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Статті в журналах з теми "Multivariate rainfall analysis"
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Nam, Woo-Sung, Tae-Soon Kim, Ju-Young Shin, and Jun-Haeng Heo. "Regional Rainfall Frequency Analysis by Multivariate Techniques." Journal of Korea Water Resources Association 41, no. 5 (May 25, 2008): 517–25. http://dx.doi.org/10.3741/jkwra.2008.41.5.517.
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Liu, Chenglin, Yuwen Zhou, Jun Sui, and Chuanhao Wu. "Multivariate frequency analysis of urban rainfall characteristics using three-dimensional copulas." Water Science and Technology 2017, no. 1 (March 7, 2018): 206–18. http://dx.doi.org/10.2166/wst.2018.103.
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Abstract Urban runoff is a major cause of urban flooding and is difficult to monitor in the long term. In contrast, long term continuous rainfall data are generally available for any given region. As a result, it has become customary to use design rainfall depth as a proxy for runoff in urban hydrological analyses, with an assumption of the same frequency for runoff and rainfall. However, this approach has lack of overall coordination and cannot fully reflect the variability of rainfall characteristics. To address this issue, this study presents a three-dimensional copula-based multivariate frequency analysis of rainfall characteristics based on a long term (1961–2012) rainfall data from Guangzhou, China. Firstly, continuous rainfall data were divided into individual rainfall events using the rainfall intensity method. Then the characteristic variables of rainfall (design rainfall depth, DRD; total rainfall depth, TRD; peak rainfall depth, PRD) were sampled using the annual maximum method. Finally, a copula method was used to develop the multivariate joint probability distribution and the conditional probability distribution of rainfall characteristics. The results showed that the copula-based method is easy to implement and can better reflect urban rainstorm characteristics. It can serve a scientific reference for urban flood control and drainage planning.
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Fontanazza, C. M., G. Freni, G. La Loggia, and V. Notaro. "Uncertainty evaluation of design rainfall for urban flood risk analysis." Water Science and Technology 63, no. 11 (June 1, 2011): 2641–50. http://dx.doi.org/10.2166/wst.2011.169.
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A reliable and long dataset describing urban flood locations, volumes and depths would be an ideal prerequisite for assessing flood frequency distributions. However, data are often piecemeal and long-term hydraulic modelling is often adopted to estimate floods from historical rainfall series. Long-term modelling approaches are time- and resource-consuming, and synthetically designed rainfalls are often used to estimate flood frequencies. The present paper aims to assess the uncertainty of such an approach and for suggesting improvements in the definition of synthetic rainfall data for flooding frequency analysis. According to this aim, a multivariate statistical analysis based on a copula method was applied to rainfall features (total depth, duration and maximum intensity) to generate synthetic rainfalls that are more consistent with historical events. The procedure was applied to a real case study, and the results were compared with those obtained by simulating other typical synthetic rainfall events linked to intensity–duration–frequency (IDF) curves. The copula-based multi-variate analysis is more robust and adapts well to experimental flood locations even if it is more complex and time-consuming. This study demonstrates that statistical correlations amongst rainfall frequency, duration, volume and peak intensity can partially explain the weak reliability of flood-frequency analyses based on synthetic rainfall events.
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Mrad, D., S. Dairi, S. Boukhari, and Y. Djebbar. "Applied multivariate analysis on annual rainfall in the northeast of Algeria." Journal of Water and Climate Change 11, no. 4 (May 15, 2019): 1165–76. http://dx.doi.org/10.2166/wcc.2019.272.
