Advances in Adjoint Functions of Connection Number in Water Resources Complex Systems: A Systematic Review.

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research.

Connection number based model for coordination development evaluation of regional water resources, social economy and ecological environment complex system.

The development of social economy often requires a large consumption of water resources, and will also discharge a large amount of pollutants to the environment. Currently, the rapid development of regional water resources, social economy and ecological environment (WSE) complex system encounters significant challenges, and the coordination development of WSE complex system becomes important and necessary condition of regional sustainable development. Therefore, to scientifically evaluate the coordination development state of WSE system, based on the establishment of evaluation index system, the connection number and distance coordination model coupling approach for the coordination development evaluation of WSE complex system was proposed in this manuscript. The application results of the proposed method in Anhui Province, China indicate that, during 2011-2020, the coordination level of Anhui province is relatively high, and the coordination grade of most cities are in grade I or II. The coordination development degree of Anhui province presented a distinct improving trend with time, from most cities in grade IV or V in 2011 to most cities in grade II in 2020, from the worst 0.0580 in 2011 to the best 0.9200 in 2020. In terms of space, the coordinated development level of southern Anhui is higher than that of northern Anhui. Meanwhile, the coordination development status of the 16 cities in Anhui province can be divided into three patterns according to its historical variation characteristics, i.e., coordination development mode, ecological environment backward mode, and social and economic backward mode. Compared with the commonly used coordination evaluation method, the method of this paper can solve the problem of homogenization, and its calculation results are more reasonable and practical.

Structure Simulation and Equilibrium Evaluation Analysis of Regional Water Resources, Society, Economy and Ecological Environment Complex System.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020-2029 was higher compared to that of 2010-2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system.

Quantitative Evaluation and Obstacle Factor Diagnosis of Agricultural Drought Disaster Risk Using Connection Number and Information Entropy.

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007-2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management.

Drought identification based on Palmer drought severity index and return period analysis of drought characteristics in Huaibei Plain China.

The threshold level method for drought identification is challenging due to the problems of selection of drought index reflecting the drought process associated with water supply and demand as well as the underlying physical meaning of drought thresholds. The frequently used hydrological drought indices (e.g., runoff) are susceptible to being affected by human activities, and drought characteristics are incapable of revealing spatial and temporal comparability. Furthermore, the drought process with the same severity but a longer duration is more likely to be evaluated as a more severe event, which contradicts the actual drought situation. In this study, the Palmer drought severity index (PDSI) method, in which the meteorological factors less influenced by human activities were taken as the input, was adopted to determine the dry/wet states and the PDSI value at each period firstly. The dry/wet states were defined with dry period, wet period, transition period, transition period in dry spell, and transition period in a wet spell. Following that, drought identification criteria were established through the dry/wet states and PDSI value according to the consistency of the identified results and the actual drought situations. Particularly, drought severity and peak intensity were taken as drought characteristics in this paper, and the joint return periods of the characteristics were estimated based on the Gumbel-Hougaard copula function. And eventually, a case study was conducted in Huaibei Plain, China. The results showed that the most severe droughts identified by PDSI had a good consistency with the actual drought situations, drought severity and peak intensity were applicable to reflect the drought impacts. It is worth noting that the implications of the joint return period and the relationships among different types of them. The occurrence probability of a multi-characteristic drought event should be calculated by the integration of joint probability density function over the region corresponding to the event of interest, and the joint frequency of drought characteristics should not be used as the occurrence probability of the drought disaster losses greater (or less) than that caused by the drought with the same characteristics. In addition, drought processes identified by PDSI and standardized precipitation indices (SPI) from monthly and seasonal scales were compared, indicating the drought identified results through PDSI are almost consistent with the actual situations.

Coordination evaluation and obstacle factors recognition analysis of water resource spatial equilibrium system.

