## 1. Introduction

[2] Ecohydrologic processes comprise nonlinear couplings between climate, soils, water cycle and vegetation [*Reiners and Driese*, 2003]. In the first part of the paper [*Ruddell and Kumar*, 2009] it is argued that in this context, system state is best represented as a pattern of couplings between the various processes, rather than by measurements of individual variables. This arrangement may be described as a network of directional couplings and feedback cycles between a system's variables at a range of spatiotemporal scale. A process network was defined as “a network of feedback loops and the associated time scales that depicts the magnitude and direction of flow of matter, energy, and/or information between the different variables” [*Ruddell and Kumar*, 2009, paragraph 3]. Process networks were developed where the strength of each directional coupling is measured by the information flow between pairs of variables at a specified time scale. Information flow is the contribution of uncertainty-reducing or predictive information provided by the time lag history of one variable to the future value of another. The transfer entropy statistic [*Schreiber*, 2000] was used to measure the asymmetric information flow between two variables.

[3] Detailed analysis of process networks constructed for drought and healthy states of an agricultural ecosystem in the Midwestern United States showed that a healthy system is characterized by a predominance of feedbacks at a variety of time scales. On the other hand a drought system is characterized by a breakdown in the number of information feedback loops in the interaction between the various variables and the system seems to shift more to a source-sink type coupling rather than a feedback driven coupling [*Ruddell and Kumar*, 2009, Figures 7 and 8].

[4] Analysis of dynamics over a network poses significant challenges [*Strogatz*, 2001]. While a number of approaches exist for the analysis of structural properties of large network such as small world [*Watts and Strogatz*, 1998] and scale-free properties [*Albert and Barabasi*, 2002; *Newman*, 2003], the study of asymmetric information flow through a network remains an open and challenging problem. If a system's state is defined as a network of feedback couplings, then one should be able to learn about system states and dynamics by observing changes in statistics that characterize the properties of information flow in the process network.

[5] The goal of the present paper is to develop measures to characterize the organization of process networks, understand how the organization changes in time, and identify and characterize network-scale emergent properties. By summarizing a complicated process network using network statistics, many system states can be quickly and quantitatively compared. The result is a powerful and flexible statistical approach to the analysis of complex ecohydrologic systems, which can resolve key characteristics such as feedbacks, time scale, and subsystem organization. The organization of the process network is analyzed by identifying feedback, sources and sinks of information, and their seasonal variability. After characterizing distinct system states, specific patterns of organization are studied and the parameters controlling the emergence of these patterns are identified.

[6] This paper is organized as follows. In section 2, statistical measures for characterizing the organization of the asymmetric information flow in a process network are derived. In section 3, the seasonal and annual ecohydrological patterns that appear in the network statistics for the years 1998–2006 are analyzed. Conclusions and discussion are given in section 4.