摘要：随着经济发展，水污染日益加剧。水体污染最突出的问题是富营养化。联合国环境规划署的一项调查表明，全球范围内30％～40％的湖泊和水库都有不同程度的富营养化。湖泊富营养化呈现发展快、危害大、治理难、修复历时长等特点，而数学模型可以综合反映系统特征，因此建模是湖泊管理中特别有用的手段。

　本文构建的模型综合考虑了水温、总氮、总磷等因素对藻类生长率的影响。通过观察N/P比值的变化，进行总磷的参数修正，回归方程的趋势线预测，得到了一个适合的藻类峰值的计算方程，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，本文采用具有绝对稳定性的多项式回归方法建立藻类生长模型。

　模型结果表明，作出的状态变量的描述是理想的，方程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。方程模拟结果与测量数值基本符合，而在有明显差异的地方又作出了相应的解释。结果表明，本文提出的藻类生长模型及其算法是有效的。

关键词：玄武湖，富营养化，AGP，生长模型

Abstract：With economic development, water pollution is increasing. And the most prominent problem is the eutrophication. A survey which came from United Nations Environment Programme showed that 30% to 40% of the lakes and reservoirs have different degrees of eutrophication. Lake eutrophication showed rapid development, large hazardous, difficult to control, and long restore time, but the mathematical model can reflect the system characteristics comprehensively, so model is particularly useful in the lake management.

　　　This model is taken into account water temperature, nitrogen, phosphorus and other factors on the growth rate of algae. By observing the N/P ratio changes, amendments to the parameters of TP, the trend of the regression equation predicted, we get an equation for calculating the peak of algae, so that it can more accurately describe the process of algal growth. Stability and accuracy is essential in the algal growth model. Therefore, absolute stability are established with a polynomial regression method of algae growth model.

　　　Model results showed that the description of the state variables was ideal, and it makes the equation is consistent with the requirements of algal growth variation, it is also a better approximation of measured values. The simulation results conform with the basic measurements, and it also explain the difference. The results showed that the algal growth model and its algorithm is effective.

Keywords: XuanWu Lake, Eutrophication, AGP, Growth model

　　　水体富营养化的危害很大，是当今世界面对的主要水污染问题之一。水体富营养化已经造成了很多有害的影响如：水质恶化、散发腥臭异味、降低水体的透明度、向水体释放有毒物质、影响供水水质并增加制水成本、影响水产养殖、湖泊水功能显著下降等。水体富营养化的关键过程也就是藻类大量繁殖的过程。富营养化水体中的藻类突发性增长受到很多因素的影响，如水体中的营养盐(氮、磷)含量、水流速度、水体温度、pH、溶解氧、光照强度等。这些因素并非独立的，而是相互作用。本试验根据实验室条件选取了文献中普遍提及的2个影响因子(氨氮、总磷)，每个影响因子选2个水平值，设计成正交试验表，进行藻类培养试验。通过试验研究得出以下结论：