DATA ASSIMILATION W.
and K. PURI
Bureau of Meteorology Research Centre Melbourne. Australia
I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Evolution of Assimilation and the FGGE . . . . . . . . . . . . . . . . . . . . . 3. Components of Four-Dimensional Assimilation Systems . . . . . . . . . . . . . . . 3.1. Observational Data Base . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Optimum Interpolation (01) . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Model Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Prediction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Characteristics of Some Current Assimilation Schemes . . . . . . . . . . . . . . . 4.1. Continuous Assimilation . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Intermittent Assimilation . . . . . . . . . . . . . . . . . . . . . . . . . 5. RoleofFour-Dimensional Assimilation in ResearchandOperations . . . . . . . . . . 5.1. Research Implications of Four-Dimensional Assimilation . . . . . . . . . . . . . 5.2. Research on Four-Dimensional Assimilation Procedures . . . . . . . . . . . . . 5.3. Long-Term Operational lmplications of Four-Dimensional Assimilation . . . . . . . 6. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Numerical weather prediction (NWP) is a central aspect of activities in all major operational weather centers throughout the world. While the capacities differ, the principles are commonly shared; i.e., the weather prediction problem is defined as an initial value marching problem. The quality of NWP hinges crucially on the accuracy of specifying the initial conditions, on the appropriateness of boundary conditions, and on the ability to model mathematically the dynamics and physical processes of the evolving atmosphere. Advances in NWP in the past 15 years have been heavily influenced by the sophistication and capacity in mathematical computation and the burgeoning data base available from space-based observing systems. In particular, the two traditionally separated functions, objective numerical analysis and numerical model prediction, have been merged to yield what is now commonly described as four-dimensional data assimilation. In this procedure the numerical prediction model is employed to coordinate in time and space the irregularly distributed asynoptic data typically available from the international community of meteorological services. The spur to this development of data assimilation has been the space-based observing systems and in particular the temperature I23 ADVANCES I N GEOPHYSICS, V O L U M E
Copyright 0 1982 by Academic Press, Inc. All rightc of reproduction in any form reserved.
W. BOURKE, R. SEAMAN, AND K. PURI
soundings from the sun-synchronous, polar-orbiting satellites, although objective analysis schemes utilizing what is now termed intermittent assimilation were in use before satellite-based temperature soundings were available. The advent of this asynoptic observational data base, on the one hand, has defined a more complex objective analysis problem but at the same time has led to a much more comprehensive use of the prediction equations. The predictive component of the assimilation system provides an additional source of information, and an objective is to obtain a sequence of fields of dependent dynamic variables that is consistent with both the observations and physical laws of atmospheric flow. The observed variables defining large-scale atmospheric motion are the three-dimensional distribution of the horizontal components of the wind, the atmospheric pressure, the temperature, and the humidity. For large-scale flow the hydrostatic equation is particularly appropriate and vertical motion may accordingly be diagnosed. Furthermore, a reference level of pressure such as mean sea-level pressure, and the temperature field together with the hydrostatic relation and the geostrophic mass-wind relationship, is sufficient to define the three-dimensional distribution of pressure, temperature, and wind except perhaps in tropical latitudes in which the geostrophic relationship is inappropriate. Charney et al. (1969) in a pioneering paper on this subject suggested that the requisite model initial conditions (in the extratropics) of pressure, temperature, and wind in numerical prediction could be obtained in principle by assimilating only temperature data such as those available from satellites. The importance of this subject was recognized at an early stage by the Global Atmospheric Research Programme (GARP) Joint Organizing Committee (JOC), which sponsored the International Symposium on Four-Dimensional Data Assimilation in Princeton at the Geophysical Fluid Dynamics Laboratory (GFDL) in April 1971. Before proceeding, it is appropriate to elaborate a little on the Global Atmosphere Research Programme. A central objective of the program was to improve our understanding and explanation of atmospheric behavior, thereby leading to more comprehensive atmospheric models and more accurate prediction. A key arm of the GARP Joint Organizing Committee was the Working Group on Numerical Experimentation (WGNE) that had been established in 1968. The main aim of the WGNE was to identify a program of numerical experiments and to coordinate the studies of co-operating research groups. Foremost among the problem areas identified by the WGNE, and given continuing attention, was four-dimensional assimilation. In the present essay, the development of four-dimensional data
assimilation through the decade of planning prior to the First CARP Global Experiment (FGGE) and its current status are reviewed. Reviews of data assimilation have already been presented by McPherson (1 975) and by Bengtsson (1975), and a more detailed account of research up until the mid-seventies will be found in these references. A monograph edited by Bengtsson et af. (1981) provides considerable technical detail on current data assimilation methods. 2. EVOLUTION OF ASSIMILATION AND
In the years immediately subsequent to the 1971 meeting in Princeton at the GFDL, there followed a significant expansion of research activity. Much of this research up until the mid-seventies was concerned with using model-simulated data in perturbed model reruns to analyze observational network requirements and assimilation procedures. The consensus of this time was that these “identical twin” experiments, while being very valuable, provided a too optimistic view of the possibilities of four-dimensional assimilation capabilities. Experiments based on real observational data approaching the FGGE global requirements became possible with the Nimbus-6 satellite launched in June 1975 that carried the most advanced infrared and microwave sounding instruments hitherto placed in orbit. This instrumentation was the precursor of the operational Tiros-N launched in October 1978 for the FGGE year. Consequently, from the mid-seventies onward it was possible to experiment with global temperature coverage such as anticipated as integral and key components both of the FGGE year and of the ensuing operational satellite program. The earlier generation of vertical temperature profile radiometer (VTPR) measurements from the NOAA-2/4 satellites had been available operationally since December 1972 and had, of course, been assessed in a number of studies in terms of impact on analyses and prediction as discussed in the review by Bengtsson (1975). However, the value of observing system simulation experiments (OSSEs) within the context of identical twin experiments in the development of four-dimensional assimilation was undoubted. The methodology of assimilation itself was established, and very important significant conclusions were obtained indicating the clear need for a reference level and the inadequacy of temperature measurements alone in defining the state of the tropical atmosphere. The inadequacy of temperature measurements alone in the tropics, as originally foreshadowed by Charney et al. (1969), was unanimously identified within the numerical experimentation conducted in the early seventies at the GFDL (Gordon et al., 1972), by
W. BOURKE, R. SEAMAN, AND K. PURI