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Abstract In recent times, there has been a growing interest in understanding precipitation variability and its predictability for periods of a few months to several years. Our work consisted of studying climatic changes in the northeastern region of Algeria based on multivariate analysis of the annual rainfall. Variability of annual rainfall was analyzed using principal component analysis (PCA) and non-hierarchical classification (cluster method). For spatial rainfall variability, due to the complexity of the region, we used the method inverse distance weighted cartography modeling. Results indicate PCA represented the accumulated yearly rainfall of correlated fields on an annual scale, only the years 1971, 1985, 1995, and 2002 had a rather high degree of correlation, translating the homogeneity of annual distribution of precipitation. Cluster method demonstrated the certainty of three groups. The first group was characterized by regions of distinguishable climatic types, such as Mediterranean climate. The second group was characterized by the Tellian Atlas, while the third group was characterized by high plateaus. Spatial analysis of average decade rainfall shows that the isohyet curves of 750 mm in the center of the study region are shifting to the south, and that the Mediterranean regime rainfall affects all the northern region.
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Jiang, Xinyu, Lijiao Yang, and Hirokazu Tatano. "Assessing Spatial Flood Risk from Multiple Flood Sources in a Small River Basin: A Method Based on Multivariate Design Rainfall." Water 11, no. 5 (May 17, 2019): 1031. http://dx.doi.org/10.3390/w11051031.
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A key issue in assessing the spatial distribution of flood risk is considering risk information derived from multiple flood sources (river flooding, drainage inundation, etc.) that may affect the risk assessment area. This study proposes a method for assessing spatial flood risk that includes flooding and inundation in small-basin areas through multivariate design rainfall. The concept of critical rainfall duration, determined by the time of concentration of flooding, is used to represent the characteristics of flooding from different sources. A copula method is adopted to capture the correlation of rainfall amounts in different critical rainfall durations to reflect the correlation of potential flooding from multiple flood sources. Rainfalls for different return periods are designed based on the copula multivariate analysis. Using the design rainfalls as input, flood risk is assessed following the rainfall–runoff–inundation–loss estimation procedure. A case study of the Otsu River Basin, Osaka Prefecture, Japan, was conducted to demonstrate the feasibility and advantages of this method. Compared to conventional rainfall design, this method considers the response characteristics of multiple flood sources, and solves the problem of flood risk assessment from multiple flood sources. It can be applied to generate a precise flood risk assessment to support integrated flood risk management.
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Gaitan, S., and J. A. E. ten Veldhuis. "Opportunities for multivariate analysis of open spatial datasets to characterize urban flooding risks." Proceedings of the International Association of Hydrological Sciences 370 (June 11, 2015): 9–14. http://dx.doi.org/10.5194/piahs-370-9-2015.
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Abstract. Cities worldwide are challenged by increasing urban flood risks. Precise and realistic measures are required to reduce flooding impacts. However, currently implemented sewer and topographic models do not provide realistic predictions of local flooding occurrence during heavy rain events. Assessing other factors such as spatially distributed rainfall, socioeconomic characteristics, and social sensing, may help to explain probability and impacts of urban flooding. Several spatial datasets have been recently made available in the Netherlands, including rainfall-related incident reports made by citizens, spatially distributed rain depths, semidistributed socioeconomic information, and buildings age. Inspecting the potential of this data to explain the occurrence of rainfall related incidents has not been done yet. Multivariate analysis tools for describing communities and environmental patterns have been previously developed and used in the field of study of ecology. The objective of this paper is to outline opportunities for these tools to explore urban flooding risks patterns in the mentioned datasets. To that end, a cluster analysis is performed. Results indicate that incidence of rainfall-related impacts is higher in areas characterized by older infrastructure and higher population density.
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Araújo, Winicius Santos, Francisco Assis Saviano Souza, José Ivaldo Barbosa de Brito, and Lourivaldo Mota Lima. "Estudo Pluvial no Nordeste do Brasil Utilizando Análise Multivariada (Rain Study in Northeast Brazil Using Multivariate Analysis)." Revista Brasileira de Geografia Física 5, no. 3 (November 5, 2012): 448. http://dx.doi.org/10.26848/rbgf.v5i3.232781.
