B题 地区降水量问题.doc

2012重庆通信学院暑期数学建模模拟竞赛B题B题 地区降水量问题降水量是衡量一个地区降水多少的数据。空气柱里含有水汽总数量也称为可降水量。它对应于空气中的水分全部凝结成雨、雪降落所能形成的降水量。降水量是指从天空降落到地面上的液态和固态（经融化后）降水，没有经过蒸发、渗透和流失而在水平面上积聚的深度。它的单位是毫米。某地区地形分布数据如附件1给出，该地区30年水量站资料如附件2给出。请你建立数学模型解决以下问题1、试作出该地区的空间三维图及等高线图，求解出流入该地区山谷区域的最大、最小、年均水量？2、估算说明在所给区域内的海拔在500米以上部分的地表面积，并分析说明其精度？3、分别考虑该地区植被完好和沙漠化两种情形对降水量是否有影响，如何影响，并给出理由？附件1：地区地形数据（三坐标分别代表其横、纵、竖坐标，单位：米）z1000998.75995.00988.69979.80968.25953.94936.75916.52893.03x050100150200250300350400450y0000000000987.42825.32800.00759.93714.14661.44600.00526.78435.89312.255005506006507007508008509009500000000000z998.55997.95996.95995.54993.73991.51988.89985.85982.40978.52x50505050505050505050y20406080100120140160180200994.77994.18993.18991.77989.95987.72985.09982.04978.57974.68970.3610010010010010010010010010010010020406080100120140160180200220965.61960.42988.48987.88986.86985.44983.62981.38978.72975.65972.1610010015015015015015015015015015024026020406080100120140160180968.25963.90959.11953.87979.59978.98977.96976.52974.68972.42969.7415015015015020020020020020020020020022024026020406080100120140966.64963.12959.17954.78949.45944.67968.04967.42966.39964.94963.0720020020020020020025025025025025016018020022024026020406080100960.78958.07954.93951.37947.36942.92938.03932.68953.73953.10952.05250250250250250250250250300300300120140160180200220240260204060950.58948.68946.36943.61940.43936.80932.74928.22923.26917.8230030030030030030030030030030035080100120140160180200220240260936.54935.90934.83933.33931.40929.03926.23922.98919.29915.15910.5535035035035035035035035035035035020406080100120140160180200220905.48899.94916.30915.64914.54913.02911.04908.63905.76902.44898.6735035040040040040040040040040040024026020406080100120140160180894.43889.72884.53878.76893.25892.13891.01889.44887.41884.93881.9940040040040045045045045045045045020022024026020406080100120140878.58874.70870.34865.51860.17854.34865.79865.10863.94862.32860.2345045045045045045050050050050050016018020022024026020406080100857.67854.63851.12847.11842.61837.62832.11826.08834.93834.21833.01500500500500500500500500550550550120140160180200220240260204060831.32829.16826.50823.35819.70815.54810.86805.67799.94793.66799.755505505505505505505505505505506008010012014016018020022024026020798.99797.75795.99793.73790.95787.65783.84779.45774.60769.16763.15600600600600600600600600600600600406080100120140160180200220240756.57759.67758.88757.56755.71753.33750.41746.93742.90738.31733.1460065065065065065065065065065065026020406080100120140160180200727.39721.04714.07713.86713.02711.62709.65707.11703.99700.29695.9965065065070070070070070070070070022024026020406080100120140160691.09685.57679.41672.61665.13661.14660.98658.71656.58653.83650.4670070070070070075075075075075075018020022024026020406080100120646.45641.79636.47630.48623.78616.36608.19599.67598.67596.99594.6475075075075075075075080080080080014016018020022024026020406080591.61587088583.44578.27572.36565.69558.21549.91540.74800800800800800800800800800100120140160180200220240260附件2：某地区1980至2010年水量站测得的降水量资料年份年降水量（mm）年内一次最大降水量（mm)备注19801434.6 80.2 19811214.1 70.1 19821516.5 73.2 19831346.3 86.1 19841321.0 50.4 19851235.0 66.9 1986858.4 70.1 19871130.1 57.6 19881233.0 71.2 1989978.1 106.8 19901329.5 95.4 19911272.1 71.5 19921159.3 59.5 19931355.8 108.5 19941440.5 86.7 19951563.9 183.4 19961187.5 75.8 19971348.0 53.6 19981303.2 120.1 19991246.7 71.5