Christine Johnson (Reading University)
(also with Prof. Brian J. Hoskins (Reading University),
Prof. Nancy K. Nichols (Reading University) and
Sue P. Ballard (Met Office)).
Baroclinic instability is characterised by a pressure field that has a westward tilt with increasing height. This vertical structure can result in the rapid development of depressions leading to severe storms. It is therefore important that a data assimilation system should be able to perform well in these situations. This work aims to understand some of the capabilities and weaknesses of four-dimensional variational data assimilation (4D Var), by applying the method to theoretical cases of baroclinic instability and rapidly growing synoptic scale features where the vertical structure is important.
The 2D Eady model is a simple linear quasi-geostrophic model which can be used to describe the vertical coupling between upper and lower boundary waves. The numerical model is used within a 4D Var system to perform identical twin experiments. The first set of experiments consider the case where only part of the flow is observed, but with enough observations so that the problem remains well posed. We investigate how information is propagated to the unobserved regions by the minimisation algorithm and model dynamics. The second set of experiments include the background state or 'Jb term' in the cost function. In reality, there are not enough observations to completely determine the state of the system and so it is necessary to find an optimal blend between a background state and the observations. In particular, the impact of a phase or displacement error in the background state is considered, as the relative phase between the upper and lower boundary waves is vital in determining the growth of the system.
These simple theoretical case studies should allow us to develop a greater understanding of the processes within 4D VAR, and the limitations of the method when used in the presence of baroclinic instability.
Zhao-Xia Pu
Goddard Earth Sciences & Technology Center
University of Maryland, Baltimore County
and
Mesoscale Atmospheric Processes Branch
Mail Code 912
NASA Goddard Space Flight Center
Greenbelt, MD 20771
Phone: (301) 614-6078
E-mail: pu@agnes.gsfc.nasa.gov
Wei-Kuo Tao
NASA Goddard Space Flight Center
William S. Olson
Joint Center for Earth Systems Technology/UMBC
Surface rainfall data, derived from the TRMM Microwave Image (TMI), are assimilated into the PSU/NCAR MM5 model using a 4DVAR technique. Preliminary experiments are performed to incorporate TRMM rainfall data into a hurricane initialization. It is found that the rainfall data assimilation is sensitive to the error characteristics of the data and the physics in the adjoint model. In addition, assimilating the rainfall data alone produces a more realistic eye and rain bands in the hurricane but cannot ensure improvements of hurricane intensity forecasts. Numerical results indicate that it is necessary to incorporate TRMM rainfall data together with other types of data such as wind data into the model, in which case the inclusion of the rainfall data will further improve the intensity forecast of the hurricane. This fact might imply that some proper constraints will be needed for the rainfall assimilation. Relevant results and issues will be presented.
G. A. Jacobs, H. E. Ngodock
The Naval Research Laboratory is using adjoint equations to understand the sensitivity of ocean processes to external forcing and measurements for assimilation systems. One example examines the sensitivity of transport through strait between Korea and Japan with respect to the wind stress throughout the area. The adjoint-derived sensitivity is compared to the correlation analysis between the regional wind stress and in-situ observed transport. The correlation analysis indicates several possible areas over which the wind stress could significantly force the transport through the strait. The adjoint results are able to more precisely discern dynamical mechanisms and connections than is possible with only the correlation analyses. Thus, the adjoint results provide significant conclusions and extension beyond results provided solely by the correlation analysis. The adjoint used in this analysis is based on linear barotropic dynamics. An extension to linear baroclinic dynamics provides an estimate of the influence of different data types (measurements of velocity, absolute sea level, and sea level change) on estimating the ocean environment using representer methods. Ocean processes of different spatial and temporal length scales of course lead to different scales of influence of the measurements. This study aims to determine the data type or types required to best estimate different processes on the continental shelf.
Thomas R. Bewley & Laura Cerviño, UC San Diego
The Complex-Step Derivative (CSD) method has already proven to be a valuable tool for the verification of adjoint codes, and has even proven to be useful in the practical solution of optimization problems involving big numerical codes when the control variable is of fairly low dimension. The CSD method computes the directional derivative in real-space optimization problems using a complex extension of all real variables in a given problem and truncation of the Taylor-series expansion: J(phi+i*eps*phi') = J(phi)+i*eps*(DJ/Dphi)*phi' + O(eps^2). Using this approach, the directional derivative of the objective function J in the direction phi', denoted (DJ/Dphi)*phi', is easily computed from any finite-difference or finite-element code simply by changing all variables in the code from real to complex, changing the control from phi to phi+i*eps*phi' (for a sufficiently small value of eps), then looking at the imaginary component of the resulting calculated value of the objective function J. In a code involving only real arithmetic, this directional derivative calculation is not plagued by the 'difference of large numbers' problem which often corrupts other techniques which might be used to compute this directional derivative. In the present work, we show how the CSD method may be modified for application to pseudospectral codes. Pseudospectral codes, which switch back and forth between physical-space representations (with real variables) and Fourier space representations (with complex variables), are well suited for spatially-periodic problems, such as the solution of the Navier-Stokes equation on a sphere. The benefit of the pseudospectral approach is that spatial derivatives may be computed extremely accurately in Fourier space, whereas nonlinear products may be computed extremely efficiently in physical space. The conversion between the Fourier and physical representations is made relatively efficient by leveraging the Fast Fourier Transform (FFT). When the modified CSD method is applied to pseudospectral simulations, the Fourier transforms combine large and small numbers and thus lead to certain numerical inaccuracies. However, our recent numerical results (to be presented at the talk) show that this pseudospectral extension of the standard CSD method is still far superior for computing directional derivatives than the other techniques currently available for computing the directional derivative in such problems.
Desroziers and Ivanov (2001) have proposed an iterative fix-point algorithm in order to evaluate both observation and background error variances and successfully tested it on simulated TEMP data. Yet, several properties of the algorithm remain insufficiently understood, and its relationships with methods such as GCV or maximum likelihood should be established. The algorithm basically depends on statistical properties of parts of the cost function at its minimum. We provide several of those properties, and examine the limit of the algorithm in two cases : 1- tuning of the observations and background error variances together; 2- tuning the observations error variances alone. We propose a theoretical evaluation of the variance of the error statistics estimators, thus providing a lower bound to the variance of their actual computation. We also examine the effect of observation error bias (or of any spatially correlated component of the observational error). These results will be illustrated in a simplified 1D or 2D assimilation scheme.
