Tangent linear analysis of the Mosaic land surface model

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Abstract

[1] In this study, a tangent linear eigenanalysis is applied to the Mosaic land surface model (LSM) [Koster and Suarez, 1992] to examine the impacts of the model internal dynamics and physics on the land surface state variability. The tangent linear model (TLM) of the Mosaic LSM is derived numerically for two sets of basic states and two tile types of land condition, grass and bare soil. An additional TLM, for the soil moisture subsystem of this LSM, is derived analytically for the same cases to obtain explicit expressions for the eigenvalues. An eigenvalue of the TLM determines a characteristic timescale, and the corresponding eigenvector, or mode, describes a particular coupling among the perturbed states. The results show that (1) errors in initial conditions tend to decay with e-folding times given by the characteristic timescales; (2) the LSM exhibits a wide range of internal variability, modes mainly representing surface temperature and surface moisture perturbations exhibit short timescales, whereas modes mainly representing deep soil temperature perturbations and moisture transfer throughout the entire soil column exhibit much longer timescales; (3) the modes of soil moisture tend to be weakly coupled with other perturbed variables, and the mode representing the deep soil temperature perturbation has a consistent e-folding time across the experiments; (4) the key parameters include soil moisture, soil layer depth, and soil hydraulic parameters. The results agree qualitatively with previous findings. However, tangent linear eigenanalysis provides a new approach to the quantitative substantiation of those findings. Also, it reveals the evolution and the coupling of the perturbed land states that are useful for the development of land surface data assimilation schemes. One must be careful when generalizing the quantitative results since they are obtained with respect to two specific basic states and two simple land conditions. Also, the methodology employed here does not apply directly to an actual time-varying basic state.

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