Kasahara and Williamson (1972) at the National Centre for Atmospheric Research (NCAR), and by Jastrow and Halem (1973) at the Goddard Institute for Space Science (GISS). This facilitated the JOC recommendation that adequate coverage of the tropical zone by geostationary satellites to enable wind specification from cloud displacements would be a critical requirement for FGGE [World Meteorologic OrganizatiodInternational Council for Scientific Unions (WMO/ICSU), 1971bl.The need for vertical wind profile sounding between IO"N and 10"s supplementing the World Weather Watch (WWW) network and the cloud vector winds was also demonstrated in these studies (WMO/ICSU, 1974). Early planning for the FGGE also identified clearly the need for a reference level in the Southern Hemisphere (WMO/ICSU, 197la). This was initially to be achieved by a fleet of 450 constant-level balloons. A modest network of drifting buoys was identified as relevant to provide data in areas of persistent cloudiness in the latitudes 50-65"s. Subsequently, the constant-level balloon program did not eventuate, but an expanded program of drifting buoys throughout the Southern Hemisphere provided one of the major observational successes of the FGGE. The value of the early observational simulation studies has clear testimony even today; the operational polar-orbiting satellites, the modest operational deployment of buoys in the Southern Hemisphere in the early eighties, and the foreshadowed increase in buoys in the mid-eighties demonstrate this. Some experiments conducted in the first half of the seventies considered among other things the question of asynoptic versus synoptic insertion of temperature soundings (Kasahara, 1972). These experiments were a little inconclusive and the range of procedures used today still reflects some uncertainty. Further and more realistic OSSEs were undertaken by extracting simulated data from sophisticated models and then utilizing lower resolution and less comprehensive models for simulated assimilation and data base studies. Simple updating of nearest grid points was at this time being replaced by the more traditional objective analysis procedures, such as the successive correction method (SCM) and optimum interpolation (01). The nonidentical twin experiments provided some indication of the influence of an incomplete data base and of observational and forecast error and highlighted the requirement for detailed knowledge of the magnitude and structure of the expected observational errors. In particular there was good qualitative agreement between experiments at the NCAR (Williamson, 1975) and at the United Kingdom Meteorological Office (UKMO) by Lorenc (1975) in nonidentical twin OSSEs in defining the overall requirements of the
assumed special observing systems; quantitatively, however, the 0 1 analysis step in the UKMO system provided superior model assimilation of data. Difficulty in drawing definitive conclusions with regard to data networks was clearly identified at this time and related to deficiencies in utilizing the information content of the observations. An important suggestion from the UKMO/OSSE studies of Lorenc (1975) was the overall improved performance over the Southern Hemisphere with a widely dispersed drifting-buoy network in comparison to a closer concentration of the buoys in regions of high variability and short longitudinal span. A second major study conference on four-dimensional data assimilation was again sponsored by the GARP/JOC and conducted in Paris late in 1975 (WMO/ICSU, 1976). Problems of particular concern in assimilation systems that were highlighted at this conference included (1) spurious excitation of gravity waves in the model atmosphere; (2) difficulties of combining observations, forecast, and climatology in the most effective and efficient manner; (3) verification procedures for assessing analyses; (4) the analysis and data problems of low latitudes; and ( 5 ) clarification of the relevant merits of the intermittent and the continuous approaches to assimilation.
Papers presented at the Paris meeting by Rutherford and by Schlatter foreshadowed a developing consensus for the 0 1 method of analysis. Rutherford presented details of a three-dimensional multivariate 01 scheme that was already operational in the Canadian Weather Service. The multivariate aspect provides mass-wind coupling through model prediction error covariances. This was a more sophisticated approach than the earlier useful demonstrations of inferring geostrophic corrections to model wind fields in the presence of assimilated mass data alone (Rutherford, 1973; Hayden, 1973). The multivariate approach was perceived to be more appropriate for intermittent data analysis than for continuous insertion where the mass-wind coupling would be achieved simply by model dynamics. Two factors associated with the general problem of assimilation, namely, the need for mass-wind coupling and the need to control excessive excitation of spurious gravitational oscillations, appeared to be handled more readily in the multivariate approach. At the meetings of the WMO Executive Committee Inter-Government Panel on FGGE in February 1976, two commitments were offered to produce FGGE level-IIIB data sets. These offers came from the European Centre for Medium Range Weather Forecasts (ECMWF) and
W. BOURKE, R. SEAMAN, AND K. PURI
the GFDL; the JOC expressed concern in April 1977 at the absence of further offers to produce level-IIIB data sets (WMO/ICSU, 1977). At this time it was also becoming apparent that the resources available for the FGGE would be less than expected. The formal observational requirements for the global experiment to be held in 1979 had been defined in the prior decade of planning and comprehensive observing systems simulation experiments. These formal requirements called for the observing systems in the extratropics of both hemispheres to provide at a lateral resolution of 500-km soundings of wind and temperature, surface pressure, humidity, and sea temperatures, with a vertical resolution of seven levels for the soundings (four troposphere, three stratosphere) and two degrees of freedom for humidity. In the equatorial tropics the formal requirements were essentially as in the extratropics but with more stringent requirements for wind data. The expense of the enhanced tropical wind observing system was such that it could only be implemented for two special observing periods. An example of the decrease in resources available for the FGGE was the omission of the constant-level balloon observing system in the Southern Hemisphere. Further OSSE studies undertaken at the UKMO (Bromley, 1978) identified a deterioration in analysis and prediction in the Southern Hemisphere upon omission of the constant-level balloons poleward of 30"sand dramatically demonstrated the need for at least one reference level in the Southern Hemisphere such as the surface-pressure observations from drifting ocean buoys. The studies by Bromley provided OSSE assessment of analysis and prediction error for three different FGGE data distributions: (1) the basic observing system corresponding to the normal meteorological observing network of WMO; (2) the basic system plus the ideal extensions via special observing systems; and (3) the basic system plus actual special observing systems then committed to FGGE.
Additional studies by Larsen et al. (1978) provided theoretical estimates of analysis error based on interpolation theory for these configurations of observations. The OSSE assimilation studies and analysis error estimates provided by Bromley (1978) and by Larsen et al. (1978) were such that the WMO Executive Committee Inter-Governmental Panel on FGGE was able to agree in early 1977 that a global-atmospheric experiment could be conducted. The observational data base had largely been identified as adequate, although the resources committed left some doubt regarding
the adequacy of the tropical observing system where the lateral resolution of wind soundings would barely meet the now proposed requirement of 700 km. It is appropriate in an essay on data assimilation to record these details on the FGGE planning. In particular, the detailed assimilation studies led to a clear commitment in the late seventies to the Global Weather Experiment by the JOC and the WMO Executive Committee InterGovernmental Panel. During the period leading up to the FGGE it had also been possible to conduct assimilation experiments on subsets of the final observing systems. In the first of these, the GARP Atlantic Tropical Experiment (GATE) conducted in 1974 provided an early opportunity to evaluate four-dimensional assimilation in the tropics. The tropical domain presented at that time and even now an especially formidable task both from the analysis and prediction viewpoint; the tropical flow is relatively decoupled from the pressure field due to the weakness of the Coriolis force, and the complex convective physical processes remain difficult to parameterize on the scales typically available to global assimilation systems. Miyakoda et al. (1976, 1982) evaluated the assimilation methodology developed at the GFDL on the GATE data, initially in near real time for the entire 101 days and subsequently for 34 days with the complete final GATE data set. The 34-day GATE assimilation was the precursor to the system used for FGGE level-IIIB production at the GFDL (Stern and Ploshay, 1983). These analyses showed that the assimilation system could produce a reasonable and consistent picture for the easterly wave disturbances in the tropical Atlantic. However, the study highlighted the difficulty of maintaining dynamical consistency between the mass and wind fields and the dependence of the analysis scheme on the parameterization of physical processes included in the predictive component of the system. A second major experimental evaluation of observing systems was designed as a prototype of the FGGE. This study was conducted at the National Meteorological Center (NMC) in Washington. It is described in the report by Desmarais et al. (1978) and was referred to as the Data Systems Test (DST). The DST in August-September 1975 (DST-5) and February-March 1976 (DST-6) produced the most extensive global meteorological data base in existence at that time. The basic observing network of the WMO was augmented by the polar-orbiting satellite Nimbus-6 temperature and moisture soundings, cloud vector winds from geostationary satellites SMS- 1 and SMS-2, constant-level balloon winds and special aircraft data. The NMC assimilation system at this time consisted of the operational spectral Hough analysis scheme (Flattery,