Desroziers G. and S. Ivanov, 2001 Diagnosis and adaptative tuning of observation error parameters in a variationnal assimilation. Q.J.R.M.S, 127, 1433-1452
Assuming is it possible to detect an anthropogenic influence on climate using a complex, coupled climate model, one would like to determine the sensitivity of that detection result to various model parameters and processes. Rather than perturbing each model parameter in turn and assessing the resulting impact, the adjoint approach is capable of providing sensitivity information with respect to all model variables and parameters in a single adjoint integration. An example of the utility of this approach is demonstrated using a simplified coupled climate model. Unfortunately, state-of-the-art coupled climate models are highly nonlinear on time-scales of 50-100 years, rendering the traditionally-employed adjoint approach worthless. Methods to recover sensitivity information in the face of severe nonlinearity include ensemble approaches, the utilization of simplified models, and the inclusion of large diffusion terms. A speculative method is presented that uses the complex forward model's complete tangent-linear model, but periodically ``knocks down'' error growth due to highly nonlinear processes. This approach allows the details of fast processes to impact the development of the slow processes, but does not allow them to grow to a level that swamps the desired slow process signal.
Marta Janiskova and Jean-Francois Mahfouf
The adjoint of various physical processes have been used in the operational ECMWF 4D-Var assimilation system since 1997. As the forecasting system is constantly evolving (higher horizontal and vertical resolutions, adjoint of semi-Lagrangian scheme, longer assimilation cycle, changes in non-linear physical parametrizations), validation of existing linearized physical parametrizations and their further improvement become important to preserve their usefulness in the system. Thorough re-evaluation of the linearized schemes reveals various hidden problems. Potential sources for improving the fit of the linearized model to the non-linear one are identified. For example, the operational package of linearized physics is improved by including more detailed radiation schemes. Using a more comprehensive set of linearized physical parametrizations in 4D-Var system shows positive impacts in terms of quality of the forecasts.
Kevin Raeder, Ronald Errico, and Martin Ehrendorfer
Twelve-hour SVs have been computed for 4 distinct synoptic cases. Initial norms include perturbation energy and variance-weighted mean squares of either mixing ratio or other fields. These variances are estimates of analysis uncertainty over the United States determined from statistics of differences between ECMWF and NCEP re-analyses. Final norms include energy or mean squared precipitation rate. The main result is the great sensitivity of the final energy norm to initial perturbations of moisture when the initial constraint is a variance weighted norm. For most cases, the SVs that maximize energy are distinct from those that maximize precipitation, although there are notable exceptions where both types of SVs are highly correlated. Furthermore, independently determined SVs for variance weighted dry and moist fields are shown to produce nearly identical final-time structures for those cases where diabatic precipitation processes are important. The net effect of combining perturbations of the dry and moist fields can therefore be greater than the effect of either alone. Further work will distinguish between convective and stratiform precipitation as well as examine some of the mechanisms for development of the SV structures.
Stephane Laroche, Monique Tanguay, Yves Delage
Meteorological Service of Canada (MSC)
This study examines the linearization properties of a simplified planetary boundary layer parameterization based on the vertical diffusion equations, in which the exchange coefficients are function of the local Richardson number and wind shear. Spurious noise, associated with this parameterization, develops near the surface in the tangent linear integrations. The origin of this problem is investigated by examining the accuracy of the linearization and the numerical stability of the scheme used to discretize the vertical diffusion equations.
It is shown that the noise is primarily due to the linearization of the exchange coefficients when the atmospheric state is near neutral static stability and when a long time step is employed. A regularization procedure based on the linearization error and a criterion for the numerical stability is proposed and tested. This regularization is compared with those recently adopted by Mahfouf (1999, Tellus, 51A, 147-166), who neglects the perturbations of the exchange coefficients, and by Janiskova et al. (1999, Mon. Wea. Rev., 127, 26-45), who reduce the amplitude of those perturbations when the Richardson number is in the vicinity of zero.
When the sizes of the atmospheric state perturbations are 1 m/s for the winds and 1 K for the temperature, which is the typical size of analysis increments, our regularization and the one proposed by Janiskova et al. perform similarly and are slightly better than neglecting the perturbations of the exchange coefficients. On the other hand, when the state perturbations are much smaller (e.g. three orders of magnitude smaller), it is shown that the linearization becomes accurate and a regularization is no longer necessary, as long as the time step is short enough to avoid numerical instability. In this case, our regularization procedure becomes inactive while the others introduce unnecessary errors.
Dacian N. Daescu
Institute for Mathematics and its Applications, University of Minnesota
and
Adrian Sandu
Department of Computer Science, Michigan Technological University
The dynamical models associated with atmospheric chemical reactions mechanisms are represented as stiff systems of nonlinear ordinary differential equations which integration requires highly stable numerical methods. Runge-Kutta-Rosenbrock (RKR) methods have been proved to be reliable chemistry solvers that have outstanding stability properties and conserve the linear invariants of the system. The derivation of the discrete and continuous adjoint model associated with atmospheric chemical reactions models, implementation, and a comparative performance analysis are presented for RKR methods. Applications to variational data assimilation and adjoint sensitivity analysis with respect to the model state and source parameters are presented. The discrete adjoint model is generated from the numerical method used during the forward integration and has the advantage that the computed gradient is exact relative to the computed cost functional. Since the complexity of the discrete adjoint code implementation is determined by the complexity of the forward model integration method, the drawbacks are related with the difficulty to generate the adjoint code when sophisticated numerical methods are used. Since RKR integration requires the Jacobian matrix, it is shown that by exploiting the particular structure of this class of methods an efficient discrete adjoint model may be generated. The continuous adjoint model is derived from the linearized continuous forward model equations. The adjoint model is then integrated with its own numerical method such that the complexity of the forward numerical integration does not interfere with the adjoint computations. While during the forward integration one has to solve a stiff nonlinear ODE's system, during the backward integration a stiff linear system must be solved. Therefore, the cost of implementing highly stable implicit methods for the continuous adjoint is relatively cheap, which is an advantage in the context of modeling stiff chemical reactions systems. Issues related to the stability and the accuracy of the discrete and continuous adjoint model for stiff dynamics are discussed. In particular, it is shown that for time-dependent sensitivity studies performed with the discrete adjoint model strong oscillations in the sensitivity values may be observed. Numerical experiments show that the amplitude of these oscillations is highly dependent on the accuracy and the method used for the forward model integration. Examples are presented for RKR methods up to order 3 using a comprehensive SAPRC99 chemical mechanism. The discrete and continuous adjoint model are generated with minimal user intervention using symbolic preprocessing software.
J. Barkmeijer (a) T. Iversen (b) and T.N. Palmer (a)
a) ECMWF, Shinfield Park, Reading, England
b) University of Oslo, Department of Geophysics, Norway
The same framework of determining fast growing perturbations in the initial time model state given by singular vectors, can also be utilized in defining sensitive structures for model tendencies. Based on so-called forcing singular vectors, small time independent tendency perturbations can be generated that may result in entirely different forecasts, even when started from the identical initial states. It will be shown how to derive forcing singular vectors and their properties will be compared with regular singular vectors.