The comprehensive evaluation analysis of water resource spatial equilibrium (WRSE) system is a fundamental and crucial facet to construct national water resource network system and implement socio-economy equilibrium development strategy in China. To clearly understanding of the structural relationship of WRSE system, we firstly proposed the definition of WRSE system from the perspective of coordination variation between water resource carrying pressure and support force subsystems in this study, then, the multi-dimensional connection cloud and coupling coordination degree approaches were applied to construct integrated evaluation model (MCCD) of WRSE system, and finally, the obstacle degree model was utilized as well to recognize the primary influence factors which resulted in the variation of WRSE system. Eventually, it can be revealed from the application results of MCCD model that, the overall situation of WRSE system in Anhui Province, China was improved obviously during the past 10 years, with the average coupling coordination degree (CCD) increased from 0.58 in 2011 to 0.68 in 2018. In addition, water resources availability per capita (S1) and agricultural irrigation quota (P8) were the two primary indicators causing the variation of water resource carrying support and pressure force subsystems. The above application analysis results were reliable and consistent with the evolution trend of actual historical observed statistics, and could also provide scientific decision-making basis for the implementation of prediction and regulation schemes of WRSE system.

Photodegradation of roxarsone in the aquatic environment: influencing factors, mechanisms, and artificial neural network modeling.

Roxarsone (ROX), an organoarsenic feed additive, can be discharged into aquatic environment and photodegraded into more toxic inorganic arsenics. However, the photodegradation behavior of ROX in aquatic environment is still unclear. To better understand ROX photodegradation behavior, the influencing factors, photodegradation mechanism, and process modelling of ROX photodegradation were investigated in this study. The results showed that ROX in the aquatic environment was degraded to inorganic As(III) and As(V) under light irradiation. The degradation efficiency was enhanced by 25% with the increase of light intensity from 300 to 800 µW/cm2 via indirect photolysis. The photodegradation was temperature dependence, but was only slightly affected by pH. Nitrate ion (NO3-) had an obvious influence, but sulfate, carbonate, and chlorate ions had a negligible effect on ROX degradation. Dissolved organic matter (DOM) in the solution inhibited the photodegradation. ROX photodegradation was mainly mediated by reactive oxygen species (in the form of single oxygen 1O2) generated through ROX self-sensitization under irradiation. Based on the data of factors affecting ROX photodegradation, ROX photodegradation model was built and trained by an artificial neural network (ANN), and the predicted degradation rate was in good agreement with the real values with a root mean square error of 1.008. This study improved the understanding of ROX photodegradation behavior and provided a basis for controlling the pollution from ROX photodegradation.

Regional water security evaluation with risk control model and its application in Jiangsu Province, China.

To reduce losses from the various disasters, regional water security evaluation and risk control model is studied. The model is built upon different kinds of indices in water security system, proceeding from the whole structure and its parts of evaluation, forewarning and decision making analysis. Based on China's national conditions, this study firstly advances an evaluation index system of regional water security, which includes three subsystems of water resource security, water environment security, and water disaster control security. Secondly, fuzzy analytic hierarchy process based on accelerating genetic algorithm (AGA-FAHP) combines with entropy weight method (EW) to determine the objective weights of evaluation indexes. The subjective and objective weights can be integrated by the principle of minimum relative information entropy. The subsystem weights are obtained by using AGA-FAHP. Then regional water security evaluation model is established. Thirdly, the comparison judging method is adopted to divide warning degree of water security with the comprehensive evaluation index and forewarning standards, and then the local conditions for proposing planning schemes. Finally, decision making analysis is employed to find the effective indices based on projection pursuit technique with the ideal point method in multi-index decision. This study takes Jiangsu province, China as an example. The evaluation results from 2000 to 2015 show that the development trend of water security is increasing on the whole except in several individual years. Risk forewarning doesn't take place in recent years. But risk is always there. So, project and non-project measures are proposed for the corresponding forewarning levels. From light warnings for three times and moderate warning for once in 2000, 2001, 2002, and 2004, index 1, 3, 4, 11, 13, 17, and 18 are selected as the effective indices to decision making analysis in common. Then, the solution schemes are given as the processing method accordingly. This conclusion is reasonable and its method is practical that match the reality. It suggests that the presented model is feasible with theory and application, which can offer advice in regional water security management to some extent.