W. BOURKE, R. SEAMAN, AND K. PURI
1970) and a global prediction model (Stackpole, 1976) with a 12-hr analysis-forecast cycle for DST-5 and 6-hr cycle for DST-6. Of particular concern in these studies was the inability to show significant impact on prediction from the use of Nimbus-6 temperature soundings in the Northern Hemisphere; the analyses in the Southern Hemisphere were assessed as improved due to the use of the satellite soundings, but the inability to define a reference level accurately was identified as a major limitation. The lack of positive impact of satellite soundings on 72-hr prediction in the Northern Hemisphere studies was accompanied by the recognition that the temperature retrievals were underestimating the spatial variance in the thermal structure of the atmosphere. These assimilation and forecast studies at the NMC were compared with similar experiments at the GFDL and the Goddard Laboratory for Atmospheric Science (GLAS), where positive impact of satellite soundings on prediction had been found. However, the NMC forecasts were identified to be superior to both the GFDL and the GLAS systems even in the absence of satellite soundings in the NMC system. It was thus apparent from these comparative studies that assimilation and data impact results were highly dependent on the inherent capabilities of the respective analysis and forecast systems (Tracton and McPherson, 1977). The NMC assessment of these experiments attributed the trivial impact of soundings in the NMC system in contrast to the beneficial impact in the GFDL and the GLAS systems, to the superior first guess of the NMC assimilation system relative to the GLAS, and to the superior analysis method at the NMC relative to the GFDL. An all-pervasive problem throughout these assimilation studies, and highlighted at the Paris study conference in 1975, had been that of the spurious excitation of inertia-gravity oscillations in the model atmosphere. Numerous algorithms to solve this problem had been suggested, but the one that now stands out as a decisive breakthrough was that of nonlinear normal mode initialization (NNMI). The NNMI procedures as now commonly used were developed by Machenhauer (1977); an equivalent algorithm was independently developed at the same time by Baer (1977). This breakthrough was not achieved in time to have a major impact on the OSSEs that contributed so decisively to the design of the FGGE observational network. However, the implementation of the dataassimilation systems at the two IIIB data producers for the entire FGGE year included the NNMI as a key component. The discussion to this point has been primarily concerned with the role of assimilation systems in the planning for the FGGE. The end product of GARP was not intended to be simply an ensemble of data sets, but a path to specific answers to physical problems arising in explaining the behavior
of the atmosphere and to practical problems of predicting its future behavior. At the outset, however, it was necessary to quantify the information content of the projected data base from observing systems that could be implemented. It was similarly recognized that these observing systems reflected a reasonable extension of existing national plans. Five years after the FGGE, the global observational network, in fact, enjoys a substantial enlargement in capacity, reflecting operational deployment of some of the FGGE special observing systems. Consequently, it is now possible to conduct not simply OSSEs, but rather observing system experiments (OSEs) utilizing the FGGE data as well as current operational data, and much of the assimilation research in the recent years has been devoted to that end. The current maturity of assimilation systems is indicated by their widespread application in operational analysis and prediction. The following sections of this chapter discuss in detail the components of a number of current four-dimensional assimilation systems, the characteristics of several specific approaches, recent research, operational results in assimilation and prediction, and an assessment of future trends.
3. COMPONENTS OF FOUR-DIMENSIONAL ASSIMILATION SYSTEMS In describing the current approach to four-dimensional assimilation, it is appropriate to consider the following four components: the observational data base, the objective analysis, the initialization algorithms, and the prediction model. These subsystems are discussed in the following sections. Some detail is provided about analysis and initialization procedures; the prediction model component is only briefly discussed as it is covered elsewhere in this volume.
3.1. Observational Data Base The WWW observing system reached an unparalleled peak in 1979 during the FGGE. In addition to the Tiros-N and NOAA-5 polar-orbiting satellites, there were, for example, five geostationary satellites from which cloud vector winds could be derived, about 300 drifting buoys in the Southern Hemisphere, an enhanced tropical system including aircraft dropwinsondes, constant-level balloons, and special tropical observing ships. The data base available in the eighties is less comprehensive than that of the FGGE year, especially in the tropics and Southern Hemisphere.
W. BOURKE, R. SEAMAN, AND K.PURI
The data base typically used in global analysis and prediction at the present time consists of (1) surface reports from land stations, (2) surface reports from ships and drifting buoys, (3) manually prepared surface reports of sea-level pressure, (4) upper-air reports from land stations and ships, ( 5 ) aircraft reports, (6) cloud motion wind vectors, (7) upper-air reports of temperature from polar-orbiting satellites, and (8) upper-air humidity data derived from satellite imagery and synoptic cloud observations.
A nontrivial aspect of all objective analysis schemes is the preprocessing of the raw data. Data need to be recognized, decoded, regrouped, and reformated, and in addition the individual messages are condensed to optimize the information content. Preliminary validation of data includes checks on internal consistency, checks relative to climatology, and a hydrostatic check on reported height and temperature. A detailed discussion of these procedures is not appropriate in the present chapter. With the basic validated data assembled and sorted with respect to observation type and time of observation and in three dimensions, the comparison of the data with the contemporaneous estimate of the prediction model then constitutes the first step in the analysis procedure. It is common practice in intermittent assimilation to group the data within 6-hr time windows centered upon the synoptic times of 0600, 1200, 1800, and 0000 GMT. With increasingly higher horizontal resolution in numerical models, this time window may be reduced to minimize the asynoptic time error. Alternatively, the data may be utilized in continuous insertion, in which case the observing and insertion times are closely synchronized in the evolving prediction model atmosphere. Some current procedures assign slightly larger observation errors to data that are off-centered relative to the nominal observing time. 3.2. Optimum Interpolation (Or} An essential component of data assimilation is objective analysis. An excellent review of that subject has been presented by Gustavsson (1981). As foreshadowed in Section 2, some consensus has emerged with the widespread use of the 01 approach, and the present discussion will focus on this procedure. The basic idea of the 01 method is to utilize the statistical covariance
properties of observational errors and background (“first guess”) field errors in order to minimize the mean square error of interpolation. Its earliest application in meteorology was by Eliassen (1954), but the approach was much further developed by Gandin (1963). Both these authors utilized a background field of climatology. The method was soon extended by Eddy (1967) to use a background field generated from the observations themselves and by Kruger ( 1969) to use a numerical prediction as a first guess. Rutherford (1973) introduced multivariate 01 that enabled the simultaneous use of mass and wind observations. With increasing computer power, fully three-dimensional multivariate schemes soon became feasible (Schlatter, 1975; Bergman, 1979; Lorenc, 1981). Probably the most appealing aspect of 01 is that it provides a logica framework within which to take the following factors into account, namely: (1) the spatial distribution of observations relative to one another and relative to grid points, (2) the error characteristics of different observing systems, (3) the information available from earlier data (by using a forecast background field and a forecast error covariance function), and (4) the quasi-geostrophic and hydrostatic relationships among variables.
