A stochastic model for tropical rainfall at a single location |
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| Institution: | 1. State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A&F University, Shaanxi, 712100, China;2. Key Laboratory of Ecohydrology of Inland River Basin, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China;3. Department of Earth and Environmental Engineering, Columbia University, New York, 10027, USA;4. Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, China;1. School of Mechatronics Engineering, Nanjing Forestry University, Nanjing, 210037, China;2. School of Mechanical Engineering, Southeast University, Nanjing, 211189, China;1. College of Water Sciences, Beijing Normal University, Beijing 100875, China;2. College of Water Conservancy and Civil Engineering, Inner Mongolia Agricultural University, Hohhot, Inner Mongolia Autonomous Region 010018, China;3. School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia;1. Department of Oral and Cranio-maxillofacial Surgery, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology, Shanghai, 200011, China;2. School & Hospital of Stomatology, Tongji University, Shanghai Engineering Research Center of Tooth Restoration and Regeneration, Shanghai, 200072, China;3. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China;4. Shanghai University of Medicine & Health Sciences, Shanghai, 201318, China;1. G-EAU, AgroParisTech, Cirad, IRD, IRSTEA, Montpellier SupAgro, Univ Montpellier, Montpellier, France;2. Department of Geography, King''s College London, WC2R 2LS, London, UK;1. Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi, India;2. MVGR College of Engineering, Vizianagaram, India;3. Central Ground Water Board, New Delhi, India |
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| Abstract: | Modelling data that correspond to rainfall accumulated over fixed periods of time presents the challenging problem of dealing with a random variable that has a point mass at zero which corresponds to dry periods that occur with positive probability. One way to overcome this difficulty is to assume that the data correspond to a normal variate w, that has been truncated and transformed. The dry periods correspond to the (unobserved) negative values and the wet periods correspond to some power of the positive ones. The serial structure that is present in rainfall can be modelled by imposing a serial structure to w. We use a dynamic linear model on w using a Fourier representation to allow for the seasonality of the data, which in the case of tropical rainfall is very marked. The model is fitted using a Markov chain Monte Carlo method that uses latent variables to handle both dry periods and missing values. We use the model to estimate and predict both the amount of rainfall and the probability of a dry period. The method is illustrated with data collected in the Venezuelan state of Guárico. |
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