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O objetivo deste trabalho foi estudar a dinâmica de variabilidade climática espacial e temporal da pluviosidade nos nove estados do Nordeste Brasileiro, utilizando as técnicas multivariadas de Análise de Componentes Principais (ACP) e Análise de Agrupamento (AA). Foram utilizadas médias mensais da precipitação pluvial e de mais 11 índices climáticos pluviais definidos pela OMM (Organização Meteorológica Mundial) obtidas a partir de dados diários de 258 estações meteorológicas e/ou postos pluviométricos, fornecidos pela antiga rede de postos da SUDENE/DCA, referentes a um período de 47 anos (1960-2006). Com base nesses dados, foram aplicadas as técnicas de ACP e AA à média pluvial e aos 11 índices pluviais. Na ACP, nove índices climáticos e a média pluvial foram representados por três componentes principais e estas explicaram mais de 90% da variância original dos dados. Na AA, nove índices apresentaram quatro grupos homogêneos de atuação. Palavras - chave: Componentes principais, agrupamento, índices pluviais. Rain Study in Northeast Brazil Using Multivariate Analysis ABSTRACTThe aim of this work was to study the dynamics of spatial and temporal climatic variability in rainfall in the nine states of Northeast Brazil, using the multivariate techniques of Principal Component Analysis (PCA) and Cluster Analysis (CA). We used monthly averages of rainfall and 11 climate indices over rain defined by WMO (World Meteorological Organization) obtained from daily data from 258 meteorological stations and/or climatic stations, supplied by the former service station network SUDENE/DCA, referring a period of 47 years (1960-2006). Based on these data, we applied the techniques the average PCA and CA rain and 11 rain indices. In ACP, nine climate indices and average rainfall were represented by three principal components and these accounted for more than 90% of the variance of the original data. In AA, nine indices showed four homogeneous groups of activity.Keywords: Principal components; cluster; rain indices.
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Nam, Woosung, Hongjoon Shin, Younghun Jung, Kyungwon Joo, and Jun-Haeng Heo. "Delineation of the climatic rainfall regions of South Korea based on a multivariate analysis and regional rainfall frequency analyses." International Journal of Climatology 35, no. 5 (October 28, 2014): 777–93. http://dx.doi.org/10.1002/joc.4182.
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Elesbon, Abrahão A. A., Demetrius D. da Silva, Gilberto C. Sediyama, Hugo A. S. Guedes, Carlos A. A. S. Ribeiro, and Celso B. de M. Ribeiro. "Multivariate statistical analysis to support the minimum streamflow regionalization." Engenharia Agrícola 35, no. 5 (October 2015): 838–51. http://dx.doi.org/10.1590/1809-4430-eng.agric.v35n5p838-851/2015.
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ABSTRACT This study aimed to develop a methodology based on multivariate statistical analysis of principal components and cluster analysis, in order to identify the most representative variables in studies of minimum streamflow regionalization, and to optimize the identification of the hydrologically homogeneous regions for the Doce river basin. Ten variables were used, referring to the river basin climatic and morphometric characteristics. These variables were individualized for each of the 61 gauging stations. Three dependent variables that are indicative of minimum streamflow (Q7,10, Q90 and Q95). And seven independent variables that concern to climatic and morphometric characteristics of the basin (total annual rainfall – Pa; total semiannual rainfall of the dry and of the rainy season – Pss and Psc; watershed drainage area – Ad; length of the main river – Lp; total length of the rivers – Lt; and average watershed slope – SL). The results of the principal component analysis pointed out that the variable SL was the least representative for the study, and so it was discarded. The most representative independent variables were Ad and Psc. The best divisions of hydrologically homogeneous regions for the three studied flow characteristics were obtained using the Mahalanobis similarity matrix and the complete linkage clustering method. The cluster analysis enabled the identification of four hydrologically homogeneous regions in the Doce river basin.