Various applications of forcing singular vectors will be discussed, such as, ensemble forecasting and data assimilation. In particular, the assimilation of precipitation data may benefit from allowing tendency perturbations during the minimization process. Properties of forcing singular vectors may also be helpful in identifying physical processes that contribute to (systematic) forecast error.
P.Gauthier, M.Tanguay, S.Pellerin, N.Ek, S.Laroche and A.Zadra
The current operational data assimilation used at the Canadian Meteorological Centre (CMC) is a 3D-Var based on a spectral formulation and on the model's own vertical levels (Chouinard et al.,2001). The analysis is driven by the Global Environmental Multiscale (GEM) model, a variable resolution semi-Lagrangian grid-point model (Cote et al.,1998). A 6-hourly 4D-Var formulation is being developed in the context of an efficient and flexible multi-processor architecture. It is built upon the same incremental 3D-Var code for both observation operators and representation of background-error covariances. The model is launched independently from the 3D-Var which sends requests to perform integrations of the direct, tangent linear or adjoint models. This bi-modular architecture will be broken up into its elementary operations allowing us to explore other data-assimilation algorithms used in meteorology and oceanography (Lagarde et al.,2001).
The optimization of the tangent linear and adjoint models of the distributed memory version of the GEM model will make it possible to run the inner loop at 2 degree resolution or higher, with the same vertical resolution as the operational model. Tangent linear and adjoint simplified physics will include vertical diffusion with surface drag (Laroche et al.,2002), sub-grid scale orographic effects and stratiform precipitation.
The coupling of the 3D-Var with the GEM model has already been tested in single observation experiments. Further work is being completed to take into account the distribution of observations over the assimilation window. Experiments including all the observations currently assimilated in the operational 3D-Var at CMC will be conducted in early 2002. At the time of the workshop, preliminary results will be presented and we will report on the current status and future development.
Steven J. Fletcher, Ian Roulstone, Nancy K. Nichols
Department of Mathematics, University of Reading, Whiteknights, PO BOX 220, Reading, Berkshire, RG6 6AX, UK.
Sasaki (1958 [1]) formulates an objective method for the analysis of meteorological data based the assumption of quasi-geostrophic and thermal wind balance. The balance conditions were substituted directly into the cost function and simple examples were studied in order to assess the effectiveness of the scheme. In this paper we extend the work of Sasaki in two important directions. First, we consider higher-order balance conditions, applied to a shallow water model, that are formally equivalent the semi-geostrophic and Charney-Bolin equations, and second, we use these constraints to determine a balanced divergent component of the analysed flow. The balance conditions used are derived from the hamiltonian description of balanced flows (McIntyre and Roulstone 1996, 2001). This work provides the theoretical basis for an approach to improving balance in the Met Office's VAR scheme in which it is desirable to quantify the relationship between balanced horizontal convergence and vertical motion.
A.S. Lawless (The University of Reading)
N.K. Nichols (The University of Reading)
and
S.P. Ballard (Met Office)
The incremental formulation of four dimensional variational assimilation (4D-Var) allows for the use of a linear model which is not exactly tangent to the full nonlinear model. The Met Office have followed the approach of deriving an approximate linearization by discretizing the continuous linearized equations, to form what is known as a perturbation forecast model. In this paper we compare the use of a perturbation forecast model with a true tangent linear model, using both direct tests of the linear models and data assimilation experiments.
Using a model of the one-dimensional shallow water equations, we first compare the behaviour of the linear models using linearization tests. An important factor in determining the accuracy of the models is found to be the representation of the background trajectory around which the model is linearized. We find that natural approximations to this trajectory may not only reduce the accuracy of the overall scheme but, within the context of semi-Lagrangian advection, may lead to a scheme which is no longer consistent.
As part of our analysis we find that the asymptotic behaviour of the linear models differ, which leads to a difficulty in testing the perturbation forecast model. In order to overcome this we propose a new method for testing such models, by which we are able to estimate the component of the linearization error which is due to nonlinear effects. This method has since been used successfully in tests of the three-dimensional model being developed for operational use at the Met Office.
In the second part of the paper we consider the use of these linear models and their adjoints in an incremental 4D-Var scheme. Identical twin experiments are used to investigate the convergence properties of the assimilation and the quality of the analysis using the two different linear models.
Carla Cardinali
In statistical linear estimation, the 'influence matrix' measures the sensitivity of the analysis to the observations, in observation space. In particular, the diagonal elements of the influence matrix represent the sensitivity of the analysis (in observation space, at observation time) to each corresponding observation, or the 'self-sensitivity'.
Self-sensitivities have been computed in ECMWF's global 4D-Var system. The computations require an estimate of the analysis error covariance, calculated using the combined Lanczos/conjugate gradient algorithm, and a tangent-linear forecast model to propagate the analysis error covariance to the observation time. The self-sensitivity shows to what extent an observation has been influential on the analysis. High self-sensitivity indicates that the analysis locally has been largely determined by a single observation. Small self-sensitivity indicates redundancy with surrounding data, or strong influence of the background information. Such diagnostics may help identify possible reasons for forecast failure due to inaccuracies in initial conditions.
G. Desroziers and P. Arbogast (Meteo-France/CNRM, France)
Potential vorticity (PV) inversion has been widely applied as a tool for diagnosing the dynamics of extratropical cyclones. It has also been used to explain or to document forecast failures.
Different techniques have been proposed for the inversion of Ertel PV or of the quasi-geostrophic pseudopotential vorticity. However, an implicit inversion technique can be obtained by introducing a PV observation operator in a variational assimilation scheme. Such a non-linear operator and its tangent-linear and adjoint expressions have been coded in the French Arpege 4D-Var. In that case the structure of the PV anomaly associated with one or several simulated PV observations is consistent with the covariances of background field errors. These statistics are those of a short-range forecast if PV observations are introduced to correct such a forecast, or those of an analysis if PV observations are added to a set of real observations available during the assimilation period.
The structure of the PV anomalies associated with single PV observations are in particular presented. It is shown that the form of these structures are dependent on the location of the observations, but that these PV structures are roughly associated with a typical horizontal wind circulation and a potential-temperature anomaly dipole oriented vertically. The structures are also different wheter observations are introduced at the beginning of the assimilation period or on the contrary at the end of this period when the PV error covariances have been implicitly evolved by the Arpege tangent-linear model and its adjoint, but also by the full resolution non-linear model in the Arpege incremental formulation. Experiments using such a 4D-Var PV inversion are conducted to diagnose a FASTEX cyclone.