Additional desirable features of 01 include in-built data checking and the availability of an interpolation error estimate. It should nevertheless be emphasized that 01 is optimal only to the extent that the presumed observational and forecast error covariances reflect the corresponding true covariances. In practice, however, 01 appears to be not unduly sensitive to small changes in the presumed covariance structure. In generalizing 01 analysis to be multivariate, the formalism requires in addition to autocovariances the introduction of cross covariances between, for example, different field types of mass and wind and the accompanying assumption that prediction errors in the mass and motion field behave in accordance with the geostrophic and hydrostatic relationships. Univariate correlations of geopotential or mass prediction errors are typically modeled in an analytic positive definite differentiable form that is horizontally isotropic. The most commonly used correlation function is the Gaussian exponential function p(r) = exp(-0.5S/b2), where r is the distance over which correlation is being considered and b is a fixed coefficient defining the horizontal scale of the parameter to be analyzed. The most common approach to obtain correlations for wind prediction errors is to apply the geostrophic wind equation
W. BOURKE, R. SEAMAN, AND K. PURI
to the isotropic correlation functions for geopotential. Similarly, cross correlations between wind and mass increments can also be derived analytically. In the tropical latitudes the geostrophic constraint is inappropriate and the multivariate schemes are gradually decoupled into univariate analyses as the equator is approached. 3.3. Model Initialization At some point in the four-dimensional assimilation cycle, it is necessary to commence model prediction from the most recent specification of the model atmosphere. There remains a serious problem. Primitive-equation models, unlike geostrophic models, admit higher-frequency gravity wave solutions that can have amplitudes substantially in excess of their counterpart in the real atmosphere. The low-frequency Rossby-mode component of the model is of prime interest, but this component can be obscured by gravitational mode oscillations occurring on a time scale similar to that of data insertion (e.g., 6 hr). These gravitational oscillations arise from imbalances between the mass and wind field. There have been a number of long-standing procedures for suppressing these spurious oscillations based on analysis of linearized forms of the equations of motion, on scale analysis, and on the fact that the large-scale atmosphere is essentially in geostrophic balance outside the tropics. These schemes usually have been formulated in pressure coordinates and have not been particularly effective or appropriate in primitive-equation models using the terrain following sigma coordinates. Implicit in the preceding remarks concerning high-frequency oscillations is the notion that the free normal modes of the discretized primitive equations can be readily evaluated. The identification of these free modes of oscillation of the primitive equation prediction model is accomplished by linearizing the equations around a simple basic state, which is commonly taken as an atmosphere at rest with temperature variation in the vertical only. The specification of a zero-wind mean state permits a simple decoupling of the three-dimensional eigenvalue problem into a series of two-dimensional eigenvalue problems. The vertical decoupling gives rise to a number of characteristic vertical modes, one corresponding to each discrete level in the model. The series of decoupled two-dimensional eigenvalue problems is equivalent to the Laplace tidal equations, where the mean free height is given by the eigenvalues or equivalent depths associated with each vertical mode. The horizontal eigenfunctions of the Laplace tidal equations are readily classified into two categories, namely, Rossby and gravity modes. For a given vertical structure, the frequency
of the modes and the pairwise existence of eastward- and westwardpropagating gravity modes permits ready identification. It is thus possible, with the common vertical structure of the atmosphere assigned to both the mass and momentum fields, to project the model state variables, or their tendency, onto the horizontal structures identifiable as either Rossby or gravity normal modes. The direct use of normal modes of the actual models was suggested by Dickinson and Williamson (1972). They proposed that initial data be expanded in terms of model-normal modes and that the amplitudes of the unwanted modes be then set to zero. This scheme was especially effective in linearized models but failed to suppress the spurious noise in the requisite nonlinear calculation. More recently Machenhauer (1977) and Baer (1977) independently proposed a nonlinear normal mode scheme (NNMI). Machenhauer proposed that rather than setting the amplitude of the unwanted modes to zero, it is the tendency of these modes that should be set to zero. This turns out to be a superb solution, but it implies a nonlinear equation, the solution of which requires an iterative process. The scheme does not have guaranteed convergence but in practice with some restrictions does converge and does lead to a very well balanced state. The iterative scheme is usually performed only for the larger-scale vertical modes. For example, in a nine level model it is usual to initialize only the first three or four vertical modes. The linearized state is that of an atmosphere at rest and this is necessary for vertical decoupling. In performing the NNMI, there is some scope for variation in the linearization specification with aspects of the dynamics omitted from the linearization implicitly included in the nonlinear term; commonly the nonlinear iteration involves only the adiabatic component of the full prediction model. One effect of excluding diabatic effects from the initialization step is a serious depletion of the tropical divergent circulations. A number of solutions has been found to alleviate this problem. One method is to replace the NNMI by an incremental linear NMI in which gravity modes in the increments in the model state due to insertion of data are removed (Pun el al., 1982). Since this scheme does not directly affect the background model field, it is designed to preserve the circulation developed by the model during data assimilation. Two types of NNMI schemes have been proposed to retain the tropical circulation. The first is based on the result that the tropical divergent circulation maintained by convective processes influence mainly the low-frequency gravity modes in a model (Puri and Bourke 1982; Puri 1983a) and these low-frequency modes are excluded from initialization by using a frequency cutoff. This scheme effectively controls the high-frequency gravity wave noise and at the same time retains the tropical divergent circulation. The second type
W.BOURKE, R. SEAMAN, AND K. PURI
of NNMI has been proposed by Wergen (1982). In this scheme the diabatic heating is obtained by integrating the model prior to initialization for a few time steps and time averaging the diabatic forcing, which is then projected onto those low-frequency large-scale modes identified with convective heating and which can then be included in the nonlinear forcing during iteration. The theory of NNMI has proved to be a very valuable practical tool in data assimilation schemes and additionally a simple diagnostic analysis of the effectiveness of model memory of inserted data. An example of the data rejection that is a major problem in data assimilation can be seen in Fig. 7 of Bourke ef al. (1982), which shows that some mass information present in initial analyses is lost during NNMI. The concept of slow and fast data manifolds developed by Leith (1980) has provided a powerful method for analyzing such problems. Daley (1978), Daley and Puri (19801, and Tribbia (1982) have investigated the effectiveness of variational constraints within NNMI schemes by using the shallow-water equations. Puri (1983b) and Temperton (1984) have applied constrained schemes to multilevel assimilation systems and demonstrated that constrained NNMI can yield a reduction in the loss of information that occurs in unconstrained NNMI. The application of the NNMI algorithm has been restricted largely to use in the global and hemispheric domain and is particularly well suited to spectral models of the atmosphere. Recent developments have seen the application of NNMI schemes to limited-area prediction models (Briere, 1982; Bourke and McGregor, 1983), and this will no doubt facilitate the development of assimilation systems for regional application. 3.4. Prediction Models
The numerical prediction models used in research and operational four-dimensional assimilation typically have been developed for the purposes of medium-range weather prediction. These models are high-resolution, comprehensively parameterized deterministic models as sophisticated, if not more so, than general circulation climate models. The models typically span the global or hemispheric domain and utilize the primitive equations. The numerical formulation of the models in recent times has seen an increasing use of spectral models that commonly have from 10 to 15 levels and a horizontal resolution of from rhomboidal-30 to triangular-63 wave number truncation. The representation of model variables in the vertical is discrete, and normal finite difference algorithms are used with constraints to ensure conservation of energy, mass, and
momentum. Accompanying the development of spectral models has been a growing consolidation in the alternative but longer-standing formulations of primitive equations in which finite differences are used in all three space dimensions. In particular, a staggered disposition of variables on latitude-longitude grids spanning the globe or hemisphere is now the most widely used method. The numerical details of both spectral and finite difference methods are reviewed in a comprehensive volume on global modeling of the atmosphere (Arakawa and Lamb, 1977; Bourke et al., 1977). Two features of prediction models that affect assimilation systems are the use of the terrain-following sigma coordinates and the use of temperature as the thermodynamic variable. In multivariate analysis a sigma coordinate system does not readily allow application of the geostrophic wind law, and temperature is less easily used than is geopotential. Accordingly, the analysis component of the assimilation cycle is frequently implemented in pressure coordinates. The model prediction is thus converted from sigma to pressure coordinates, corrected by available data, and the resultant increments or changes interpolated back to the model sigma domain. Univariate analysis in sigma coordinates is quite tractable and diagnostic increments to provide mass-wind coupling are also possible. However, in such schemes cross validation of the first guess and observations of different variables is not available, and variationally constrained blending is relatively complicated in other than pressure coordinates. The physical parameterizations of the prediction models routinely used in research and operational application of four-dimensional assimilation are quite comprehensive. These parameterizations may include (1) radiative forcing with climatological absorber amount specification (cloud amount may be diagnosed or quite commonly specified in terms of zonal mean values), (2) stability-dependent modeling of the constant flux layer of the boundary layer, (3) convective process parameterization yielding both large-scale condensation and small-scale penetrative convection, (4) hydrologic cycle modeling over land including prediction of surface and subsurface temperature and soil moisture content (sea-surface temperature is specified by monthly mean climatology), and (5) horizontal and vertical diffusive parameterizations.