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Thayakaran, R., and N. I. Ramesh. "Multivariate models for rainfall based on Markov modulated Poisson processes." Hydrology Research 44, no. 4 (January 2, 2013): 631–43. http://dx.doi.org/10.2166/nh.2013.180.
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Point process models for rainfall are constructed generally based on Poisson cluster processes. Most commonly used point process models in the literature were constructed either based on Bartlett–Lewis or Neyman–Scott cluster processes. In this paper, we utilize a class of Cox process models, termed the Markov modulated Poisson process (MMPP), to model rainfall intensity. We use this class of models to analyse rainfall data observed in the form of tip time series from rain gauge tipping buckets in a network of gauges in Somerset, southwest England, recorded by the Hydrological Radar Experiment (HYREX). Univariate and multivariate models are employed to analyse the data recorded at single and multiple sites in the catchment area. As the structure of this proposed class of MMPP models allows us to construct the likelihood function of the observed tip time series, we utilize the maximum likelihood methods in our analysis to make inferences about the rainfall intensity at sub-hourly time scales. The multivariate models are used to analyse rainfall time series jointly at four stations in the region. Properties of the cumulative rainfall in discrete time intervals are studied, and the results of fitting three-state models are presented.
Дисертації з теми "Multivariate rainfall analysis"
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Martinengo, Marta. "Improving some non-structural risk mitigation strategies in mountain regions: debris-flow rainfall thresholds, multi-hazard flooding scenarios and public awareness." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/353702.
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Hydrogeological hazards are quite diffuse rainfall-induced phenomena that affect mountain regions and can severely impact these territories, producing damages and sometimes casualties. For this reason, hydrogeological risk reduction is crucial. Mitigation strategies aim to reduce hydrogeological risk to an acceptable level and can be classified into structural and non-structural measures. This work focuses on enhancing some non-structural risk mitigation measures for mountain areas: debris-flow rainfall thresholds, as a part of an Early Warning System (EWS), multivariate rainfall scenarios with multi-hazard mapping purpose and public awareness. Regarding debris-flow rainfall thresholds, an innovative calibration method, a suitable uncertainty analysis and a proper validation process are developed. The Backward Dynamical Approach (BDA), a physical-based calibration method, is introduced and a threshold is obtained for a study area. The BDA robustness is then tested by assessing the uncertainty in the threshold estimate. Finally, the calibrated threshold's reliability and its possible forecast use are assessed using a proper validation process. The findings set the stage for using the BDA approach to calibrate debris-flow rainfall thresholds usable in operational EWS. Regarding hazard mapping, a multivariate statistical model is developed to construct multivariate rainfall scenarios with a multi-hazards mapping purpose. A confluence between a debris-flow-prone creek and a flood-prone river is considered. The multivariate statistical model is built by combining the Simplified Metastatistical Extreme Value approach and a copula approach. The obtained rainfall scenarios are promising to be used to build multi-hazard maps. Finally, the public awareness within the LIFE FRANCA (Flood Risk ANticipation and Communication in the Alps) European project is briefly considered. The project action considered in this work focuses on training and communication activities aimed at providing a multidisciplinary view of hydrogeological risk through the holding of courses and seminars.
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Mahbub, S. M. Parvez Bin. "Impact of urban traffic and climate change on water quality from road runoff." Thesis, Queensland University of Technology, 2011. https://eprints.qut.edu.au/47139/1/Parvez_Mahbub_Thesis.pdf.
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Urban traffic and climate change are two phenomena that have the potential to degrade urban water quality by influencing the build-up and wash-off of pollutants, respectively. However, limited knowledge has made it difficult to establish any link between pollutant buildup and wash-off under such dynamic conditions. In order to safeguard urban water quality, adaptive water quality mitigation measures are required. In this research, pollutant build-up and wash-off have been investigated from a dynamic point of view which incorporated the impacts of changed urban traffic as well as changes in the rainfall characteristics induced by climate change. The study has developed a dynamic object classification system and thereby, conceptualised the study of pollutant build-up and wash-off under future changes in urban traffic and rainfall characteristics. This study has also characterised the buildup and wash-off processes of traffic generated heavy metals, volatile, semi-volatile and non-volatile hydrocarbons under dynamic conditions which enables the development of adaptive mitigation measures for water quality. Additionally, predictive frameworks for the build-up and wash-off of some pollutants have also been developed.