James Beck, Tim Payne, Andy White, Amos Lawless and Sue Ballard
The Met Office, Bracknell, UK
The Met Office is trialling a new formulation non-linear forecast model for introduction operationally in 2002. The linear and adjoint models developed for a 4D-Var system are based on this new formulation dynamics. The non-linear model is semi-implicit and non-hydrostatic with semi-lagrangian advection and height based vertical co-ordinate with Charney-Philips vertical grid stagger. There is no basic state removal so a 3D GCR solver is used to solve a helmholtz equation for pressure adjustments.
The approach taken for development of the linear and adjoint models was that rather than derive the exact tangent linear version a perturbation forecast model should be developed that makes approximations to save cost and removes the need for linearization of the departure point calculations and solver method. Approximations include neglect of the advection of the vertical velocity and some deep atmosphere terms. The advection by wind increments is treated as an Eulerian forcing term rather than a linearization of the semi-lagrangian scheme. Most of the adjoint model is coded explicitly from the linear model code, e.g. advection, physics and updating. However in order to deal with the 3D solver for the pressure correction term a second equation is derived, from the adjoint of the discrete PF model equations, requiring the same basic solver for the adjoint pressure correction.
This paper will show results from linearization tests of the PF model. It will discuss the sensitivity to strong gradients in the linearization state, the need for good preconditioning and convergence of the solver in the both the forward and adjoint models to ensure that the adjoint test is passed, and the need for a revised treatment of the coriolis terms to avoid coupling all points in the adjoint model due to the implicit formulation used in the non-linear dynamics.
J. Lewis, K. Raeder, and R. Errico
A return flow event in the Gulf of Mexico is examined with benefit of the MAMS (Mesoscale Adjoint Modeling System). The aspect is essentially moisture return to the USA continent in a laterally narrow and vertically restricted zone (a cross section perpendicular to the horizontal wind in the lower troposphere). This aspect (J) is the product of wind and specific humidity at a given time during the forecast (48 h forecast). The model simulation is faithful to the moisture return pattern. We examine the Grad J where Grad is the gradient with respect to every element of the control vector. We find, as expected, that those elements of Grad J related to the sea surface temperature boundary condition are relatively large. They are not uniformly large over the entire Gulf; the largest values are tied to that area associated with low-level trajectories that flow into the cross section. This is expected. The pattern of the Grad J is unexpected in that couplets appear (+ and - regions lying next to each other). In short, increasing the SST in one area will lead to an increase in the aspect, whereas a decrease in a neighboring area will also lead to an increase. This is certainly not expected on intuitive grounds. It remains to understand the physical meaning of such patterns, albeit the structure and its influence on the aspect can be validated by perturbing the control vector and examining its impact on J.
POSTER
Saroja Polavarapu, Shuzhan Ren*, Yves Rochon, David Sankey* and David
Tarasick
Meteorological Service of Canada
*University of Toronto
A data assimilation scheme has been developed for the Canadian Middle Atmosphere Model (CMAM). The goal of this work is to improve our understanding of middle atmosphere dynamics by confronting the climate model with data and learning about model errors in the process. The CMAM is a state-of-the-art general circulation model extending from the ground to the top of the neutral atmosphere (95 km) with fully interactive chemistry, radiation and dynamics. The CMAM can depict a realistic ozone climatology and obtain a QBO-like signal. We use a T47L65 configuration with gas-phase stratospheric chemistry (44 species, 18 tracers). The Canadian Meteorological Center's (CMC) operational 3DVAR scheme was adapted by raising the lid to 95 km, generalizing the vertical coordinate and creating interfaces for the climate model state to 3DVAR. A particular challenge was the creation of new background error statistics based only on CMAM model climate runs. Our first results with the new system for Jan 1994 involve only conventional observations and SATEMs below 10 mb. The results compare well against UKMO analyses and against observations. Improvements to the system which are in progress include: replacing the digital filter initialization with an incremental filter or incremental analysis updates, upgrading to the new operational 3DVAR which assimilates temperature observations and introducing a bias correction algorithm. The next steps are to exploit the power of the 3DVAR scheme through the assimilation of current day observations such as AMSU-A, and to assimilate ozone from, for example, TOMS and SBUV/2.
Bartosz Protas & Thomas Bewley
University of California, San Diego
bprotas@ucsd.edu, bewley@ucsd.edu
Data assimilation is an inverse problem which is usually ill-posed.
Consequently, its solution using adjoint-based methods generally
requires attention to a variety of regularization issues. We address
these issue in a general framework by showing how the choice of the
functional settings for
a) the observation operator,
b) the governing evolution equations, and
c) the gradient
affects the reconstruction. Attention to each of these items
is necessary to
(a) focus the optimization procedure on the physics of interest,
(b) formulate computationally tractable problems for the state
and adjoint systems, and
(c) extract properly preconditioned gradients.
Modifying the cost functional by incorporating integral or differential operators acting on the measurements allows one to give more weight to large or small structures present in the measurements. In a similar manner, identifying the G\^ateaux differential of the functional with the scalar product in the space with desired regularity (e.g. Sobolev space) makes it possible to extract gradients smoother than in the space L_2, and may therefore be used as preconditioning. These aspects allow us to more effectively tackle the multiscale nature of the data assimilation problem. Theoretical arguments will be supported with computational results obtained for systems with varying degrees of complexity (the periodic Kuramoto-Sivashinsky equation, turbulent channel flow governed by the Navier-Stokes system, etc.). The ideas developed here are also pertinent to a range of adjoint-based control and estimation problems.
More about the ongoing research can be found at: http://turbulence.ucsd.edu/~bprotas/Forecast/root.html
Liang Xu, Tom Rosmond and Roger Daley*
Naval Research Laboratory, Monterey, California.
In this study we introduce a natural follow-on to NAVDAS (NRL Atmospheric Variational Data Assimilation System), NAVDAS-AR, where the AR stands for accelerated representer. NAVDAS-AR consists three major components. They are (1) data quality control preprocessing and generating the innovation vector; (2) minimizing a chosen cost function using a minimization algorithm, such as the accelerated representer algorithm; (3) postprocessing to produce analysis products and diagnostic information. Because (1) and (3) are essentially the same as for the current NAVDAS, we mainly focus on (2) for NAVDAS-AR in this study. The minimization algorithm used in NAVDAS-AR is based on the accelerated representer algorithm. The accelerated representer algorithm is the dual of the standard 4DVAR algorithm. That is, while the standard 4dvar algorithm (as implemented at ECMWF) is an analysis grid-space algorithm, the accelerated representer algorithm is an observation-space algorithm (as is NAVDAS itself). The non-linear, tangent linear and adjoint models of NOGAPS (Navy Operational Global Atmospheric Prediction System) are used in NAVDAS-AR for development and testing purpose. To quicken the pace of the development, a Burgers equation model (1D univariate problem) and a shallow water equation model (2D multivariate problem) are also used as the test beds to conduct quick data assimilation experiments. Preliminary results from various NAVDAS-AR experiments are shown.