Construction and application of comprehensive drought index based on uncertainty cloud reasoning algorithm.

The establishment of comprehensive drought index is a fundamental task for the analysis of drought hazard system evolution. To fully explore the characteristics of drought variation process, the cloud uncertainty reasoning method was applied to construct comprehensive drought index integrating precipitation with soil moisture indicators. The application results of the proposed drought index in Anhui Province, China revealed that, (1) The overall drought evolution presented significant intensifying trend with the drought occurrence frequency increasing from 32% to 41% from south to north in Anhui Province, and the primary drought type in the northern area was moderate-level drought events and above, while the drought type in the central and southern region was dominated by light-level drought events. (2) Autumn drought was the dominant type from 1960 to 2007 in Anhui Province, with the average drought occurrence frequency of 40%. In addition, the evolution of spring and autumn drought all presented intensifying trends from 1960 to 2007, while the summer and winter drought evolution trends were opposite. (3) The Mann-Kendall trend test results revealed that the drought evolution presented evidently intensifying trend from August 1967 to February 1969, but slight declining trend from May 1974 to August 1978, July 1989 to August 2001 and February 2003 to December 2007, and the mutation of drought evolution occurred in November 1972, February 1978 and August 1998, etc. The above results were basically consistent with the historical statistics, indicating that the proposed comprehensive drought index and its construction framework were reliable, which can be further applied in the related research field of regional drought risk management.

Spatio-Temporal Evolution Analysis of Drought Based on Cloud Transformation Algorithm over Northern Anhui Province.

Drought is one of the most typical and serious natural disasters, which occurs frequently in most of mainland China, and it is crucial to explore the evolution characteristics of drought for developing effective schemes and strategies of drought disaster risk management. Based on the application of Cloud theory in the drought evolution research field, the cloud transformation algorithm, and the conception zooming coupling model was proposed to re-fit the distribution pattern of SPI instead of the Pearson-III distribution. Then the spatio-temporal evolution features of drought were further summarized utilizing the cloud characteristics, average, entropy, and hyper-entropy. Lastly, the application results in Northern Anhui province revealed that the drought condition was the most serious during the period from 1957 to 1970 with the SPI12 index in 49 months being less than -0.5 and 12 months with an extreme drought level. The overall drought intensity varied with the highest certainty level but lowest stability level in winter, but this was opposite in the summer. Moreover, drought hazard would be more significantly intensified along the elevation of latitude in Northern Anhui province. The overall drought hazard in Suzhou and Huaibei were the most serious, which is followed by Bozhou, Bengbu, and Fuyang. Drought intensity in Huainan was the lightest. The exploration results of drought evolution analysis were reasonable and reliable, which would supply an effective decision-making basis for establishing drought risk management strategies.

Early Warning Method for Regional Water Resources Carrying Capacity Based on the Logical Curve and Aggregate Warning Index.

The sustainable utilization of water resources is a significant factor in the development of the national economy and society. Regional water resources carrying capacity (RWRCC) is an appropriate method for evaluating the balance in such utilization. In this paper, we combined time difference correlation analysis and set pair analysis firstly to identify the early warning sign index (EWSI) for RWRCC, and warning limits were determined using a logical curve. Analytic hierarchy process based on the accelerating genetic algorithm (AGA-AHP) method was used to improve the KLR model by determining weights objectively. We took advantage of the new improved model to build the aggregate warning index (AWI). Then, according to the corresponding relationship between EWSI and AWI, the early warning system for regional water resources carrying capacity (EWS-RWRCC) was established, and a case study was carried out in Anhui Province. The results showed there are eight effective EWSI obtained through the early warning analysis process of RWRCC in Anhui Province, among which the repetitive use rate of industrial water and average daily coefficient have a greater impact on AWI. Basically, the EWS-RWRCC can describe RWRCC changes in Anhui Province. From 2006 to 2014, more than half the signal lights in Anhui Province were yellow and orange, which indicated a poor state. It has been proved that the constraints of population, GDP growth and water supply capacity on the utilization of water resources in the future will be further tightened, which should be considered for future monitoring and early warning. The early warning method we used here can be widely applied into other fields; the results will enhance monitoring capacity and scientifically guide regional water resources management.

