameters (wet-to-wet and dry-to-dry transition probabilities) to simulate rainfall occurrence and a gamma distribution with two parameters (mean and standard deviation of wet day rainfall) to simulate wet day rainfall depths. Starting with the traditional MC-gamma model with deterministic parameters, this study has developed and assessed four other variants of the MC-gamma model with different parameterisations. The key finding is that if the parameters of the gamma distribution are randomly sampled each year from fitted distributions rather than fixed parameters with time, the variability of rainfall depths at both short and longer temporal resolutions can be preserved, while the variability of wet periods (i.e. number of wet days and mean length of wet spell) can be preserved by decadally varied MC parameters. This is a straightforward enhancement to the traditional simplest MC model and is both objective and parsimonious.

A stochastic description of temporal daily rainfall patterns

1984 ◽  
Vol 11 (2) ◽  
pp. 234-238 ◽  
Author(s):  
Van-Thanh-Van Nguyen
Keyword(s):  
Markov Chain ◽  
Stochastic Model ◽  
Exponential Distribution ◽  
Daily Rainfall ◽  
Stochastic Approach ◽  
Rainfall Event ◽  
Event Duration ◽  
Rainfall Occurrence ◽  
Rainfall Patterns

A stochastic approach to characterization of temporal rainfall patterns is proposed wherein a rainfall event is defined as an unbroken sequence of consecutive daily rainfalls. A stochastic model is developed to determine the probability distribution of cumulative rainfall amounts at the end of each day within a total rainfall event duration of n days. The model is structured such that the distribution of daily rainfall depths can be approximated by an exponential distribution and the rainfall occurrence process can be described by a first-order stationary Markov chain. An illustrative example was presented, using a 32-year daily rainfall record at Dorval Airport on Montreal Island. The results of this example have demonstrated the adequacy and descriptive capabilities of the model. It can be concluded that the methodology proposed here seems to be more general and more flexible than those that have been used in previous investigations. Key words: daily rainfall process, temporal rainfall pattern, stochastic model, stochastic hydrology, exponential distribution, Markov chain.

scholarly journals A Markov chain model for daily rainfall occurrences  at east Thanjavur district

MAUSAM ◽  
2022 ◽  
Vol 46 (4) ◽  
pp. 383-388
Author(s):  
M. THIYAGARAJAN ◽  
RAMA DOSS ◽  
RAMA RAJ
Keyword(s):  
Markov Chain ◽  
Poisson Process ◽  
State Estimation ◽  
Statistical Inference ◽  
Markov Chain Model ◽  
Daily Rainfall ◽  
Chain Model ◽  
New Approach ◽  
State 1 ◽  
Rainfall Occurrences

 The occurrences and non-occurrences of the rainfall can be described by a two-state Markov chain. A dry date is denoted by state 0 and wet date is denoted by state 1. We have taken the sample which follows a Poisson process with known parameter. Using this Poisson sample we have given a new approach to affect statistical inference for the law of the Markov chain and state estimation concerning un-observed past values or not yet observed future values. The paper aims at comparing the earlier fit of the data with the new approach.      

scholarly journals Development and Evaluation of a Stochastic Daily Rainfall Model with Long Term Variability

2017 ◽  
Author(s):  
A. F. M. Kamal Chowdhury ◽  
Natalie Lockart ◽  
Garry Willgoose ◽  
George Kuczera ◽  
Anthony S. Kiem ◽  
...  
Keyword(s):  
Gamma Distribution ◽  
Transition Probabilities ◽  
Daily Rainfall ◽  
Primary Objective ◽  
Generation Model ◽  
Gamma Model ◽  
Rainfall Occurrence ◽  
Rainfall Model ◽  
Two Parameters

Abstract. The primary objective of this study is to develop a stochastic rainfall generation model that can match not only the short resolution (daily) variability, but also the longer resolution (monthly to multiyear) variability of observed rainfall. This study has developed a Markov Chain (MC) model, which uses a two-state MC process with two parameters (wet-to-wet and dry-to-dry transition probabilities) to simulate rainfall occurrence and a Gamma distribution with two parameters (mean and standard deviation of wet day rainfall) to simulate wet day rainfall depths. Starting with the traditional MC-Gamma model with deterministic parameters, this study has developed and assessed four other variants of the MC-Gamma model with different parameterisations. The key finding is that if the parameters of the Gamma distribution are randomly sampled from fitted distributions prior to simulating the rainfall for each year, the variability of rainfall depths at longer resolutions can be preserved, while the variability of wet periods (i.e. number of wet days and mean length of wet spell) can be preserved by decade-varied MC parameters. This is a straightforward enhancement to the traditional simplest MC model and is both objective and parsimonious.

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