A Time-Varying Causality Formalism Based on the Liang–Kleeman Information Flow for Analyzing Directed Interactions in Nonstationary Climate Systems

Abstract

The interaction between the land surface and the atmosphere is of significant importance in the climate system because it is a key driver of the exchanges of energy and water. Several important relations to heat waves, floods, and droughts exist that are based on the interaction of soil moisture and, for instance, air temperature and humidity. Our ability to separate the elements of this coupling, identify the exact locations where they are strongest, and quantify their strengths is, therefore, of paramount importance to their predictability. A recent rigorous causality formalism based on the Liang–Kleeman (LK) information flow theory has been shown, both theoretically and in real-world applications, to have the necessary asymmetry to infer the directionality and magnitude within geophysical interactions. However, the formalism assumes stationarity in time, whereas the interactions within the land surface and atmosphere are generally nonstationary; furthermore, it requires a sufficiently long time series to ensure statistical sufficiency. In this study, we remedy this difficulty by using the square root Kalman filter to estimate the causality based on the LK formalism to derive a time-varying form. Results show that the new formalism has similar properties compared to its time-invariant form. It is shown that it is also able to capture the time-varying causality structure within soil moisture–air temperature coupling. An advantage is that it does not require very long time series to make an accurate estimation. Applying a wavelet transform to the results also reveals the full range of temporal scales of the interactions.

Quantifying the Responses of Evapotranspiration and Its Components to Vegetation Restoration and Climate Change on the Loess Plateau of China

“…These products have been largely used to detect ET trends [4] and statistically regress and correlate ET and environmental factors, such as land cover types, surface temperature, precipitation, and wind speed [6,19,31,32]. The correlation values cannot quantitatively reflect the contribution of certain factors to ET, and assuming linear relationships between ET and climatic factors is inconsistent with reality because the relationship is nonlinear [33].…”

An Evaluation of Soil Moisture Anomalies from Global Model-Based Datasets over the People’s Republic of China

“…In climate, weather, and hydrological systems, surface soil moisture plays an important role as it regulates the terrestrial water and energy cycles. There are numerous studies that have linked the impact of soil moisture anomalies to land-atmosphere interactions [1][2][3] and extreme events such as flooding and heat waves [4], as well as weather and climate monitoring in operational services [5]. It has, therefore, become significantly important to properly monitor soil moisture globally and regionally.…”

“…Several studies have used model-simulated soil moisture estimates to study regions over the globe, where soil moisture impacts the atmosphere significantly [1,4,14]. Additionally, these products have become a reliable source of information within merging schemes of satellite and ground observation datasets as references.…”

Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction

“…The formalism has been successfully applied to the studies of many real world problems, among them are the El Niño-Indian Ocean Dipole relation [18], global climate change [27], soil moisture-precipitation interaction [28], glaciology [29], and neuroscience problems [30], to name a few. Here, we particularly want to mention the study by Stips et al [27], who, through examining with (5) the causality between the CO 2 index and the surface air temperature, identified a reversing causal relation with time scale.…”