Homepage of Martin Dubrovsky Martin Dubrovsky, 1995: Met&Roll - The weather generator
for the crop growth model. In: Regional Workshop on Climate
variability and climate change vulnerability and adaptation (proceedings),
September 11-16, 1995, Praha; Institute of Atmospheric Physics,
Praha - U.S. Country Studies Program, Washington, D.C.
includes: 5 figures and 1 table
Martin Dubrovsky
Institute of Atmospheric Physics, Hradec Kralove, Czech
Republic
The weather generator Met&Roll was designed to provide daily weather data for the crop model to study potential impacts of climate change on crop production. The model variables include precipitation amount, solar radiation, maximum and minimum temperatures. Precipitation is modelled by 1st order Markov chain (occurrence) coupled by Gamma distribution for the precipitation amount. Remaining quantities are modelled by 1st order autoregressive model. To validate the generator, the statistics derived from the observed series are compared with model-related statistics or those derived from the synthetic series.
Note: Symbols GAMMA, ALPHA, BETA and CHI are used instead of the appropriate greek characters.
Weather generators (WG's) are used to produce synthetic series of given weather variables with desired stochastic structure. GUENNI (1994) names three reasons to develop a stochastic weather model: (i) to provide a means to extend historical weather records in time, (ii) to generate weather sequences in locations without historical information in order to evaluate the impact of weather variability on hydrological and water resource planning and ecological management at ungauged locations, (iii) to produce climate data that resembles actual and future climate conditions (climate change impact studies).
The weather series may consist of single variable - hourly or daily solar radiation data while designing solar conversion systems [GOH and TAN (1977); SPIRKL and RIES (1986); AMATO et al. (1986, 1988); AGUIAR et al. (1988)]; hourly or daily precipitation amount for hydrological studies, designing irrigation systems and agricultural or urban drainage systems [GABRIEL and NEUMANN (1962); GREGORY et al (1993); see WOOLHISER (1992) for a review] - or several variables, e.g. daily extreme temperatures, precipitation amount and solar radiation [RICHARDSON (1981), WILKS (1992)] for the crop models. The synthetic weather series are generated either for single site or simultaneously for several sites within given region (catchment area in the hydrological studies; e.g. BARDOSSY and PLATE (1992), WILSON and LETTENMAIER (1992), BOGARDI et al. (1993)).
The development of WG consists of (1) identifying variables to be generated (2) selecting type of the model and (3) determining parameters of the model (most frequently by analysis of the learning series). GUENNI (1994) presents the technique of interpolating parameters of the generator if the weather series is to be generated for location without historical records.
WG's often employ Markov chain models and autoregressive models of first or higher order. Some recent WG's - especially those designed to generate multi-location weather series - are linked with circulation patterns (BARDOSSY and PLATE (1992); WILSON and LETTENMAIER (1992); BOGARDI et al. (1993); WILBY (1994)). In this case, the primary series relates the course of the circulation patterns. The secondary series consists of local weather variables and their values are conditioned on circulation patterns. The series of circulation patterns may be either (1) observed, (2) stochastically generated using an appropriate model (e.g. Markov chain or semi-Markov chain ) or (3) derived from the air pressure distribution output of a GCM [BARDOSSY and PLATE, 1992].
The crop models are often employed [BACSI and HUNKAR, 1994; MEARNS et al., 1992] to study impacts of climatic variations on crop production (fig.1). The crop model simulates daily incrementing taking into account plant genetics, daily weather conditions, soil properties and management factors. The climate change impacts are assessed based on comparison of crop model runs with present-climate weather series and changed-climate weather series. The weather series for changed climate conditions is obtained either by direct modification of the existing time series or stochastically generated by the weather generator (application of the direct GCM output is not recommended because of the inaccuracy of their present versions). The former approach is simple and guarantees reproduction of selected features of the stochastic structure of the weather series without need to deal with its model representation. The disadvantage of the direct modification method is, that the length of the synthetic series is limited by length of the observed series. In a latter approach, the data are stochastically generated according to the model the parameters of which are estimated from the learning data and modified in accordance with the climate change scenario. The weather generator may produce arbitrarily long weather series for given climate conditions, which allows one to perform detailed sensitivity analysis of climate-crop relations.
