Weather Generators
Weather generators are statistical models that aim simulating realistic random sequences of atmospheric variables such as temperature, precipitation and wind at a fast pace (Wilby et al., 2004). The 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 by Weather generators. They focus on small spatial scales (typically a few sites within a region extending over few kilometers), and are computationally very fast to provide numerous random realizations and they produce distributional properties as the same as observed time series, mainly at the daily or sub daily scales. In contrast, climate models have to reproduce the behavior of the whole atmosphere and its interactions with other components of the Earth system (vegetation, oceans, etc.) at the global scale and for a long time period. The limitation of this method is that only few runs can be provided by global climate models and they do not represent a specific site as they are computed for large spatial grids. The simulations from Weather Generators are then used as the inputs of the process-based models, typically electricity demand models or crop models.
Rainfall occurrences at a single site were represented by a two-state Markov chain and their intensities by independent exponential or Gamma random variables. In this model, weather states correspond to the states of the Markov chain, i.e. to dry and wet states. Seasonal cycle and conditionally on the weather type, residuals of these variables were viewed as a multivariate autoregressive process independent on rainfall amounts. Recently, impact questions with respect to large scale climate changes have spurred a strong interest in linking local and global climate variables, leading the way to the so-called downscaling methods. There are strong links between downscaling approaches and WGs, mainly focusing on how to make the connection between circulation patterns and local atmospheric variables at the daily scale. The two weather types were defined in order to capture the changes between wet and dry days at a single site. A day was qualified as wet if the precipitation amount was greater than a certain limit of daily total rainfall (Richardson, 1981). Beyond the natural difference between wet and dry events, weather types intend to capture recurrent patterns by breaking spatio- temporal information into a finite number of blocks.
By breaking the spatio-temporal information into four blocks, one can assign a weather type for each winter day. As impact study requirements and datasets at hand moved from one single variable towards multivariate random vectors (precipitation, temperature, wind, etc.), it was natural to wonder if the definition and the numbers of weather types could benefit from the extended database. Flecher et al., 2010 decomposed the wet and dry contrast into finer nuances. Sub-regimes of wet (respectively dry) days were obtained by running a clustering algorithm on variables such as daily minimum and maximum temperature, radiation and wind speed recorded at the same single site. Additional large scale information such as pressure fields, synoptic patterns, etc. can also improve the definition of weather types. Any given day can be attached to a specific weather type, or circulation pattern, by running a clustering algorithm on large scale atmospheric variables.
Single site Models
Precipitation has always been a key variable of interest in hydrology and climatology, in particular for the first WGs. From a statistical point of view, precipitation modeling is complex because it mixes a Bernoulli random variable corresponding to dry or wet events with a positive random variable corresponding to the rainfall intensity, therefore leading to a strong departure from the classical Gaussian framework. Given the weather type sequence, precipitation amounts have been classically assumed to be conditionally independent in time. More recent developments propose to take the temporal dependence into account. During wet days, a large class of distributions can be fitted to rainfall amounts. The Gamma distribution may not be flexible enough to capture all rainfall amount behaviors. For example, precipitation can be heavy-tailed at some sites. Alternatives are thus needed to model extreme amounts. A second difficulty is the lack of a clear path on how to extend the Gamma distribution to a multivariate and/or spatial setting. This leads to the idea of transforming data into the Gaussian world that offers a simple dependence structure, the covariance matrix. This is not limited to precipitation, and for instance the square root of the wind intensity is often considered instead of its raw value. Although powerful and flexible, these transformations complicate the assessment of uncertainties and render the interpretability challenging, the measurement unit being lost. Overall, despite all these drawbacks, the Gamma density has still a lot of attractive mathematical properties and remains a strong candidate to capture basic rainfall amount properties at the daily scale, and it should be viewed as an important yardstick.
Multisite Models
If only one single weather type drives a multisite weather generator, a simple multisite modeling strategy is to assume that, given this weather type, the sites are mutually independent in space and time. Modeling the dependence structure within weather types becomes necessary, but is challenging even when only a unique weather type is considered. Few tractable models for spatial processes exist and Gaussian processes are often considered. As marginal may not be normally distributed, Gaussian processes cannot be used directly and marginal transformation may be needed. In the literature on multisite WGs with regional weather type, different avers exist to make the link between a non-Gaussian multivariate random vector and it’s normally distributed counterpart.
References
Flecher, C., Naveau, P., Allard, D., & Brisson, N. (2010). A stochastic daily weather generator for skewed data. Water Resources Research, 46(7), 1–15. https://doi.org/10.1029/2009WR008098
Richardson, C. W. (1981). Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research, 17(1), 182–190. https://doi.org/10.1029/WR017i001p00182
Wilby, R. L., Charles, S. P., Zorita, E., Timbal, B., Whetton, P., & Mearns, L. O. (2004). Guidelines for Use of Climate Scenarios Developed from Statistical Downscaling Methods. IPCC, 27(August), 1–27. https://doi.org/citeulike-article-id:8861447
