综合环境承载能力的定量模型

1、综合环境承载力的定量模型白宏涛环境承载力的表征 n环境承载力是在限制因子的约束条件下发展因子阈值矢量。 n发展因子和限制因子均可表示为n维空间的矢量：ndddd,21ncccc,21发展因子发展因子限制因子限制因子环境承载力的表征 n实际上，对某种限制因子，总有若干发展因子与之相关联，其间存在某种反映发展因子与限制因子间关系的函数 if)(iiidfc 环境承载力的表征 n研究区域内的环境承载力即为不突破限制因子阈值前提下，发展变量的阈值：ndddd,21*max( )( )ddcf dc矢量表征矢量表征优化模型优化模型环境承载力的计算n为方便数据收集和计算，通常将人口为方便数据收集和计算，通

2、常将人口O和产业总产值和产业总产值作为发展因子的度量。优化模型简化为：作为发展因子的度量。优化模型简化为：n因此，因此，确定函数确定函数 成为分析环境承载力的关键所在。成为分析环境承载力的关键所在。n灰色预测、多元统计回归分析、线性规划灰色预测、多元统计回归分析、线性规划 12*12max()max( )(,)miimPPPOcf dcdgO P PPif分析示例n已有数据（发展变量）已有数据（发展变量）人口人口Y1（万人）（万人）GDPY2（十亿元）（十亿元）工业增加值工业增加值Y3（十亿元）（十亿元）总用水量总用水量Y4（百万（百万m3）天然气用量天然气用量Y5(百万百万m3)电力用量电力

3、用量Y6（亿（亿度）度）道路建设里程道路建设里程Y7（百公里）（百公里）20006.703.492.876.409.52.433.0120017.807.287.157.7222.13.023.3720029.508.177.229.1639.34.083.91200311.029.958.1612.2746.25.104.56200412.3013.0612.3512.6751.15.754.74分析示例n已有数据（限制因子）已有数据（限制因子）PM10排放量排放量X1(千吨千吨)NOx排放量排放量X2(百吨百吨)废水排放量废水排放量X3（百万（百万m3）COD排放量排放量X4(百吨百吨)生

4、活垃圾产生生活垃圾产生量量X5（万吨）（万吨）夜间生活区夜间生活区声级声级X6(分贝分贝)工业用地工业用地X7（百公顷）（百公顷）20003.37212.204.455.253.4242.31.19520013.61114.685.446.194.1642.91.72720023.89117.006.467.204.8138.51.95520034.11218.418.768.295.6346.12.93420044.41819.769.069.626.3045.83.84灰色预测法预测变量dxdtxuxxtt( )( )( )( )111110 xxueukk1110( )( )()uB B

5、B YTT ()1时间序列变化趋势拟合预测n人口:X(k1)= 5.9999072e0.14605459knGDP：X(k1)= 4.509584e0.206546k n工业增加值:X(k1)= 4.060246e0.20736k; n总用水量:X(k1)= 5.716658e0.1671115kn天然气消耗: X(k1)= 17.82933e0.22048kn电力消耗:X(k1)= 2.170458e0.19982k ; n道路建设:X(k1)= 2.7711618e0.1125376knPM10排放量: X(k1)= 3.171937 e 0.06594946k nNOx排放量: X(k1

6、)= 12.482121 e0.094156kn废水排放量:X(k1)= 3.984583e0.17227404knCOD排放量:X(k1)= 4.619788e0.1461757kn生活垃圾产生量: X(k1)= 3.17817908e0.1381162kn生活区夜间噪声值:X(k1)= 45.293e0.0034896k n工业用地: X(k1)= 5.667029 e0.1490649k人口Y1（万人）GDPY2（十亿元）工业增加值Y3（十亿元）总用水量Y4（百万m3）天然气用量Y5(百万m3)电力用量Y6（亿度）道路建设里程Y7（百公里）20006.703.492.876.409.52

7、.433.0120017.807.287.157.7222.13.023.3720029.508.177.229.1639.34.083.91200311.029.958.1612.2746.25.104.56200412.3013.0612.3512.6751.15.754.74200514.4115.5714.0915.5866.947.205.444200616.6819.1517.3418.4283.458.796.092200719.3023.5321.3221.76104.010.736.818200822.3428.9426.2525.72129.713.117.63200925

8、.8535.5732.2930.40161.716.018.539201029.9143.7339.7335.93201.619.559.556201134.6253.7748.8942.47251.323.8710.69201240.0666.1160.1550.19313.329.1511.97201346.3681.2874.0259.32390.635.613.39201453.6599.9691.0970.11486.943.4814.99201562.09122.8112.182.86607.053.0916.78201671.86151.0137.997.93756.764.84