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BARRETO, Aldinete Bezerra. "Eventos extremos de chuva em salvador: uma abordagem matemático-estatística do ambiente atmosférico." Universidade Federal de Campina Grande, 2012. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1627.
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O objetivo deste estudo é caracterizar o regime de chuvas de Salvador em várias escalas de tempo, com foco em eventos extremos de chuva, e identificar padrões da circulação atmosférica de grande escala relacionados com tais eventos. O período de estudo é de 1964 a 2009. Métodos matemático-estatísticos (Percentil, Correlação Linear, Análise de Ondeletas, Análise de Componentes Principais (ACP) e Análise de Agrupamento) foram aplicados a dados observacionais de precipitação e dados em ponto de grade de reanálise. A técnica do percentil aplicada à série temporal dos dados diários de precipitação possibilitou classificar como eventos extremos os totais diários com valor igual ou maior do que 50 mm. O principal período chuvoso, abril a julho, detém 61% de todos os eventos da série. A análise de correlação linear mostrou uma relação direta entre a ocorrência dos eventos extremos e total mensal de chuva acima da média. A análise de ondeletas indicou que os eventos estão relacionados com, pelo menos, três tipos de oscilação na escala intrassazonal: de até 12 dias, de 12-24 dias e de 48-96 dias, o que sugere a contribuição de sistemas de escala sinótica como os distúrbios de leste e os sistemas frontais, e de circulações de escala planetária como a Oscilação de Madden-Julian. A ACP aplicada a dados de reanálise identificou padrões nos baixos níveis com configuração indicativa da presença do cavado equatorial/ZCIT, ondas de latitudes médias austrais e ZCAS, essa última relacionada com eventos dos meses de verão (dezembro-janeiro-fevereiro). O padrão do principal período chuvoso tem estrutura ondulatória no escoamento de oeste do hemisfério sul. Todos os padrões apresentam um cavado invertido no leste do Nordeste e área oceânica próxima, resultante da propagação/interação de sistemas atmosféricos da área tropical-extratropical. Nos altos níveis (200 hpa), o padrão relacionado com os eventos de verão mostra a Alta da Bolívia deslocada para nordeste, e o cavado de ar superior posicionado sobre o Atlântico tropical. A estrutura dominante nos padrões de inverno (junho-julho-agosto) é: (a) ondas de latitudes médias austrais com propagação em latitudes baixas, ou (b) uma área de difluência próxima ao equador relacionada com a ZCIT.
The objective in this study is to characterize the rainfall regime of Salvador on various time scales, with a focus on extreme rainfall events, and to identify large scale atmospheric circulation patterns related to such events. The period of study is from 1964 to 2009. Mathematical-statistical methods (Percentiles, Linear Correlation, Wavelet Analysis, Principal Component Analysis (PCA), Cluster Analysis) were applied to observational precipitation and gridpoint reanalysis data. The percentile technique applied to daily precipitation time series allowed to classify as extreme events daily rainfall totals equal to or greater than 50 mm. The main rainy period, from April to July, has 61% of all events. The linear correlation analysis identified a direct relation between the occurrence of extreme events and above-normal monthly rainfall totals. The wavelet analysis indicated that the events are related to, at least, three types of oscillations on the intraseasonal time scale: up to 12 days, 12-24 days and 48-96 days, suggesting the contribution of synoptic scale systems such as easterly disturbances and frontal systems, and planetary scale circulations as the Madden-Julian Oscillation. The PCA applied to reanalysis data identified low level patterns depicting the equatorial trough/ITCZ, southern mid-latitude waves and SACZ, the last one related to summer month events (December-January-February). The pattern of the main rainy period has a wavelike structure in the southern westerlies. All patterns show an inverted trough in eastern Northeast and the nearby oceanic area, a result of the propagation /interaction of tropical-extratropical atmospheric systems. At high levels (200 hpa), the summer pattern shows the Bolivian high displaced northeastward, and the upper level trough located over the tropical Atlantic. The dominating structure in the winter patterns (June-July-August) is: (a) southern mid-latitude waves propagating toward low latitudes, or (b) a difluence area close to the equator related to the ITCZ.
