For many applications, particularly those in agriculture and hydrology, existing data records are insufficient for analysis of impacts. Weather generators aim to address this shortcoming by providing a statistical method to produce data series of arbitrary length which possess the same statistical properties as the observed data. This page describes a newly developed model which is based on spectral methods. The spectral weather generator was developed at Florida State University’s Center for Ocean-Atmospheric Prediction Studies (COAPS) and enhanced through a collaborative effort between Florida State University and Southern Illinois University Carbondale and produces daily values of precipitation (mm), maximum and minimum surface air temperatures (oC), and total daily solar radiation (MJ m-2). The model is described in two publications: Schoof JT, Arguez A, Brolley J, O'Brien JJ (2005) "A new weather generator based on spectral properties of surface air temperatures," Agricultural and Forest Meteorology, 135, 241-251. Schoof JT (2008) "The multivariate spectral weather generator: improvements and an application to diverse climates within the contiguous United States," Agricultural and Forest Meteorology, 148, 517-521. Any questions about this site or the spectral weather generator should be sent to: jschoof@siu.eduPrecipitation Occurrence and Amount Like most weather generators, the spectral model uses a Markov-chain to describe the precipitation occurrence process. However, most previous models have used a simple first-order model which has been shown to be adequate for many regions. For some parts of the United States, however, the first-order model produces series with too few long dry spells. Therefore, the spectral weather generator employs a second-order Markov model, in which precipitation on the current day is dependent on the two previous days. This model has four parameters: p001, p011, p101, and p111, where a 0 represents a dry day and a 1 represents a wet day. For example if the previous two days were wet, a uniform [0,1] random number is generated and compared to p111. If the random number is smaller than p111, the current day is considered wet. Otherwise it is considered dry. These four transition probabilities are computed from the observed data and are defined separately for each calendar month. Once the precipitation occurrence part of the weather generator produces a wet day, a precipitation amount must be determined. The spectral weather generator employs a mixed-exponential distribution. As the name implies, the mixed-exponential distribution is a mixture of two exponential distributions and its probability density function is given by:  where &beta1 is the mean of the first distribution, &beta2 is the mean of the second distribution, and &alpha is the mixing parameter. The first distribution is chosen with probability &alpha, while the second is chosen with probability 1-&alpha . The parameters of the mixed-exponential distribution are fitted separately for each month using maximum likelihood methods. Temperatures and Solar Radiation The spectral method is based on (1) computation and averaging of monthly spectral estimates to reveal average variability as a function of frequency and (2) introduction of high frequency variability to the smoothed spectra in the form of white noise. The former helps the generated series maintain a level of variability similar to the observed series, while the latter ensures a realistic level of day-to-day variability. The process of data generation for an individual variable begins with computing a set of statistics describing the data. These include the wet- and dry-day mean values for each day of the year, and the average skewness and lag-0 and lag-1 correlation matrices for each month. Consider the time series of a variable for a single month, Tt. The data are first standardized according to precipitation occurrence and subjected to a discrete Fourier transform to produce the spectral estimates, TfTf*, which represent the variance present in the data across different frequencies. By averaging these for each calendar month over the length of the time series, an ensemble mean spectral estimate, HfHf*, is produced. The square roots of the average spectral estimates, |Hf|, represent the amplitude of the variability across frequencies. To generate data for a particular calendar month, a skewed random number series is generated is generated with length equal to the month of interest, xt. The spectrum of the random noise series, XfXf*, is theoretically constant, but actually exhibits some sampling variability. By multiplying the ensemble amplitude spectra and the discrete Fourier transform of the white noise series, a new vector Yf=|Hf|Xf is produced. The inverse Fourier transform of Yf, Yt, is a new time series of appropriate length containing anomalies of the original variable. The final monthly time series is obtained by adding in the wet- and dry-day means. The procedure described above produces data series that closely resemble the observed series in terms of the means, variances, and skewness of the daily data. Reproducing multivariate data series with the proper inter-variable relationships represents an additional challenge. In the current model formulation, the user can enter the desired level of agreement between observed and generated correlation coefficients. Executables and Instructions Executable files for the spectral weather generator has been provided below. The following considerations should be made when using the spectral weather generator: There are two executables included here: spectral_par_2007.exe and spectral_gen_2007.exe. The former computes the weather generator parameters while the latter generates the data. The program spectral_par_2007.exe will prompt the user for the input file name. Once the command to run the spectral weather generator has been invoked, the user is prompted for five pieces of information: the input file name, the output file name, the number of years to generate, the level of agreement for cross-correlations and a positive seed for for the random number generator. This can be any positive integer. The input data file must have the following format: Year, Month, Day, Year-Day (1-365), Tmax, Tmin, Solar Radiation, Precipitation The output file will have the following format: Year, Month, Day, Precipitation Occurrence (binary), Precipitation Amount, Tmax, Tmin, Solar Radiation Note that the units of the output variables will be the same as those of the input variables. Click on the link to download a zip file containing the executables: spectral_2007.zip The spectral weather generator has recently been upgraded for use with the DSSAT crop modeling system. The zip file contains two executable programs. The program spectral_par_2007_wthman.exe reads a weather (.wth) file and writes the spectral weather generator parameters in a climate (.cli) file. The program spectral_gen_2007_wthman.exe reads the climate file, prompts the user for information and generates data using the spectral method. Click on the link to download the Weatherman compliant executables: spectral_2007_weatherman.zip Results from US Stations The spectral weather generator has been applied to a large number of stations within the contiguous USA. The interactive map below contains links to the results from a subset of stations. These results were obtained by performing a 100-year run with a correlation threshold of 0.2. Click on a station to view graphics detailing a number of model performance evaluations.  Acknowledgements COAPS receives its base support from the Applied Research Center, funded by NOAA Office of Global Programs awarded to Dr. James O'Brien. Additional support has been provided by the USDA , CSREES, and the USDA-Risk Management Agency through the Southeast Climate Consortium. Additional funding for this work was provided to J.T. Schoof of Southern Illinois University Carbondale through a subcontract from Florida State University. |