Adaptive management of water resources based on an advanced entropy method to quantify agent information

Adaptive management, which originated in the 1970s, enables managers to undertake scientific actions to adjust strategies through information feedback for the enhancement of management effectiveness when facing uncertainty problems (Lessard 1998). Although research on this management method has just begun, it has attracted the attention and interest of researchers in many fields, including resource management, socio-ecological systems, and human-nature adaptation (Christopher et al. 2013; Peter 2014; Cheng et al. 2015).

A water resources management system is a complex system that integrates economic, societal, and ecological considerations, exhibiting multidimensional, dynamic, open, and nonlinear characteristics (Brookfield & Gnau 2016; Li et al. 2016). Adaptive management has shown good advantages in addressing these characteristics, so it has been widely used in water resources management in recent years. Geldof (1995) considered adaptive water resources management as an entire process for the integrated management of water resources, in which strategies can be adjusted and balanced through constant adaptations to changes. In view of the complexity and uncertainty of basin water resources systems, Sophocleous (2000) noted that the sustainable management of basin water resources must be based on adaptive management. Folke et al. (2002) undertook an integrated management of water resources based on the theme of adaptive management, which rendered results closer to the actual situation. Based on an analysis of the adaptive mechanism of a regional water resources system, Zhao (2003) constructed a new model for analyzing a water resources adaptive management system. Wang et al. (2007) considered adaptive management as a dynamic adjustment process, in which system health and resource sustainability are achieved, and by focusing on the uncertainty of system management, a series of activities that include designing, planning, monitoring, and managing resources are carried out to ensure the integrity and coordination of the system. Knüppe & Pahl-Wostl (2011) introduced adaptive mechanisms into complex groundwater management and expanded the application of adaptive management in water resources systems. Fu et al. (2016) introduced adaptive management into reservoir-water rights transactions and applied a two-stage interval-stochastic programming model to solve the problem. These studies emphasized the important role of adaptive management in water resources management from different perspectives.

In adaptive management, it is necessary to uniformly measure the amount of information transformation in a complex system, and entropy theory (Shannon 1948) is very effective to quantify the energy flow in a given process. Bao & Zou (2018) used entropy to confirm the weight of the objective and study the degree of conflict between water shortage and human activity. Amiri et al. (2014) analyzed information of each parameter through information entropy in a study of groundwater quality. Wu et al. (2017) used entropy theory to determine the information of indicators in the study of surface water quality. Tanyimboh (2017) and Saleh & Tanyimboh (2016) used an advanced entropy model to study the optimal allocation of water resources. Malekian & Azarnivand (2016) utilized Shannon entropy to analyze flood risk. Huang et al. (2014) made use of entropy theory to study the temporal and spatial variation of potential evaporation in a basin in order to improve the drought resistance ability. Entropy theory is widely used in water resources research, but there are few studies that perform quantitative analysis and track management processes using entropy theory.

With the goal of the coordinated development of water resources and the social economy, under the constraints of the total annual available water resources and water use efficiency policy goals for 2015 and 2030, which were written in the ‘Opinions on the practice of the strictest water resources management system’ promulgated by the State Council of China in 2012, the advanced theory of a complex system multi-agent model was used for the adaptive management of regional water resources. Information entropy was introduced to water resources adaptive management for monitoring and evaluating the management status, in order to provide countermeasure for regional water resources management.

Heilongjiang Province, China, is located in mid-latitude eastern Eurasia (see Figure 1). Its geographical coordinates are 121°11′ to 135°05′ east longitude and 43°25′ to 53°33′ north latitude. It includes the 13 administrative regions of Harbin, Qiqihar, Mudanjiang, Jiamusi, Daqing, Jixi, Shuangyashan, Yichun, Qitaihe, Hegang, Heihe, Suihua, and Daxing-anling. Within its territory is the world-famous black soil belt, and it is an important commodity grain base in China. In the study area, the average annual water resource is 8.11 × 10¹⁰ m³ (the amount of surface water resources and groundwater resources are added, and the amount of repetition between them is deducted). The per capita amount of water resources is 2.16 × 10³ m³. According to Heilongjiang Provincial Bureau of Statistics & Survey Organization of Heilongjiang of NBS (2016), the total water supply was 3.55 × 10¹⁰ m³, the proportions of agricultural, industrial, domestic, and ecological water consumption were 0.88:0.07:0.05:0.01. As observed above, the utilization level of regional water resources was low, and agricultural production consumed most of the available water resources, with a low water resources utilization benefit (the water consumption per 10,000-yuan production value was 2.36 × 10² m³, and the amount of water consumption was 2.65 times the nationwide average). Therefore, it is necessary to optimize the management of water resources so that managers can make timely adjustments to their management strategies and promote the rational utilization of water resources in this region.

