Agricultural water allocation with climate change based on gray wolf optimization in a semi-arid region of China

Study area

The study area was the Aksu Valley (75°35′–82°00′E, 40°00′–42°27′N, excluding Akqi) in Xinjiang, China. The area is approximately 3.6 × 10⁴ km², including six counties or cities in the Aksu area (Aksu, Wensu, Awati, Wushi, Keping and Alar). It is served by the western upper reaches of the Tarim River Basin (Fig. 1) and sand dunes are the predominant landform (El-Tantawi et al., 2019). The water used for agricultural irrigation makes up more than 95% of the total regional water consumption. The most important irrigated crop is cotton, which has increased in annual planting area (Li et al., 2020a; Li et al., 2020b).

Data sources

Meteorological data were obtained from the China Meteorological Science Data Network (1961–2005) (http://data.cma.cn/). Large-scale climate variables (predictors) for the current climate and future scenarios under the RCPs in years 1961 to 2050 obtained from Canadian Climate Data and Scenarios (http://climate-scenarios.canada.ca/). We used grid resolution 2.815° latitude by 2.815° longitude. River discharge data (1961–2005) were from the Aksu Valley Chronicles (Aksu River Basin Management Office, 2006). Socio-economic data were gathered from the Aksu Region Yearbook and Xinjiang Construction Corps Yearbook (Bureau of Statistics of Xinjiang Production and Construction Corps, 2009).

Simulation of climate scenarios

Estimation of water demand and supply in Aksu River Basin

Multi-objective optimal allocation model of water and soil resources

The multi-objective optimal allocation model must cover the balance of the economic, social and ecological benefits. We used the gross national product (GDP) as the economic indicator, the maximum benefit of water per cubic meter as the social indicator and ecological green equivalent as the ecological indicator. The computational formula is: (10)${\displaystyle {\mathrm{F}}_1\left(\mathrm{X}\right)=max{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{a}}_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{ij}}}$ (11)${\displaystyle {\mathrm{F}}_2\left(\mathrm{X}\right)=max\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{a}}_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{ij}}}{\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{b}}_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{ij}}}}$ (12)${\displaystyle {\mathrm{F}}_3\left(\mathrm{X}\right)=max\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{c}}_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{ij}}}$ (13)${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{b}}_{\mathrm{ij}}{\mathrm{X}}_{\mathrm{ij}}\le {\mathrm{W}}_{\mathrm{s}}}$ (14)${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{X}}_{\mathrm{ij}}=\mathrm{T}}$ (15)${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{X}}_{1\mathrm{j}}\ge {\mathrm{PL}}_{\min }}$ (16)${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{X}}_{2\mathrm{j}}\ge {\mathrm{FL}}_{\mathrm{now}}}$ (17)${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{X}}_{3\mathrm{j}}\ge {\mathrm{CL}}_{\mathrm{now}}}$ (18)${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{X}}_{4\mathrm{j}}\ge {\mathrm{WL}}_{\mathrm{now}}}$ (19)${\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{X}}_{5\mathrm{j}}={\mathrm{NL}}_{\mathrm{now}}}$ where F₁(X) is total GDP, F₂(X) is the utilization of maximum benefits per cubic meter of water, F₃(X) is the ecological green equivalent of the river basin, X_ij is the area of land types in each area (km²), a_i is gross national product per unit area of each land type (10,000 yuan/km²), b_i isthe water demand per unit area of each land use type (m³), and c_i is the green equivalent value of each area of each land type. T is the total area (km²), PL_min is the red line of cultivated land in the study area (km²), FL_now is the current forest area (km²), BL_now is the current construction land area, WL_now is the current water area, and NL_now is the current unused land area.

The MOGWO algorithm and the optimal solution

Design of MOGWO algorithm

We modified the grey wolf algorithm (GWO) to incorporate two new components (storing non-dominated Pareto optimal solutions archive and a leader selection strategy) to comprise the MOGWO (Mirjalili et al., 2016). The detailed procedures are described in Fig. 2.

We obtained a set of non-dominated solutions for the multi-objective model. The parameter settings were number of wolves = 100, achieve = 100, range = 20% and iterations = 100.

The best optimal value for multi-objective model based on analytic hierarchy process method (AHP)

To establish a judgment matrix, the relative weight of each target is determined. At the same time, the consistency index of the judgment matrix is calculated to verify the validity of the weight. The consistency of the matrix is considered acceptable when the consistency ratio (CR) is less than 0.1. We determined importance indicators for establishing the judgment matrix (Table 2) and the proportions and test indicators of the three planning goals calculated by the analytic hierarchy process (Table 3).

Projected future climate and water resource change

We projected temperatures and precipitation at the Aksu Basin using the downscaled global climate models (GCMs) (Fig. 3). Warming was predicted for this area’s subregions. By the year 2050 (starting in 2020), the projected temperature could increase up to 1.3, 0.9, 0.8, and 0.2 °C, at Aksu, Keping, Alar, and Akqi under RCP4.5, respectively. Under the RCP8.5 climate scenarios, the temperatures were predicted to increase at a faster rate. As opposed to temperature trends, the precipitation showed decreasing trends except at the Keping station.

The minimum and maximum temperatures predicted by SDSM from 2006 to 2050 change over the whole basin’s ET₀ (Figs. 4 and 5). ET₀ values of the four weather stations showed an upward trend during the period 2010–2050. There was no significant difference between the RCP4.5 and RCP8.5 climate scenarios during the first years, but ET₀ has an increasingly higher value under RCP8.5 scenarios relative to RCP4.5 after 2035. The difference value is expected to be as high as 50 mm by 2050.

By using the neural network model to estimate the runoff flow of the hydrological station, the available surface water in the basin gives a trend of slow future increase (Fig. 6). Until 2050, the annual average run off is predicted to increase 7. 963 × 10⁸ m³ and 10. 41 × 10⁸ m³ under RCP4.5 and RCP8.5, respectively. The amount of runoff was higher under the RCP8.5 scenario than the RCP4.5 scenario (Table 4).

The optimal allocation of the water and land resources

Future water shortage is predicted to be about 5.83 × 10⁸m³ in the basin (Table 5). The Pareto frontier under the five scenarios obtained by MOGWO is shown in Fig. S1; the specific values of water and soil resource allocation in the basin are shown in Tables S2–S7. Due to the high emission concentration (RCP8.5), with the exception of construction land, the water demand per unit area of the other land types is higher compared to the low emission concentration (RCP4.5). Although the total cultivated area in the basin under the two climate scenarios is similar, the change of cultivation in each region of the basin differs. Water and land resource allocation in the recent-term (2020), medium-term (2035), and long-term (2050) plan under two emission concentrations showed, in general, a trend of decreasing arable land and grassland and increasing other land (Fig. 7). The arable land areas of Awati, Aksu, and Alar exhibited a continuous downward trend as the result of the policy for restoring farmland to save water, but the arable land areas was likely to continue to increase in Wushi County (Fig. 8). In addition, the area of grassland in the Wushi and Wensu regions was trending downward, while the Alar was increasing (Fig. 9).