Of additional concern is the question of the assimilation cycle requiring refinements in parameterization. A conspicuous omission from the preceding list is the inclusion of a diurnal forcing in the radiative heating
W. BOURKE, R. SEAMAN, AND K. PURI
calculations. Given that the time scale of assimilation cycles is of the order of 6 hr and that the diurnal changes in thermal fields within the atmosphere and at the surface over continents can be substantial on this time scale, the absence of such a diurnal component in the model may lead to biases in the background fields and to spurious rejection of observed data. Preliminary experiments with diurnal forcing in assimilation studies have, however, been very limited, and there is surprisingly little evidence to suggest that this is an important requirement. The time-step integration of the prediction model component of the assimilation cycle is typically effected by a semi-implicit algorithm in spectral models (Robert, 1969; Bourke, 1974) and increasingly by economical split-explicit schemes in finite difference models (Gadd, 1978). The computational overhead of implicit time differences in spectral models is only slight. Both of the time integration schemes allow the model evolution to proceed on time scales of significance in the meteorological context and not to be constrained unnecessarily by the small time steps associated with the time scale of the low-amplitude, high-frequency gravitational modes occurring in the models.
4. CHARACTERISTICS OF SOMECURRENT ASSIMILATION SCHEMES
As mentioned in Section 2, two approaches to insertion were under serious consideration in the mid-seventies, namely, continuous assimilation and intermittent assimilation. Originally, continuous assimilation implied insertion of data only at the nearest model time step (Bengtsson, 1975), but it is now understood to include continuous insertion in which the same data may be repeatedly inserted within a short time span. Also all current assimilation systems proceed only in the forward direction, with the implication that later data do not influence the analyses at earlier times, as would be possible in iterative schemes such as discussed by Talagrand ( 1981). At present both continuous and intermittent approaches are in use, reflecting in some sense the lack of consensus with regard to the most appropriate way to proceed. Continuous insertion of data is the basis of the assimilation systems used at the GFDL (Stern and Ploshay, 1983) and the UKMO (Bell, 1983); intermittent assimilation is the basis of the systems used at the ECMWF (Bengtsson et al., 1982), at the NMC (Kistler and Parrish, 1982), at the Japan Meteorological Agency (JMA) (Kanamitusu et al., 1983), at the Canadian Weather Service (Rutherford, 1975), and at the ANMRC (Bourke et al., 1982). The intermittent analysis schemes are usually multivariate in that the complete atmospheric
representation of all dynamic variables is analyzed simultaneously, while the continuous schemes are more often univariate. These distinctions are not necessarily rigid, since intermittent univariate analysis is also commonly used. However, multivariate continuous insertion appears not to have been tested among the various research and operational groups, perhaps due to the substantial computational requirement. To illustrate the basic differences between the two approaches, the operational system at the ECMWF (Bengtsson et al., 1982) utilizing the intermittent multivariate approach will be considered, together with the research scheme at the GFDL (Stern and Ploshay, 1983) that utilizes the continuous insertion in a univariate framework. These two centers operated such schemes in the production of the FGGE analyses, as the official level-IIIB data producers. Variations within these two basic approaches, as developed by other groups, will be noted as appropriate. 4.1. Continuous Assimilation
The essential characteristic of this approach is the continuous insertion of data into the model at each time step. As used at the GFDL, these data are determined by three-dimensional univariate 01 in pressure coordinates. The univariate statistical interpolations to a regular latitude-longitude grid are performed at 2-hr intervals within each 12-hr span, on 19 mandatory pressure levels from 1000 to 0.4 mb, at the model grid points for u , u, T, q and p s . The six separate 01 analyses within the 12-hr span are provided with the most recent synoptic analysis for the first guess. The preprocessed 01 data are then inserted into the evolving model forecast with a weighting corresponding to their reliability. In the absence of data the model is unperturbed, while with highly reliable data the model solution would be essentially replaced by the insertion data at appropriate grid points. The continuous component of the GFDL assimilation involves the repeated insertion of the 0 1 analyzed data at each time step within the 2-hr time interval. To provide time continuity for the repeated insertion, the six individual 2-hr analyses are interpolated in time defining a time base of preprocessed data that is continuous for the 12-hr span. A schematic of the GFDL assimilation scheme shown in Fig. la illustrates these procedures. The NNMI is performed every 6 hr. The GFDL scheme initializes the first 7 of 18 vertical modes via four iterations of the NNMI. A frequency cutoff restricts the initialization to those free modes having a characteristic oscillation period of less than 6 hr. The prediction model component of the GFDL assimilation scheme, summarized in
- llb Observations -
- Dynamcal Analysis & initialization - Archived Dlb Analyses
0 r u u u k Ikml 00022 I A0
* method * variables
* grid * *
first guess application
prepared by 3-dimensional. u n i v a r i a t e , optimum i n t e r p o l a t i o n on p r e s s u r e l e v e l s (no PSL.u.v.T.q d a t a i n s e r t e d a t upper two m d e l levels) N40 gaussian, 1 9 p r e s s u r e l e v e l s 12-hr a s s i m i l a t i o n r e s u l t s every 1 2 h r (+ 1-hr d a t a window)
* * *
d a t a injected i n t o a global s p e c t r a l model, using weighted t i m e i n t e r polation uariabtee P*.T. 5 ( v o r t i c i t y ) , D(divergence), q on s i p a l e v e l s resolution R30L18 (rhomboidal t r u n c a t i o n a t 30 wavea. 1 8 a l e v e l s ) time integration semi-implicit @t-8%20 minutesf u n c t i o n of CFL c r i t e r i o n ) lateral diffueion I(D2 vertical mixing l e n g t h method ( t o 3 Irm depth), diffusion d r y convective adjustment (above l e v e l 18) boundary Zayer Monia-Obukhov process s p e c t r a l l y truncated topography developed by F e l s and Schwarrkopf radiation
(i) clouds - c l i m a t o l o g i c a l monthly mean for each l a t i t u d e (ii)application-diurnal variation; short- and long-wave r a d i a t i o n c a l c u l a t i o n every 2 h r
sea-surface temperature land-surface temperature moisture
0052 - 3 x ) O W
0223 - b
O m -13
O W -14
0901 --150W. 0948 --16OA!