The model formulation of the weather generator implemented in Met&Roll was taken from WILKS (1992). The model variables are 4 daily weather characteristics: total sun radiation (SRAD), maximum temperature (TMAX), minimum temperature (TMIN) and precipitation amount (RAIN). An occurrence of the precipitation is modelled by a non-stationary first-order Markov chain, precipitation amount is modelled by gamma distribution, GAMMA(ALPHA,BETA). The remaining quantities - or more exactly, the standardized deviations from their mean annual courses - are modelled by a first-order autoregressive process.
The main procedures available in Met&Roll are:
The purpose of the stochastic generator is to produce
data which are statistically similar to the observed
series. In other words, the statistics (including means,
variances, frequency of occurrence of extremes,
correlations and lag-correlations between variables)
derived from the synthetic data are to be statistically
insignificantly different from those derived from the
observed data. To validate the generator, the statistics
derived from the observed series were compared with model-based
statistics or with those derived from the synthetic
series. The 30-years (1961-1990) daily weather series
from 16 Czech stations were used for that purpose. The
results obtained for Hradec Kralove (11649) are discussed
below.
(a) Testing reproduction of the parameters of the
generator (tab.I) (comparing parameters derived from
the observed and synthetic series) has revealed no
discrepancies beyond the range of random errors. This
fact, however, cannot be considered as a quality
certificate of the generator's model but rather a proof
of numerical correctness of the analysis and generation
procedures.
(b) Testing normality of SRAD, TMAX
and TMIN (assessment of the series of
skewness and kurtosis coefficients calculated for
individual weeks of the year from the observed 30y series):
The tests have revealed that some important features
of the statistical structure of the daily weather series
are not satisfactorily preserved by the stochastic
weather generator. For better reproduction of the
stochastic structure of the time series, one might either
think of totally different approach (e.g. linkage with
circulation patterns) or consider some modifications of
the above weather generator, e.g.:
Whatever the changes to the weather generator will be, it must be borne in mind that increasing number of parameters of the model may decrease the accuracy of parameters derived from the observed learning series and consequently may even worsen the statistical similarity of observed and synthetic series. Thus the detailed quality analysis must be performed to confirm the improvement.
Fig.1.
Schematic conceptual framework for estimating effects of
the climatic change on crop production [inspired by WILKS
(1992)]. Procedures in the rounded rectangle are
accessible from Met&Roll. A: analysis of observed
daily weather data (retrieving parameters of the
generator); MP: modification of parameters of the
generator according to the climate change scenario; G:
generation of the synthetic time series by weather
generator; MW: direct modification of daily weather data.
Fig.2.
The weekly series of skewness (lower symbols) and
kurtosis (upper symbols) of SRAD. The coefficients are
rescaled in order their sample values have N(0,1)
distribution for normally distributed variable.
Fig.
3. Reproduction of the variability of monthly and
annual means. The figure displays ratios of standard
deviations of monthly and annual averages of SRAD (square),
TMAX (+), TMIN (x) and RAIN (triangle) derived from 30y
observed and synthetic time series. The horizontal lines
delineate (from below) 0.5%, 2.5%, 97.5% and 99.5%
quantiles (squared values of the quantiles of F30,30
distribution) of the ratios under assumption of equal
variance of both observed and synthetic series.
Figs. 4-5. Lag-0 correlations (upper graph) and
lag-1 correlations (bottom graph) between standardized
values of TMAX and remaining quantities calculated
for individual weeks. The vertical bars at the right part
of the graphs mark 95% confidence interval about the all-year
correlations used by the weather generator's AR(1) model.
Tab.I. Parameters of the stochastic generator and their storage on disk.
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characteristic | description | stored
| | values
| |per year
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P1, P01 | probabilities the first-order | 365
| Markov chain model |
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ALPHA and BETA | parameters of the gamma | 12
| distribution |
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M(x|dry), S(x|dry), | smoothed annual courses of | 365
M(x|wet), S(x|wet) | averages and standard |
where x is element | deviations of SRAD, TMAX and |
of {SRAD,TMAX,TMIN} | TMIN; separately for dry and |
| wet days) |
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A and B | matrices of the first-order | 1
| autoregressive model for |
| standardized values of SRAD, |
| TMAX and TMIN |
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