system: [SYSTEM]

user: 2. 模型构建 完全分解模型由Sun [ 13 ] 于1998年提出，是指数分解法中的一种重要模型，本文利用该模型分解长江三角洲地区用水量时空差异的驱动效应。 假定地区用水总量W由公式(1)表示： W = ∑ i = 1 3 W i = ∑ i = 1 3 P × G P × G i G × W i G i (1) 式中，P和G分别代表人口数和国内生产总值， G i 和 W i 分别表示第i产业增加值和用水量，并且满足 G = ∑ i = 1 3 W i ( i = 1 ， 2 ， 3 )。 将公式(1)进一步改写成公式(2)的形式： W = ∑ i = 1 3 P × I n c × S i × I i (2) 式中， I n c = G / P 表示人均国内生产总值， S i = G i / G 表示第i产业增加值占国内生产总值的比重， I i = W i / G i 表示第i产业用水强度。 假定时间从0变化到t，用水总量变化量 Δ W 可以由公式(3)表示： Δ W = W t − W 0 = ∑ i = 1 3 P t × I n c t × S i t × I i t − ∑ i = 1 3 P 0 × I n c 0 × S i 0 × I i 0 (3) 可以将用水总量变化量 Δ W 分解为4个驱动效应，如公式(4)所示： Δ W = Δ W P + Δ W I n c + Δ W S + Δ W I (4) 依据“共同创造，平等分配”原则 [ 13 ] ，4个驱动效应分别如公式(5)~(8)所示： 人口效应： Δ W P = ∑ i = 1 3 Δ P ⋅ I n c 0 ⋅ S i 0 ⋅ I i 0 + 1 2 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ S i 0 ⋅ I i 0 + Δ S i ⋅ I n c 0 ⋅ I i 0 + Δ I i 0 ⋅ I n c 0 ⋅ S i 0 )                                                 + 1 3 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ Δ S i ⋅ I i 0 + Δ I n c ⋅ Δ I i ⋅ S i 0 + Δ S i ⋅ Δ I i ⋅ I n c 0 )                   + 1 4 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ Δ S i ⋅ Δ I i ) (5) 收入效应： Δ W I n c = ∑ i = 1 3 Δ I n c ⋅ P 0 ⋅ S i 0 ⋅ I i 0 + 1 2 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ S i 0 ⋅ I i 0 + Δ S i ⋅ P 0 ⋅ I i 0 + Δ I i ⋅ P 0 ⋅ S i 0 )                                                   + 1 3 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ Δ S i ⋅ I i 0 + Δ P ⋅ Δ I i ⋅ S i 0 + Δ S i ⋅ Δ I i ⋅ P 0 )                       + 1 4 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ Δ S i ⋅ Δ I i ) (6) 结构效应： Δ W S = ∑ i = 1 3 Δ S i ⋅ P 0 ⋅ I n c 0 ⋅ I i 0 + 1 2 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ I n c 0 ⋅ I i 0 + Δ I n c ⋅ P 0 ⋅ I i 0 + Δ I i ⋅ P 0 ⋅ I n c 0 )                                                 + 1 3 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ Δ I n c ⋅ I i 0 + Δ P ⋅ Δ I i ⋅ I n c 0 + Δ I n c ⋅ Δ I i ⋅ P 0 )                   + 1 4 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ Δ I n c ⋅ Δ I i ) (7) 强度效应： Δ W I = ∑ i = 1 3 Δ I i ⋅ P 0 ⋅ I n c 0 ⋅ S i 0 + 1 2 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ I n c 0 ⋅ S i 0 + Δ I n c ⋅ P 0 ⋅ S i 0 + Δ S i ⋅ P 0 ⋅ I n c 0 )                                               + 1 3 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ Δ I n c ⋅ S i 0 + Δ P ⋅ Δ S i ⋅ I n c 0 + Δ I n c ⋅ Δ S i ⋅ P 0 )                 + 1 4 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ Δ I n c ⋅ Δ S i ) (8) 式中， Δ W P 、 Δ W I n c 、 Δ W S 和 Δ W I 分别表示人口效应、收入效应、结构效应和强度效应，分别反映人口规模变化、经济增长、产业结构调整、产业用水强度变化对用水总量变化量 Δ W 的影响。 公式(4)~(8)展现了用水总量W从时间0变化到t时，用水总量变化量 Δ W 的驱动效应。若存在两个地区，分别用R0和R1表示，用水总量的空间差异如公式(9)所示： Δ W = W R 1 − W R 0 = ∑ i = 1 3 P R 1 × I n c R 1 × S i R 1 × I i R 1 − ∑ i = 1 3 P R 0 × I n c R 0 × S i R 0 × I i R 0 (9) 式中各变量的含义与公式(3)相同，只不过公式(9)表示空间差异，而公式(3)表示时间差异。 