Analysis of daily streamflow complexity by Kolmogorov measures and Lyapunov exponent

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 * Corresponding author tel. +55 81 996593064 E-mail address: borkostosic@gmail.com (B. Stosic) 2 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.

The Choice of an Appropriate Information Dissimilarity Measure for Hierarchical Clustering of River Streamflow Time Series, Based on Calculated Lyapunov Exponent and Kolmogorov Measures

“…The values of KC and KCM of standardized daily discharge data are shown in Table 2 , which shows that the KC values for all daily streamflow time series were relatively small, ranging in the interval from 0.200 to 0.474. Similar behavior was observed for KCM, having values in the intervals from 0.252 to 0.682, which is expected for lowland rivers in contrast to mountain rivers, whose KC values can be up to 0.98 [ 51 , 52 ]. From Table 2 it is seen that there were three peaks for KC: 0.474, 0.352, and 0.316 for stations 3_08088610 (Graford), 7_08093100 (Aquilla), and 9_08098290 (Highbank), respectively.…”

“…The highest value of LLE (0.394) for 3_08088610 (Graford) station is a result of changed river streamflow dynamics because of the Sheppard Hydroelectric Power Plant at Morris Sheppard Dam (Possum Kingdom Reservoir) that is built on the Brazos River in Palo Pinto County. More details about the change in the nonlinearity and randomness of streamflow for this gauge station can be found in [ 51 ].…”

“…In stochastic analysis, a random process is considered predictable if it is possible to infer the next state from previous observations. In many models; however, randomness is a phenomenon which “spoils” predictability [ 51 ]. Deterministic chaos does not mechanically denote total predictability, but means that at least it improves the prognostic power.…”

Mapping regularities in the solar irradiance data using complementary complexity measures

“…More specifically, the analysis of solar irradiation time series, obtained either by measurement or by prediction is difficult since their dynamics are almost always chaotic or just on the edge of chaos. However, the knowledge of their chaotic behaviour is useful in assessment of the predictability via the Lyapunov time (which is inversely proportional to the Lyapunov exponent)as well as the Kolmogorov time (Mihailović et al 2019).…”

Analysis of Streamflow Complexity Based on Entropies in the Weihe River Basin, China

“…Streamflow, as a key component of the hydrologic cycle, is significantly influenced, and its natural variability is being complicated by climate change and human activities, which may introduce extra chaotic information into discharge records [ 1 ]. It is characterized with a stochastic, nonlinear, non-stationary and time-varying nature by a multitude of uncertain information and represents a complex system [ 2 , 3 , 4 ].…”