Study on Soil Water Resource Carrying Capacity Based on Multi-objective Model in Hebei

Based on analysis and summary of the present achievements concerned soil water resource, the conception and connotation of soil water resource were defined and its carrying capacity was given in this study. According to characteristics of soil water resource carrying capacity, the multi-objective model of soil water resource carrying capacity was established for Hebei province. In the model, objective functions consists of 4 parts, including agriculture output value, grain yield, proportion of agricultural water consumption and eco-environmental water consumption, each crop’s planting area is defined as decision variable. After changing the multiple objectives into a single objective by fuzzy binary contrast method, this multi-objective model was solved by using the method of single objective programming. The results show that the agriculture output value and grain yield could be increased steadily and agricultural water consumption is decreased contrarily by the soil water resource optimum scheme in comparison with present situation. The consumptions of soil water resource are 6.80 and 7.62 billion m3 respectively in 2020 and 2030 by developing agricultural technology of the water-saving irrigation, straw returning, film-covering planting and greenhouse cultivation. The amount of saving water for agriculture is 0.75 and 1.79 billion m3 respectively in 2020 and 2030 year.


INTRODUCTION
Hebei is one of the most severe water shortage areas of China, Where the average annual water resources are 20.49 billion m 3 , the water resources per capita are only 307 m 3 and water resources per hectare are 3165 m 3 .The total water consumption is up to 19.37 billion m 3 in 2010.The water supply quantity of surface water is 3.61 billion m 3 , its development and utilization rate is 94.6%; the exploitation of groundwater is 15.76 billion m 3 , some of which the 5.44 billion m 3 is overexplored every year.At present, the gap between water supply and water demands is 5 to 6 billion m 3 in Hebei.The traditional water resources could not support the sustainable socio-economic development.
However, it is rich in soil water resource in Hebei.According to the evaluation of soil water resource, the average annual rainfall is 99.79 billion m 3 ; more than 70% transform directly into soil water.Therefore, the development and utilization of soil water resource is an effective measure for helping ease the shortage of water resources in Hebei.

Soil water resource:
The resource is defined as the general term of natural environment factors that can generate economic value and improve current and future human welfare in the certain period by United Nations Environment Programme (UNEP).Soil water exists ubiquitously in soil and it can be absorbed and utilized by crops and improve the agricultural environment.Soil water has characteristics of natural resources and is the most convenient fresh water to use in world.Therefore, soil water is a kind of resource.Nputotulu (1974) scholar first proposed the concept of soil water resource and then many scholars studied on soil water resource (Pariva et al., 2012;Liu et al., 2009;Xia and Li, 2001;Yu and Xiong, 2003;Yang et al., 2004;Wang et al., 2006;Shen, 2008;Li and Zheng, 2009;Bandyopadhyay and Mallick, 2003;Franz et al., 2012).
Based on analysis and summary of the present achievements concerned soil water resource, the conception and connotation of soil water resource were defined in the study.In General, soil water resource is the amount of water stored between the ground water table and the surface of the soil, which it can be recycled.In a narrow sense, soil water resource refers to the fresh water with update capabilities in a period of time, which it is recharged by precipitation and stored in soil evaluation layer, can be utilized for agricultural production and ecological environment under natural conditions.In mountainous areas with shallow soil layer, soil water resource refers to effective rainfall stored in the entire soil layer.Plains where soil layer is thicker and groundwater is deep, soil water resource refers only to soil water bodies in the upper unsaturated soil which can be absorbed by vegetation root.Soil water that exists in the lower soil layer only exchanges with gravity water and cannot be absorbed and utilized by vegetation.This part of soil water can be regarded as static reserve.The soil evaluation layer is shown in Fig. 1.