将地区R1和地区R0用水总量空间差异 Δ W R 1 − R 0 也分解为4个驱动效应，即人口效应、收入效应、结构效应和强度效应，如下所示： Δ W R 1 − R 0 = Δ W P R 1 − R 0 + Δ W I n c R 1 − R 0 + Δ W S R 1 − R 0 + Δ W I R 1 − R 0 (10) Δ W P R 1 − R 0 = ∑ i = 1 3 Δ P ⋅ I n c R 0 ⋅ S i R 0 ⋅ I i R 0                                                                                 + 1 2 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ S i R 0 ⋅ I i R 0 + Δ S i ⋅ I n c R 0 ⋅ I i R 0 + Δ I i ⋅ I n c R 0 ⋅ S i R 0 )                                                                                 + 1 3 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ Δ S i ⋅ I i R 0 + Δ I n c ⋅ Δ I i ⋅ S i R 0 + Δ S i ⋅ Δ I i ⋅ I n c R 0 )                                                                                   + 1 4 ∑ i = 1 3 Δ P ⋅ ( Δ I n c ⋅ Δ S i ⋅ Δ I i ) (11) Δ W I n c R 1 − R 0 = ∑ i = 1 3 Δ I n c ⋅ P R 0 ⋅ S i R 0 ⋅ I i R 0                                                                                     + 1 2 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ S i R 0 ⋅ I i R 0 + Δ S i ⋅ P R 0 ⋅ I i R 0 + Δ I i ⋅ P R 0 ⋅ S i R 0 )                                                                                     + 1 3 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ Δ S i ⋅ I i R 0 + Δ P ⋅ Δ I i ⋅ S i R 0 + Δ S i ⋅ Δ I i ⋅ P R 0 )                                                                                     + 1 4 ∑ i = 1 3 Δ I n c ⋅ ( Δ P ⋅ Δ S i ⋅ Δ I i ) (12) Δ W S R 1 − R 0 = ∑ i = 1 3 Δ S i ⋅ P R 0 ⋅ I n c R 0 ⋅ I i R 0                                                                                   + 1 2 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ I n c R 0 ⋅ I i R 0 + Δ I n c ⋅ P R 0 ⋅ I i R 0 + Δ I i ⋅ P R 0 ⋅ I n c R 0 )                                                                                   + 1 3 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ Δ I n c ⋅ I i R 0 + Δ P ⋅ Δ I i ⋅ I n c R 0 + Δ I n c ⋅ Δ I i ⋅ P R 0 )                                                                                   + 1 4 ∑ i = 1 3 Δ S i ⋅ ( Δ P ⋅ Δ I n c ⋅ Δ I i ) (13) Δ W I R 1 − R 0 = ∑ i = 1 3 Δ I i ⋅ P R 0 ⋅ I n c R 0 ⋅ S i R 0                                                                                 + 1 2 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ I n c R 0 ⋅ S i R 0 + Δ I n c ⋅ P R 0 ⋅ S i R 0 + Δ S i ⋅ P R 0 ⋅ I n c R 0 )                                                                                 + 1 3 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ Δ I n c ⋅ S i R 0 + Δ P ⋅ Δ S i ⋅ I n c R 0 + Δ I n c ⋅ Δ S i ⋅ P R 0 )                                                                                 + 1 4 ∑ i = 1 3 Δ I i ⋅ ( Δ P ⋅ Δ I n c ⋅ Δ S i ) (14) 式中， Δ W P R 1 − R 0 、 Δ W I n c R 1 − R 0 、 Δ W S R 1 − R 0 和 Δ W I R 1 − R 0 也分别表示人口效应、收入效应、结构效应和强度效应，分别反映地区R1与地区R0人口规模差异、经济增长差异、产业结构差异和产业用水强度差异对用水总量空间差异 Δ W R 1 − R 0 的影响。