太湖藻类生长模型研究

Ecological Simulation of Algae Growth in Taihu Lake

本文提出了一个改进的藻类生长模型及其新颖的计算机模拟算法 .该模型不但考虑了水温、总氮、总磷、浮游动物和辐射等因素对藻类生长率的影响 ,而且根据水温、总磷和藻类浓度等因素对藻类死亡率进行了修正 ,从而能更加精确地描述藻类生长的过程 .在藻类生长模型计算机模拟中 ,稳定性和计算精度是至关重要的 ,因此 ,本文建立了具有绝对稳定性和二阶精度的数值算法求解藻类生长模型中的偏微分方程组 .此外 ,为了进一步验证该藻类生长模型的性能 ,本文采用了 1998年度太湖中有关采样点总氮、总磷、水温及日辐射量等的实测值进行模拟 .由于实测值为每个月中某一天的测量值 ,为了模拟过程能正确进行 ,本文采用样条插值的方法估计出每一天的总氮、水温及辐射量等数值 .由于在藻类生长模型中 ,藻类与总磷有直接的耦合 ,不能简单地用插值等方法 .本文提出了一种广义拟合的方法 ,使得总磷既符合藻类生长模型要求的变化规律 ,又较好地逼近实测值 .计算机模拟结果与测量数值基本符合 ,而在有明显差异的地方 ,文中作出了相应的解释 .结果表明 ,本文提出的藻类生长模型及其算法是有效的 。

This paper presents a modified ecological model of algae growth in Taihu Lake and its novel numerical algorithm. In this model, many important factors, such as the water temperature, total nitrogen, total phosphor, the biomass of the zooplankton, radiation, etc., are taken into account for the growth rate of the algae. Moreover, the mortality rate of the algae is considered and modified according to the value of water temperature, total phosphorus and the biomass of the algae. As a result, a more accurate description of the behavior of the algae is obtained. The performance of stability and accuracy is very important for the correct simulation procedure. A numerical algorithm that has the property of absolute stability and second order accuracy is proposed, and is used to solve the partial differential equations in the ecological model. In order to perform a further validation of the model, the field measured data in Taihu Lake in 1998 are adopted in the simulation. Because only one set of the field measured data per month, i.e., total twelve sets of data are available, estimated data of every day are required to perform the simulation correctly. In this paper, the estimated data of the water temperature, total nitrogen, the biomass of the zooplankton and radiation are obtained by interpolation method. In the ecological model, there is a direct coupling between the algae and total phosphorus; therefore, the estimated data of phosphorus can not be obtained by simple interpolation. A generalized fitting method is then developed to solve this problem. With this method, the characteristic of the total phosphorus obeys the ecological model. Meanwhile, the values of the simulated total phosphorus are approached to the field measured data optimally. Basically, the simulated results fairly agree with the field measured results. Explanations are given to some distinct differences between the simulated results and field measured results. It is demonstrated that the ecological model and the algorithm are reliable and efficient for the simulation of the actual ecological behavior of algae.