A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail. iii Contents List of Figures vii 1 Introduction 1 2 Description of the Moisture Parameterization Scheme 1 2.1 Cumulus Parameterization Package of the NASA GEOS-1 GCM . . . . . . 5 2.2 Description of the Discretization of the Moisture Physics Parameterization . 12 3 Tangent Linear Model of the Moist Process Physics Package 17 3.1 Linearized Discrete Dynamical Equations . . . . . . . . . . . . . . . . . . . 23 3.2 Coding of the Tangent Linear Model . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Notational Convention for Variables and Subroutines Used in the Tangent Linear Model Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Adjoint Model of the M...

The equatorial Pacific is a region with strong negative feedbacks. Yet coupled general circulation models (GCMs) have exhibited a propensity to develop a significant SST bias in that region, suggesting an unrealistic sensitivity in the coupled models to small energy flux errors that inevitably occur in the individual model components. Could this “hypersensitivity ” exhibited in a coupled model be due to an underestimate of the strength of the negative feedbacks in this region? With this suspicion, the feedbacks in the equatorial Pacific in nine atmospheric GCMs (AGCMs) have been quantified using the interannual variations in that region and compared with the corresponding calculations from the observations. The nine AGCMs are the

Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connecting them with current and future data assimilation approaches. Estimation theory provides a broad and natural mathematical foundation for data assimilation science. Stochastic--dynamic modeling and stochastic observation modeling are described first. Optimality criteria for linear and nonlinear state estimation problems are then explored, leading to conditional--mean estimation procedures such as the Kalman filter and some of its generalizations, and to conditional--mode estimation procedures such as variational methods. A detailed derivation of the Kalman filter is given to illustrate the role of key probabilistic concepts and assumptions. Extensions of the Kalman filter to nonlinear observat...

This document presents a description of the development of the tangent-linear and the adjoint models of the adiabatic version of the GEOS-2 GCM. The dierence between this GCM and the GEOS-1 GCM, the development and validation of the tangent-linear and adjoint models as well as the multitasking of the above models are documented, described and accompanied with illustrative examples. i Contents List of Figures iii List of Tables iv 1 Introduction 1 2 Description of the NASA GEOS-2 GCM 1 2.1 Atmospheric dynamic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Discretization of the NASA GEOS-2 GCM and its dierence from GEOS-1 GCM . . 3 2.3 Structure and ow chart of the adiabatic NASA GEOS-2 GCM . . . . . . . . . . . . 4 3 Tangent linear model of the adiabatic version of NASA GEOS-2 GCM 8 3.1 Notational convention for the tangent linear model . . . . . . . . . . . . . . . . . . . 8 3.2 Verication of the tangent linear model . . . . . . . . . . . . . . . ...

The general circulation simulated by Version 1 of the Goddard Earth Observing System (GEOS-1) general circulation model is compared with the five-year reanalysis recently completed using the GEOS-1 data assimilation system. Emphasis is on the comparison of dynamical quantities, such as heat and momentum fluxes. The results indicate that, while many features are well simulated, the model exhibits a number of severe biases. These include: a cold bias at both poles and an associated westerly bias at upper levels, a strong low-level westerly bias during northern hemisphere winter, a dry tropical boundary layer and excessive moisture at all levels outside the tropics, too much poleward heat and momentum flux by transient eddies, and too little heat flux by stationary eddies. The effects on these biases of increasing resolution and order of accuracy, of including a parameterization of gravity wave drag, and of increasing the vertical extent of the model are also examined. The mai...

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail. iii Contents List of Figures vii 1 Introduction 1 2 Description of the Moisture Parameterization Scheme 1 2.1 Cumulus Parameterization Package of the NASA GEOS-1 GCM . . . . . . 5 2.2 Description of the Discretization of the Moisture Physics Parameterization . 12 3 Tangent Linear Model of the Moist Process Physics Package 17 3.1 Linearized Discrete Dynamical Equations . . . . . . . . . . . . . . . . . . . 23 3.2 Coding of the Tangent Linear Model . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Notational Convention for Variables and Subroutines Used in the Tangent Linear Model Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Adjoint Model of th...

this document are intended to give a general overview of the quality and consistency of the GEOS--1 DAS output. The results show that many of the time--mean prognostic fields are quite similar to those of the ECMWF analyses, though substantial systematic differences do occur in some regions. It is unclear how many of these differences are the result of model bias, or whether they reflect differences in the input observations, or how closely each system draws to the same observations. Other quantities, such as the zonal mean meridional wind, show substantial differences. These quantities are only weakly constrained by the observations and appear to reflect model biases. The impact of model bias is clearest in the hydrological cycle. This is reflected in the list of known deficiencies (summarized in Fig. 96, see also the Appendix), which are dominated by biases in the moisture field, clouds, and precipitation.

A three--day workshop on results from the Data Assimilation Office (DAO) five--year assimilation was held March 6--8, 1995 at Goddard Space Flight Center. The primary objective of the workshop was to provide timely feedback from the data users concerning the strengths and weaknesses of version 1 of the Goddard Earth Observing System (GEOS--1) assimilated products. A second objective was to assess user satisfaction with the current methods of data access and retrieval. There were a total of 49 presentations, with about half (23) of the presentations coming from scientists outside of Goddard. The total attendance was about 120. The first two days were devoted to applications of the data: these included studies of the tropical circulation, geodynamics applications, constituent transport, momentum and energy diagnostics, precipitation and diabatic heating, hydrological modeling and moisture transport, cloud forcing and validation, various aspects of intraseasonal, seasonal and ...