*Roger Daley (deceased August 2001)
Ian Roulstone (Met Office)
In this paper we examine and compare three different methods for calculating increments to vertical motion. The objective of this work is to provide suitably balanced increments to vertical velocity for use in a programme to improve the treatment of moisture, cloud and precipitation in VAR. In Richardson's 1992 book on numerical weather prediction, he derived an equation for diagnosing a dynamically consistent vertical velocity for a hydrostatic model by combining the thermodynamic and continuity equations. This equation also arises as a consistency condition in the hamiltonian description of the hydrostatic primitive equations. We show how additional balance constraints can be imposed within the hamiltonian framework to obtain a balanced vertical velocity from suitably balanced horizontal divergent wind increments. Results obtained from Richardson's equation will be discussed and compared with those obtained by integrating the continuity equation and the quasi-geostrophic omega equation.
Tom Rosmond
NRL Monterey
Carolyn Reynolds
NRL Monterey
Ron Errico
NCAR
Rolf Langland
NRL Monterey
Perturbations suitable for ensemble forecasting purposes are designed to have vertical and horizontal correlations like those found between the reanalysis data sets from NCAR/NCEP and ECMWF. Formulation of these perturbations also includes consideration of the (daily varying) analysis error variance information produced by NAVDAS, the Navy's new 3Dvar analysis system developed by the late Roger Daley.
Therefore, while these perturbations are generated using random numbers, they are constrained to have spatial structures similar to those found in analysis differences or analysis errors, and also reflect fluctuations in analysis error variance due to daily changes in the observation network.
Singular Vector-based ensembles produce optimally growing perturbations. At the other end of the spectrum, purely random perturbations will, for the most part, decay initially. It is expected that while the perturbations considered here will not grow as rapidly as SV-based perturbations, their spatial correlations will result in growth that is considerably faster than purely random perturbations. This generation method is considerably less expensive than an SV-based method, and will also not suffer from convergence of the perturbations, which can happen when using a method that cycles the perturbations simply by rescaling them.
The nature of the ensemble dispersion will be investigated considering, among other things, the projection of the initial perturbations onto singular vectors.
Y. Tremolet, ECMWF
The ECMWF assimilation system is based on the incremental formulation of 4DVAR. In that framework, the control variable for the minimization is the analysis increment. The computation of the cost function is based on the integration of the linearized version of the forecast model and its gradient is computed using the adjoint model. In addition to the linear approximation, because of computational cost, the minimization is performed at a lower resolution than the non linear forecast.
The linear approximation is usually tested in a perfect framework which is necessary for the validation of the linearized code. In this presentation we will instead focus on testing the validity of the tangent linear approximation and of the incremental 4DVAR formulation in the context of operational assimilation. In that case, the linear and adjoint models are run at a lower resolution than the non linear model and the physics may be different in the two models.
Comparisons have been made between the linear model output and the finite difference obtained by running the non linear model twice, with and without adding the analysis increment. We present measures of the accuracy with respect to the resolution used in the linear model, the physics used in the linear model, and the length of the assimilatyion window. Deficiencies in the implementation as well as limitations in the incremental assimilation method can be shown by these diagnostics.
The results should be useful to guide future improvement in the variational assimilation algorithm at ECMWF and to assess the improvements due to further developments in linearized physics.
T J Payne, A C Lorenc, S P Ballard, M R Dubal and J Beck (The Met. Office)
The Met Office is developing an incremental 4D-Var scheme in which linearisation states are interpolated to lower resolution from non-linear model runs and updated in an outer loop. This paper describes aspects of this scheme, notably the "double inner loop" and in the linear model the Helmholtz solver and recent progress with the physical parametrisations.
With the aim of simplifying development and reducing CPU time the linear model used for the prediction of increments, called the perturbation forecast (PF) model, is not exactly tangent linear to the non-linear dynamics (for the approximations made see the paper "Issues arising in development of the linear and adjoint models for use in 4D-Var with a semi-lagrangian, semi-implicit, non-hydrostatic model"). Most of the adjoint model is coded explicitly from the linear model code, e.g. advection, physics and updating. However in order to deal with the 3D solver for the pressure correction term a second equation is derived, from the adjoint of the discrete PF model equations, requiring the same basic solver for the adjoint pressure correction.
To reduce the cost of the 4D-Var minimisation a "double inner loop" scheme is employed whereby the observation operator used in each inner-inner loop is a linearisation of the full version (thereby making the cost function exactly quadratic), the linearisation recalculated in the outer-innner loop. This scheme has been used operationally in the Met Office 3D-Var since 1999.
A major outstanding challenge in the development of 4D-Var is the inclusion of physical parametrisations into the PF-Adjoint model. Some results will also be presented on recent progress in this direction.
Martin Leutbecher
The future network of observations for weather forecasting may be envisaged to include an adaptive component. One would like to know a priori how the use of a set of additional observations will affect the forecast error. Here, a measure of the statistically expected change of the magnitude of forecast error is introduced. It uses the Hessian of the cost function of a variational assimilation scheme to obtain information on the distribution of initial errors. Two distributions of initial errors are considered. One for the routine observing network and one for the modified network. The intermittent modification of the observing network is accounted for in the computation of the Hessian by changing the observation term in the cost function. The distributions of initial errors are evolved with the tangent-linear version of the forecast model. Then, the forecast errors are projected into a subspace of leading singular vectors. Without the projection the method would be equivalent to an extended Kalman filter. The projection reduces the rank of the forecast error covariance matrix. Due to the rank reduction the problem remains computationally tractable even for realistic NWP models.
To illustrate, the method is applied to the 2-day forecast of an extra-tropical cyclone. The expected reduction of forecast error is computed for various hypothetical adaptive components of the observing network that differ by spatial coverage, observation density and the type of observation.
Mike Fisher
It is well known that the vertical and horizontal scales of background error covariance are non-separable: large horizontal scales tend to have deeper vertical correlations than small horizontal scales. The ECMWF four-dimensional variational data assimilation system recognizes this fact by providing different vertical correlation matrices for each total wavenumber of the spherical harmonic expansion of vorticity background error. The resulting model of background error is homogeneous for vorticity.
A non-homogeneous, non-separable model of background error covariance will be presented. The model is based on a wavelet expansion for the sphere, defined in terms of radial basis functions (i.e. functions of great-circle distance). An advantage of the chosen wavelet basis is the complete absence of "pole problems". However, a necessary consequence is that the expansion is non-orthogonal.
