A stochastic model of runoff‐producing rainfall for summer type storms

Duckstein, Lucien; Fogel, Martin M.; Kisiel, Chester C.

doi:10.1029/wr008i002p00410

Cited by 43 publications

(15 citation statements)

References 6 publications

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“…Gaiha et al (2010) used negative binomial regression to assess the likely count of natural disasters in various countries. Duckstein et al (1972) showed that the distribution for mean areal rainfall in arid climates could be described by a negative binomial probability mass function (pmf). Czamara et al (1997) used negative binomial (Pascal) distribution to analyse number of droughts in time interval (0, r) along with chisquare tests of goodness of fit at the 0.05 level.…”

Section: Methodsmentioning

confidence: 99%

Analysing the Variability of Rainfall for Drought Progonosis in Jharkhand State: A Statistical Approach

Pandey

Kumar

Chakraborty

et al. 2011

Irrigation and Drainage

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Agriculture in the state of Jharkhand depends on the southwest monsoon which brings about 80% of the mean annual precipitation. The high variability in rainfall generally leads to meteorological drought conditions, demanding a large time domain analysis of rainfall behaviour. In the present paper, daily rainfall data for 49 years of Ranchi District, Jharkhand state of India, were analyzed for the probability and variability of rainfall. The monsoon weeks, i.e. the 21st to the 41st, were considered and it was found that the rainfall distribution can be modeled by a negative binomial distribution. Additionally, by denoting a wet week by W and a dry week by D, the unconditional probability P(W) and the conditional probabilities P(W/W) and P(W/D) for these weeks were evaluated using a first-order Markov chain at three probability levels (30, 50 and 70 mm). The results were checked against a uniform model with the help of the Kolmogorov-Smirnov test and it was found that in most cases they supported the uniform distribution assumption. Lower probability (less than 0.50) of getting 70 mm of rainfall under any probability conditions during the 27th to 38th weeks indicated the proneness of the region to drought during the crop growth and maturity stage under condition of initial rainfall failure during the crop sowing stage. RÉSUMÉ L'agriculture dans l'État de Jharkhand dépend de la mousson de sud-ouest qui apporte environ 80% de la moyenne des précipitations annuelles. La forte variabilité des précipitations conduit généralement à des conditions de sécheresse météorologique, dont l'analyse du comportement exige une analyse de longues périodes d'observation.. Dans le présent document, les précipitations journalières pour les 49 années du district de Ranchi, dans l'état de Jharkhand en Inde ont été analysées pour caractériser les probabilités et la variabilité des précipitations. Seules les précipitations de mousson ont été retenues, soit de la 21 ème à la 41 ème semaine, et il a été constaté que la répartition de la pluie pouvait être modélisée par une loi binomiale négative. En outre, en désignant une semaine humide par W et une semaine à sec par D, la probabilité inconditionnelle P (W) et les probabilités conditionnelles P (W / W) et P (W / D) pour ces semaines ont été évaluées à l'aide d'une chaine de Markov à trois niveaux de probabilité (30, 50 et 70 mm). Les résultats ont été vérifiés par rapport à un modèle uniforme à l'aide du test de Kolmogorov-Smirnov et il a été constaté que, dans la plupart des cas ils ont appuyé l'hypothèse de distribution uniforme. La probabilité faible (moins de 0,50) d'obtenir 70 mm de pluie sous toutes conditions de probabilité pendant les semaines 27 à 38 indique la prédisposition de la région à la sécheresse au cours des stades croissance et de maturation des cultures quand la région a déjà connu un défaut de précipitations au moment du semis des cultures.

