Article
An Empirical Study for Real Options of Water Management in
the Three Gorges Reservoir Area
Zuliang Lu
1,2,
*, Xiankui Wu
1
, Fei Cai
1
and Fei Huang
1
Citation: Lu, Z.; Wu, X.; Cai, F.;
Huang, F. An Empirical Study for
Real Options of Water Management
in the Three Gorges Reservoir Area.
Sustainability 2021, 13, 11255.
https://doi.org/10.3390/
su132011255
Academic Editors: João Carlos de
Oliveira Matias and Paolo Renna
Received: 18 July 2021
Accepted: 17 September 2021
Published: 12 October 2021
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1
Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University,
Chongqing 404000, China; xiankuiwu@126.com (X.W.); feicaizyy@126.com (F.C.); feihuangc@126.com (F.H.)
2
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics,
Tianjin 300222, China
* Correspondence: zulianglu@csrc.ac.cn
Abstract:
This paper investigates an empirical evaluation of water management on agricultural
irrigation. To address this problem, a real options model was proposed. This model analysis the
choice of investment in water savings. Also, the model discusses a linear complementary problem
that can be transformed into the inequalities of parabolic variational. By using a power penalty
method, we solved the parabolic variational inequalities. The results depicted that the nonlinear
parabolic equations’ solution is converges to the rate of order
O(h
−
k
2
)
. A numerical example is
given at the end of the paper to demonstrate the theoretical analysis follows from the Three Gorges
Reservoir Area.
Keywords: water management; Three Gorges Reservoir Area; water price
1. Introduction
Water resource security is recognized as one of the most severe challenges with which
mankind is facing, especially in agriculture. There is a critically uneven distribution of
water resources in agricultural irrigation water resources in China [
1
]. Per capital available
water is bountiful in the south, but few in the north. The irrigation of China in water
consumption needs not only large but also excess waste. Especially in the areas with
abundant water resources [
2
], they possess no strong sense for saving water and have low
utilization efficiency of irrigation water.
The Three Gorges Reservoir Area [
3
] is such a region we mentioned. Since the
establishment of the Three Gorges Dam, it directly inundated the 682 square kilometers
of the valley area and spread to 19 counties and cities with an area of 6 square kilometers.
This leads to plenty of water resources with the poor ability of soil and water inadequate
conservation in the Three Gorges Reservoir Area. Even, there have led to a significant
decline in forest coverage because the hill slope area accounted for 97.3 percent of which
the slope area over 30 degrees is more than half of the slope area, unreasonable farming
practices on arable land and deforestation [
4
]. Affected by the flooding of the reservoir
and the second occupation of land by immigrants, the per capita cultivated land area in
the Three Gorges Reservoir Area decreased from 73 square meters to 60 square meters. So
challenges are seriously confronted with the sustainable development of agriculture.
According to the survey [
5
], however, the current effective irrigation rate is only 25.9%.
The rest which depends on rains belongs to no irrigation facilities. Paddy field is the main
part of the current irrigation areas, accounting for 47.3% of the total irrigation areas, but
the only 59.6% of paddy fields can be irrigated, while only 16.4% of drylands and 19.5%
of garden lands can be irrigated. The main source of irrigation water is small-scale water
supply projects [
6
]. In the existing projects, pond reservoir is the main body of water supply,
accounting for 62.3% of the total water supply capacity. Followed by reservoirs, accounting
Sustainability 2021, 13, 11255. https://doi.org/10.3390/su132011255 https://www.mdpi.com/journal/sustainability