O W -17
o m -1aoo;
RAND monthly c l i m a t o l o g i c a l nornmls. y e t varying d a i l y
determined by s u r f a c e h e a t balance. using 3 s o i l l e v e l s t o model h e a t f l u x l a r g e - s c a l e condensation a t 80%humidity s a t u r a t i o n , cumulus p a r a m e t e r i z a t i o n by moist convective adjustment n o n l i n e a r normal mode, 7 v e r t i c a l modes (only modes with p e r i o d s s h o r t e r than 6 h r a d j u s t e d ) every 6 h r (m/s). T(.K). mixing r a t i o (g/g). g e o p o t e n t i a l h e l g h t (geop. meters). RH(%), v e r t i c a l v e l o c i t y ( m b / s ) , s u r f a c e wind s t r e s s T ~ ,T~ (N/m2)
1.875’ l a t i t u d e l l o n g i t u d e , 19 p r e s s u r e l e v e l s (9 Pressure l e v e l s for MR and RH)
Fig. Ib, is an 18-level global spectral model truncated at rhomboidal wave number 30. A detailed description of the model is given in Gordon and Stem (1982). Aspects of the GFDL scheme that are particularly distinctive include the extent of preprocessing and the insertion of data at each model time step. Continuous insertion is also utilized in the operational and research assimilation system developed at the UKMO. This system uses repeated interpolation and insertion of data at each time step of the forward-running forecast model. The time integration of the model is an economical split explicit scheme. The basic assimilation procedure was developed by Lorenc (1976) and used in the FGGE planning OSSEs discussed earlier. The UKMO scheme employs univariate 01 and the ongoing model forecast is adjusted by weighted corrections. The UKMO scheme derives the weights from the 6-hourly application of the 0 1 algorithm and keeps these constant for the 6-hr period. No explicit initialization procedures are used. 4.2. Intermittent Assimilation
The intermittent method of assimilation is perhaps the most widespread approach taken at present. Here the observations from a time span, typically within 3 hr of a nominal analysis time, are used to correct a 6-hr forecast made from the previous analysis. This approach ignores the asynoptic error associated with grouping the data into time blocks of 6 hr and relies entirely on the prediction model capability to coordinate the data in the time domain. A very comprehensive example of the intermittent assimilation is that utilized at the ECMWF. Here 01 employed at 6-hourly intervals, is applied in a three-dimensional multivariate form. The simultaneous analysis of geopotential and wind data is performed in pressure coordinates at 15 standard levels from 1000 to 10 mb. To the extent that the effective observational data base changes only slowly from grid point to grid point, the analyzed increments of geopotential and wind on pressure surfaces are locally close to nondivergent. Outside the tropical latitudes, the multivariate aspect of the scheme also retains an almost FIG. 1 . The GFDL assimilation system: (a) Schematic overview of the data-processing system during the FGGE. OPI denotes optimum interpolation, and the dashed arrows indicate the first guess used for OPI. Data are inserted into the model every time step as indicated by the full arrows, and a nonlinear normal mode initialization, denoted by N , is performed every 6 hr. (b) Model configuration. [From Stern and Ploshay (1983).]
W. BOURKE, R. SEAMAN, AND K. PURI
geostrophic relationship between analyzed geopotential and wind corrections. The incremental changes to the 6-hr forecast first-guess fields are interpolated from pressure to sigma coordinates and applied as corrections to the current model state in the sigma domain. A distinctive aspect of the ECMWF multivariate scheme is the definition of large overlapping analysis volumes from 660 to 1330 km square and one-third of the atmosphere deep. The multivariate 0 1 may utilize up to 200 separate observations in this three-dimensional volume to define increments of height and wind simultaneously, thus reflecting an appropriate mass-wind relationship. The final analyzed increments consist of weighted combinations of the increments from the overlapping volumes. The ECMWF prediction model is currently a 15-level global spectral model truncated at triangular wave number 63. The FGGE IIIB analyses were produced by utilizing a grid-point precursor to this model that effectively had a slightly lower resolution. A schematic of the ECMWF assimilation scheme and a summary of the prediction model are shown in Fig. 2a, b, respectively. At the completion of each 6-hourly 0 1 , the NNMI is applied, with two iterations and initialization of four vertical modes. Although not implemented in the IIIB-analysis system, an innovation is the inclusion of diabatic forcing in the initialization (Wergen, 1982). This is similar in effect to a frequency cutoff as used at the GFDL in that the model prediction and analysis of the divergent circulations in the tropics are better preserved. The United States operational global analysis and prediction system as developed at the NMC are very similar in broad strategy to that used at the ECMWF. The prediction model is a global spectral model, and the archived analysis is produced from a multivariate 01 applied at 6-hourly intervals, utilizing the NNMI. Other centers utilizing an intermittent assimilation scheme include the Canadian Weather Service, the JMA, and the ANMRC. The Canadian approach parallels that of the ECMWF scheme. The last two groups use spectral models in the prediction step, while 01 is applied as a two-dimensional multivariate scheme at the JMA and as a univariate scheme at the ANMRC. The discussion hitherto has neglected to mention the analysis and prediction of the moisture content of the atmosphere. While moisture is undoubtedly a key aspect of the thermodynamics of the atmosphere, Smagorinsky et al. (1970) discussed whether the moisture specification needs to be defined explicitly, since the forward-running model dynamics may be sufficient to generate an appropriate moisture specification. A
detailed discussion of the analysis of moisture in the context of the ECMWF scheme has been given by Tibaldi (1982). This scheme reflects the widespread use of a simple SCM analysis of moisture, as part of the normal assimilation cycle. The data base for moisture analysis is substantially inferior to that of the thermal field, although the polar-orbiting satellites do provide profiles of the precipitable water between several layers in the troposphere, in addition to temperature soundings. However, the quality of these data are such that they have not been used routinely in operational or research application. 5. ROLEOF FOUR-DIMENSIONAL ASSIMILATION IN RESEARCH A N D OPERATIONS
Four-dimensional assimilation has been developed during the past 15 years to the point that it is an essential component of numerical analysis and prediction systems in both research and operations. In research the most visible demonstration of this has been the production of twice-daily global analyses for the entire FGGE year by the ECMWF and the GFDL. In operations, the improving performance of medium-range global and hemispheric prediction at centers such as the ECMWF, the UKMO, and the NMC are clear evidence of the practical benefits of research in this area. 00 GMT
Interpolation O + P
3-Dimensional Analysis Interpolation P * O
* +6 * hr
1 2 CHT
FIG.2. The ECMWF assimilation system: (a) schematic overview of the data-processing system during the FGGE and (b) model configuration. [From Bengtsson er a / . (1982). From Birlletin ofrhe American Mereorologicd Sociefy, copyright 1982 by the American Meteorological Society.]
p(mb) 10 20 30 50 70
100 150 200 2 50 300 400
500 700 850 1000
0.025 (al) 0.077 0.132 0.193 0.260 0.334 0.415 0.500 0.589 0.678 0.765 0.845 0.914 0.967
Vertical and horizontal (latitude-longitude) grids and dispositions of variables in the’analysis (left) and prediction (right) coordinate systems. ANALYSIS
Independent variab Zes Dependent variub l e s Grid
First guess D a t a assimi~ationfrequency
3-dimens ional multivariate
A , cp, P # t 6 , u.
