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Research Report

Subject Development of Weather Generator for Statistical Downscaling (Korean)
Author Dr. Moosup Kim Date 2016.01.01
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GCM (Global Circulation Model) is a basic and fundamental tool for predicting future climate conditions. Unfortunately, its output is so coarse in space and time that it cannot be directly applied to application fields. Currently, there is a large amount of research focused on closing the gap between resolutions of GCM output and application data. This process, called downscaling, produces climate data of high resolution from coarse GCM outputs. Downscaling schemes have mainly been studied in two approaches - dynamical and statistical downscaling. Dynamical downscaling is based on RCM (Regional Circulation Model), which is a dynamical circulation model with higher spatial resolution and more detailed regional topography than GCM. Thus, it can produce climate data of fine resolution adapted for a target basin. On the other hand, statistical downscaling is based on statistical models describing basin weather and its relation with climate predictors. Since it can rapidly downscale GCM output without expensive computational costs, it has been employed in a variety of application fields. Recently, a hybrid approach has been studied to further increase the spatial resolution of dynamically downscaled data and correct the distributional bias using observation data.

 

In this report, we concentrate on statistical downscaling. There are several approaches for statistical downscaling. One of the most prominent approaches is a regression model which links basin weather variables with climate predictors so that climate prediction can be reflected on the basin weather. Since climate prediction is provided in coarse spatial resolution, it is viewed as spatial disaggregation. Another approach employs a weather generator, which generates weather scenarios day to day by using a statistical model for basin weather. As such, it can be viewed as a tool for temporal disaggregation.

 

This report focuses on weather generators. Many weather generators have already been developed. Since weather generators are based on statistical models for basin weather, statistical modeling is the most prominent factor in developing a new weather generator. One of the most widespread models was proposed by Richardson, His model deals with precipitation, daily maximum/minimum temperatures, and solar radiation; it is a multivariate but site-specific model. The modeling approach is fully parametric: the precipitation model assumes that wet/dry-spells follow a first-order 2-state Markov model and rainfall amount is distributed according to a gamma distribution. In the temperature model, the daily mean trends are estimated by fitting Fourier series and the anomalies are modeled by the Vector AR (Auto Regressive) process that can describe their correlation structure. The precipitation model was modified by Racsko et al. As the parametric model may have model bias, the discrepancy between real world model and assumed model, thus non-parametric approach, is often employed. Racsko et al. adopted a wet/dry-spell alternation scheme instead of the Markov model. Moreover, rainfall amount is modeled by a semi-empirical distribution. Now in many publications, Richardson and Racsko models are called WGEN and LARS-WG, respectively. The site-specific model has been extended to a multi-site one for covering an entire basin rather than a specific site. Since a multi-site model is definitely more complicated than a site-specific one, non-parametric approach is preferred to parametric due to its flexibility. Apipattanavis et al. proposed a multi-site multivariate weather generator that assumes a parametric Markov model for wet/dry-spells but adopts the k-NN method for simulating conditional distribution of weather variables, which is a non-parametric resampling method.

 

In this study, we aim to develop a new weather generator for statistical downscaling of climate prediction. For the purpose, the weather generator is required to have the following abilities:

 

• covering multiple sites;

 

• being linkable with climate predictors.

 

For spatial disaggregation of climate prediction, the weather generator has to be capable of simulating multi-site weather. Furthermore, for producing climate data of high resolution, spatial interpolation is applied to weather scenarios retaining spatial correlation. The second ability above is related to the inter-annual variation of climate. Typically, weather generator models are calibrated for generating climatological weather that ignores the inter-annual variation of climate. Thus, for such variations to be reflected, the weather generator has to be linkable with climate predictors. Motivated by these demands, we have developed a new multi-site multivariate weather generator for statistical downscaling. The weather generator deals with precipitation and daily maximum/minimum temperatures.

 

Now, we introduce the underlying statistical models of the proposed weather generator. First, the precipitation model is described in detail. As in the LARS-WG precipitation model, wet/dry-spells are simulated by a wet/dry-spells alternation model where each spell is generated independently. Especially, the lengths of dry-spells are generated by using a corresponding empirical distribution. As mentioned before, this method allows us to circumvent the model bias problem arising in Markov modeling. Generating wet-spell is more complicated than dry-spell since multi-site rainfall generation is involved. In particular, at-site distribution of rainfall amount is discontinuous at zero amount and multi-site distribution is far from multivariate normal. Thus, we take into account copula models that provide a general framework for modeling multivariate distributions. Actually, two approaches are considered for copula modeling: semi-empirical and Gaussian. The semi-empirical approach can be viewed as a multi-site version of the semi-empirical distribution method of LARS-WG. As it is flexible, model fitting is rather simple. However, as the number of sites under consideration increases, it suffers from sparsity. On the other hand, Gaussian model is parametric, and thus sparsity problem vanishes but model bias may be involved.

 

In rainfall amount modeling, it is important to deal with extreme precipitation because it has enormous impacts on application fields. For appropriate extreme rainfall generation, extreme value models are employed; generalized Pareto distribution is fitted to extreme rainfall data at every site and Spatial Gaussian Extremes Modeling is adopted for describing inter-site coherence of extreme precipitation.

 

Next, the temperature model is described. The daily mean trends are estimated by local polynomial regression method instead of with Fourier series. The local polynomial regression seems to estimate mean trends more accurately than Fourier series. It is also notable that the daily mean is affected by precipitation. WGEN temperature model estimates daily mean trends of wet and dry days, separately, thus the magnitude of the effect is determined by whether the day is wet or dry. However, actual daily mean is observed to respond to rainfall intensity too: as the intensity gets stronger, daily mean falls down much more. This observation motivates the use of a regression model for mean down-shift against the intensity of precipitation that differentiates the proposed model from WGEN model. Temperature anomalies are obtained from standardization as in WGEN model, but they exhibit autocorrelation in space as well as time. To capture the correlations, we also consider the Vector AR model. Note that in multi-site model, the Vector AR model gets more complex (the number of parameters estimated is large) as the number of sites increases, thus we need to consider dimension reduction. It can be accomplished by EOF analysis, which provides a suitable set of principal component series. The Vector AR model is fitted to the vector series of the principal components rather than anomalies directly. This enable us to capture the correlation structure efficiently.

 

We evaluated the performance of the proposed weather generator by carrying out a case study focusing on the Nakdong basin in the Korean peninsula. ASOS (Automatic Synoptic Observation System) daily data is readily available and 14 observation stations are located nearby. A 26 year observation period was used (January 1, 1988 - December 31, 2013). We fit the models described above to the ASOS data and generated 1,000 sets of simulation data, whose period is from January 1 to December 31. The performance was measured by the similarity between statistical characteristics of observation and simulation data. In the evaluation, we took the following characteristics into consideration: daily distribution; spatial correlation, temporal correlation of temperatures; correlation between maximum and minimum daily temperatures; monthly accumulation and maximum of precipitation; wet-day frequency; and monthly averages of temperatures. As the result, most of characteristics were reproduced well by the proposed weather generator, except monthly averages of temperatures where the synthetic averages revealed a narrower spread than observations. In calibrating the weather generator model, inter-annual variation of climate was ignored but significantly detected in real climate. We guess that excluding this variation causes the flaw in the monthly averages of temperatures. In future studies, we will investigate climate predictors and link them to weather generators for piping inter-annual variation of climate to basin weather.