Stochastic weather generators: an overview of weather type models

Ailliot, Pierre; Allard, Denis; Monbet, Valérie; Naveau, Philippe

Journal de la société française de statistique, Tome 156 (2015) no. 1, pp. 101-113.

Pour réaliser des études d’impact dans lesquelles le climat est un paramètre d’entrée important, un problème fréquemment rencontré consiste à produire des séries temporelles de variables climatiques telles que températures, précipitation, vent ou humidité relative, en plusieurs sites simultanément, au pas de temps journalier et parfois horaire. Ces séries doivent être faciles à générer. Elles doivent aussi être réalistes en ce sens que les distributions des statistiques liées à la dynamique spatio-temporelle, telles que les corrélation entre variables, la persistence temporelle et les différentes sources de variabilité doivent être correctement reproduites. De nombreux générateurs stochastiques de conditions météorologiques ont été proposés dans ce but. Dans cet article, nous proposons de passer en revue la classe particulière des générateurs stochastiques à base de types de temps. En règle générale, un type de temps est une caractérisation grossière des conditions atmosphériques journalières. Il existe de nombreuses façons de définir les types de temps, qu’ils soient observés ou cachés dans une structure latente, et d’en inférer leur propriétés. Cette revue a pour objet d’aider les statisticiens, les scientifiques du climat et les utilisateurs de produits climatiques à appréhender les concepts et modèles probabilistes utilisés dans les générateurs stochastiques de conditions météorologiques et d’en cerner les avantages et leurs limites.

A recurrent issue encountered in environmental, ecological or agricultural impact studies in which climate is an important driving force is to provide fast and realistic simulations of atmospheric variables such as temperature, precipitation and wind at a few specific locations, at daily or hourly temporal scales. Spatio-temporal dynamics and correlation structures among the variables of interest, as well as weather persistence and natural variability have to be reproduced accurately in a distributional sense. This quest leads to a large variety of so-called stochastic weather generators (WGs) in the literature. Here, we provide an up-to-date overview of weather type WG models. Weather types classically represent daily characteristics of the relevant atmospheric information at hand. There are many ways to build such weather states, either hidden or observed, and to infer their properties. This overview should help statisticians as well as meteorologists and climate product users to understand the probabilistic concepts and models behind weather type WGs, and to identify their advantages and limits.

Keywords: Stochastic Weather Generators, Precipitation, Regime Switching Models, Weather Type
Mot clés : Générateurs aléatoires de conditions météorologiques, Précipitations, Modèles à Changements de Régimes, Type de temps

[1] Allard, D.; Bourotte, M. Disaggregating daily precipitations into hourly values with a transformed censored latent Gaussian process, preprint (2014)

[2] Ailliot, P.; Bessac, J.; Monbet, V.; Pène, F. Non-homogeneous hidden Markov-switching models for wind time series, Journal of Statistical Planning and Inference (2014) | Zbl

[3] Ailliot, P.; Thompson, C.; Thomson, P. Space time modeling of precipitation using a hidden Markov model and censored Gaussian distributions, Journal of the Royal Statistical Society, Series C (Applied Statistics), Volume 58 (2009) no. 3, pp. 405-426

[4] Bellone, E.; Hughes, J.P.; Guttorp, P. A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts, Climate Research, Volume 15 (2000), pp. 1-12

[5] Bardossy, A.; Plate, E. Modeling daily rainfall using semi-Markov representation of circulation pattern occurrence, Journal of hydrology, Volume 122 (1991), pp. 33-47

[6] Bardossy, A.; Plate, E. Space-time model for daily rainfall using atmospheric circulation patterns, Water Resources Research, Volume 28(5) (1992), pp. 1247-1260

[7] Chilès, J.P..; Delfiner, P. Geostatistics: Modeling Spatial Uncertainty, Second Edition, Wiley, 2012 | Zbl

[8] Carey-Smith, Trevor; Sansom, John; Thomson, Peter A hidden seasonal switching model for multisite daily rainfall, Water Resources Research, Volume 50 (2014) no. 1, pp. 257-272

[9] Chandler, R. E.; Wheater, H.S. Analysis of rainfall variability using generalized linear models: A case study from the west of Ireland, Water Resources Ressearch, Volume 38 (2002) no. 10 | DOI