(15-analysis levels, see above)
Nonstaggered, standard pressure levels
6-hr forecast ( complete prediction mode 1 )
6-hr (f3-hr w ndow)
N o n l i n e a r n o r m a l mode, 5 v e r t i c a l modes, n o n a d i a b a t i c
T , u, v , q , P,
S t a g g e r e d i n t h e h o r i z o n t a l (Arakawa C - g r i d ) . Uniform h o r i z o n t a l ( r e g u l a r l a t / l o n g ) . Nonuniform v e r t i c a l s p a c i n g O f l e v e l s ( s e e above).
Finite difference scheme
Second o r d e r a c c u r a c y
(At = 15 min) ( t i m e f i l t e r w = 0.05) 15 m4 s-l L i n e a r , f o u r t h o r d e r ( d i f f u s i o n c o e f f i c i e n t = 4.5.10 )
A l b e d o , r o u g h n e s s , s o i l m o i s t u r e , snow, and i c e s p e c i f i e d g e o g r a p h i c a l l y . A l b e d o , s o i l , m o i s t u r e and snow time d e p e n d e n t .
I n c l u d e d , m o d e r a t e l y smooth.
Boundary eddy f l u x e s d e p e n d e n t on r o u g h n e s s l e n g t h and l o c a l s t a b i l i t y (Monin-Obukov) F r e e - a t m o s p h e r e t u r b u l e n t f l u x e s d e p e n d e n t on m i x i n g l e n g t h and R i c h a r d s o n number
( i i i ) Kuo c o n v e c t i o n scheme
(iv) (v) (vi) (vii)
F u l l i n t e r a c t i o n between r a d i a t i o n and c l o u d s F u l l hydrological cycle Computed l a n d t e m p e r a t u r e , no d i u r n a l c y c l e Climatological sea-surface temperature
W. BOURKE, R. SEAMAN, AND K. PURI
5.1. Research Implications of Four-Dimensional Assimilation It is now clear, after the FGGE and the production of the level-IIIB analyses, that the meteorological community has widely disseminated global analyses of very high quality. The assimilation systems that were developed for the FGGE, and a subset of the FGGE observing system has been maintained, enabling global analyses to be produced routinely at centers such as the ECMWF, the NMC, and the UKMO and more recently at the JMA. With these high-quality global analyses now available for a period of 5 years it is possible to address a range of questions fundamental to meteorological science. These include
(1) What are the limits to predictability, not only of day-to-day weather, but also of the aggregated atmospheric variables referred to as climate on the intra- and interseasonal time scales? (2) What are the factors governing intra- and interseasonal variations in weather? Of particular interest at the time of writing is the research program into the tropical oceans and global atmosphere, formally known as TOGA. This program is concerned with assessing the extent to which the time-dependent behavior of the tropical-ocean global-atmosphere system is predictable on the time scales of months and years. An essential component of TOGA is the ability to define the variations in the global atmospheric circulation, thermodynamics, and hydrological cycle. The 1982/1983, El Nifio episode has given particular emphasis to these studies. Indeed the TOGA program has drawn attention to the development of data-assimilation systems for the description of the temperatures, circulation, and pressure fields of the upper layers of the global ocean. An operational ocean-thermal-analysis forecast system has been developed by Clancy and Pollak (1983). The atmospheric data-assimilation system in these pioneering studies is providing the surface stress and the heat flux at the air-sea interface, and the concept of assimilation has thus already been expanded to the coupled atmosphere-ocean domain. As the atmospheric assimilation systems have improved, numerical weather prediction has been usefully extended in time scale. Medium-range weather prediction is now considered to be successful for time scales of the order of 1 week in the Northern Hemisphere mid-latitudes and to 4 days in the Southern Hemisphere. The limit to medium-range predictability has been addressed by Lorenz (1982). He
concludes that estimates of instantaneous weather patterns that are better than guesswork nearly 2 weeks in advance appear to be possible, and efforts to achieve this are clearly warranted. Such useful extensions in skill will no doubt depend on ability to enhance current assimilation systems as well as the prediction models themselves.
5.2. Research on Four-Dimensional Assimilation Procedures In the preceding discussion much has been said of the current four-dimensional assimilation procedures. The refinements to this approach are an ongoing activity at all the major research and operational numerical weather centers throughout the world. The various assimilation systems now available differ in detail in many respects from each other. Intercomparisons of data-assimilation schemes have been undertaken in a joint study by the ECMWF, the UKMO, and the NMC (Hollingsworth et al., 1985). These intercomparisons have concentrated on use of the FGGE data set. Certain differences in the quality of prediction to 3 days can be attributed to differences in the respective analyses and thereby to the assimilation systems. Even with the FGGE data base, it is evident that the current assimilation schemes do not always define the three-dimensional, global large-scale flow in a similar fashion. Although these differences no doubt reflect inevitable uncertainties in the initial state, it is also likely that the exploitation of the data base is less than optimum. Procedures for assimilating single-level data, such as surface pressure and cloud vector winds in particular, remain less than well defined. Indeed, differences in some of the rather ad hoc methods adopted in various approaches could only be expected to give rise to differing analyses. Many analysis differences in the intercomparison study cited above were also associated with differences in quality control and data selection. For example, the ECMWF system in some cases was assessed to be averaging inconsistent data, the NMC system to be rejecting some data, and the UKMO system to be accepting most data but sometimes in an unbalanced fashion. The absence of an explicit geostrophic constraint between mass and wind in the UKMO system at that time was identified as a contributory factor to poor forecasts in the Southern Hemisphere. A global energetics study of the FGGE analyses produced by the GFDL and the ECMWF for the two special observing periods has been conducted by Kung and Tanaka (1983). There are sharp contrasts in the energy transformations depicted in the analyses that are attributed to
W. BOURKE, R. SEAMAN, AND K . PURI
specific differences in the four-dimensional assimilation procedures. The major differences are thought to be associated with (1) the differing NNMI and in particular the initialization of selected modes in the GFDL scheme and (2) the more geostrophic character of the multivariate analyses from the ECMWF in comparison to the univariate approach at the GFDL. In seeking to improve assimilation methods there are many areas of potential modifications. Given the widespread use of 01, it is necessary to specify expected prediction error covariances among all variables and positions that are to be analyzed. The assumed relationships in widespread use are unlikely to be optimum, and by using the large amounts of data accumulated from operational systems it is now possible to derive better models of auto- and cross-correlation functions for prediction error. Such studies are in progress at a number of centers, and although these results will be system dependent, it is anticipated that as assimilation procedures improve some consensus in modeling prediction error could be reached. Improvements in assimilation will also accompany improved realism in the predictive model component. The forecast models provide both the first-guess specification for 01 and often the fields for preliminary quality control of observations. The view of the study conference in Exeter (WMO/ICSU, 1982), as part of the numerical experimentation program on observing systems, was that considerable improvements can still be made in models using higher resolution, better numerical techniques, and improved parameterizations. The breakthrough in initialization now attributed to the NNMI is undoubted. However, the role of the NNMI in the tropics and in the vicinity of high orography is not fully understood. To some extent, the broad specification of the Hadley circulation can be retained by including some diabatic forcing in the initialization step (Wergen, 1982) or by simply bypassing the initialization of the low-frequency large-scale modes associated with the Hadley flow (Puri and Bourke, 1982; Puri, 1983a). Also the detailed specification of the diabatic heating at the initial forecast time is considered necessary if the divergent wind field over the tropics in particular is to be analyzed and predicted correctly. The ability both to analyze and to predict in the vicinity of high orography is clearly of relevance as evidenced by close attention given to specification of the numerically enhanced or “envelope orography” (Wallace et al., 1983). This approach has resulted in some improvement in prediction beyond 4 days, although it is also associated with some degradation at 1 day.