The adaptive management of water resources is a dynamic process such that when conducting water resources management, the needs and conflicts among different stakeholders are balanced and coordinated, and continuous learning and adjustment are adopted. In doing so, planning and management decisions directed towards water resources are improved, and the adaptability of the water resources system is increased.

In this paper, based on the decision-making process of water resources management, a multi-agent model was used to present a formal description of the management process. Based on the objectives and requirements of regional water resources management, the stakeholders of water resources systems were divided into different agents in the model. Information entropy was used to determine the weight of the objective and to quantify the adaptive performance (competition and cooperation among agents in order to realize their objectives) of each agent to evaluate the management results. The input and output methods were selected to describe the internal behaviors of the agents. A nested genetic algorithm was used to perform simulations for the agents to determine, in turn, the decision-making plan of water resources adaptive management (see Figure 2).

The multi-agent model was proposed by the Santa Fe Institute, NM, USA, to solve practical applications of the theory of complex adaptive systems. Its essence lies in that, during the interactions between a given agent and the environment or other agents, its own behavioral rule undergoes constant changes such that it is adapted to the environment and participates in coordinated development with other agents (Holland 1995, 1998). Therefore, this approach fits the needs of adaptive management very well and is an important means of addressing the complex issues associated with water resources systems (Bazrkar et al. 2017).

The administrative agent simulates the administrators and organizers of a water resources system. Under the premise of controlling the total amount of water resources, the administrative agent carries out resource allocation based on the principle of ceding priority to ecological environment protection, promotes the coordinated sustainable development of water resources and the social economy, and alleviates the imbalance between the supply and demand of regional water resources.

The behavioral rules are as follows.

Agent inputs: These include ecological benefits, the satisfaction degrees of water use, agricultural and industrial production value, and the grain yield.

Agent outputs: These include all the information for the water-demand agents.

According to the characteristics of water users and industries, the water-demand agents are divided into four types: agricultural, industrial, domestic, and ecological. The behavioral rules and constraints are shown in Table 1, and the adaptive performances are now discussed.

Quantifying information in the management process is the basis for choosing a management strategy. According to information entropy (Shannon 1948), an advanced theory to quantify the information uncertainty, the information of individuals in the model simulation process was first quantified. The weight of each objective was then accordingly determined, and the benefits of a given agent were obtained. To effectively overcome the influence of the large objective difference and prevent the occurrence of objective weight 0, the interaction between objectives was considered fully, and the individual standard deviation was introduced to improve the traditional entropy method.

Step 2: Calculate the entropy of each objective.

The initial data for the water-demand agents are shown in Table 2. The amounts of water consumption, production values, grain yield, and acreage of land occupied were obtained from the Heilongjiang Provincial Bureau of Statistics & Survey Organization of Heilongjiang of NBS (2016) and National Bureau of Statistics of China (2016). The net irrigation quota were derived from the water quota for local standards in Heilongjiang Province, China (DB23/T 727-2010). The production value of the agricultural agent was taken from the Ministry of Agriculture of the People's Republic of China (2016). The irrigation water use coefficient, water use efficiency of industrial agent, and the reference amount of initial water consumption of the agents in 2030 were taken from the stipulation in ‘Opinions on the practice of the strictest water resources management system (http://www.gov.cn/zhengce/content/2012-02/15/content_2311.htm)’ and ‘Assessment methods on the practice of the strictest water resources management system (http://www.gov.cn/zwgk/2013-01/06/content_2305762.htm)’. The initial satisfaction degree of water use for the water-demand agents were obtained based on the water consumption amounts and initial water-demand amounts.

Initial data for the water-demand agents in the study area are shown in Table 2. During model execution, each agent would undergo adaptive evolution by following the behavioral rules and undergo reorganization through continuous learning and feedback. The results converge when the allocation of available water is stable, and a way emerges to coordinate water use with other agents and the environment, which is the result of adaptive management (see Figure 4). The adaptive management result for water resources allocation in 2015 was obtained. The validity of the result was verified by comparing it with the real data for 2015 (see Figure 5). Then, considering the ‘Opinions on the practice of the strictest water resources management system’, the data of 2030 in Table 2 were input into the model, and the adaptive management results in the study area were compared under the two conditions of changeless and increased water use efficiency (see Figure 6). The required improvement in water use efficiency for meeting the above policy goal in 2030 was achieved.