[10] Furrer, E.M.; Katz, R.W. Improving the simulation of extreme precipitation events by stochastic weather generators, Water Resources Research, Volume 44 (2008) no. 12

[11] Flecher, C.; Naveau, P.; Allard, D.; Brisson, N. A stochastic daily weather generator for skewed data, Water Resources Research, Volume 46 (2010)

[12] Fuentes, Montserrat; Reich, Brian; Lee, Gyuwon Spatial-temporal mesoscale modeling of rainfall intensity using gage and radar data., Annals of Applied Statistics, Volume 2 (2008) no. 4, pp. 1148-1169 | Zbl

[13] González-Farías, G.; Domínguez-Molina, J. Armando; Gupta, A.K. The closed skew-normal distribution, Skew-elliptical distributions and their applications: a journey beyond normality, Chapman & Hall/CRC, Boca Raton, FL, 2004, pp. 25-42

[14] Gupta, Arjun K.; González-Farías, Graciela; Domínguez-Molina, J.Armando A multivariate skew-normal distribution, Journal of Multivariate Analysis, Volume 89 (2004) no. 1, pp. 181-190 | Zbl

[15] Gabriel, K.R.; Neumann, J. A Markov chain model for rainfall occurrence at Tel-Aviv, Quart. J. R. met. Soc., Volume 88 (1962), pp. 90-95

[16] Hughes, J.P; Guttorp, P.; Charles, S.P. A non-homogeneous hidden Markov model for precipitation occurrence, Applied Statistics, Volume 48 (1999) no. 1, pp. 15-30 | Zbl

[17] Holzmann, H.; Munk, A.; Suster, M.; Zucchini, W. Hidden Markov models for circular and linear circular time series, Environmental and Ecological Statistics, Volume 13 (2006), pp. 325-347

[18] Hutchinson, MF Stochastic space-time weather models from ground-based data, Agricultural and Forest Meteorology, Volume 73 (1995) no. 3, pp. 237-264

[19] Katz, R.W. Precipitation as a chain-dependant process, Journal of Applied Meteorology, Volume 16 (1977), pp. 671-676

[20] Khalili, M.; Brissette, F.; Leconte, R. Stochastic Multi-Site Generation of Daily Weather Data, Stochastic Environmental Research and Risk Assessment, Volume 23 (2009) no. 6, pp. 837-849

[21] Kim, Y.; Katz, R. W.; Rajagopalan, B.; Podestá, G. P.; Furrer, E. M. Reducing overdispersion in stochastic weather generators using a generalized linear modeling approach, Climate research, Volume 53 (2012), pp. 13-24

[22] Kleiber, W.; Katz, R.W.; Rajagopalan, B. Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes, Water Ressources Research, Volume 48 (2012)

[23] Khalili, M.; Leconte, R.; Brissette, F. Stochastic Multi-Site Generation of Daily Precipitation Data Using Spatial Autocorrelation., Journal of Hydrometeorology, Volume 8 (2007) no. 3, pp. 396-412

[24] Kenabatho, P.K.; McIntyre, N.R.; Chandler, R.E.; Wheater, H.S. Stochastic simulation of rainfall in the semi-arid Limpopo basin, Botswana, International Journal of Climatology (2012) no. 32, pp. 1113-1127

[25] Koch, E.; Naveau, P. A frailty-contagion model for multi-site hourly precipitation driven by atmospheric covariates, Water Resources Research (2015) | DOI

[26] Katz, R.W.; Parlange, M.B. Generalizations of chain-dependent processes: Application to hourly precipitation, Water Resources Research, Volume 31 (1995) no. 5, pp. 1331-1341

[27] Lee, D.; An, H.; Lee, Y.; Lee, J.; Lee, H.S.; Oh, H.S. Improved multisite stochastic weather generation with applications to historical data in South Korea, Asia-Pacific Journal of Atmospheric Sciences, Volume 46 (2010) no. 4, pp. 497-504

[28] Lennartsson, J.; Baxevani, A.; Chen, D. Modelling precipitation in Sweden using multiple step Markov chains and a composite model, Journal of Hydrology, Volume 363 (2008) no. 1, pp. 42-59