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Fann, Jyr-shiuan, and 范植軒. "Establishing rainfall-runoff ANN model in watershed with multivariate analysis." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/40407392207447601078.
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碩士逢甲大學
水利工程與資源保育研究所
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Different spatial distribution and environmental change on the simulation of rainfall-runoff process has a considerable impact in watershed. Artificial intelligence has prove to be an efficient way for hydrological modeling and widely used for rainfall-runoff process modeling in recent years. By clarifying the relationship between the physiographic and hydrological, allows us to understand how to make the spatial variability affect hydrological. This fact proves that the different of physiographic for the modeling of rainfall-runoff is very important. The study will use the factor analysis and structural equation modeling to filter important physiographic factor which has enough to represent watershed. Structural equation modeling (SEM) is different from factor analysis, that has the theory of priority and the purpose is to improve the model fit. We use a back-propagation neural network (BPN) which has input layer, hidden layer and out layer, and the form was considered by time distribution of rainfall-runoff and the space distribution of watershed environment. Besides, the form operates in learning by input-output that in order to combine and construct the system which are simulating. We expect the study can establish the nonlinear relationship among the physiographic factors, precipitation, and outflow of the specific watershed. Further more, we hope it can estimate the outflow of the sub-watershed or the other watershed which is an area of physiographic factors that are similar to the watershed. With validation tests at Wu-Xi watershed, it performed concluded fair forecast results and which could effectively simplify the model.
Частини книг з теми "Multivariate rainfall analysis"
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Manoj, S., C. Valliyammai, and V. Kalyani. "Multivariate Regression Analysis of Climate Indices for Forecasting the Indian Rainfall." In Lecture Notes in Networks and Systems, 713–20. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-3172-9_67.
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Hudnurkar, Shilpa, Vidur Sood, Vedansh Mishra, Manobhav Mehta, Akash Upadhyay, Shilpa Gite, and Neela Rayavarapu. "Multivariate Time Series Forecasting of Rainfall Using Machine Learning." In Artificial Intelligence of Things for Weather Forecasting and Climatic Behavioral Analysis, 87–106. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-3981-4.ch007.
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Predicting rainfall is essential for assessing the impact of climatic and hydrological changes over a specific region, predicting natural disasters or day-to-day life. It is one of the most prominent, complex, and essential weather forecasting and meteorology tasks. In this chapter, long short-term memory network (LSTM), artificial neural network (ANN), and 1-dimensional convolutional neural network LSTM (1D CNN-LSTM) models are explored for predicting rainfall at multiple lead times. The daily weather parameter data of over 15 years is collected for a station in Maharashtra. Rainfall data is classified into three classes: no-rain, light rain, and moderate-to-heavy rain. The principal component analysis (PCA) helped to reduce the input feature dimension. The performance of all the networks are compared in terms of accuracy and F1 score. It is observed that LSTM predicts rainfall with consistent accuracy of 82% for 1 to 6 days lead time while the performance of 1D CNN-LSTM and ANN are comparable to LSTM.