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Section: Methodsmentioning

confidence: 99%

Analysing the Variability of Rainfall for Drought Progonosis in Jharkhand State: A Statistical Approach

Pandey

Kumar

Chakraborty

et al. 2011

Irrigation and Drainage

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show abstract

“…Outside hydrology there have as yet been only few applications of this socalled 'Box-Jenkins' approach to pure time series; notable exceptions are the work by Bennett et al (1976) modelling atmospheric pollution at Kew, an analysis of soil tension by Lai (1976) and of sediment yield by Duckstein et al (1976). Rather more work has been carried out using the same approach but analysing distance series in which time is replaced by distance along some natural transect such as down a river or downslope.…”

Section: Markov Processesmentioning

confidence: 98%

Statistical methods in physical geography

Unwin

1977

Progress in Physical Geography: Earth and Environment

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This essay presents a state of the art review of statistical applications in physical geography. Initially, methods drawn from traditional statistics based upon classical probability theory are described and evaluated. It is argued that explicitly, or, more usually, implicitly such methods assume independence of the observations in both space and time making it incumbent upon statistical physical geography to reject what one authority has called its former 'timebound preoccupation' (Chorley, 1962, 6) in favour of time-less 'equilibrium' morphological systems analysis. Next, I go on to examine the development and potential of models based upon the theory of stochastic processes as it relates to the evolution of systems in space and time in which observations are not assumed to be independent of each other. It is suggested that many problems are better cast in this, or a mixed stochastic/deterministic framework which will allow the time dimension to be reincorporated into physical geography..In a review of this kind, traditional subdivisions of physical geography do not form an adequate organizational framework and are becoming increasingly irrelevant to what physical geographers actually do. Instead, statistical concepts and techniques will be discussed according to the method of systems analysis to which they are most suited. According to Chorley and Kennedy ( t g7 i ), four levels of systems analysis are possible. Morphological systems deal with networks of structural relationships between parts of systems; these have been analysed by classical statistical methods. Cascading systems are defined by the paths followed by throughputs of energy and mass, and like process-response systems in which these cascade flows are linked to morphological transformations, can be analysed using stochastic process theory. Finally, physical geographers are also interested in control systems resulting from the interaction of human decision-making and physical process-response for which statistical decision theory provides a useful analytic framework but which will not be considered in the present work. Although this classification was designed for geomorphological work, a similar scheme for climatological studies has been proposed and exemplified by Terjung (1976). I The analysis of morphological systems At this level of analysis, statistical methods are used to investigate the

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“…Exponential, gamma, Weibull and lognormal probability distributions have been applied. Duckstein et al (1972) fitted the exponential distribution. Mills (1981) modelled total amount with the lognormal distribution, observing the mean to be a function of duration and the variance to be independent.…”

Section: Modelling Rainfall Amounts On Wet Daysmentioning

confidence: 99%

A stochastic model of low flows

Lawal

Watt

Watts

1997

Stochastic Hydrol Hydraul

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Abstract:A model is developed for annual low flow hydrographs. Its two primary components reflect the fact that hydrologic processes during streamflow rise (function of water input) and recession (function of basin storage) are different. Durations of periods of rise (wet intervals) and recession (dry intervals) are modelled by discrete probability distributions -negative binomial for dry intervals and negative binomial or modified logarithmic series for wet intervals depending on goodness of fit. During wet intervals, the total inflow is modelled by the lognormal distribution and daily amounts are allocated according to a pattern-averaged model. During dry intervals, the flow recedes according to a deterministie-stocha~stic recession model.The model was applied to three Canadian basins with drainage area ranging from 2210 to 22000 km 2 to generate 50 realizations of low flow hydrographs. The resulting two standard-error confidence band for the simulated probability distribution of annual minimum 7-day flows enclosed the probability distribution estimated from the observed record. A sensitivity analysis for the three basins revealed that in addition to the recession submodel, the most important submodel is that describing seasonality. The state of the basin at the beginning of the low flow period is of marginal importance and the daily distribution of input is unimportant.

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A stochastic model of runoff‐producing rainfall for summer type storms

Cited by 43 publications

References 6 publications

Analysing the Variability of Rainfall for Drought Progonosis in Jharkhand State: A Statistical Approach

Analysing the Variability of Rainfall for Drought Progonosis in Jharkhand State: A Statistical Approach

Statistical methods in physical geography

A stochastic model of low flows

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