Regional water resource carrying capacity evaluation based on multi-dimensional precondition cloud and risk matrix coupling model.

Water resource carrying capacity modelling is a fundamental task to explore the interaction mechanism between socio-economic development and water resource carrying system. To reasonably quantify regional water resource carrying capacity, firstly, the water resource carrying system was divided into pressure, support and regulation forces subsystems, then the multi-dimensional precondition cloud algorithm was introduced to quantify the belonging degree of single evaluation index, and the comprehensive belonging degree of each sample was further obtained through risk matrix and index weight, and finally the multi-dimensional precondition cloud and risk matrix coupling model (PCRM) was established to recognize carrying grade and reveal carrying mechanism. The application results of PCRM model indicated that water resource carrying capacity in Anhui province, China presented a slightly improving trend in both provincial and city scales during 2005 to 2015. Meanwhile, evaluation result of PCRM model was more approaching to the average characteristic value of different approaches, which indicated that PCRM coupling model is effectively to explore properties of indexes and subsystems of water resource carrying system, and could be further applied in other system evaluation and regulation research fields in the future.

Optimal Water Resources Regulation for the Pond Irrigation System Based on Simulation-A Case Study in Jiang-Huai Hilly Regions, China.

Due to the importance and complexity of water resources regulations in the pond irrigation systems of the Jiang-Huai hilly regions, a water allocation simulation model for pond irrigation districts based on system simulation theory was developed in this study. To maximize agricultural irrigation benefits while guaranteeing rural domestic water demand, an optimal water resources regulation model for pond irrigation districts and a simulation-based optimal water resources regulation technology system for the pond irrigation system were developed. Using this system, it was determined that the suitable pond coverage rate (pond capacity per unit area) was 2.92 × 105 m3/km2. Suitable water supply and operational rules for adjusting crop planting structure were also developed the water-saving irrigation method and irrigation system. To guarantee rural domestic water demand, the multi-year average total irrigation water deficit of the study area decreased by 4.66 × 104 m3/km2; the average multi-year water deficit ratio decreased from 20.40% to 1.18%; the average multi-year irrigation benefit increased by 1.11 × 105 RMB (16,128$)/km2; and the average multi-year revenue increased by 6.69%. Both the economic and social benefits were significant. The results of this study provide a theoretical basis and technological support for comprehensive pone governance in the Jiang-Huai hilly regions and promote the establishment of a water allocation scheme and irrigation system for pond irrigation districts, which have practical significance and important application value.

Quantitative Assessment and Diagnosis for Regional Agricultural Drought Resilience Based on Set Pair Analysis and Connection Entropy.

Assessment and diagnosis of regional agricultural drought resilience (RADR) is an important groundwork to identify the shortcomings of regional agriculture to resist drought disasters accurately. In order to quantitatively assess the capacity of regional agriculture system to reduce losses from drought disasters under complex conditions and to identify vulnerability indexes, an assessment and diagnosis model for RADR was established. Firstly, this model used the improved fuzzy analytic hierarchy process to determine the index weights, then proposed an assessment method based on connection number and an improved connection entropy. Furthermore, the set pair potential based on subtraction was used to diagnose the vulnerability indexes. In addition, a practical application had been carried out in the region of the Huaibei Plain in Anhui Province. The evaluation results showed that the RADR in this area from 2005 to 2014 as a whole was in a relatively weak situation. However, the average grade values had decreased from 3.144 to 2.790 during these 10 years and the RADR had an enhanced tendency. Moreover, the possibility of RADR enhancement for six cities in this region decreased from east to west, and the drought emergency condition was the weak link of the RADR in the Huaibei Plain.