It will be shown that, when implemented in the ECMWF four-dimensional data assimilation system, the wavelet-based covariance model retains the non-separable characteristics of the existing covariance model, while demonstrating a significant degree of geographical variation of both vertical and horizontal correlation.
M.A. Wlasak (The University of Reading)
N.K. Nichols (The University of Reading) - presenter
I. Roulstone (Met Office)
The measured data available for assimilation into a numerical weather prediction (NWP) model are not sufficient to determine all the degrees of freedom in the model. The evolution of weather systems is dominated by 'balanced' flow patterns, however, and prior knowledge of the balanced structures in the atmosphere can be used to resolve the indeterminacy. A weakness of current operational data assimilation schemes is the definition of balance used. Spurious imbalances can lead both to inaccuracies in the forecast and to inherent uncertainty over the meteorologically significant features in the initial conditions. Undesirable results include the excitation of spurious gravity-inertial waves.
In this paper we formulate a new technique for generating a 'balanced' analysis of data based on the conservation of potential vorticity (PV). Control variable transforms are derived using a linear PV inversion method that produces a balanced rotational wind and an associated balanced height. These transforms enable a best match between observations and the balanced components in the analysis to be achieved. The new transforms have been tested in a 2-D global shallow water model on a spherical geometry. Results have been successfully obtained for a variety of different weather regimes, characterized by Burger number.
For regimes with high Burger number, the new control variable transforms are shown to capture the balance observed in the winds. In these regimes, the streamfunction, currently used in the Met Office system to derive the balanced components of the system, produces essentially same results as the new method. For regimes with low Burger number, however, the balanced flow is no longer captured by the streamfunction, primarily because the energy is held predominantly as potential energy. In these regimes the balance is held in the height field, which is well represented by the new control variables in these regimes. The new technique is thus able to capture the balanced atmospheric flow over a full range of weather regimes.
Further tests examining the divergence tendencies of the balanced flow fields derived by the new transforms are now being carried out in order to measure how well gravity waves are controlled by this technique.
Anthony WEAVER, Sophie RICCI and Andrea PIACENTINI
Centre Europeen de Recherche et de Formation Avancee
en Calcul Scientifique (CERFACS),
42, avenue Coriolis, 31057 Toulouse Cedex, France
In a recent paper by Weaver and Courtier (2001) (WC01), a practical algorithm was described for modelling correlation functions within a background-error covariance matrix. The algorithm is based on the numerical integration of a generalized diffusion equation (GDE). In its most basic form, the GDE describes a family of isotropic correlation functions. A notable feature of these functions is that their variance spectrum at high wavenumbers decays at least as rapidly as the spectrum of the Gaussian. Certain observational evidence suggests, however, that some geophysical variables have a much more gradual spectral decay rate. For these variables, the GDE may not be an appropriate correlation model.
In this presentation, we describe an extension of the GDE algorithm which allows us to model correlation functions that have a much wider range of spectral characteristics. The new algorithm is based on an implicit time-discretization of the GDE. In the limit of a large number of "time" iterations, the implicit scheme reproduces the functions of WC01, with sharply decaying spectrums; with a reduced number of iterations, the scheme permits new functions with slowly decaying spectrums. These new correlations functions are in fact closely related to those generated by smoothing splines.
>From a more practical viewpoint, the implicit scheme introduces the possibility of substantially reducing the computational cost of the algorithm. This is particularly important for flow-dependent, anisotropic versions of the GDE which, with an explicit time-discretization, require many iterations to remain numerically stable. The GDE is well suited for application in bounded domains and within ``square-root'' operators often used in preconditioning transformations in variational assimilation. Examples will be presented from a variational assimilation system for the OPA ocean general circulation model.
John Derber(NCEP), Russ Treadon(NCEP) and Paul van Delst (NCEP and CIMSS)
Building upon the infrastructure developed at NCEP over the last 10 years, a series of additional advances have been made in the NCEP global data assimilation system. The most recent enhancements include the addition of additional satellite measured radiances and satellite based precipitation estimates. The satellite measured radiances include the addition of microwave data over land, AMSU-B data and GOES imagery data. Each of these data (and other satellite radiance data previously used ) required unique developments for the quality control and bias correction, but use the same improved version of a clear column radiative transfer algorithm. This radiative transfer (and it^Òs adjoint) has been developed to be usable by a wide range of users and to be easily adaptable to new instruments.
The satellite based precipitation observations from TRMM and SSM/I were also incorporated into global data assimilation system. The inclusion of this data required the incorporation of a version of the forecast model^Òs precipitation parameterization and their adjoints. Some modification of the parameterizations were necessary because of discontinuities. The inclusion of these data has also required development of quality control and bias correction appropriate for this data. Brief presentations of both of the quality control, bias correction, forward models and model impact for these new data sources will be presented.
R. Giering, T. Kaminski, R. Todling, and S.-J. Lin
We are applying FastOpt's new Automatic Differentiation tool Transformation of Algorithms in Fortran (TAF) to the joint NASA/NCAR climate model's dynamical core. The dynamical core formulation is based on work of Lin and Rood. All physical parameterizations (including the land surface model) are derived from the NCAR CCM version 3. The model is written in Fortran 90. TAF automatically generates the tangent linear and adjoint models. We list the modifications to the model code and the extensions to TAF, which were necessary to achieve this. We explain the automatic generation of the check pointing scheme, which allows long integrations of the adjoint in a memory/disk efficient way. We describe how parallelization of the tangent linear and ajdoint models of the parallel code version is achieved automatically.
T. Kaminski and R. Giering
We present FastOpt's new Automatic Differentiation (AD) tool Transformation of Algorithms in Fortran (TAF). >From a model code in Fortran 77/90/95 TAF automatically generates the tangent linear and adjoint models. Applying TAF twice, yields second derivative (Hessian) code. Compared to its predecessor Tangent linear and Adjoint Model Compiler (TAMC), TAF has a number of advantages: TAF is more robust in that it avoids a number of TAMC bugs and in that it handles more complex control flows. Also it supports almost the full language standard, whereas TAMC was restricted to Fortran 77 with some Fortran 90 extensions. Furthermore, owing to improved internal algorithms, the code generation is speeded up considerably and is much more memory efficient. Another advantage is that we are providing support and consulting to TAF users. TAF generated code is very efficient. We give a brief description of TAF, and list the few restrictions that still apply. TAF is available since the end of 2000, and there is a set of first applications, which include one atmospheric GCM and two oceanic GCMs. We give an overview on the first TAF applications and highlight special features of particular applications, such as memory efficient handling of the main time loop or generation of Hessian code. Finally we give the perspectives of future TAF development.
