基于混沌理论的河流藻类生长特性分析--以德国易北河为例

Analysis of the growth characteristics of river algae based on chaos theory:a case study of Elbe River

针对藻类生长具有高度非线性特征和实际采样样本间隔稀疏的问题,采用了混沌理论对采样序列的混沌特征量进行估计。采用C-C方法估计时间序列的嵌入维和延迟时间,采用G-P算法对关联维进行估计,并采用小数据量法估计最大Lyapunov指数,最终可实现对最长可预测时长的估计。以易北河为例,对易北河水体叶绿素a 1997年至2001年间各年的观测序列进行了混沌分析,分析结果表明,各年的叶绿素a观测序列均具有低维混沌特性,关联维D=2.75—4.02,各年的叶绿素a序列的最长预测时间变化范围为8.01—18.94d,平均为13.98d(约2周)。采用同样方法对5a易北河连续日径流量时间序列分析表明,该径流量也具有低维混沌特性(最大Lyapunov指数λ1=0.0125),径流量的最长预测时间估计约为80d。气候因素的混沌特性对藻类生长表现出的混沌特征的影响可能要大于径流量等水文因素的影响。

Algal growth at equilibrium is not sustainable in a river or lake experiencing point or non-point source pollution, which is likely to change with season, location, and human activity. Chlorophyll a, as a common indictor, is an important reference point for water resource management. It oscillations, and chaotic fluctuations. Algal growth can be affected by the biodiversity of species, as a resuk of their has many highly nonlinear characteristics. The characteristics that differ among species, however, are all susceptible to change under external disturbance. It is difficult to provide a comprehensive and detailed description of nonlinear algal Variations in chlorophyll a tend to maintain certain regularity; for example, seasonal variation and the 24 hour cycle, which also display self-similarity. However, it is difficult to observe similar variations at different times from the studied sampling series. These features are similar to aspects of chaotic motion, such as boundedness, ergodicity, and inherent randomness. The sampling of the indictor chlorophyll a is typically performed on an hourly, weekly, or even monthly basis. With higher sampling frequency, the sampling series of chlorophyll a in the field becomes more unstable and appears to be more chaotic. Therefore, this paper aims to study the variations in a chlorophyll a series sampled from the field, rather than constructing a theoretical model to recapitulate the field data. While there is extensive research on algae in many lakes or rivers, few studies discuss the prediction of algal growth times in aquatic environments. The aspects of algal growth times are partially addressed in this study The variation characteristics of the algal data series dimensional time series were recovered by reconstruction were analyzed using chaos theory. The characters of the one- into the multi-dimensional phase space, using phase space reconstruction. The reconstruction parameters, namely the embedding dimension m and time delay 7, were estimated using the correlation integral method （C-C method）. The correlation strange attractor, which is the main characteristic of a chaotic dimension, D, is the basic mathematical description of the system. D was calculated using the Grassberger-Procaccia algorithm （G-P algorithm）. Only the largest Lyapunov exponent, A l, was estimated through the small data method to evaluate the diffusion degree of the phase trajectory. The reciprocal of A l is the upper bound of the deterministic prediction time in the chaotic system, which is designated as the Lyapunov time t0. This property indicates that the system is unpredictable beyond t0. In this paper, the chaotic characteristics of hourly chlorophyll a concentrations and the daily runoff time series of the Elbe River over a five year period （ 1997--2001 ） were analyzed. It was found that both sequences had the properties of low-dimension chaos withλ1〉0, D = 2.75--4.02 for the chlorophyll a series, and D = 1.84 for the runoff series. The average value of to（ 14 days） was estimated for the five-year chlorophyll a sequence data. These findings were remarkably close to the current biggest day-to-day weather forecast time （ two to three weeks）. A much longer value of to for the runoff series, for the same period, was 80 days. This result indicated that compared to the weather factors, the runoff factor is clearly weaker in affecting the chaotic characteristics of chlorophyll a.