Rainfall Network Optimization And Design Based On Information Entropy Theory

Rainfall is one of the most fundamental components of the water cycle.As an important source of rainfall data,rainfall networks provide basic data for water resources management and support decision-making process.Therefore,the spatial design and optimal layout of rainfall networks need theoretical and reasonable validation.The optimized rainfall networks thereby not only save resources and economic costs,but also provide more efficient information for hydrological study and scientific research.Information entropy theory quantifies the uncertainty of random variables and can be used to measure the information acquisition and transmission ability of hydrological data collection system.In recent years,it has also been widely studied in the field of hydrometric network optimization and design.Based on the application of information entropy theory on the optimization and design of rainfall network,this study summarizes and improves three entropy-based solutions.The first solution is to provide optimal sets of stations or rankings for existing monitoring networks or potential stations.Rankings emerge either from sorting based on a specific metric or from applying a greedy ranking algorithm,which generates ranking step by step based on an objective function.The second solution evaluates the rainfall network by investigating the spatial information transmission pattern between stations and deriving a minimum geographical distance between two stations or by using information maps.The third solution uses multi-objective optimization to generate a Pareto front of optimal sets of rainfall stations,among which the optimal networks are diversified.Firstly,for a greedy ranking algorithm based on Maximum Information Minimum Redundancy(MIMR)criteria,temporal variability analysis is introduced in the network optimization process.Under sliding time series and different meteorological conditions,two rainfall networks in Shanghai(Yangtze River basin)and Xi 'an(Yellow River basin)are optimized and analyzed.It is found that the optimal rainfall networks obtained by using time series with different starting days or different meteorological conditions are different,which indicates that the spatial and temporal boundary conditions and meteorological forcing factors should be fully considered during the optimization and design of rainfall network.Therefore,we propose a dynamic network evaluation framework for considering temporal variability,which ranks stations under time series with different starting days using a fixed time window.With ranking disorder index(RDI)and ranking variability,we can identify the rainfall stations which are temporarily of importance or redundancy and provide some useful suggestions for decision makers.Secondly,we compare two models,information transfer model based on information-distance spatial transmission pattern and data transfer model based on geostatistical kriging interpolation technique,for rainfall network design.We also apply and evaluate two models for adding stations.In regions where either there is limited data or data is not available,it is a common challenge to add stations for network design.The entropy theory-based information transfer model and geostatistical interpolation techniques are two solutions to meet the challenge.Results showed that the information transfer model estimated transinformation between station pairs better than did the data transfer model.Directional Information Transfer(DIT)index is used to calculate and evaluate the information transfer between different representative stations and other stations.For the information transfer model and data transfer model,the region with the least information redundancy is selected as the optimal site for new station through minimizing multivariate transinformation(information redundancy)from multiple representative stations to the target location.Finally,we propose a two-stage rainfall network optimization framework,especially for streamflow simulation by integrating multi-objective optimization and artificial neural network,verifying the feasibility of combining the optimization of rainfall networks with model application.In the first stage,we use the total correlation as an indicator of information redundancy among stations,multivariate transinformation as an indicator of information transfer from rainfall to runoff,and Nash-Sutcliffe coefficient as the areal rainfall estimation index.Non-dominated Sorting Genetic Algorithms with elitist strategy(NSGA-II)is used for solving multi-objective optimization.In the second stage,the neural network model is used for runoff simulation to validate the optimized network.Using Huaxian station,an important exit hydrological station in the Wei River Basin,as the target station for runoff simulation,the results showed that the optimized rainfall network can achieve a balance between network design efficiency and runoff prediction accuracy.The main innovative contribution of this paper lies in:(1)for network system with dynamic changes in boundary conditions,a dynamic rainfall network evaluation framework is proposed based on sliding time window,MIMR ranking algorithm and ranking disorder index,which helps integrate spatial-temporal analysis into the optimization and design of rainfall networks;(2)in view of spatial correlation and information transfer pattern among stations,especially for adding new stations or lack of data,the advantages of information transfer model in describing the spatial information distribution are demonstrated;(3)combining multi-objective optimization and artificial neural network,we propose a rainfall network optimization method which can be applied to runoff prediction.Using the transinformation between rainfall and runoff during the network design process,the method promotes the rainfall network optimization and design from the perspective of hydrological forecast.