Alexander Beck, Patrick Haas, and Martin Ehrendorfer
In current operational implementations of four dimensional variational data assimilation (4D-Var) no explicit cycling of background error covariances takes place. Propagation of error covariances by means of the full (extended) Kalman filter (EKF) is not possible due to the high computational cost. Hence one seeks an efficient approximation to the full EKF which allows for some flow-dependent cycling of errors. The reduced rank Kalman filter (RRKF) is a primary candidate for providing dynamical prediction-error statistics at low numerical cost. The basic idea is that the dynamical propagation of errors is only applied in a subspace of relatively small dimension. This subspace can be defined by the so-called Hessian singular vectors (HSVs) which are obtained solving a general eigenproblem. The approximation to the fully evolved forecast error covariance matrix is constructed through combining information contained in the set of HSVs and the static background error covariance matrix B. The RRKF has been implemented based on quasigeostrophic (QG) dynamics as part of a QG 4D-Var system. Within this system the importance of the specification of the background term is studied in a series of cycling experiments with different configurations for the background formulation. These configurations include static B, the RRKF in various configurations (i.e., dimension of the subspace) and the evolved forecast error covariance matrix obtained from a full EKF. Special emphasis is placed on studying the impact of the RRKF on the quality of the analyses and subsequent forecasts in view of the full EKF. Preliminary results suggest that the performance of the RRKF strongly depends on the overall level of variance implied through B and that a relatively large number of HSVs is needed to obtain flow-dependent features when blending the static background and the evolving unstable subspace. Other results concern the question to what extent the flow-dependent covariance information at a given cycle is propagated to the next cycle or, in other words, if there is an overlap of the unstable subspaces at successive analysis cycles.
In this presentation, evolutions of singular vectors (SVs) from a hierarchy of rather simple QG models (Eady and Green models) are described, and their evolutions are diagnosed using piecewise PV inversion and wave activity diagnostics. In addition, SV calculations for a variety of norms are computed for observed basic flows associated with observed surface cyclogenesis events using the adjoint and tangent linear propagator of a mesoscale numerical weather prediction model. These singular vectors will be related to the particular synoptic characteristics of the of the observed cyclogenesis events. Adjoint-based forecast sensitivities will also be calculated at various stages of a cyclone life-cyclone to better understand how the sensitivity of a cyclone forecast changes as the cyclone progresses through its life-cycle. These results, taken together with the aforementioned SV calculations will aid in better understanding the importance of mid-tropospheric forecast sensitivity maxima noted in many previous studies.
Adrian Sandu
Computer Science Department, Michigan Technological University
and
Dacian Daescu
Institute for Mathematics and its Applications, University of Minnesota
Comprehensive chemistry-transport models (CTMs) are used to study the fate of pollutants in the atmosphere. A "best estimate" of the chemical state of the atmosphere can be obtained by assimilating the measurements into the model predictions. Building the tangent linear model and its adjoint is very challenging due to the presence of stiff chemical terms. In this talk we present newly-developed software tools that automatically generate the adjoint models for chemical kinetic systems.
The Kinetic preprocessor KPP (co-developed by the authors) is a software environment for solving chemical kinetic problems. KPP reads reaction files and produces C or Fortran code for the time derivative function and its Jacobian. A sparsity analysis of the Jacobian is performed, and species are reordered to minimize the fill-in. KPP provides a suite of stiff numerical integrators for simulating the time evolution of the system. Efficient, sparse routines for solving the linear algebra required by implicit integration are also generate by KPP.
Recently the KPP capabilities were extended to generate efficient code for adjoint computations. More exactly, the Hessian of the chemical system in sparse format is automatically calculated; this is integrated with adjoint Runge-Kutta-Rosenbrock methods and with optimization routines. The resulting code is extremely efficient due to the aggresive exploitation of sparsity.
In this talk we present an overview of KPP; theoretical issues associated with the adjoint modeling of stiff ODE systems will be reviewed; the KPP adjoint-code generating capabilities will be discussed in detail; and results will be shown for atmospheric pollution modeling problems.
Carolyn Reynolds, Tom Rosmond, Rolf Langland
Naval Research Laboratory, Monterey, CA
Recent work has shown that the full (nonlinear) growth of perturbations in atmospheric ensemble forecasts can depart significantly from tangent linear growth after relatively short time periods (2-days). This may have significant implications for applications in which tangent linear perturbation growth is assumed, as in, for example, the use of adjoint-based techniques for targeted observing applications.
In this study we examine the energetics of the tangent linear and nonlinear growth of singular vector perturbations scaled to have initial amplitudes consistent with estimates of analysis uncertainty. The potential and kinetic contributions to perturbation energy are examined as a function of wave number and altitude. Preliminary results indicate that nonlinearities are far more significant on small spatial scales than on synoptic scales. Application of the relative nonlinearity index of Gilmour et al. (2001) indicates that nonlinearities are less significant when considering relatively smooth fields, such as geopotential height, than when considering fields that have more small-scale structure. This suggests that it may be possible to extend the utility of tangent linear-based tools through a judicious choice of metric. Examination of twin (positive and negative) perturbations illustrates how the spatial perturbation patterns can still exhibit a large degree of symmetry (with a phase shift) even when the nonlinearity index is large. Implications for ensemble generation and targeted observing will be discussed.>
P Rogel, A Weaver, E Machu, S Ricci, A Piacentini
CERFACS, Toulouse, France
J Vialard
LODyC, Paris, France
In the perspective of providing ocean initial conditions to a coupled seasonal climate prediction system, a global ocean variational assimilation system is being developed at CERFACS. It based on a 3D-Var/4D-Var approach. The 3D-Var configuration allows for a thorough computation of the innovation vector by comparing data and model equivellent at the exact time (First Guess at Appropriate Time - FGAT [1]). The 4D-var is based on an incremental approach using the Tangent Linear physics in an inner loop. This dual development is aimed at better validating a multivariate background and observation error statistical scheme, which is based on the separation between physically balanced components of the error [2], and a univariate scheme which computes the space distribution of the error [3]. The error model validity is then checked independently from the development of the TL-adjoint system.
An original aspect of this system is the use of the PALM flow-chart approach [4], which splits the assimilation problem into its physical and algebraic parts. This allows for an increased modularity and flexibility of the algorithm, an optimisation of the algebraic part, and a full potential for paralellisation. A short presentation of the PALM software developed at Cerfacs will be given.
Results will show an early evaluation of the global 3D-Var scheme performance when assimilating in-situ temperature data, its internal consistancy, and its comparison to a former version, restricted to the tropical Pacific, of the system.