In Figure 5(a), the water consumption of the ecological agent in the study area for 2015 was fully guaranteed after adaptive management: the lowest satisfaction degrees of water use increased from 0.67 for the domestic agent to 0.69 for the agricultural agent (an increase of 2.90%); the satisfaction degrees of water use of the agricultural agent decreased from 0.74 to 0.69; and the satisfaction degrees of water use of the industrial agent, domestic agent, and ecological agent increased from 0.81, 0.67, and 0.15 to 0.94, 0.80 and 1.00, respectively. In Figure 5(a′), the production value of the agricultural agent increased from 2.91 × 10¹¹ yuan to 3.30 × 10¹¹ yuan; the production value of the industrial agent increased from 3.23 × 10¹¹ yuan to 3.75 × 10¹¹ yuan; the grain yield increased from 6.32 × 10⁷ t to 6.76 × 10⁷ t; and the ecological benefit decreased from 2.59 × 10⁷ hm² to 2.50 × 10⁷ hm² (a decrease of 3.63%). In Figure 5(b), the land acreage for rice, corn, soybean, wheat, and other crops of the agricultural agent increased from 3.84 × 10⁶ hm², 7.72 × 10⁶ hm², 2.49 × 10⁶ hm², 7.50 × 10⁴ hm², and 2.01 × 10⁵ hm² to 4.18 × 10⁶ hm², 8.06 × 10⁶ hm², 2.76 × 10⁶ hm², 9.28 × 10⁴ hm², and 2.57 × 10⁵ hm² (after the adaptive management, it increased by 8.84%, 4.35%, 11.02%, 23.76%, and 27.97%, respectively). The land acreage for forest land, grassland, and wetland of the ecological agent decreased from 2.18 × 10⁷ hm², 2.06 × 10⁶ hm², and 4.31 × 10⁶ hm² to 2.11 × 10⁷ hm², 1.93 × 10⁶ hm², and 4.19 × 10⁶ hm² (after the adaptive management, it decreased by 3.53%, 6.31%, and 2.82%, respectively).

After adaptive management in 2015, the economic benefit of the whole region, namely, the total production value of industry and agriculture, increased from 6.14 × 10¹¹ to 7.05 × 10¹¹ yuan. Combined with the amount of water consumption allocated of the agricultural and industrial agent (2.90 × 10¹⁰ m³ and 2.77 × 10⁹ m³), the benefit of water use was calculated to be 22.17 yuan/m³, which is 14.81% higher than the 19.31 yuan/m³ before the adaptive management. The amount of water consumption allocated of the agricultural agent was 7.10% less than that before adaptive management. The major reason is that the study area is one of the important commodity grain bases in China, and agricultural water consumption is always high in order to ensure national food security (Ren et al. 2018), which, to a certain extent, limits the development of other industries in the region and also leads to the overall economic development of the region below the national level. Under the constraints of water balance of the administrative agent, this part of water resources was transferred to other water-demand agents, resulting in improvement of the satisfaction degrees of water use of the industrial, domestic, and ecological agents (after the adaptive management, it increased by 16.3%, 19.5%, and 585.0%, respectively), which effectively promotes the balance between supply and demand. This is conducive to the development of other industries in the region and the rationalization of industrial structure. The grain yield increased by 6.89% after adaptive management; the stable growth of the grain yield is of great significance for ensuring national food security. Under the constraints of land balance of the administrative agent, the increase in land acreage of the agricultural agent resulted in a reduction in the land acreage of the ecological agent; the formula for the ecological benefit shows that this is the reason for the decline in the ecological benefit. However, the adaptive management implemented provision of ecological compensation to the ecological agent, the water consumption allocated of the ecological agent increased to 1.78 × 10⁹m³, making the satisfaction degree of water use of the ecological agent increase from 0.15 to 1, thus achieving the Pareto optimum of water resource management (Nouiri 2014). In practice, ensuring ecological water demand to be met for 100% can be accomplished by means of comprehensive implementation of the ‘river chief system’ (Ren 2015) and other regulatory means to control river water intake, prevent and control water pollution, improve water environment, and restore water ecology.

In a word, adaptive management in the study area coordinates water use of each water-demand agent, and effectively alleviates the regional water use imbalance. At the same time, after the adaptive management of the agricultural agent in the study area, the amount of water consumption was reduced, but there was still an increase in the water demand caused by the increase in the land acreage of the grain crops; thus, it is necessary to improve the efficiency of irrigation water use.

