干湿持续期随机模拟
Stochastic Simulation for Dry and Wet Spell
-
摘要: 该文应用数据建模技术, 实现干湿期随机建模。主要包括:利用历史气象资料, 从中采集干湿期数据; 应用实测数据, 创建干湿期经验分布函数; 应用Monte Carlo方法和经验分布参数, 随机生成干湿期序列, 通过和Markov链模型输出的对比分析, 讨论生成序列的统计误差, 测试结果显示, 与两状态Markov链方法相比, 所建模型性能更好。Abstract: Rainfall models are the most important component in stochastic weather generator. Two-state, firstorder Markov chain model is generally applied to simulate rainfall occurrence.The monthly statistics of time series of dry and wet days simulated by the model shows it may work well, but it is not satisfying when focusing on the persistent drought or prolonged wet in the series, although the difference between the simulated monthly mean of rainy days and the actually observed one are not marked.A stochastic model of dry and wet spells (DWS) is described, in which defined stochastic variables are the length of dry or wet spells, numbering in days, other than dry and wet day state. It is obvious that the variable itself has expressed the persistency of rainy or drought weather. Data modeling method is applied too. The related techniques include designing an algorithm for obtaining observed data of dry and wet spells from history records of daily rainfall; constructing empirical distribution function of the length of dry and wet spells monthly, and creating the parameter tables mapping the accumulated frequency distribution monthly; deriving a stochastic sampling formula for generating a dry or wet spell based on direct sampling principle and an algorithm of daily weather (dry or wet) on computer based on Monte Carlo simulation technique with previous sampling formula and parameter tables. Dry and wet spell simulation has been implemented using Java language. Users can select some run time parameters, for example, the name of observed location, the thread value for rainy day, and so on.Model validation test are done using history data from three locations, Beijing, Taiyuan and Zhengzhou. 100 years of rainfall data are generated for each location with the help of DWS simulator respectively. Its statistic items monthly includes : maximum of spell, mean of spell, variance of spell and mean number of rainy days. The mean absolute deviation of simulated value from observed one for all statistical items are about 1.8—2.0, 0.1—0.4, 0.4—0.6, 0.08—0.09 and 0.2—0.4, respectively.The t-tests are done in order to detect significant differences between observed and simulated value for maximum, mean and variance. No significant differences are found at α=0.01. For comparison betw een dry and wet spell model and two-state, first-order Markov chain model, the same statistics are obtained by running Markov chain model. Results indicate that the accuracy of dry and wet spell model is higher than two-state, first-order Markov chain for all statistical items, especially for maximum dry spells.Although dry and wet spell model is available and better than two-state, first-order Markov chain, its weakness is that the parameters in dry and wet spell model are more than those in Markov chain model, lacking in aesthetic feeling of mathematics.
-
Key words:
- dry and wet spell;
- stochastic modeling;
- weather simulator
-
表 1 模拟与实测降水序列统计平均值差异显著性t-检验 (t0.01=2. 819, df=22)
Table 1 Significance test of difference between simulated and observed daily rainfall
表 2 DWS和Mc模拟值的绝对误差
Table 2 Absolute deviations of simulated values with DWS and Mc
-
[1] Richardson C W, Wright D A. WGEN: A Model for Generating Daily Weather Variables. USDA, ARS-8 Washington D C, 1984. http://www.worldcat.org/title/wgen-a-model-for-generating-daily-weather-variables/oclc/12460768 [2] Johnson G L, Hanson C L, Hardegree S P, et al. Stochastic weather simulation-Overview and analysis of two commonly used models. J App Meteorol, 1996, 35:1878-1896. doi: 10.1175/1520-0450(1996)035<1878:SWSOAA>2.0.CO;2 [3] Larsen G A, Pense R B. Stochastic simulation of daily climatic data for agronomic models. Agronomy Journal, 1982, 74:510-514. doi: 10.2134/agronj1982.00021962007400030025x [4] 林而达, 张厚宣, 王京华, 等.全球气候变化对中国农业影响的模拟.北京:中国农业科技出版社, 1997:23-53. [5] Semenov M A, Brooks R J, Barrow E M, et al. Comparison of the WGEN and LARS-WG stochastic weather generators for diverse climates. Climate Research, 1998, 10 : 95-107. doi: 10.3354/cr010095 [6] 王世耆.随机天气模拟原理与模拟系统WG4E.计算机与农业 (增刊).作物管理软件研究专集, 1997, :67-82. [7] Shu Geng. A Simple Method for Generating Daily Rainfall Data. Agricultural and Forest Meteorology, 1986:363-376. https://www.researchgate.net/profile/I_Supit/publication/256434270_A_simple_method_for_generating_daily_rainfall_data/links/55e7637308ae3e1218420bd3.pdf [8] Richardson C W. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research, 1981, 17(1):182-190. doi: 10.1029/WR017i001p00182 [9] Jorgenson D L. Persistency of rain and no-rain periods during the winter at San Francisco. Mon Wea Rev, 1949, 77(9):303. doi: 10.1175/1520-0493(1949)077<0303%3APORANP>2.0.CO%3B2 [10] Steinhausser H. Trocken-und Niederschlagsperioden und ihre Theoretische Behandlung. Arch Met Geoph Biokl, 1959, 10 (1):38-58. doi: 10.1007/BF02243118 [11] Gabriel K R, Neumann J. On distribution of weather cycles by length. Quart J R Met Soc, 1957, 83:357-375. doi: 10.1002/qj.49708335714/full?scrollTo=references [12] Longley R W. The length of dry and wet periods. Quart J R Met Soc, 1953, 79:342-520. doi: 10.1002/(ISSN)1477-870X [13] 么枕生.气候统计.北京:科技出版社, 1963:170-172. [14] William H P, Brian P F, Saul A T, et al. Numerical Recipes in C:The Art of Scientific Computing. Cambridge:University Press, 1988: 517-518. [15] 诸叶平, 王世耆.随机天气模型及其JAVA实现.电子学报, 2007, 35(12):25-29. http://www.cnki.com.cn/Article/CJFDTOTAL-DZXU200712006.htm [16] 复旦大学数学系.统计数学.上海:上海科技出版社, 1960:67-69.