[1] M Fisher and E Andersson: Developments in 4D-Var and Kalman
Filtering, ECMWF Tech. Memor. 347, (2001).
[2] J Derber and F Bouttier: A reformulation of the background error
covariance in the ECMWF global data assimilation system, Tellus
(1999), Vol 51A, 195-221.
[3] A. Weaver and P. Courtier: Correlation modelling on the sphere
using a generalized diffusion equation, Q.J.R.M.S. (2001)
[4] Th. Lagarde, A. Piacentini and O. Thual: A new representation of
data assimilation methods: the PALM flow charting approach. Q.J.R.M.S.
(2001), Vol. 127 , pp. 189-207
Nancy L. Baker
Naval Research Laboratory
Monterey, CA 93943-5502
The adjoint of the NRL Atmospheric Variational Data Assimilation System (NAVDAS) is used to compute the sensitivity of the forecast error to the observations and background (and implicitly, the statistical assumptions about their respective error covariances). Observation sensitivity may be used to estimate the potential impact of satellite observations on the analysis and forecast, and to illustrate the effects of different data selection choices. The sensitivity to an observation is largest when (1) the observations are relatively isolated or an abrupt change in observation density occurs, (2) the observations are assumed to be accurate relative to the background, and (3) the observations are located in a region with strong sensitivity of to the initial temperature and wind fields. In the present NAVDAS configuration, ATOVS brightness temperatures over land and ice are eliminated since they are more difficult to assimilate properly. This can create an abrupt change in the observation density along coastlines and ice-edge boundaries. The brightness temperatures along these boundaries contain contributions from the different surface types and have larger representativeness errors than the brightness temperatures over the open oceans. Abrupt changes in the data density also occur for the less accurate observations along the edges of the satellite scan. If the observation errors are incorrectly assumed to be spatially homogeneous, and the observations are in regions of strong sensitivity to the initial temperatures and wind fields, the sensitivity to the relatively inaccurate observations along the data-rich/data-sparse boundary will be larger than the sensitivity to the more accurate (data dense) observations. This implies that the less accurate observations have greater potential to change the forecast and influence the analysis. Increasing the assumed observation error variance decreases both the observation sensitivity and the influence of the observation on the analysis. These results highlight the importance of properly specifying the observation errors.
Qingnong Xiao, Dale Barker (NCAR/MMM)
Development of the Weather Research and Forecasting (WRF) model is a collaborative effort between NOAA/NCEP, NOAA/FSL, NCAR, the US Air Force Weather Agency (AFWA) and Oklahoma University. WRF is designed for both operational and research use and is targeted towards the <1-10km range. WRF dynamics, software architecture and data assimilation codes are being designed from scratch. The majority of physics routines so far implemented are legacy codes from the models WRF will potentially replace (MM5, ETA, RUC, ARPS).
In this poster, a description of the current status of the nascient WRF data assimilation system will be given. At present, a basic 3DVAR capability is in place which allows assimilation of conventional and some non-conventional (e.g. retrievals of TPW from ground-based GPS stations, SSM/I radiances) observations. Results of tests to date will be presented, including mesoscale applications of 3DVAR in east-Asian and US domains.
Finally, plans for future additional WRF data assimilation capabilities, both variational (e.g. incremental 4DVAR) and non-variational (Ensemble Kalman Filter) will be briefly discussed.
(poster presentation)
Patrick Haas, Alexander Beck (U. Vienna)
Martin Ehrendorfer (U. Innsbruck)
The general aim of this work is to incorporate flow-dependent information into static background error covariances (denoted as B) by a computationally feasible method. This goal can be achieved by a reduced rank Kalman filter (RRKF) that generates a dynamically evolved forecast error covariance matrix P by combining dynamic information given by Hessian singular vectors (HSVs) and B. Hereby only an unstable subspace spanned by a small number of HSVs is evolved. The RRKF represents a formulation where the inverse of P as needed in a variational assimilation system is approximated. Theory and results relevant for the RRKF (such as how the approximation to P depends on the number of HSVs included) will be presented. The alternative approach in which P (rather than its inverse) is approximated will be discussed briefly.
M. Naughton and W. Bourke (Bureau of Meteorology) and R. Buizzaa (ECMWF)
A global ensemble prediction system, has been developed and implemented and is now running in the Bureau of Meteorology operational schedule. The approach adopted at the BoM has followed the strategies pioneered at the ECMWF in the use of singular vector based perturbations. The system utilises an ensemble of 33 members of the BoM global spectral model at a resolution of T119/L19; the pertubations are linear combinations of SVs (Total Energy Norm) evaluated at T42/L19 - the present deterministic operational global model operates at T239/L29. The quantitative performance of this system will be described together with some examples of the diagnostics generated from the system. A detailed intercomparison of the BoM EPS system with that of the ECMWF has been conducted for the period of April to August of 2001; results of this intercomparison will be discussed.
P.Steinle, R.Seaman, J.Paevere and Y.Xiao
A new 3d-variational assimilation scheme developed at BMRC is currently undergoing parallel trial. This scheme is posed in observation space so as to allow for more flexibility in the specification of the background error covariances. As a prelude to exploring an Ensemble Kalmen filter, the use of background error covariances from an ensemble of analyses is also being investigated. This talk will cover issues raised during these two investigations.
Ricardo Todling, Yanqiu Zhu, Jing Guo and Stephen E. Cohn
For the past few years the Data Assimilation Office has been developing a Retrospective Data Analysis/Assimilation System (RDAS). The RDAS is aimed at improving analyses generated by the GEOSDAS Terra system by making use of observations ahead of the analysis time. The procedure is based on a formulation of the fixed-lag Kalman smoother and is now finally implemented in the context of the physical-space statistical analysis system.
In this presentation we will show results from a statistical evaluation of the the performance of the RDAS when compared against results obtained with our regular assimilation system. We will also show results from the performance of the RDAS in dealing with synoptically challenging situations. Finally, we will present a brief discussion on plans to implement retrospective data assimilation capabilities in the newly developed DAO finite-volume data assimilation system.
Luc Fillion, Stephane Belair
In view of improving the presence of physics in adjoint applications like singular vector computations, precipitation sensitivity in mesoscale weather forecast, and 4D-Var data assimilation, we examined the linearization aspects of the Kain-Fritsch (KF) moist convective scheme. This scheme being recognized as one of the most appropriate for mesoscale applications and is planned to be operational at the Canadian Meteorological Center (CMC) for regional data assimilation and weather forecasting. Examination of process contributions to the response and sensitivity of KF for a wide range of convective cases was used to formulate an efficient approximation to the classical adjoint of the KF scheme. The degree of validity of the linearization of KF scheme will also be discussed in view of various adjoint applications.