The optimum order of a Markov chain model for daily rainfall in Nigeria

Jimoh, O. D.; Webster, Peter J.

doi:10.1016/s0022-1694(96)03015-6

Cited by 53 publications

(35 citation statements)

References 14 publications

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“…However, Hurvich and Tsai (1989) provided a correction for AIC for model selection in small samples and the corrected AIC does not over fit the models as the AIC tends to do. Jimoh and Webster (1996) determined the optimum order of a Markov chain model for daily rainfall occurrences at five locations in Nigeria using AIC and BIC. The AIC consistently gave a higher order for the Markov chain than the BIC.…”

Section: Markov Chainsmentioning

confidence: 99%

Stochastic generation of annual, monthly and daily climate data: A review

Srikanthan

McMahon²

2001

Hydrol. Earth Syst. Sci.

293

175

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The generation of rainfall and other climate data needs a range of models depending on the time and spatial scales involved. Most of the models used previously do not take into account year to year variations in the model parameters. Long periods of wet and dry years were observed in the past but were not taken into account. Recently, Thyer and Kuczera (1999) developed a hidden state Markov model to account for the wet and dry spells explicitly in annual rainfall. This review looks firstly at traditional time series models and then at the more complex models which take account of the pseudo-cycles in the data. Monthly rainfall data have been generated successfully by using the method of fragments. The main criticism of this approach is the repetitions of the same yearly pattern when only a limited number of years of historical data are available. This deficiency has been overcome by using synthetic fragments but this brings an additional problem of generating the right number of months with zero rainfall. Disaggregation schemes are effective in obtaining monthly data but the main problem is the large number of parameters to be estimated when dealing with many sites. Several simplifications have been proposed to overcome this problem. Models for generating daily rainfall are well developed. The transition probability matrix method preserves most of the characteristics of daily, monthly and annual characteristics and is shown to be the best performing model. The two-part model has been shown by many researchers to perform well across a range of climates at the daily level but has not been tested adequately at monthly or annual levels. A shortcoming of the existing models is the consistent underestimation of the variances of the simulated monthly and annual totals. As an alternative, conditioning model parameters on monthly amounts or perturbing the model parameters with the Southern Oscillation Index (SOI) result in better agreement between the variance of the simulated and observed annual rainfall and these approaches should be investigated further. As climate data are less variable than rainfall, but are correlated among themselves and with rainfall, multisite-type models have been used successfully to generate annual data. The monthly climate data can be obtained by disaggregating these annual data. On a daily time step at a site, climate data have been generated using a multisite type model conditional on the state of the present and previous days. The generation of daily climate data at a number of sites remains a challenging problem. If daily rainfall can be modelled successfully by a censored power of normal distribution then the model can be extended easily to generate daily climate data at several sites simultaneously. Most of the early work on the impacts of climate change used historical data adjusted for the climate change. In recent studies, stochastic daily weather generation models are used to compute climate data by adjusting the parameters appropriately for the future climates assumed.

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Section: Markov Chainsmentioning

confidence: 99%

Stochastic generation of annual, monthly and daily climate data: A review

Srikanthan

McMahon²

2001

Hydrol. Earth Syst. Sci.

293

175

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“…Instead of adjusting daily rainfall to match the mean monthly precipitation, we perform the bias adjustment on a set of (pseudo) stationary stochastic parameters that describe the rainfall process in terms of frequency, intensity, and the autocorrelation of wet and dry periods [16][17][18]. This approach addresses the key limitations of time series based bias adjustment:…”

Section: Introductionmentioning

confidence: 99%

Bias adjustment of satellite rainfall data through stochastic modeling: Methods development and application to Nepal