5.3. Long-Term Operational Implications of Four-Dimensional Assimilution
The immediate operational implications of current assimilation systems are evidenced by the quality of medium-range predictions routinely available. The longer-term implications arise from the ability to conduct ( I ) OSEs with the enhanced data base available from the FGGE year and (2) OSSEs with proposed future enhancements of observational systems. The JOC study conference in Exeter (WMO/ICSU, 1982) drew attention to the importance of research utilizing the FGGE data. At this meeting the particular concern was the coordination of numerical experimentation of relevance to the design of the future WWW system. The meeting considered a number of observing systems, including satellite temperature soundings, cloud vector winds, and drifting-buoy pressure observations and their relevance to maintaining accurate global analyses. The current range of assimilation systems enabled certain conclusions to be drawn about the observational requirements for global analysis and prediction. Among these conclusions were the following: (1) Atmospheric soundings from polar-orbiting satellites are an essential element of the global observing system, (2) cloud vector winds contribute significantly to tropical and Southern Hemisphere analysis although showing little impact on prediction, (3) drifting buoys in the Southern Hemisphere provide large positive impact on analysis and prediction, and (4) the impact of single-level observing systems is significantly dependent on the particular assimilation system used.
The ability to identify these factors in OSEs highlights the current value of existing assimilation systems. It is unlikely that the WWW network will approach the comprehensiveness of the FGGE year in the near future, and it is therefore crucial to carefully identify those components of key importance. There is now widespread activity in the numerical experimentation community to assess further the impact of particular observing systems in a closely controlled manner. For example, the same data base and broad strategies are to be utilized by a number of operational and research centers using data from the first special observing period of the FGGE. This intercomparison will highlight the response of analysis and prediction systems to degradation of the data base and should provide some further limited but quantitative measures of the impact of various observing systems. It should be noted that OSEs are inherently difficult
W. BOURKE, R. SEAMAN, AND K. PURI
and expensive and that the results are not necessarily as decisive and quantitative as the designers of observing systems require. It is also clear that the utilization of the current observational data base could be enhanced. An obvious example is the potential for very-highresolution temperature soundings from the operational polar-orbiting satellites. These data are presently available at a horizontal resolution of from 250 to 500 km. With enhanced global processing, such as performed locally at a number of centers, the global data base for temperature soundings could approach a resolution of the order of 100 km. The numerical resolution of the assimilation and prediction systems under current development at the NMC, the GFDL, the ECMWF, and the UKMO could be expected to require that data base in the near future. In addition to improving the horizontal resolution of temperature soundings, the scope for improving the quality of the soundings themselves is also of considerable importance and is strongly coupled to present-day assimilation endeavors. In particular, recent reconsideration of direct inversion methods (Smith et al., 1984), in contrast to current operational statistical retrieval methods, affords the promise of more accurate soundings using first-guess temperature information from the assimilation systems. The present data base supporting global assimilation and prediction systems is almost totally dependent on space-based observing systems. Proposed enhancements of these satellite systems include substantially improved temperature soundings from an infrared interferometer (Smith, 1979, 1984) and the possibility of improved direct determination of wind fields. A particularly interesting system under consideration, known as WINDSAT, could provide high-quality wind measurements over the globe at horizontal resolutions of less than 100 km (Huffaker, 1978). The WINDSAT project is particularly exciting in view of the known behavior of current assimilation prediction systems. The wind measurements via a satellite-based infrared Doppler radar have been suggested as a long-term solution to the wind field specification necessary for improved prediction. The information content of wind measurements is relatively more valuable than mass measurements in the tropical domain and for smaller scales over the entire globe. However, the lead time of space-based sensors is long and even now the earliest practical demonstration of the WJNDSAT technique is proposed for a Space Shuttle flight in 1990. Accordingly, it is necessary to simulate the capabilities of such a system if indeed it is to materialize. The current assimilation systems and largescale prediction models afford the option to assess quantitatively such proposed new observing systems.
6. CONCLUSION Four-dimensional assimilation has reached substantial maturity following the decade of research leading up to the FGGE and the more recent implementation of operational assimilation systems at centers throughout the world. The value of the assimilation OSSE studies in the seventies has been verified by the success of the current observing and assimilation systems in providing the meteorological community with comprehensive analyses spanning the global atmosphere for the first time. Thirteen years after the first conference o n four-dimensional assimilation in 1971 under the sponsorship of the JOC and hosted by Dr. Smagorinsky at the GFDL, it is clear that great progress in this field has been made. The capacity to develop global assimilation and prediction systems further and to design an optimum observing system for WWW in the decade ahead is a sign of great vitality in this important component of meteorological science. REFERENCES Arakawa, A., and Lamb, V . R. (1977). Computational design of the basic dynarnical processes of the UCLA general circulation model. Methods Comput. Phys. 17, 174-265. Baer, F. (1977). Adjustments of initial conditions required to suppress gravity oscillations in non-linear flows. Beitr. Phys. Atmos. 50, 350-366. Bell, R. S. (1983). The Meteorological Office operational global data assimilation and forecast system. Prepr., Con$ Numer. Wearher Predict., 6th, 1983, pp. 269-274. Bengtsson, L. (1975). Four-dimensional assimilation of meteorological observations. CARP Pub/. Ser. 15. Bengtsson, L., Ghil, M., and KaIIen, E., eds. (1981). “Dynamic Meteorology: Data Assimilation Methods.” Springer-Verlag, Berlin and New York. Bengtsson, L., Kanamitsu, M., Kallberg, P., and Uppala, S. (1982). FGGE Four-dimensiond assimilation at ECMWF. Bull. Am. Meteorol. SOC. 63, 29-43. Bergman, K. H. (1979). Multivariate analysis of temperatures and winds using optimum interpolation. M o n . Weather Reu. 107, 1423- 1444. Bourke, W . (1974). A multi-level spectral model. I . Formulation and hemispheric integrations. Mon. Weather Reu. 102, 687-701. Bourke, W . , and McGregor, J. L. (1983). A non-linear vertical mode initialization scheme for a limited area prediction model. Mon. Weather Reu. 111, 2285-2297. Bourke, W., McAvaney, B., Puri, K . , and Thurling, R. (1977). Global modelling of atmospheric flow by spectral methods. Methods Comput. Phys. 17, 267-324. Bourke, W., Pun, K . , Seaman, R . , McAvaney, B., and Le Marshall, J. (1982). ANMRC data assimilation for the southern hemisphere. Mon. Weather Rev. 110, 1749-1771. Briere, S. (1982). Nonlinear normal mode initialization of a limited area model. Mon. Weather Reu. 110, 1166-1 186. Bromley, R. A. (1978). Simulation experiments to assess the effectiveness of the observing
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