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Dai, Q., D. Han, and P. K. Srivastava. "Radar Rainfall Sensitivity Analysis Using Multivariate Distributed Ensemble Generator." In Sensitivity Analysis in Earth Observation Modelling, 91–102. Elsevier, 2017. http://dx.doi.org/10.1016/b978-0-12-803011-0.00005-7.
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Moazami, S., and S. Golian. "Ensemble-Based Multivariate Sensitivity Analysis of Satellite Rainfall Estimates Using Copula Model." In Sensitivity Analysis in Earth Observation Modelling, 273–94. Elsevier, 2017. http://dx.doi.org/10.1016/b978-0-12-803011-0.00014-8.
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Al-Thukair, Assad, Yasin Jemal, and Alexis Nzila. "Influence of Climatic Factors on the Abundance and Profusion of Mosquitoes in Eastern Province, Saudi Arabia." In Mosquito Research - Recent Advances in Pathogen Interactions, Immunity, and Vector Control Strategies [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.104615.
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This study was performed to evaluate the change in seasonal abundance and distribution of individual mosquito vectors (Culex, Anopheles, and Aedes) in relation to the climatic factors in Eastern Province, Saudi Arabia, for the study period of 2014. The association between mosquito abundance and environmental parameters was investigated using bivariate and multivariate analysis. The study showed the range of temperature and relative humidity required for individual mosquito larvae abundance varies for Culex, Anopheles, and Aedes. However, no variation was observed in the range of temperature and relative humidity required for the abundance of adult Culex and Anopheles. The results revealed a negative relationship between mosquito larval/adult abundance and temperature (Total number of larva/adult is 671/11 in July, While it is 2462/221 in January). There is a link between relative humidity and rainfall, as the three climatic factors together were responsible for 33.1% (R2 = 0.331), 54.6% (R2 = 0.546), and 86.6% (R2 = 0.866) of the variance on Culex, Anopheles, and Aedes larvae, respectively. The effects of the three climatic parameters of temperature, relative humidity, and rainfall on mosquito larval and adult abundance were discussed. In addition, influences of other environmental factors on larval/adult mosquito distribution and abundance were also explained.
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Polyak, Ilya. "Second Moments of Rain." In Computational Statistics in Climatology. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195099997.003.0010.
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The first part of this chapter presents a description of the GATE rain rate data (Polyak and North, 1995), its two-dimensional spectral and correlation characteristics, and multivariate models. Such descriptions have made it possible to show the concentration of significant power along the frequency axis in the spatial-temporal spectra; to detect a diurnal cycle (a range of variation of which is about 3.4 to 5.4 mm/hr); to study the anisotropy (as the result of the distinction between the north-south and east-west transport of rain) of spatial rain rate fields; to evaluate the scales of the distinction between second-moment estimates associated with ground and satellite samples; to determine the appropriate spatial and temporal scales of the simple linear stochastic models fitted to averaged rain rate fields; and to evaluate the mean advection velocity of the rain rate fluctuations. The second part of this chapter (adapted from Polyak et al., 1994) is mainly devoted to the diffusion of rainfall (from PRE-STORM experiment) by associating the multivariate autoregressive model parameters and the diffusion equation coefficients. This analysis led to the use of rain data to estimate rain advection velocity as well as other coefficients of the diffusion equation of the corresponding field. The results obtained can be used in the ground truth problem for TRMM (Tropical Rainfall Measuring Mission) satellite observations, for comparison with corresponding estimates of other sources of data (TOGA-COARE, or simulated by physical, models), for generating multiple rain samples of any size, and in some other areas of rain data analysis and modeling. For many years, the GATE data base has served as the richest and most accurate source of rain observations. Dozens of articles presenting the results of the GATE rain rate data analysis and modeling have been published, and more continue to be released. Recently, a new, valuable set of rain data was produced as a result of the TOGA-COARE experiment. In a few years, it will be possible to obtain satellite (TRMM) rain information, and a rain statistical description will be needed in the analysis of the observations obtained on an irregular spatial and temporal grid.