## 1 Introduction  
The seasonal rate of change in atmospheric carbon dioxide (CO\({}_{2}\)) above temperate regions is largely driven by the net sum of two opposing processes: carbon (C) uptake through Gross Primary Production (_GPP_) and carbon release from the vegetation and soil through plant and microbial respiration. The magnitude of the annual ecosystem-driven change to the global soil C pool is such that even a small increase in soil respiration (\(R_{s}\)) rates could result in a net reduction in net terrestrial C sink strength and an increase in atmospheric CO\({}_{2}\) concentration [1; 2; 3]. The soil ecosystem comprises a multitude of organisms acting over a broad range of spatial and temporal scales, from heterotrophic soil fauna to plant roots, all embedded in a complex and highly variable physical environment [4]. This variation is both spatial, through differences in soil microbial communities and root structural characteristics, and temporal, through fluctuations in energy and water dynamics and through disturbances. A principal challenge to understanding biogeochemical cycles is identifying the causal agents of process rates, which requires separation of endogenous dynamics from the effects of the time-dependent, and often correlated, forcing variables. Any coupling among ecological variables induced by external drivers is difficult to distinguish from the endogenous correlation structures generated by the core ecological system. Major complications arise from the inter-correlation of external forcing variables, indirect effects of one variable over another, and feedbacks. For example, air and soil temperatures are strongly correlated to incoming shortwave radiation. Part of this energy reaching the surface, stems and leaves, is transformed into sensible heat, which warms the air above, and into soil heat flux, which warms the soil below. Sensible and latent heat fluxes are correlated, as both are constrained by available energy (net radiation minus soil heat flux) [5]. Soil moisture can limit plant metabolic rates and microbial activity and therefore controls, with other drivers, the reaction rates of many biogeochemical processes in the soil. Hence, it is not surprising that in ecological time series analysis, one of the main challenges is to determine how one state (or rate) variable relates to or \"causes\" the magnitude or dynamics of another. The problem is naturally compounded when both the affecting and affected variables are subjected to multiple periodic and external forcings, and when state changes lag behind causal agents. The conventional approach to studying the relationships between affected variables and the forcing that drives them employs correlation [6]. However, the existence of correlation itself does not necessarily demonstrate causation. First, due to the symmetric nature of correlation it cannot distinguish between the causal roles of the affected and affecting variable. Second, correlation cannot distinguish whether both variables are directly interacting or if the appearance of correlation is a result of both variables being forced by a common third variable. Identification of causality, based on the argument that the response cannot precede the perturbation, has been at the core of a number of disciplines of prediction [7]. Among the more popular measures of causality are the so-called Granger causality (hereafter referred to as G-causality)--the main subject of this study--and transfer entropy. For Gaussian variables it has been demonstrated that these two approaches are equivalent [8], and this result has been extended to other common types of distributions [9]. The concept of G-causality originated in econometrics [10, 11] but is now being used in a wide range of different fields, among them the analysis of climatic and environmental time series [12, 13, 14, 15]. Compared to several information-theory driven methods that are used in ecohydrology [16, 17] the main advantage of G-causality is that it has an explicit spectral and non-parametric formulation [18, 19].