[29] Maraun, D.; Wetterhall, F.; Ireson, A.M.; Chandler, R.E.; Kendon, E.J.; Widmann, M.; Brienen, S.; Rust, H.W.; Sauter, T.; Themeßl, M. Precipitation downscaling under climate change: Recent developments to bridge the gap between dynamical models and the end user, Reviews of Geophysics, Volume 48 (2010) no. 3

[30] Parlange, M.B.; Katz, R.W. An extended version of the Richardson model for simulating daily weather variables, Journal of Applied Meteorology, Volume 39 (2000), pp. 610-622

[31] Qian, B.; Corte-Real, J.; Xu, H. Multisite stochastic weather models for impact studies, International Journal of climatology, Volume 22 (2002) no. 11, pp. 1377-1397

[32] Richardson, C.W. Stochastic simulation of daily precipitation, temperature, and solar radiation, Water Resources Research, Volume 17 (1981) no. 1, pp. 182-190

[33] Racsko, P.; Szeidl, L.; Semenov, M. A Serial Approach to Local Stochastic Weather Models, Ecological Modelling, Volume 57 (1991), pp. 27-41 | DOI

[34] Semenov, A.M.; Brooks, R.J.; Barrow, E.M.; Richardson, C.W. Comparison of the WGEN and LARS-WG stochastic weather generators for diverse climates, Climate Research, Volume 10 (1998), pp. 95-107

[35] Srikanthan, R; McMahon, TA Stochastic generation of annual, monthly and daily climate data: A review, Hydrology and Earth System Sciences Discussions, Volume 5 (2001) no. 4, pp. 653-670

[36] Sansom, J.; Thomson, P.; Carey-Smith, T. Stochastic seasonality of rainfall in New Zealand, Journal of Geophysical Research: Atmospheres, Volume 118 (2013) no. 10, pp. 3944-3955

[37] Thompson, C.; Thomson, P.; Zheng, X. Fitting a multisite rainfall model to New Zealand data, Journal of Hydrology, Volume 340 (2007), pp. 25-39

[38] Todorovic, P.; Woolhiser, D. A A stochastic model of n-day precipitation., Journal of Applied Meteorology, Volume 14 (1975), pp. 17-24

[39] Vrac, M.; Stein, M.; Hayhoe, K. Statistical downscaling of precipitation through non homogeneous stochastic weather typing, Climate Research, Volume 34 (2007), pp. 169-184

[40] Wilks, D.S. Use of stochastic weather generators for precipitation downscaling, Wiley Interdisciplinary Reviews: Climate Change, Volume 1 (2010) no. 6, pp. 898-907

[41] Wilks, D.S. Stochastic weather generators for climate-change downscaling, part II: multivariable and spatially coherent multisite downscaling, Wiley Interdisciplinary Reviews: Climate Change, Volume 3 (2012) no. 3, pp. 267-278

[42] Wilks, D.S. Multisite generalization of a daily stochastic precipitation generation model, Journal of Hydrology, Volume 210 (1998) no. 1, pp. 178-191

[43] Wilson, L.L.; Lettenmaier, D.P.; Skyllingstad, E. A hierarchial stochastic model of large-scale atmospheric circulation patterns and multiple station daily precipitation, Journal of Geophysical Research, Volume 97(D3) (1992), pp. 2791-2809

[44] Wilks, D.S; Wilby, R.L The weather generation game: a review of stochastic weather models, Progress in Physical Geography, Volume 23 (1999) no. 3, pp. 329-357

[45] Wilby, R.L.; Wigley, T.M.L.; Conway, D.; Jones, P.D.; Hewitson, B.C.; Main, J.; Wilks, D.S. Statistical downscaling of general circulation model output: a comparison of methods, Water Resources Research, Volume 34 (1998), pp. 2995-3008

[46] Yang, C.; Chandler, R.E.; Isham, V.; Wheater, H.S. Spatial-temporal rainfall simulation using generalized linear models, Water ressources research, Volume 41 (2005) no. 11

[47] Zucchini, W.; Guttorp, P. A hidden Markov model for space-time precipitation, Water Resources Research, Volume 27 (1991), pp. 1917-1923

[48] Zucchini, W.; McDonald, I.L. Hidden Markov models for time series : an introduction using R, Chapman & Hall/CRC, London, 2009 | Zbl