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 Nonparametric Stochastic Approach for Disaggregation of Daily to Hourly Rainfall Using 3-Day Rainfall Patterns

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2306
Author(s):  
Heeseong Park ◽  
Gunhui Chung
Keyword(s):  
Time Series Data ◽  
Daily Rainfall ◽  
Rainfall Event ◽  
Rainfall Data ◽  
Series Data ◽  
K Nearest Neighbor ◽  
Urban Catchment ◽  
Urban Flood ◽  
Hourly Rainfall ◽  
Rainfall Patterns

As infrastructure and populations are highly condensed in megacities, urban flood management has become a significant issue because of the potentially severe loss of lives and properties. In the megacities, rainfall from the catchment must be discharged throughout the stormwater pipe networks of which the travel time is less than one hour because of the high impervious rate. For a more accurate calculation of runoff from the urban catchment, hourly or even sub-hourly (minute) rainfall data must be applied. However, the available data often fail to meet the hydrologic system requirements. Many studies have been conducted to disaggregate time-series data while preserving distributional statistics from observed data. The K-nearest neighbor resampling (KNNR) method is a useful application of the nonparametric disaggregation technique. However, it is not easy to apply in the disaggregation of daily rainfall data into hourly while preserving statistical properties and boundary continuity. Therefore, in this study, three-day rainfall patterns were proposed to improve reproducible ability of statistics. Disaggregated rainfall was resampled only from a group having the same three-day rainfall patterns. To show the applicability of the proposed disaggregation method, probability distribution and L-moment statistics were compared. The proposed KNNR method with three-day rainfall patterns reproduced better the characteristics of rainfall event such as event duration, inter-event time, and toral amount of rainfall event. To calculate runoff from urban catchment, rainfall event is more important than hourly rainfall depth itself. Therefore, the proposed stochastic disaggregation method is useful to hydrologic analysis, particularly in rainfall disaggregation.

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. 

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

Characterization of HIV infection and seroconversion by a stochastic model of the HIV epidemic

1995 ◽  
Vol 126 (1) ◽  
pp. 81-123 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Sho Rong Lee ◽  
Si Chin Tang
Keyword(s):  
Hiv Infection ◽  
Stochastic Model ◽  
Hiv Epidemic

Strong ergodicity for continuous-time, non-homogeneous Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 692-694 ◽  
Author(s):  
Mark Scott ◽  
Barry C. Arnold ◽  
Dean L. Isaacson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Homogeneous Markov Chain ◽  
Strong Ergodicity

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

A Characterization of the Exponential Distribution

1994 ◽  
Vol 44 (1-2) ◽  
pp. 123-126
Author(s):  
E. S. Jebvanand ◽  
N. Unnikrishnan Nair
Keyword(s):  
Exponential Distribution ◽  
Prior Distribution ◽  
Future Observation ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Continuous Population

In this note we prove that the exponential distribution is characterized by the property [Formula: see text] where Y is a future observation and x1, x2,…, x n are identical and independently distributed observations from a continuous population with density f( x; a), where a is assumed to have a non-informative prior distribution

Sign in / Sign up

Export Citation Format

Share Document