基于马尔可夫过程的湖泊生态需水保障不确定性研究

Estimating the Ecological Water Demand in Lakes and the Degree of Certainty based on the Markov Process

湖泊生态需水对维持其基本生态功能具有重要作用,保障生态需水已成为湖泊生态保护的重要组成部分。目前湖泊生态需水的保障方法都是在同一时间尺度下维持一个确定的水量,但湖泊水位是一个随机过程,其生态状况与湖泊水位波动密切相关,随着水位波动,湖泊生态系统的结构和功能在不断变化,导致其生态需水量也发生变化,只确定一个生态水量,不足以应对湖泊生态需水量未来可能出现的各种情况,也无法应对未来生态需水保障的不确定性,亟需对湖泊生态需水进行不确定性研究,以保障不同时期的生态需水量。以白洋淀为例,将其水位划分为5个区间,代表5个水位时期,再分析各时期的生态环境状况,得出每个时期有利于湖泊生物多样性的生态需水量。结果表明,白洋淀在枯水期、偏枯期、平水期、偏丰期、丰水期的生态水位分别为6.347、6.681、7.276、8.617、9.177 m。根据马尔可夫过程,利用改进加权马尔可夫链模型,计算出未来湖泊水位处于各个时期的概率,从而确定湖泊生态需水量的保障程度,并对未来生态需水保障情况进行预测。

Ecological water demand(EWD) is the water inflow to a lake required to give the depth necessary for maintaining basic ecological functions and sustaining the ecological services provided by the lake. Determining and maintaining the EWD has become an important part of lake management and protection. Previous studies mainly focused on maintaining a single EWD value over time, but the water level of lakes naturally fluctuates and the fluctuations are closely related to lake biodiversity. As water level fluctuates, lake ecosystem functions change synchronously, leading to the variation in the EWD. Methods that ensure one particular EWD are not sufficient to deal with the varying condition of lakes, nor can they deal with the uncertainty of guaranteeing a given EWD. In this study, we took Baiyangdian Lake as a case study and used the improved weighted Markov Chain model to predict the probability of maintaining the EWD of Baiyangdian Lake and to explore the uncertainty of maintaining the EWD. The water level of Baiyangdian Lake was divided into five states:(1) dry(5.200-6.382 m),(2) relatively dry(6.382-7.042 m),(3) normal(7.042-8.362 m),(4) relatively wet(8.362-9.021 m) and(5) wet,(9.021-11.150 m). After analyzing ecological conditions, the optimal EWD for biological diversity in each state was determined and the results were as follows: dry, 6.347 m;relatively dry, 6.681 m;normal 7.276 m;relatively wet, 8.617 m;wet, 9.177 m. The improved weighted Markov Chain model was then used to calculate the probability of a given water level in January 2001 based on the water level data for Baiyangdian Lake in 2000. The predicted water flow in January 2001 was 0.550×10~8m^3 and the measured flow was 0.490×10~8m^3, an error of 12.24%. The degree of certainty for maintaining the EWD in Baiyangdian Lake in January 2001 was 0.981. The annual degree of certainty for EWD in Baiyangdian Lake changed little, with a value of 0.167 in both 2001 and 2002. Our results show that the method used in this study is reliable for predicting future monthly and annual degrees of certainty for the EWD of lakes and to support decision making related to sustaining the EWD in lakes with large seasonal fluctuations in water level.