## 1. Introduction

[2] A land surface model (LSM) or soil-vegetation-atmosphere-transfer (SVAT) scheme exhibits variability on a wide range of timescales from hours to months, and even years through atmospheric interactions [e.g., *Delworth and Manabe*, 1988, 1993; *Entekhabi*, 1995; *Robock et al.*, 1998]. These timescales are strongly influenced by external forcing, especially precipitation and downward short-wave and long-wave radiation at the surface. They are also modulated by the internal dynamics and physics of land surface systems, in particular by soil moisture dynamics. There are numerous studies on the variability of land surface models. Approaches to date include: (1) performing numerical simulations, (2) performing numerical sensitivity tests, and (3) building relatively simple land surface models that can be solved analytically.

[3] In the first approach, either a general circulation model (GCM) which includes an LSM or a stand-alone LSM is integrated over long time periods [e.g., *Dickinson*, 1984; *Sato et al.*, 1989; *Koster and Suarez*, 1994]. These studies have demonstrated the main variability of the land surface system, as modeled, and the pronounced effect of the land surface on atmospheric variability. In the second approach, using either an LSM coupled to a GCM or a stand-alone LSM, sensitivity experiments are usually performed with a change in one particular parameter or parameterization scheme [e.g., *Henderson-Sellers et al.*, 1995; *Xue et al.*, 1996a, 1996b]. The results are then compared with a control integration to reveal the impact of the change. This type of sensitivity experiment identifies important parameters or parameterizations in land surface models. The third approach, solving equations of a simple LSM analytically, estimates characteristic timescales of land surface variables in simplified cases [e.g., *Delworth and Manabe*, 1988; *Brubaker and Entekhabi*, 1995; *Yang et al.*, 1995]. This approach simplifies complex land surface processes. For example, one can represent the evaporation and runoff process as a bucket model or treat the soil moisture system as a first-order Markov process.

[4] These three approaches mainly reveal the impact of external forcing [*Entekhabi*, 1995; *Delworth and Manabe*, 1988, 1993] on the land surface variability, because the forcing terms exert the dominant control on the variability of land surface models. In the data assimilation context, we need to understand the impact of internal dynamics and physics on the variability of a land surface model. For this purpose we employ tangent linear analysis to an LSM in this study.

[5] There are two reasons for studying the internal dynamics and physics of land surface models with the tangent linear approximation. First, the linear behavior of the internal dynamics and physics alone controls the evolution of small land surface state perturbations, which are defined as the departures from a solution of a nonlinear model called the trajectory. These perturbations might be considered to be errors in the true state values. The study of this linear behavior allows us to identify the main relationships, or balance, among these errors in an LSM. An example of such a balance is the effect of errors in surface soil moisture on the surface temperature and moisture. This kind of error correlation may be used to formulate background error covariances of an assimilation scheme. Second, with an understanding of the internal features, we can efficiently identify key parameters and parameterizations of the model with minimum influence of the external forcing. By efficiently we mean that one run can reveal multiple key parameters or parameterizations. By minimum influence of the external forcing we mean that the evolution of the perturbed state variables is not explicitly controlled by the external forcing at a particular time, though the mean trajectory is controlled by the external forcing and the perturbation behavior may vary with different mean states.

[6] In this paper, we apply tangent linear model (TLM) analysis to study the linear behavior of the internal physics and dynamics of the Mosaic LSM [*Koster and Suarez*, 1992]. In a recent review paper, *Errico* [1997] describes the development and applications of TLM and their corresponding adjoint models in meteorology. Although the use of TLM and adjoint models has recently increased rapidly, applications to land surface modeling and assimilation require specific consideration due to the complex physical features and nonlinearity of LSMs.

[7] In section 2, we briefly describe the Mosaic LSM. In section 3, we derive the TLM based on the prognostic equations of the Mosaic LSM, and we describe the experimental design and precautions taken in deriving the TLM numerically. In section 4, we present the results of the TLM eigenanalysis, including characteristic timescales and modes of the land surface state perturbations. In section 5, we obtain a linearized soil moisture subsystem and examine the role of soil moisture dynamics. We find explicit relationships between the timescales and the Mosaic LSM parameters. Finally, in section 6, we summarize the main results and discuss their application to land surface data assimilation.