In Figure 6(a), the water consumption of the ecological agent in the study area before and after the improvement of water use efficiency was fully guaranteed: the lowest satisfaction degrees of water use increased from 0.41 to 0.55 for the industrial agent (an increase of 34.29%), and the satisfaction degrees of water use of the agricultural agent and domestic agent increased from 0.73 and 0.58 to 0.85 and 0.61 (increases of 16.44% and 5.17%), respectively. In Figure 6(a′), the production value of the agricultural agent decreased from 3.33 × 10¹¹ to 3.28 × 10¹¹ yuan, the production value of industrial agent increased from 2.84 × 10¹¹ to 4.19 × 10¹¹ yuan, the grain yield decreased from 7.04 × 10⁷ to 6.81 × 10⁷t, and the ecological benefit increased from 2.50 × 10⁷ to 2.54 × 10⁷hm². In Figure 6(b), the land acreages of rice, corn, soybean, wheat, and other crops of the agricultural agent changed from 4.59 × 10⁶hm², 8.31 × 10⁶hm², 2.45 × 10⁶hm², 8.90 × 10⁴hm², and 2.37 × 10⁵hm² to 4.53 × 10⁶hm², 7.87 × 10⁶hm², 2.51 × 10⁶hm², 8.96 × 10⁴hm², and 2.39 × 10⁵hm², the land acreages of rice and corn decreased by 1.25% and 5.29%, and those of soybean, wheat, and other crops increased by 2.53%, 0.69%, and 0.88%, respectively. The land acreage of main crops increased or decreased, reflecting changes in planting structure. The land acreages of forest land, grassland and wetland of the ecological agent increased from 2.11 × 10⁷hm², 1.86 × 10⁶hm², and 3.89 × 10⁶hm² to 2.15 × 10⁷hm², 1.90 × 10⁶hm², and 3.90 × 10⁶hm², respectively (increases of 1.8%, 2.34%, and 0.16%).

After improvement in the water use efficiency in 2030, the economic benefit of the whole region, namely, the total production value of industry and agriculture, increased from 6.16 × 10¹¹ to 7.47 × 10¹¹ yuan. Combined with the amount of water consumption allocated of agricultural and industrial agents (3.10 × 10¹⁰m³ and 2.57 × 10⁹m³), the benefit of water use was calculated to be 22.18yuan/m³, which is 21.14% higher than the 18.31yuan/m³ before improving the water use efficiency. The satisfaction degrees of water use of all water-demand agents were improved. Under the policy of the changeless total amount of water consumption, the water consumption of each water-demand agent in the region was effectively coordinated, promoting socioeconomic development. The ecological benefit in the study area increased by 1.78% relative to that when water use efficiency was unchanged; combined with the decrease in the ecological benefit in 2015, it can be concluded that constant water resources adaptive management can improve the ecological benefit in 2030. Clearly, the adaptive management of water resources while improving water use efficiency not only helps realize policy goals but also improves the ecological environment of the study area. After improving the water use efficiency, the amount of water consumption of agricultural agent decreased by 0.59% relative to that when the water use efficiency was unchanged, and the total land acreage for agriculture decreased by 4.32 × 10⁵hm² (a decrease of 2.76% relative to that when the water use efficiency was unchanged); at the same time, the grain yield decreased by 3.16%, and the change rates of the grain yield relative to the amount of water consumption and land acreage were 5.28 and 1.14, respectively. The grain yield was greatly affected by the amount of water consumption. Considering the loosening of China's population policy, the population will inevitably increase, and since the volume of international grain trade is limited, the demand for grain is bound to exhibit a rigid growth trend. Therefore, improving the efficiency of agricultural irrigation water is necessary to ensure national food security. Combining the amount of water consumption with the production value of the industrial agent, the amount of water consumption per 10,000-yuan production value was 61.37m³, a decrease of 16.73% relative to the value of 73.90m³ in 2015. Therefore, in order to achieve the policy goal, the industrial agent must ensure that the annual decrease in the amount of water consumption per 10,000-yuan production value is 1.21%. The total amount of water consumption of the domestic agent increased by 4.64% relative to that when the water use efficiency was unchanged, but according to the logistic model for population growth in this paper, the population of the study area will reach 4.11 × 10⁷ in 2030, so the water quota per capita was decreased from 0.12m³ to 0.11m³ per day. Therefore, we should encourage people to save water via adaptive management.

In conclusion, the adaptive management of water resources by improving water use efficiency is conducive to realizing policy goals, to promote the sustainable development of society, the economy, and ecology, and to providing direction for managers to make water resources management decisions.

