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232
Recipes for Adjoint Code Construction
"... this paper, is the Adjoint Model Compiler (AMC). ..."
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Cited by 255 (23 self)
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this paper, is the Adjoint Model Compiler (AMC).
ADOLC: A Package for the Automatic Differentiation of Algorithms Written in C/C++
, 1995
"... The C++ package ADOLC described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked ..."
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Cited by 187 (26 self)
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The C++ package ADOLC described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked with C. The numerical values of derivative vectors are obtained free of truncation errors at a small multiple of the run time and randomly accessed memory of the given function evaluation program. Derivative matrices are obtained by columns or rows. For solution curves defined by ordinary differential equations, special routines are provided that evaluate the Taylor coefficient vectors and their Jacobians with respect to the current state vector. The derivative calculations involve a possibly substantial (but always predictable) amount of data that are accessed strictly sequentially and are therefore automatically paged out to external files.
Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter
 Physica D
, 2007
"... Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become availab ..."
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Cited by 147 (11 self)
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Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast ” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, I describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “Ensemble Kalman Filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. I discuss both the mathematical basis of this approach and its implementation; my primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. 1
Ensemble Kalman Filter Assimilation of Doppler Radar Data with a Compressible Nonhydrostatic Model: OSS Experiments
, 2004
"... A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general pur ..."
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Cited by 127 (78 self)
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A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multiclass ice microphysics. New aspects compared to previous studies include the demonstration of the ability of EnKF method in retrieving multiple microphysical species associated with a multiclass ice microphysics scheme, and in accurately retrieving the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of radial velocity and reflectivity data as well as their spatial coverage in recovering the full flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside precipitation regions, are used. Significant positive impact of the reflectivity assimilation
OnLine Estimation of Error Covariance Parameters for Atmospheric Data Assimilation
, 1994
"... We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is ..."
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Cited by 122 (10 self)
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We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the singlesample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: timedependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be th...
Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part I: Model development and simulated data experiments
 J. Atmos. Sci
, 1997
"... The purpose of the research reported in this paper is to develop a variational data analysis system that can be used to assimilate data from one or more Doppler radars. In the first part of this twopart study, the technique used in this analysis system is described and tested using data from a simu ..."
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Cited by 92 (8 self)
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The purpose of the research reported in this paper is to develop a variational data analysis system that can be used to assimilate data from one or more Doppler radars. In the first part of this twopart study, the technique used in this analysis system is described and tested using data from a simulated warm rain convective storm. The analysis system applies the 4D variational data assimilation technique to a cloudscale model with a warm rain parameterization scheme. The 3D wind, thermodynamical, and microphysical fields are determined by minimizing a cost function, defined by the difference between both radar observed radial velocities and reflectivities (or rainwater mixing ratio) and their model predictions. The adjoint of the numerical model is used to provide the sensitivity of the cost function with respect to the control variables. Experiments using data from a simulated convective storm demonstrated that the variational analysis system is able to retrieve the detailed structure of wind, thermodynamics, and microphysics using either dualDoppler or singleDoppler information. However, less accurate velocity fields are obtained when singleDoppler data were used. In both cases, retrieving the temperature field is more difficult than the retrieval of the other fields. Results also show that assimilating the rainwater mixing ratio obtained from the reflectivity data results in a better performance of the retrieval procedure than directly assimilating the reflectivity. It is also found that the system is robust to variations in the Z–qr relation, but the microphysical retrieval is quite sensitive to parameters in the warm rain scheme. The technique is robust to random errors in radial velocity and calibration errors in reflectivity. 1.
Using the Extended Kalman Filter with a Multilayer QuasiGeostrophic Ocean Model
 J. Geophys. Res
, 1992
"... this paper the extended Kalman filter is used with a nonlinear multilayer quasigeostrophic (QG) model. This provides us with both a realistic ocean model and a very sophisticated error statistics scheme. The extended Kalman filter is an extension of the common Kalman filter and may be used when the ..."
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Cited by 83 (16 self)
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this paper the extended Kalman filter is used with a nonlinear multilayer quasigeostrophic (QG) model. This provides us with both a realistic ocean model and a very sophisticated error statistics scheme. The extended Kalman filter is an extension of the common Kalman filter and may be used when the model dynamics or the measurement equation is nonlinear. It consists of an approximative equation for the propagation of error covariances, and also approximative filter equations if the measurement equation is nonlinear. When changing from a linear system to nonlinear dynamics the possible existence of a wide variety of phenomena which are nonexistent in the linear theory is introduced. Nonlinear systems may have solutions with multiple equilibria, where the solutions sometimes abruptly undergo transitions from one equilibrium to another as parameters change (bifurcations). Also chaotic behavior occurs in many deterministic systems, where solutions exhibit an apparently random behavior. The Lorenz [1963] model is probably the best known example of chaotic systems. It has solutions which undergo "unpredictable" transitions between two different equilibria (chaos). As discussed by Miller and Ghil
Construction of the Adjoint MIT Ocean General Circulation Model and Application to Atlantic Heat Transport Sensitivity
 J. Geophys. Res
, 1999
"... We first describe the principles and practical considerations behind the computergeneration of the adjoint to the MIT ocean general circulation model (GCM), using R. Giering's software tool Tangentlinear and Adjoint Model Compiler (TAMC). The TAMC's recipe for (FORTRAN) linebyline gene ..."
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Cited by 77 (19 self)
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We first describe the principles and practical considerations behind the computergeneration of the adjoint to the MIT ocean general circulation model (GCM), using R. Giering's software tool Tangentlinear and Adjoint Model Compiler (TAMC). The TAMC's recipe for (FORTRAN) linebyline generation of adjoint code is explained by interpreting an adjoint model strictly as the operator that gives the sensitivity of the output of a model to its input. Then, the sensitivity of 1993 annualmean heat transport across 29 N in the Atlantic, to the hydrography on 1 January 1993, is calculated from a global solution of the GCM. The "kinematic sensitivity" to initial temperature variations is isolated, showing how the latter would influence heat transport if they did not affect density and hence the flow. Over one year, the heat transport at 29 N is influenced kinematically from regions up to 20 upstream in the western boundary current, and up to 5 upstream in the interior. In contrast, the dynamica...
A coarse grid threedimensional global inverse model of the atmospheric transport 1. Adjoint model and Jacobian matrix
, 1996
"... . TM2 is a global threedimensional model of the atmospheric transport of passive tracers. The adjoint of TM2 is a model that allows the efficient evaluation of derivatives of the simulated tracer concentration at observational locations with respect to the tracer's sources and sinks. We des ..."
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Cited by 65 (9 self)
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. TM2 is a global threedimensional model of the atmospheric transport of passive tracers. The adjoint of TM2 is a model that allows the efficient evaluation of derivatives of the simulated tracer concentration at observational locations with respect to the tracer's sources and sinks. We describe the generation of the adjoint model by applying the Tangent linear and Adjoint Model Compiler in the reverse mode of automatic differentiation to the code of TM2. Using CO 2 as an example of a chemically inert tracer, the simulated concentration at observational locations is linear in the surface exchange fluxes, and thus the transport can be represented by the model's Jacobian matrix. In many current inverse modeling studies, such a matrix has been computed by multiple runs of a transport model for a set of prescribed surface flux patterns. The computational cost has been proportional to the number of patterns. In contrast, for differentiation in reverse mode, the cost is independ...
A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation
 IN REVIEW
, 2005
"... A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assump ..."
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Cited by 48 (4 self)
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A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radialvelocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.