Analysis of Daily Streamflow Complexity by Kolmogorov Measures and Lyapunov Exponent

TL;DR

This study assesses the complexity and predictability of daily streamflow data in Texas using Kolmogorov complexity and Lyapunov exponents, revealing human influence effects and long-term memory in the data.

Contribution

It introduces the combined use of Kolmogorov complexity and Lyapunov exponents to analyze streamflow variability and anthropogenic impacts.

Findings

Higher complexity at Graford station due to human activities

Complexity decreases with larger catchments, indicating less human influence

Inverse relationship between Kolmogorov complexity and Lyapunov predictability

Abstract

Analysis of daily streamflow variability in space and time is important for water resources planning, development, and management. The natural variability of streamflow is being complicated by anthropogenic influences and climate change, which may introduce additional complexity into the phenomenological records. To address this question for daily discharge data recorded during the period 1989-2016 at twelve gauging stations on Brazos River in Texas (USA), we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures to assess complexity, and Lyapunov time (LT) to assess predictability. We find that all daily discharge series exhibit long memory with an increasing downflow tendency, while the randomness of the series at individual sites cannot be definitively concluded. All Kolmogorov complexity measures have relatively small values with the exception of the USGS (United States Geological Survey) 08088610 station at Graford, Texas, which exhibits the highest values of these complexity measures. This finding may be attributed to the elevated effect of human activities at Graford, and proportionally lesser effect at other stations. In addition, complexity tends to decrease downflow, meaning that larger catchments are generally less influenced by anthropogenic activity. The correction on randomness of Lyapunov time (quantifying predictability) is found to be inversely proportional to the Kolmogorov complexity, which strengthens our conclusion regarding the effect of anthropogenic activities, considering that KC and LT are distinct measures, based on rather different techniques.