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Fourth Study Conference on BALTEX Scala Cinema Gudhjem

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- 183 -<br />

Generating Synthetic Daily Weather Data for Modelling of Envir<strong>on</strong>mental<br />

Processes<br />

Leszek Kuchar<br />

Institute of Meteorology and Water Resources, ul. Parkowa 30, PL-51616 Wroclaw (Poland)<br />

Agricultural University of Wroclaw, Department of Applied Mathematics, ul. Grunwaldzka 53, PL-50357 Wroclaw (Poland)<br />

1. Introducti<strong>on</strong><br />

For the needs of envir<strong>on</strong>mental models, particularly simulati<strong>on</strong><br />

models daily data of solar radiati<strong>on</strong>, maximum and minimum<br />

temperature, and total precipitati<strong>on</strong> are most often required. If<br />

there are no required data or they are missing, applicati<strong>on</strong>s of<br />

models are very limited. The situati<strong>on</strong> menti<strong>on</strong>ed occurs if<br />

there is a lack of a meteorological stati<strong>on</strong> or new envir<strong>on</strong>mental<br />

c<strong>on</strong>diti<strong>on</strong>s or when new records of data are not available. First<br />

methods generating data for the needs of agricultural modelling<br />

were c<strong>on</strong>structed by Richards<strong>on</strong>, mainly for crop simulati<strong>on</strong>s<br />

for a new climate scenarios.<br />

2. Methods<br />

Daily records of data were simulated by means of general<br />

climate informati<strong>on</strong>. Weather generators like many envir<strong>on</strong>mental<br />

statistical models, use Markov chains to determine<br />

occurrence of wet/dry days, and gamma or exp<strong>on</strong>ential probability<br />

distributi<strong>on</strong> for amount of rainfall. Daily values of solar<br />

radiati<strong>on</strong>, temperature maximum and minimum are c<strong>on</strong>sidered<br />

as a weakly stati<strong>on</strong>ary process and generated by general linear<br />

model (GLM). Depending <strong>on</strong> locati<strong>on</strong> of future applicati<strong>on</strong><br />

more studies were related to choosing an appropriate probability<br />

distributi<strong>on</strong> for each climate variable. Generated data series<br />

are required to have the same statistics as climate data including<br />

means, variati<strong>on</strong>s and cross, lag and lag-cross correlati<strong>on</strong>s<br />

of solar radiati<strong>on</strong> and temperature. The amount of precipitati<strong>on</strong><br />

and its variati<strong>on</strong> is also expected to be the same as from observed<br />

data. While means and variati<strong>on</strong>s of generated data<br />

(except variati<strong>on</strong> of precipitati<strong>on</strong>) sufficiently estimate moments<br />

of theoretical distributi<strong>on</strong>, there are still poor fitting in<br />

precipitati<strong>on</strong> variati<strong>on</strong>, precipitati<strong>on</strong> extremes and correlati<strong>on</strong>s<br />

between variables.<br />

3. Results<br />

In Richards<strong>on</strong>’s weather generator, the cross, the lag and the<br />

cross-lag correlati<strong>on</strong> illustrate seas<strong>on</strong>al and spatial relati<strong>on</strong><br />

between variables, are c<strong>on</strong>stant through locati<strong>on</strong>s and over the<br />

year. Recently, spatial and m<strong>on</strong>thly course of correlati<strong>on</strong> are<br />

introduced to the models by staircase functi<strong>on</strong>. Correlati<strong>on</strong>s<br />

differ from m<strong>on</strong>th to m<strong>on</strong>th and locati<strong>on</strong>, however c<strong>on</strong>stant<br />

within the given m<strong>on</strong>th. Transiti<strong>on</strong> probabilities and parameters<br />

of rainfall probability distributi<strong>on</strong> are fixed m<strong>on</strong>thly or biweekly<br />

as a set of 12 or 26 values or estimated by strait functi<strong>on</strong>.<br />

In this presentati<strong>on</strong> new trends of data generating as parametrizati<strong>on</strong><br />

of serial correlati<strong>on</strong>, transiti<strong>on</strong> probability, and α parameter<br />

of Γ probability distributi<strong>on</strong> will be presented.<br />

References<br />

Bruhn J.A., Fry W.E., Fick G.W., 1980: Simulati<strong>on</strong><br />

of Daily Weather Data Using Theoretical Probability<br />

Distributi<strong>on</strong>s. J. Appl. Meteorol., 19,<br />

1029-1036.<br />

Gates W.L., 1985: The use of general circulati<strong>on</strong><br />

models in the analysis of the ecosystem impacts<br />

of climatic change. Clim. Change, 7, 267-284.<br />

Hayhoe H.N., 1998: Relati<strong>on</strong>ship between weather<br />

variables in observed and WXGEN generated<br />

time series. Agric. For. Meteorol., 90, 203-214.<br />

Hunt L.A., Kuchar L., Swant<strong>on</strong> C.J., 1998: Estimati<strong>on</strong><br />

of solar radiati<strong>on</strong> for use in crop modelling.<br />

Agric. For. Meteorol., 91, 293-300.<br />

Kuchar L., 2004: Using WGENK to generate synthetic<br />

daily weather data for modelling of agricultural<br />

processes. Math. Comp. Simul., 65(2) /in<br />

print/.<br />

Larsen G., Pense R., 1982: Stochastic Simulati<strong>on</strong> of<br />

Daily Climatic Data for Agr<strong>on</strong>omic Models.<br />

Agr<strong>on</strong>. J., 74, 510-514.<br />

Matalas N.C., 1967: Mathematical assessment of<br />

synthetic hydrology. Water Resources Res., 3(4),<br />

937-945.<br />

Michaels<strong>on</strong> J., 1987: Cross-Validati<strong>on</strong> in Statistical<br />

Climate Forecast Models. J. of Climate and Appl.<br />

Meteorol., 26, 1589-1600.<br />

Richards<strong>on</strong> C.W., Wright D.A., 1984: WGEN: A<br />

model for generating daily weather variables.<br />

U.S. Department of Agriculture, Agricultural Research<br />

Service, ARS-8, 83pp.<br />

Richards<strong>on</strong> C.W., 1985: Weather simulati<strong>on</strong> for<br />

crop management models. Trans. ASAE., 28,<br />

1602-1606.<br />

SAS Institute Inc., 1988: SAS/STAT User’s Guide.<br />

Release 6.03 Editi<strong>on</strong>. Cary, North Carolina.<br />

Wilks D.S., 1992: Adapting stochastic weather generati<strong>on</strong><br />

alghoritms for climate change studies.<br />

Clim. Change, 22, 67-84.

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