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 can be affected by the biodiversity of species, as a result of their oscillations, and chaotic fluctuations. Algal growth 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 growth. 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 were analyzed using chaos theory. The characters of the one-dimensional time series were recovered by reconstruction into the multi-dimensional phase space, using phase space reconstruction. The reconstruction parameters, namely the embedding dimension m and time delay τ, were estimated using the correlation integral method (C-C method). The correlation dimension, D, is the basic mathematical description of the strange attractor, which is the main characteristic of a chaotic system. D was calculated using the Grassberger-Procaccia algorithm (G-P algorithm). Only the largest Lyapunov exponent, λ₁, was estimated through the small data method to evaluate the diffusion degree of the phase trajectory. The reciprocal of λ₁ 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 with λ₁>0, D = 2.75-4.02 for the chlorophyll a series, and D = 1.84 for the runoff series. The average value of t₀ (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 t₀ 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.