9、18.77201783.16185.7169.6115.80943.479.1821.01201896.23228.3208.7136.80117696.6923.512019111.4280.7256.8161.701466118.126.312020128.9345.0315.9191.101828144.229.45社会经济发展变量预测表社会经济发展变量预测表 PM10排放量X1(千吨)NOx排放量X2(百吨)废水排放量X3（百万m3）COD排放量X4(百吨)生活垃圾产生量X5（万吨）夜间生活区声级X6(分贝)工业用地X7（百公顷）20003.37212.204.455.253.4242

10、.31.19520013.61114.685.446.194.1642.91.72720023.89117.006.467.204.8138.51.95520034.11218.418.768.295.6346.12.93420044.41819.769.069.626.3045.83.8420054.71221.9611.2111.107.2846.36.57820065.03324.1313.3112.858.3646.47.63520075.37626.5215.8114.889.6046.68.86320085.74229.1318.7817.2211.0246.710.2920096

11、.13432.0122.3219.9312.6546.911.9420106.55235.1626.5123.0614.5247.113.8620116.99938.6331.4926.6916.6747.216.0920127.47642.4537.4130.8919.1447.418.6820137.98646.6444.4535.7621.9847.621.6820148.5351.2552.8041.3925.2347.725.1620159.11156.3062.7347.9028.9747.929.2120169.73361.8774.5255.4533.2648.133.9201

12、710.3967.9788.5764.1738.1848.239.35201811.1174.68105.1874.2743.8448.445.68201911.8682.05124.9385.9650.3348.653.02202012.6790.15148.4299.5357.7948.761.54社会经济限制因子预测表社会经济限制因子预测表 多元统计回归分析法构建函数n以PM10排放量为例，EXCEL工具拟合n假设因变量和解释变量主要是线性关系nMarkov模型中的误差相互独立n误差服从正态分布并具有等变异性01 122yxx77 +x回归结果讨论三个问题：问题问题1：选择的解释变量能否

13、足以解释因变量的变化？：选择的解释变量能否足以解释因变量的变化？回归统计回归统计Multiple RMultiple R0.9999960.999996R SquareR Square0.9999920.999992Adjusted R SquareAdjusted R Square0.9999880.999988标准误差标准误差0.0100360.010036观测值观测值2121R2=SSR/SST残差SSE=SST-SSR R2度量了回归模型中解释变度量了回归模型中解释变量所解释的量所解释的y y变异的比例（相变异的比例（相对测度）对测度）回归结果讨论三个问题：问题问题2：解释变量与因变量

14、是否可以用线性函数来描述？：解释变量与因变量是否可以用线性函数来描述？方差分析方差分析dfdfSSSSMSMSF FSignificance Significance F F回归分析7 7163.0548163.054823.2935423.29354231245.1231245.14.44E-324.44E-32残差13130.001310.001310.0001010.000101总计2020163.0561163.0561Significance F是个非常小的概率，不能拒绝是个非常小的概率，不能拒绝“因变量与至少一个解释变量因变量与至少一个解释变量之间存在线性关系之间存在线性关系”的假

15、设。的假设。回归结果讨论三个问题：问题问题3：是否每个解释变量都对因变量存在显著影响？：是否每个解释变量都对因变量存在显著影响？CoefficieCoefficientsnts标准误差标准误差t Statt StatP-valueP-valueLower 95%Lower 95%Upper 95%Upper 95%下限下限 95.0%95.0%上限上限 95.0%95.0%InterceptIntercept0.9781990.9781990.0464380.04643821.0647821.064781.97E-111.97E-110.8778770.8778771.0785221.0785

16、220.8778770.8778771.0785221.078522Y1Y1-0.08775-0.087750.0279390.027939-3.14067-3.140670.0078110.007811-0.14811-0.14811-0.02739-0.02739-0.14811-0.14811-0.02739-0.02739Y2Y20.1535820.1535820.0852680.0852681.8011751.8011750.0949050.094905-0.03063-0.030630.3377910.337791-0.03063-0.030630.3377910.337791Y3

17、Y3-0.06564-0.065640.0613210.061321-1.07046-1.070460.3038850.303885-0.19812-0.198120.0668340.066834-0.19812-0.198120.0668340.066834Y4Y4-0.27356-0.273560.0332870.033287-8.21816-8.218161.66E-061.66E-06-0.34547-0.34547-0.20165-0.20165-0.34547-0.34547-0.20165-0.20165Y5Y5-0.01623-0.016230.0032980.003298-4

18、.92079-4.920790.000280.00028-0.02335-0.02335-0.0091-0.0091-0.02335-0.02335-0.0091-0.0091Y6Y60.2347680.2347680.0362150.0362156.4826086.4826082.06E-052.06E-050.156530.156530.3130050.3130050.156530.156530.3130050.313005Y7Y71.3191531.3191530.0505290.05052926.106726.10671.29E-121.29E-121.2099911.2099911.