Soil water resource carrying capacity: Carrying
Capacity refers to that objects can withstand the maximum load without incurring any damage.The concept of carrying capacity was introduced to study the potential of resource utilization.Resource carrying capacity is defined by UNESCO as follows: A country or region's resource carrying capacity refers to the population of the country or region that can be continuing to provide in the foreseeable period by the use of local natural resources, energy, intelligence, technology and other conditions in keeping with its social and cultural living standard.
With the research on the resource carrying capacity increasingly, the water resource carrying capacity and water environment carrying capacity are hot field (Ashok, 2011;Al-Juaidi et al., 2014;Karasev and Suntsova, 2001).However, there is less work on soil water resource carrying capacity (Xu, 2001).
According to the characteristics of soil water resource, this study put forward the concept of soil water resource carrying capacity.Soil water resource carrying capacity refers to the ability that can be continuing to support the region's agricultural economic development and maintain a good ecological system under natural conditions (considering only precipitation, such as rain-fed agriculture and natural pasture) or natural-artificial binary mode (considering the natural rainfall and irrigation, such as artificial grassland, grain and cotton cultivation area) in a certain stage of development of social economy and science and technology condition.The evolution process of soil water resource carrying capacity is shown in Fig. 2.
Objective functions: According to the connotation of soil water resource capacity, the supporting objective is agriculture and ecology and its carrying ability represents the scale of the agriculture, forestry, animal husbandry and ecological environment.The target of development and utilization of soil water resource is the maximum comprehensive benefits, including economic, social and ecological benefits.
Economic benefits are the total output value of agriculture in region; the food security and the rational allocation of water resources need to be considered for social benefits.The conventional water resources for agricultural production can be replaced through development and utilization of soil water resource and this part of water can be used for life and industrial production.To a certain extent, this method can alleviate competitive water problems.The more conventional water replacement out, the ratio of agricultural water consumption is smaller.Therefore, social benefits are the total grain output and the ration of agricultural water consumption.Ecological benefits are agricultural ecological water consumption, that is, the leakage of agricultural irrigation water.Water leakage is inevitable in the process of agricultural irrigation.In irrigation works condition and the management level, irrigation area is greater, the more water leakage and it is advantageous to restore ecological environment and improve the situation of groundwater overdraft.
In the model, objective functions consists of 4 parts, including agriculture output value, grain yield, proportion of agricultural water consumption and ecoenvironmental water consumption, each crop's planting area is defined as decision variable.

Objective function 1:
The maximum agriculture output value, which reflects economic benefits: where, x j and x' j = Crops irrigation area and the non-irrigation area respectively y j and y' j = Crop yield per unit area of irrigation and non-irrigation area p j = Crop price j = 1, 2, …, m m = The amount of crop species Object function 2: The maximum grain yield, which reflects social benefits: Object function 3: The maximum agro-ecological environmental water consumption, which reflects ecological benefits: where, m j = Irrigation quota under soil water utilization η j = Effective utilization coefficient of irrigation water k = Leakage recharge coefficient of the irrigation water

Object function 4:
The minimum proportion of agricultural water consumption, which reflects social benefits: where, W t represents the total amount of water.
The objective function 4 is taken minus sign to transform the maximum function as follows: Constraint conditions:  Arable land constraints: where, A is arable land; k f is multiple cropping index. Planting structural constraints: where, x j min and x j max are minimum and maximum suitable arable land in irrigation land; x' j min and x' j max are minimum and maximum suitable arable land in non-irrigation land. Water resources constraints: The present agricultural water use is the upper limit of agricultural water consumption: where, W togr is present agricultural water use. Agro-ecological environmental water constraints as follows: where, W emin is minimum agro-ecological environmental water.
 Soil water resource constraints: Other constraints: Other constraints include the policy of agricultural development, the level of agricultural science and technology development, agricultural planning, water conservancy planning and planting habit in local.

SOLUTION OF THE MULTI-OBJECTIVE MODEL
Normalization of the multi-objective function: In order to eliminate the difference of each goal in quantity and dimension, it is necessary to normalize objectives.Firstly, in the constraint condition, the single objective optimization results were calculated and regarded as maximum potential value.F1max, F2max, F3max, F4max represent maximum potential value of four objectives respectively.Secondly, normalization value of objective is the ratio of actual value and maximum potential value.The calculation formula is as follows: Synthesis of the multi-objective function: The multiple objectives were transferred into singular objective by weighted method.Singular objective is shown as follows: Weightiness: Weightiness is determined by designing the questionnaire and with fuzzy binary contrast method (Wang et al., 2003;Chen and Fu, 2005).For elements a k and a l in set A = {a 1 a 2 ….a n } which is being compared, Pairwise comparisons on importance (excellence or other properties) are made by using three scales 0, 0.5 and 1 and the following rules: If a k is more important than a l , then give a scale e kl = 1, e lk = 0 If a k and a l make no distinction, then give a scale e kl = 0.5, e lk = 0.5 If a l is more important than a k , then give a scale e kl = 0, e lk = 1 where, k = 1 2 …n; l = 1 2 … n.After making comparisons between n elements, the qualitative sorting matrix is gained: Binary contrast matrix of four objective functions is shown as follows: sum 0.5 1 1 1 3.5 0 0.5 1 1 2.5 0 0 0.5 1 1.5 0 0 0 0.5 0.5 The importance of objective functions are in sequence: the total output value of agriculture>the total grain yield>agro-ecological environmental water consumption>agricultural water consumption Table 1.
Based on the importance of objective functions in questionnaire and the relationship between mood operator and quantitative scales, quantitative scales of objective functions are shown in Table 2.
Solution method of single objective model: When the multi-objective model is merged into a single objective model, it is solved by using the method of single objective programming through MATLAB software.Linprog function is used to solve this single objective linear programming in optimization toolbox.Using method of Linprog function is as follows:

