Predictability of monthly streamflow by considering complexity measures

•All rivers had high permutation entropy (PE)•Lyapunov exponent (LE) of monthly streamflow time series is positive for all rivers.•Streamflow time series can exhibit a large value of PE and lower LE at the same time.•Chaos, turbulence, and complexity were inter-related.•Rivers were classified based on their flow predictability. Natural fluid flow systems exhibit turbulent and chaotic behavior that determines their high-level complexity. Chaos has an accurate mathematical definition, while turbulence is a property of fluid flow without an accurate mathematical definition. Using the Kolmogorov complexity (KC) and its derivative (KC spectrum), permutation entropy (PE), and Lyapunov exponent (LE), we considered how chaos affected the predictability of natural fluid flow systems. This paper applied these measures to investigate the turbulent, complex and chaotic behaviors of monthly streamflow of rivers from Bosnia and Herzegovina, the United States, and the Mendoza Basin (Argentina) and evaluated their time horizons using the Lyapunov time (LT). Based on the measures applied for river streamflow, we derived four modes of the interrelationship between turbulence, complexity, and chaos. Finally, using the measures, we clustered rivers with similar time horizons representing their predictability.