Multi-Level Decision-Making for Inter-Regional Water Resources Management with Water Footprint Analysis and Shared Socioeconomic Pathways

Abstract

This study develops a synergistic optimization framework for planning inter-regional water resources management system under shared socioeconomic pathways; this framework integrates multi-level and robust flexible programs. The upper-level model determines minimum social loss induced by water exploitation, the middle-level one focuses exclusively on pollutant emissions, and the lower-level one aims to achieve maximum economic benefits. An improved multi-level interactive algorithm is proposed to balance the satisfaction degree of constraints and goals to achieve optimal. The effectiveness of the developed multi-level model is illustrated through a real-world case in Wuhan City Circle. Results indicate that the overall water resources performance in Wuhan City Circle is satisfactory, especially in Xianning and Huanggang, whereas some water footprint deficits exist in Wuhan, Xiaogan, and Tianmen. Climate scenarios have a remarkable effect on social loss but only slightly affect water supply strategies, pollutant emissions, and economic benefits. A high satisfactory degree results in a low risk of insufficient water supply and excessive pollutant emissions. Thus, satisfactory degree can be used as an evaluation indicator for identifying the amount of credible and reliable risk on final decisions. The findings of this study can enable stakeholders to grasp the inherent conflicts and trade-offs between environmental and economic interests.

Appendix

1.1 Sets

j :

the type of water sources (j = 1for surface water; 2 represents groundwater);

i :

administrative region (i = 1 for Wuhan, 2 for Huangshi, 3 for Ezhou, 4 for Huanggang, 5 for Xiaogan, 6 for Xianning, 7 for Xiantao, 8 for Qianjiang, 9 for Tianmen);

k :

represents the index for planning horizon (k = 1 for 2020, 2 for 2025);

m :

the index for capacity expansion;

g:

the type of pollutant; g = 1 for COD and 2 for ammonia nitrogen;

1.2 Parameters and decision variables

BZ :

a ratio of production water consumption to total water consumption;

CM :

the wastewater emission coefficient of the primary industries;

CN :

the wastewater emission coefficient of the secondary industries;

CO :

the wastewater emission coefficient of the tertiary industries;

CP :

the wastewater emission coefficient of the domestic;

EB :

the system economic benefit (RMB ¥);

EM :

the benefit coefficient of water use in terms of the primary industries (RMB ¥/m³);

EN :

the benefit coefficient of water use in terms of the secondary industries (RMB ¥/ m³);

EO :

the benefit coefficient of water use in terms of the tertiary industries (RMB ¥/ m³);

EP :

the benefit coefficient of water use in terms of the domestic (RMB ¥/ m³);

f :

the agent equation of water footprint and water consumption at different sectors;

FQ :

the minimum amount of grain yield (ton);

GDWL :

the minimum water use for per unit gross domestic product (m³/10⁴ RMB ¥);

GDWU :

the maximum water use for per unit gross domestic product (m³/10⁴ RMB ¥);

GM :

gross domestic product of the primary industries (RMB ¥);

GML :

the lower-bound economic indicators;

GMU :

the upper-bound economic indicators;

GN :

gross domestic product of the secondary industries (RMB ¥);

GNL :

the lower-bound economic indicators;

GNU :

the upper-bound economic indicators;

GO :

gross domestic product of the tertiary industries (RMB ¥);

GOL :

the lower-bound economic indicators;

GOU :

the upper-bound economic indicators;

K :

the loss rate of maximum economic impact of water pollution on each calculation sub-item (where K₁, K₂, K₃, and K₄ correspond to the domestic, primary, secondary, and tertiary industries, respectively);

L :

the length of the planning horizon (day);

PCM :

pollutant concentration of wastewater from the primary industries (mg/L);

PCN :

pollutant concentration of wastewater from the secondary industries (mg/L);

PCO :

pollutant concentration of wastewater from the tertiary industries (mg/L);

PCP :

pollutant concentration of wastewater from the domestic (mg/L);

PDWL :

the minimum per capita water consumption (m³/person);

PDWU :

the maximum per capita water consumption (m³/person);

PE :

the system pollutant emissions (10⁴ tones);

PN :

the population scale of each region;

PNL :

the lower-bound demographic indicators;

PNU :

the upper-bound demographic indicators;

Q :

the availabilities of different water resources (m³);

SB :

the system social benefits (RMB ¥);

TPP :

the amount of available pollutant emissions (10⁴ tones);

TWP :

the amount of available wastewater emissions (10⁴ m3);

UCW :

the treatment cost for per wastewater (RMB ¥/ m³), which is related to the regional water quality;

UEC :

the cost for unit expansion (RMB ¥/ m³);

UFP :

the amount of grain yield per unit of water use (ton/ m³);

VM :

the cost coefficient with regard to the primary industries (RMB ¥/ m³);

VN :

the cost coefficient with regard to the secondary industries (RMB ¥/ m³);

VO :

the cost coefficient with regard to the tertiary industries (RMB ¥/ m³);

VP :

the cost coefficient with regard to the domestic sector (RMB ¥/ m³);

WCP :

the wastewater treatment capacity (m³/day);

WF :

largest per capita water footprint in different regions and periods, which equals to 2 in this study.

WMAX :

the variation range of average water quality of lakes in the region;

WMIN :

the variation range of average water quality of rivers in the region;

xm :

the optimal amount of water allocation to the primary industries (m³);

XMMAX :

the maximum amount of water demand in terms of the primary industries (m³);

XMMIN :

the minimum amount of water demand in terms of the primary industries (m³);

xn :

the optimal amount of water allocation to the secondary industries (m³);

XNMAX :

the maximum amount of water demand in terms of the secondary industries (m³);

XNMIN :

the minimum amount of water demand in terms of the secondary industries (m³);

xo:

the optimal amount of water allocation to the tertiary industries (m³);

XOMAX :

the maximum amount of water demand in terms of the tertiary industries (m³);

XOMIN :

the minimum amount of water demand in terms of the tertiary industries (m³);

xp :

the optimal amount of water allocation to the domestic (m³);

XPMAX :

the maximum amount of water demand in terms of the domestic (m³);

XPMIN :

the minimum amount of water demand in terms of the domestic (m³);

y :

the binary variable with a value of 0 (no expansion) or 1 (expansion);

αm :

the fairness coefficient of the primary industries water use;

αn :

the fairness coefficient of the secondary industries water use;

αo :

the fairness coefficient of the tertiary industries water use;

αp :

the fairness coefficient of the domestic water use;

η :

the removal rate of pollutants;

λm :

economic loss rate caused by pollution from the primary industries (%);

λn :

economic loss rate caused by pollution from the secondary industries (%);

λo :

economic loss rate caused by pollution from the tertiary industries (%);

λp :

the individual economic losses caused by domestic water pollution (RMB ¥).