RESULTS AND DISCUSSION
Model parameters: Hebei is located in the Haihe River Basin and a semi-humid and semi-arid continental monsoon climate area, where cultivated area is 6.33 million hectare and effective irrigation area is 4.56 million hectare.The main planting crops consist of winter wheat, summer corn, cotton, vegetables and other crops.The cropping index is 137%.Since irrigation agriculture is dominant in Hebei, natural-artificial binary model of soil water resource carrying capacity is built.Selected 2010 as the base year, based on investigation of crop planting area, yield, prices, etc., agricultural irrigation area, irrigation water utilization coefficient, the unit area crop yield were predicted with the trend methods in 2020 (short-term planning) and 2030 (long-term planning) respectively.According to analysis test data, it was obtained the amount of the improved utilization of soil water resource by the different agricultural saving-water technology.The parameters are shown in Table 3.

Result analysis:
When the parameters of soil water resource carrying capacity model is determined, it is to solve by linprog function in optimization toolbox.The optimization results are shown in Table 4.
Table 5 shows that agriculture output value is 262.17 and 181.08 billion Yuan respectively for normal year (P = 50%) and slight dry year (P = 75%) in 2020; Grain yield is 48.14 and 39.74 million t; Agricultural water consumption is 13.04 and 12.52 billion m 3 and its ratio is 59% and 61.6%;The soil water resource

CONCLUSION
Based on analysis and summary of the present achievements concerned soil water resource, the conception of soil water resource carrying capacity was defined in the study.Soil water resource carrying capacity refers to the ability that can be continuing to support the region's agricultural economic development and maintain a good ecological system under natural conditions (considering only precipitation, such as rainfed agriculture and natural pasture) or natural-artificial binary mode (considering the natural rainfall and irrigation, such as artificial grassland, grain and cotton cultivation area) in a certain stage of development of social economy and science and technology condition.
The multi-objective model of soil water resource carrying capacity was established in Hebei.In the model, objective functions consists of 4 parts, including agriculture output value, grain yield, proportion of agricultural water consumption and eco-environmental water consumption, each crop's planting area is defined as decision variable.After changing the multiple objectives into a single objective by fuzzy binary contrast method, this multi-objective model was solved by using the method of single objective programming.
The results show that the agriculture output value and grain yield could be increased steadily and agricultural water consumption is decreased contrarily by the soil water resource optimum scheme in comparison with present situation.The consumptions of soil water resource are 6.80 and 7.62 billion m 3 respectively for normal year (P = 50%) in 2020 and 2030 by developing agricultural technology of the water-saving irrigation, straw returning, film-covering planting and greenhouse cultivation.The agriculture saving water is 0.75 and 1.79 billion m 3 respectively for normal year (P = 50%) in 2020 and 2030.

Fig. 1 :
Fig. 1: The diagrammatic sketch of soil water resource evaluation layer 10) where, W s min = Minimum utilization of soil water resource W tsoial = Total amount of soil water resource W soial = The utilization of soil water resources  Nonnegative constraints: E = (e kl ) n×n is called the sorting scale matrix of the criteria set regarding importance, whose element e kl satisfies: E = (e kl ) n×n is consistent, if it is subject to: 2, …, n.The above conditions are necessary and sufficient for E being the sorting consistency scale matrix.
where, f = Linear objective function vector A = Matrix for linear inequality constraints b = Vector for linear inequality constraints Aeq = Matrix for linear equality constraints beq = Vector for linear equality constraints set Aeq = [] and beq = [] if no equalities exist; lb and ub is vector of lower and upper bounds on decision variables respectively.

Table 1 :
The mood operator and quantitative scales of objective functions

Table 3 :
The amount of the improved utilization of soil water resource by different agricultural technology

Table 4 :
The optimization results of soil water resource carrying capacity model

Table 5 :
The effect of soil water resource utilization in 2020 and 2030