A stochastic weather generator (WG) produces synthetic time series of weather data of unlimited length for a location based on the statistical characteristics of observed weather at that location. Models for generating stochastic weather data are conventionally developed in two steps (Hutchinson 1987). The first step is to model daily precipitation and the second step is to model the remaining variables of interest, such as daily maximum and minimum temperature, solar radiation, humidity and windspeed conditional on precipitation occurrence. Different model parameters are usually required for each month, to reflect seasonal variations both in the values of the variables themselves and in their cross-correlations.

The "Richardson" and "serial" types

Perhaps the best known approach for developing weather generators was reviewed by Richardson (1981), and WGs based on the approach are often referred to as the "Richardson-type". At the first step, the estimation of precipitation involves first modelling the occurrence of wet and dry days using a Markov procedure, and then modelling the amount of precipitation falling on wet days using a functional estimate of the precipitation frequency distribution. The remaining variables are then computed based on their correlations with each other and with the wet or dry status of each day. The Richardson-type of generator has been used very successfully in a range of applications in hydrology, agriculture and environmental management.

One criticism of the Richardson-type WG is its failure to describe adequately the length of dry and wet series (i.e. persistent events such as drought and prolonged rainfall). These can be very important in some applications (e.g. agricultural impacts). For this reason an alternative, "serial approach" has been developed (Racsko et al., 1991), which first models the sequence of dry and wet series of days and then models other weather variables like precipitation amount and temperature as dependent on the wet or dry series.

Using WGs in impact assessment

The decision to apply a weather generator in an impact assessment may be determined by one or more of the following requirements:

Long time series of daily weather, which are not available from observational records;
Daily weather data in a region of data sparsity
Gridded daily weather data for spatial analysis (e.g. of risk)
The ability to investigate changes in both the mean climate and its inter-daily variability

Once the decision is made, a suitable WG should then be selected. The criteria for selection will depend upon what models are available and how their documented features suit the needs of the impact assessment. It may be necessary to test a number of models to assess their suitability. After selecting a model, several steps of analysis are required to parameterise and test the WG:

Data collection - observed daily climatological data for the variables and site(s) of interest should be collected, quality controlled and correctly formatted. If the WG is to be parameterised for a 1961-1990 baseline period, as much data as possible from this period will be required. On the other hand, if it important to model low frequency, high magnitude events, it will be desirable to obtain the longest possible observed time series. For spatial applications, between-site consistency of the observational time period may also be important.
Parameterisation - the parameters of the model are estimated using methods documented for the weather generator. If spatial analysis is also being undertaken, this will require parameter estimation at many sites and subsequent interpolation of the parameters to a grid or other spatial field. Some WG programs have automatic procedures for parameter estimation.
Model testing - time series of weather are generated and their statistics analysed and compared with the observed data on which they were based. The significance of any discrepancies between the WG-derived and observed series can be assessed by running both series through an impact model. Again, automatic model testing procedures are built in to some public domain WG programs.
Climate scenarios - if the WG is to be used to create weather time series representing a changed climate, procedures will also be required for applying climate change information (e.g. on climate variability change from GCMs) as adjustments to the parameters of the WG. Some WG software also handles climate scenarios.

Applying WGs over space

Weather generators using different approaches have been tested and applied in climate impact assessment (e.g. Wallis and Griffiths, 1995; Harrison et al., 1995), and the approaches have also been compared (e.g. Johnson et al., 1996; Semenov et al., 1998). While they are most commonly applied at sites, methods have also been developed to interpolate the site parameters of WGs over space, facilitating spatial analysis (e.g. of risk). However, because WG time series are usually site-independent and ignore the observed spatial correlation of climate, this can limit the value of some spatial impact assessments.

For example, a WG may simulate the occurrence of 3 prolonged droughts in a 30 year time series at location A. It may also simulate the same number of droughts at a nearby location B, but in different years. On the other hand, the observed climate at both locations may also show three drought years, but it is likely that these are the same years at both locations, since drought is commonly a widespread phenomenon. Thus, while the WG may provide an accurate statistical representation of the observed situation at each individual site (i.e. the risk of drought and its local impact), taken together, the droughts are not simultaneous and the aggregate impact (e.g. on water resources or agriculture) is likely to be less severe than in the real situation, where widespread drought affects a large area.

A further discussion of this problem and of efforts being made to develop stochastic space-time weather models can be found in Hutchinson (1995), and the role of WGs in climate scenario development is provided in Mearns et al. (2001).