Formulas (I)–(III) were used to calculate the weights of the objectives before and after adaptive management for the year 2015, and before and after improving the water use efficiency for the year 2030 (see Table 3). In Table 3, when the agent has one or two targets, the weights of the objectives are essentially equal (e.g., industrial agents) during the model execution. When there are more than three objectives, the weights vary greatly (e.g., the weight of agricultural agent production value has changed from 0.315 to 0.448 for the year 2015). For the same agent, the order of the weights of each objective are also different (e.g., in 2015 and 2030, the order of the objectives for the administrative agent are d₄ > d₃ > d₁ > d₂ and d₄ > d₃ > d₂ > d₁). This shows that no matter what the conditions, the ecological benefit of the study area is vitally important. The second most important is grain yield, the reason for this being that the study area is one of the important commodity grain bases in China. The weight order of satisfaction degree and production value have changed before and after adaptive management for the year 2015, and before and after improving the water use efficiency for the year 2030; this is related to the strict requirement of the total annual available water resources in the region and after improving the water use efficiency, the administrative agent pays more attention to production value than water. In total, under the condition of improving the ecological environment and not affecting the grain yield too much, the study area should actively improve the water use efficiency of the water-demand agent, and find ideas and measures to promote the development of a high-quality economy.

It can be seen from the above that the weights given according to individual information entropy are different from the previous weighting methods, and can better reflect the differences between the objectives of the agent during model execution. Moreover, the imbalance between supply and demand of water resources has been improved in the water resources management of the study area in 2015 and 2030, which verifies the feasibility and rationality of the method in practical application.

In this paper, a research method for adaptive management of regional water resources is proposed. The information entropy is used to solve the problem of information transmission during the model execution. The traditional information entropy is improved by using the standard deviations of individuals, the interference of the abnormal value to the agent evolution information is reduced, the state of the agent is tracked and modified, and a nested genetic algorithm is employed to perform the simulation of each agent. The method can effectively coordinate the benefit conflict among the water-demand agents and the benefit conflict between the water-demand agents and administrative agent. A water allocation scheme with high comprehensive benefits is obtained through individual selection, crossover, and mutation. This research about water resources management provides a valuable solution to the whole water resources management problem, which is applicable to the optimization and simulation of regional water resources management and other complex systems. However, the model does not reflect the impact of socioeconomic development on the crop unit price and irrigation water efficiency, nor does it provide a detailed analysis of the uncertain relationship between conservation of the ecological environment and ecological water use. This will be an important direction to improve the method in future work.

In this paper, regional water resources adaptive management research is conducted based on the advanced theory of complex systems, which is applicable to the optimization and simulation of regional water resources management and other complex systems. Under the condition of giving priority to ecological water use, the benefits relationship among different agents are considered from two aspects: administrative agent and water-demand agents. The adaptive management model is tested by using the actual data of Heilongjiang Province in 2015. After adaptive management, the proportions of agricultural, industrial, domestic, and ecological water consumption changes to 0.817:0.078:0.055:0.050, which alleviates the imbalance of regional water use, and the validity of regional water resources adaptive management has been confirmed. According to strict control requirement of the regional total annual available water resources in 2030, water resources adaptive management before and after improving the water use efficiency are conducted. It was concluded that water resources adaptive management can change the proportions of agricultural, industrial, domestic, and ecological water consumption to 0.835:0.069:0.046:0.050, which further shows that the constant water resources adaptive management coordinates the water use among the water-demand agents.

The traditional information entropy is improved by introducing the standard deviation of individuals, which reduces the interference of abnormal value to the agent evolution information, prevents the occurrence of weight ‘0’, and quantifies the states of agents so that managers can track and manage. Unlike previous ones, the differences among the objectives of agents during the model execution can be reflected well, and a new method to determine the weight of multi-objectives is provided.

In addition, taking Heilongjiang Province, the main grain-producing region in China as an example, after adaptive management for the year 2015, the weight of production value increased by 42.22%, indicating that the agricultural agent pays more attention to production value than grain yield, but the weight of grain yield still accounted for 55.2%. When improving the water use efficiency for the year 2030, the weight difference between the two is only 0.017. Therefore, in order to realize adaptive management, the study area needs to continuously improve agricultural production value under the condition of ensuring grain yield, and create a good external environment for regional agricultural products' processing industry.

This research was funded by the Natural Science Foundation of Heilongjiang Province (No. E2017006), the National Natural Science Foundation of China (No. 51609039), the China Postdoctoral Science Foundation (funded project No. 2016M601410), and the Heilongjiang Province Postdoctoral Science Foundation (funded project No. LBH-Z16025), Key Laboratory of Efficient Use of Agricultural Water Resources, Ministry of Agriculture, P.R. China (No. 2017008).