Müller

Thompson

2013

Advances in Water Resources

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a b s t r a c tEstimating precipitation over large spatial areas remains a challenging problem for hydrologists. Sparse ground-based gauge networks do not provide a robust basis for interpolation, and the reliability of remote sensing products, although improving, is still imperfect. Current techniques to estimate precipitation rely on combining these different kinds of measurements to correct the bias in the satellite observations. We propose a novel procedure that, unlike existing techniques, (i) allows correcting the possibly confounding effects of different sources of errors in satellite estimates, (ii) explicitly accounts for the spatial heterogeneity of the biases and (iii) allows the use of non overlapping historical observations. The proposed method spatially aggregates and interpolates gauge data at the satellite grid resolution by focusing on parameters that describe the frequency and intensity of the rainfall observed at the gauges. The resulting gridded parameters can then be used to adjust the probability density function of satellite rainfall observations at each grid cell, accounting for spatial heterogeneity. Unlike alternate methods, we explicitly adjust biases on rainfall frequency in addition to its intensity. Adjusted rainfall distributions can then readily be applied as input in stochastic rainfall generators or frequency domain hydrological models. Finally, we also provide a procedure to use them to correct remotely sensed rainfall time series.We apply the method to adjust the distributions of daily rainfall observed by the TRMM satellite in Nepal, which exemplifies the challenges associated with a sparse gauge network and large biases due to complex topography. In a cross-validation analysis on daily rainfall from TRMM 3B42 v6, we find that using a small subset of the available gauges, the proposed method outperforms local rainfall estimations using the complete network of available gauges to directly interpolate local rainfall or correct TRMM by adjusting monthly means. We conclude that the proposed frequency-domain bias correction approach is robust and reliable compared to other bias correction approaches.

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“…If the chain has converged at time n 0 , then the two means θ A and θ B should be equal and Geweke's statistic has an asymptotically standard normal distribution as Equation (12).…”

Section: Geweke's Diagnosticmentioning

confidence: 99%

Applicability of Zero-Inflated Models to Fit the Torrential Rainfall Count Data with Extra Zeros in South Korea

Lee¹,

Kim²

2017

Water

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Several natural disasters occur because of torrential rainfalls. The change in global climate most likely increases the occurrences of such downpours. Hence, it is necessary to investigate the characteristics of the torrential rainfall events in order to introduce effective measures for mitigating disasters such as urban floods and landslides. However, one of the major problems is evaluating the number of torrential rainfall events from a statistical viewpoint. If the number of torrential rainfall occurrences during a month is considered as count data, their frequency distribution could be identified using a probability distribution. Generally, the number of torrential rainfall occurrences has been analyzed using the Poisson distribution (POI) or the Generalized Poisson Distribution (GPD). However, it was reported that POI and GPD often overestimated or underestimated the observed count data when additional or fewer zeros were included. Hence, in this study, a zero-inflated model concept was applied to solve this problem existing in the conventional models. Zero-Inflated Poisson (ZIP) model, Zero-Inflated Generalized Poisson (ZIGP) model, and the Bayesian ZIGP model have often been applied to fit the count data having additional or fewer zeros. However, the applications of these models in water resource management have been very limited despite their efficiency and accuracy. The five models, namely, POI, GPD, ZIP, ZIGP, and Bayesian ZIGP, were applied to the torrential rainfall data having additional zeros obtained from two rain gauges in South Korea, and their applicability was examined in this study. In particular, the informative prior distributions evaluated via the empirical Bayes method using ten rain gauges were developed in the Bayesian ZIGP model. Finally, it was suggested to avoid using the POI and GPD models to fit the frequency of torrential rainfall data. In addition, it was concluded that the Bayesian ZIGP model used in this study provided the most accurate results for the count data having additional zeros. Moreover, it was recommended that the ZIP model could be an alternative from a practical viewpoint, as the Bayesian approach used in this study was considerably complex.

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The optimum order of a Markov chain model for daily rainfall in Nigeria

Cited by 53 publications

References 14 publications

Stochastic generation of annual, monthly and daily climate data: A review

Stochastic generation of annual, monthly and daily climate data: A review

Bias adjustment of satellite rainfall data through stochastic modeling: Methods development and application to Nepal

Applicability of Zero-Inflated Models to Fit the Torrential Rainfall Count Data with Extra Zeros in South Korea

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