Water Resources Carrying Capacity Evaluation and Diagnosis Based on Set Pair Analysis and Improved the Entropy Weight Method.

To quantitatively evaluate and diagnose the carrying capacity of regional water resources under uncertain conditions, an index system and corresponding grade criteria were constructed from the perspective of carrying subsystem. Meanwhile, an improved entropy weight method was used to determine the objective weight of the index. Then, an evaluation model was built by applying set pair analysis, and a set pair potential based on subtraction was proposed to identify the carrying vulnerability factors. Finally, an empirical study was carried out in Anhui Province. The results showed that the consistency among objective weights of each index was considered, and the uncertainty between the index and grade criterion was reasonably dealt with. Furthermore, although the carrying situation in Anhui was severe, the development tended to be improved. The status in Southern Anhui was superior to that in the middle area, and that in the northern part was relatively grim. In addition, for Northern Anhui, the fewer water resources chiefly caused its long-term overloaded status. The improvement of capacity in the middle area was mainly hindered by its deficient ecological water consumption and limited water-saving irrigation area. Moreover, the long-term loadable condition in the southern part was due largely to its relatively abundant water resources and small population size. This evaluation and diagnosis method can be widely applied to carrying issues in other resources and environment fields.

Chlorine stress mediates microbial surface attachment in drinking water systems.

Microbial attachment to drinking water pipe surfaces facilitates pathogen survival and deteriorates disinfection performance, directly threatening the safety of drinking water. Notwithstanding that the formation of biofilm has been studied for decades, the underlying mechanisms for the origins of microbial surface attachment in biofilm development in drinking water pipelines remain largely elusive. We combined experimental and mathematical methods to investigate the role of environmental stress-mediated cell motility on microbial surface attachment in chlorination-stressed drinking water distribution systems. Results show that at low levels of disinfectant (0.0-1.0 mg/L), the presence of chlorine promotes initiation of microbial surface attachment, while higher amounts of disinfectant (>1.0 mg/L) inhibit microbial attachment. The proposed mathematical model further demonstrates that chlorination stress (0.0-5.0 mg/L)-mediated microbial cell motility regulates the frequency of cell-wall collision and thereby controls initial microbial surface attachment. The results reveal that transport processes and decay patterns of chlorine in drinking water pipelines regulate microbial cell motility and, thus, control initial surface cell attachment. It provides a mechanistic understanding of microbial attachment shaped by environmental disinfection stress and leads to new insights into microbial safety protocols in water distribution systems.

Forewarning model for water pollution risk based on Bayes theory.

In order to reduce the losses by water pollution, forewarning model for water pollution risk based on Bayes theory was studied. This model is built upon risk indexes in complex systems, proceeding from the whole structure and its components. In this study, the principal components analysis is used to screen out index systems. Hydrological model is employed to simulate index value according to the prediction principle. Bayes theory is adopted to obtain posterior distribution by prior distribution with sample information which can make samples' features preferably reflect and represent the totals to some extent. Forewarning level is judged on the maximum probability rule, and then local conditions for proposing management strategies that will have the effect of transforming heavy warnings to a lesser degree. This study takes Taihu Basin as an example. After forewarning model application and vertification for water pollution risk from 2000 to 2009 between the actual and simulated data, forewarning level in 2010 is given as a severe warning, which is well coincide with logistic curve. It is shown that the model is rigorous in theory with flexible method, reasonable in result with simple structure, and it has strong logic superiority and regional adaptability, providing a new way for warning water pollution risk.