# 不同时间尺度下水资源配置效应Effects of Time Scales on Water Resources Allocation

Abstract: The water resources allocation is an important means to solve the problem of uneven distribution of water resources in time and space. However, there are few studies on the effects of time scales on water resources allocation. The effects caused by the variation of time scale are often ignored and lead to underestimation of water shortage risks in water resources management. IRAS water resources allocation model which can adjust the time step flexibly to adapt to different time scales, is employed to the middle and lower reaches of the Hanjiang River basin as a case study. There are three types of time scales (year, season and month) to be chosen for discussing the effects of time scales on water resources allocation. The results show that the effects of time scales on water resources allocation mainly depend on water resources conditions and the regulating capacity of the water system. Water shortage is few to find in all three-time scales if the water resources are enough to satisfy the water demand. However, the effects of time scales on water resources allocation are more sensitive in areas with water shortage and weak regulating capacity of the water system. As the variability of water inflow and demand water can be smoothed at long-term scale, the water shortage ratio at long-term scale is lower than that at a short-term scale. The results of the study have not only analyzed the effects of time scales on water resources allocation, but also warned the risks of water resources management at different time scales.

1. 引言

2. IRAS模型结构与原理

IRAS是一款能够灵活调整计算时间步长，适用于多种时间尺度条件的水资源配置模拟模型，目前该模型已经在英国泰晤士河流域、墨西哥瓜纳华托河流域与葡萄牙瓜迪亚纳河流域等地区得到了成功应用。模型以物理水网为基础，通过分析水资源系统中供、用、耗、排等主要环节中所涉及的要素和相互连接关系，结合水资源系统的来水序列、需水序列、各类参数以及约束条件，在不同的调度运行规则下，模拟系统内水资源的配置过程。其原理如图1所示：

Figure 1. Framework of the IRAS model

2.1. 系统概化

IRAS模型水资源系统中所涉及的实体元素可以分为节点与有向线段两种类型。节点用于描述研究区域中的工程设施、控制结构与用水单元，根据实体元素的属性可将其分为水源节点、来水节点、用水节点、分流节点、汇流节点。有向线段用于描述节点之间存在的水量传输与影响关系，根据水流是否能够双向流动可将其分为双向线段与单向线段。其中单向线段又可进一步分为需水线段、分流线段、天然线段，参与到地表水的输送与分配过程之中；双向线段通常结合达西定律用于地下水的模拟。

2.2. 参数设置

2.3. 运行规则

1) 时间步长划分

IRAS模型以年为周期进行模拟计算，其时间步长可灵活调整，以适应不同时间尺度数据的输入，为在日、旬、月、季、年等时间尺度条件下水资源配置模拟计算提供了支持。每个时间步长可进一步划分为不同子时间步长(最小为1天)，子时间步长的数目越多，模拟过程越精细，配置结果精度越高，所需计算时间越长。

2) 缺水计算

${W}_{st}^{e}=\frac{\underset{1}{\overset{st}{\sum }}{W}_{st}^{in}-\underset{1}{\overset{st}{\sum }}{W}_{st}^{r,in}}{st-1}\ast \left(tst-st+1\right)$ (1)

${W}_{st}^{d}=\frac{{W}_{t}^{dem}-{W}_{t}^{dem}\ast f-\underset{1}{\overset{st-1}{\sum }}{W}_{st}^{in}-{W}_{st}^{e}}{tst-st+1}$ (2)

$E{W}_{st}^{k,out}=\underset{i=1}{\overset{N}{\sum }}{W}_{st}^{i,d}\ast {\alpha }_{st}^{i,k}$ (3)

3) 供水计算

Figure 2. Calculation diagram of water supply discharge of the main reservoir

${P}_{t}=t/T$ (4)

${V}_{\mathrm{max}}^{t}={V}_{\mathrm{max}}^{b}\ast \left(1-{P}_{t}\right)+{V}_{\mathrm{max}}^{e}\ast {P}_{t}$ (5)

${V}_{\mathrm{min}}^{t}={V}_{\mathrm{min}}^{b}\ast \left(1-{P}_{t}\right)+{V}_{\mathrm{min}}^{e}\ast {P}_{t}$ (6)

${q}_{\mathrm{max}}^{t}={q}_{\mathrm{max}}^{b}\ast \left(1-{P}_{t}\right)+{q}_{\mathrm{max}}^{e}\ast {P}_{t}$ (7)

${q}_{\mathrm{min}}^{t}={q}_{\mathrm{min}}^{b}\ast \left(1-{P}_{t}\right)+{q}_{\mathrm{min}}^{e}\ast {P}_{t}$ (8)

${P}_{v}=\left({V}^{t}-{V}_{\mathrm{min}}^{t}\right)/\left({V}_{\mathrm{max}}^{t}-{V}_{\mathrm{min}}^{t}\right)$ (9)

${q}^{t}={q}_{\mathrm{min}}\ast \left(1-{P}_{v}\right)+{q}_{\mathrm{max}}\ast {P}_{v}$ (10)

4) 配水与耗水计算

2.4. 约束条件

1) 计算分区水量平衡约束

${W}_{st}^{i}=\underset{m=1}{\overset{M}{\sum }}{W}_{st}^{m}\cdot {\beta }_{st}^{i,m}+\underset{k=1}{\overset{K}{\sum }}{W}_{st}^{k,out}\cdot {\alpha }_{st}^{i,k}+{W}_{st}^{i,in}-\underset{j=1}{\overset{J}{\sum }}{W}_{st}^{i,j}\cdot {c}_{st}^{i,j}-{W}_{st}^{i,l}-{W}_{st}^{i,t}$ (11)

2) 水库约束

① 水库水量平衡约束

${V}_{st+1}^{k}={V}_{st}^{k}+{W}_{st}^{k,in}-{W}_{st}^{k,out}-{W}_{st}^{k,l}$ (12)

② 水库库容约束

${V}_{\mathrm{min}\text{}st}^{n}\le {V}_{st}^{n}\le {V}_{\mathrm{max}\text{}st}^{n}$ (13)

3) 非负约束

${W}_{st}^{i,j}\ge 0$ (14)

4) 需水约束

${W}_{st}^{i,j}\le D{W}_{st}^{i,j}$ (15)

5) 供水能力约束

$\underset{j=1}{\overset{J}{\sum }}{W}_{st}^{i,j}\le A{W}_{st}^{i}$ (16)

3. 汉江流域中下游地区水资源配置模型构建

3.1. 研究区——汉江流域中下游地区概况

3.2. 计算单元划分

3.3. 模型输入

1) 水平年及计算步长

Figure 3. Spatial distribution of computing units and reservoirs in the middle and lower reaches of Hanjiang River basin

Figure 4. Schematic diagram of the middle and lower reaches of Hanjiang River basin

2) 来水条件与需水条件

Table 1. Annual off-stream water demand in the present and planning years (100 million m3)

3) 参数设置

Table 2. Regression coefficient of every type of water use in the Hanjiang River basin

4. 结果分析

Table 3. Total water scarcity in the middle and lower reaches of Hanjiang River basin (10,000 m3)

Table 4. Water scarcity in every city in the middle and lower reaches of Hanjiang River basin (10,000 m3)

5. 结论

Figure 5. The process of water inflow and water demand in Jingmen city under seasonal and monthly scales

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