Dependency and Redundancy: How Information Theory Untangles Three Variable Interactions in Environmental Data

Exploring water fluxes between hydrological model (HM) components is essential to assess and improve model realism. Many classical metrics for HM diagnosis rely solely on streamflow and hence provide limited insights into model performance across processes. This study applies an information theory measure known as "transfer entropy" (TE) to systematically quantify the transfer of information among major HM components. To test and demonstrate the benefits of TE, we use the Framework for Understanding Structural Errors (FUSE) model to mimic and compare four commonly used HM structures, VIC, PRMS, SACRAMENTO, and TOPMODEL, across 671 catchments spanning a variety of hydrologic regimes in the conterminous United States. We explore connections between HM components and catchment landscape characteristics (e.g., climate, topography, soil, and vegetation) and characterize their nonlinear associations using distance correlation and Spearman correlation coefficients. Our results indicate that while the information transferred from precipitation to runoff is similar across model structures (likely as a result of calibration), the information transferred among other components can vary significantly from a FUSE structure to another. We find that aridity, precipitation duration and frequency, snow fraction, mean elevation, forest area, and leaf area index are often significantly associated with TE between the main HM components. We propose that the presence of meaningful nonlinear associations can be used to diagnose process representation in HMs. Our results highlight the necessity to enhance the conventional streamflow-only calibration approach for a more realistic representation of water dynamics in the models.

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Exploring Hydrologic Model Process Connectivity at the Continental Scale Through an Information Theory Approach

Konapala

Kao

Addor

2020

“…If k and/or l are chosen to be large, the reliability of the estimate of transfer entropy is decreased (Hlinka et al, ). This decrease in reliability is a fundamental issue with estimating high‐dimensional probability distributions due to the curse of dimensionality (Weijs et al, ). To minimize these effects, we set τ = 1, ω = 1, k = 0, and l = 0 and use the temporal resolution of the time series as the method of choosing a timescale.…”

Section: Methodsmentioning

confidence: 99%

Quantifying Process Connectivity With Transfer Entropy in Hydrologic Models

Bennett

Nijssen

et al. 2019

Quantifying the behavior and performance of hydrologic models is an important aspect of understanding the underlying hydrologic systems. We argue that classical error measures do not offer a complete picture for building this understanding. This study demonstrates how the information theoretic measure known as transfer entropy can be used to quantify the active transfer of information between hydrologic processes at various timescales and facilitate further understanding of the behavior of these systems. To build a better understanding of the differences in dynamics, we compare model instances of the Structure for Unifying Multiple Modeling Alternatives (SUMMA), the Variable Infiltration Capacity (VIC) model, and the Precipitation Runoff Modeling System (PRMS) across a variety of hydrologic regimes in the Columbia River Basin in the Pacific Northwest of North America. Our results show differences in the runoff of the SUMMA instance compared to the other two models in several of our study locations. In the Snake River region, SUMMA runoff was primarily snowmelt driven, while VIC and PRMS runoff was primarily influenced by precipitation and evapotranspiration. In the Olympic mountains, evapotranspiration interacted with the other water balance variables much differently in PRMS than in VIC and SUMMA. In the Willamette River, all three models had similar process networks at the daily time scale but showed differences in information transfer at the monthly timescale. Additionally, we find that all three models have similar connectivity between evapotranspiration and soil moisture. Analyzing information transfers to runoff at daily and monthly time steps shows how processes can operate on different timescales. By comparing information transfer with correlations, we show how transfer entropy provides a complementary picture of model behavior.Plain Language Summary Building a complete picture of the hydrologic system is a difficult task. When the hydrologic community builds computer models to simulate the hydrologic cycle, we often must make approximations, which introduce error and uncertainty. It is common to attempt to control the error in our predictions by choosing the level of complexity of the hydrologic model or by choosing model parameter values so that model results match observations most closely. Neither approach can identify whether we may simply be compensating for poor choices in the way that the model operates. This study evaluates a statistical method, which relies on an information theoretic measure called transfer entropy that provides insight into the internal operations of a model. We apply this method to examine the different components of water flow within three different models in four different regions across the Columbia River Basin in the Pacific Northwest of North America. We found that the method was able to disentangle the complex way in which these models operate and provide high-level insight into the similarities and differences across different models and sites. We propose that this is ...

“…We denote a precipitation time series as P t , and streamflow as Q t . An important consideration in applying IT measures to data is the discretization of variables and the pdf estimation method (Gong et al, 2014; Weijs et al, 2018). In this study, we transform our precipitation data into a binary data set, with a value of 1 assigned to each day within the study period with precipitation occurring above a threshold magnitude M (mm), and a value of 0 assigned to each day within the study period below the threshold.…”

Section: Information Measures To Capture Time Dependenciesmentioning

confidence: 99%

Information Flows: Characterizing Precipitation‐Streamflow Dependencies in the Colorado Headwaters With an Information Theory Approach

Franzen

Farahani

Goodwell

2020

Watersheds aggregate precipitation signals of many intensities and from many locations into a single observable streamflow at an outlet point. This dependency between precipitation and streamflow varies seasonally and can shift over time due to changes in land cover, climate, human water uses, or changes in properties of precipitation events themselves. We apply information theory-based measures to capture temporal linkages, or information transfers, from daily precipitation occurrence at different locations in a basin to streamflow at an outlet. We detect critical magnitudes of precipitation and lag times associated with the strongest precipitation-streamflow relationships, and further partition information transfers to determine relative contributions from the knowledge of wet versus dry past states. Based on an analysis of daily U.S. Geological Survey (USGS) streamflow and Climate Prediction Center (CPC) gridded gauge-based precipitation data sets in the Colorado Headwaters Basin, this dependency is strongest in fall, the longest dominant lag times occur in spring, and the strengths of dependencies have increased in spring and summer over the past 65 years. These features relate to both seasonal and spatial characteristics of precipitation and the landscape. A partitioning of information components shows that in this basin, the particular knowledge of a lagged, or past, wet state tends to be more informative to flow than a lagged dry state, even though dry days are more frequent. This study introduces several signatures of precipitation-streamflow relationships that can also more broadly characterize strengths, thresholds, and timescales associated with various interconnected processes.