19、4283151.4283151.2099911.2099911.4283151.428315剔除不显著变量的回归结果回归统计回归统计Multiple RMultiple R0.9999960.999996R SquareR Square0.9999910.999991Adjusted R SquareAdjusted R Square0.9999880.999988标准误差标准误差0.0100890.010089观测值观测值2121方差分析方差分析dfdfSSSSMSMSF FSignificance FSignificance F回归分析回归分析6 6163.0547163.054727.1

20、7578275267003.51.4E-341.4E-34残差残差14140.0014250.0014250.0001020.000102总计总计2020163.0561163.0561剔除不显著变量的回归结果CoefficCoefficienientsts标准误标准误差差t Statt StatP-valueP-valueLower Lower 95%95%Upper Upper 95%95%下限下限 95.95.0%0%上限上限 95.95.0%0%IntercepIntercept t0.988990.988991 10.045560.045566 621.70

21、4721.70473.54E-3.54E-12120.891260.891262 21.086721.086720.891260.891262 21.086721.08672Y1Y1- -0.10.10820821 10.020480.020486 6- -5.25.28188189 90.000110.000116 6- -0.10.15215214 4- -0.00.06426427 7- -0.10.15215214 4- -0.00.06426427 7Y2Y20.062490.062490.005430.005434 411.500511.50053 31.61E-1.61E-080

22、80.050830.050836 60.074140.074144 40.050830.050836 60.074140.074144 4Y4Y4- -0.20.24084082 20.013200.013201 1- -18.18.2422427 73.73E-3.73E-1111- -0.20.26916913 3-0.2125-0.2125- -0.20.26916913 3-0.2125-0.2125Y5Y5- -0.00.01311313 30.001590.00159- -8.28.25755756 69.45E-9.45E-0707- -0.00.01651654 4- -0.0

23、0.00970972 2- -0.00.01651654 4- -0.00.00970972 2Y6Y60.244990.244997 70.035110.035113 36.977376.977377 76.48E-6.48E-06060.169680.169687 70.320300.320307 70.169680.169687 70.320300.320307 7剔除不显著变量的回归结果限制因子限制因子PMPM1010排放量与发展变量的函数关系可排放量与发展变量的函数关系可初步表示为：初步表示为：X1=0.9890-0.1082y1+0.06249y2- 0.2408y4- 0.013

24、13y5 + 0.2450y6 + 1.316y7残差分析n线性的判断X1与sin（yi）的残差分析X1与sin（yi）的分析CoefficCoefficienientsts标准误标准误差差t Statt StatP-valueP-valueLower Lower 95%95%Upper Upper 95%95%下限下限 95.95.0%0%上限上限 95.95.0%0%IntercepIntercept t6.183866.183863 30.938400.938406 66.589756.589751 11.21E-1.21E-05054.171184.171182 28.196548.1

25、96545 54.171184.171182 28.196548.196545 5y1y11.257141.257147 71.282931.282934 40.97990.97990.343760.343766 6- -1.41.49449447 74.008764.008767 7- -1.41.49449447 74.008764.008767 7y2y2- -3.43.44954953 32.356072.356074 4-1.4641-1.46410.165250.165258 8-8.5028-8.50281.603751.603751 1-8.5028-8.50281.60375

26、1.603751 1y4y4- -0.00.07177178 81.179911.179911 1- -0.00.06086083 30.952350.952353 3- -2.62.60240243 32.458882.458882 2- -2.62.60240243 32.458882.458882 2y5y51.877731.877731.553211.553211 11.208931.208934 40.246710.24671- -1.41.45355358 85.209035.209037 7- -1.41.45355358 85.209035.209037 7- -1.81.86036034 4- -1.81.86036034 4如何处理？残差分析n正态性检验当当n n不是足够大时，利用残差的正态概率图来检不是足够大时，利用残差的正态概率图来检验误差的正态性。验误差的正态性。最终的回归结果限制因子限制因子PMPM1010排放量与发展变量的函数关系表排放量与