Dynamics of Zonal-Mean Flow Assimilation and Implications for Winter Circulation Anomalies

Eric DeWeaver Department of Meteorology, University of Maryland, College Park, Maryland

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Sumant Nigam Department of Meteorology, University of Maryland, College Park, Maryland

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Abstract

Seasonally averaged 200-mb circulations for recent winters (1987/88 and 1988/89) that represent opposite phases of El Niño and a zonal-mean zonal flow index cycle are diagnosed using data assimilated by the Goddard Earth Observing System (GEOS) and operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF). The comparison is undertaken to determine whether there are significant differences in the 200-mb vorticity dynamics implied by the mean meridional circulations in the two datasets and whether these differences can be related to the Incremental Analysis Update (IAU) method used in the GEOS assimilation.

The two datasets show a high degree of similarity in their depictions of the large-scale rotational flow, but there are substantial differences in the associated divergent circulations. For the zonal-mean flow, the zonal winds are substantially the same, but the meridional wind in the Tropics and subtropics is considerably weaker in the GEOS assimilation than its counterparts in both the ECMWF data and the GEOS analyses used to produce the assimilation.

The authors examine the assimilation of the Hadley circulation using a zonally symmetric f-plane model. For this model, the IAU method easily assimilates the rotational flow but fails to assimilate the divergent circulation. This deficiency of the IAU method may explain the weakness of the Hadley cell in the GEOS assimilation, at least in relation to the GEOS analysis.

For this simple model, an alternative assimilation method, based on constraints imposed by the analyzed potential vorticity and mean meridional circulation fields, is proposed that simultaneously assimilates both rotational and divergent flow components.

Barotropic modeling suggests that an accurate representation of mean meridional flow anomalies can be important for the diagnosis of both zonal-mean and eddy rotational flow perturbations, particularly during extreme phases of the zonal-mean zonal flow fluctuation.

Corresponding author address: Dr. Eric DeWeaver, Department of Meteorology, University of Maryland, College Park, MD 20742.

Email: eric@atmos.umd.edu

Abstract

Seasonally averaged 200-mb circulations for recent winters (1987/88 and 1988/89) that represent opposite phases of El Niño and a zonal-mean zonal flow index cycle are diagnosed using data assimilated by the Goddard Earth Observing System (GEOS) and operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF). The comparison is undertaken to determine whether there are significant differences in the 200-mb vorticity dynamics implied by the mean meridional circulations in the two datasets and whether these differences can be related to the Incremental Analysis Update (IAU) method used in the GEOS assimilation.

The two datasets show a high degree of similarity in their depictions of the large-scale rotational flow, but there are substantial differences in the associated divergent circulations. For the zonal-mean flow, the zonal winds are substantially the same, but the meridional wind in the Tropics and subtropics is considerably weaker in the GEOS assimilation than its counterparts in both the ECMWF data and the GEOS analyses used to produce the assimilation.

The authors examine the assimilation of the Hadley circulation using a zonally symmetric f-plane model. For this model, the IAU method easily assimilates the rotational flow but fails to assimilate the divergent circulation. This deficiency of the IAU method may explain the weakness of the Hadley cell in the GEOS assimilation, at least in relation to the GEOS analysis.

For this simple model, an alternative assimilation method, based on constraints imposed by the analyzed potential vorticity and mean meridional circulation fields, is proposed that simultaneously assimilates both rotational and divergent flow components.

Barotropic modeling suggests that an accurate representation of mean meridional flow anomalies can be important for the diagnosis of both zonal-mean and eddy rotational flow perturbations, particularly during extreme phases of the zonal-mean zonal flow fluctuation.

Corresponding author address: Dr. Eric DeWeaver, Department of Meteorology, University of Maryland, College Park, MD 20742.

Email: eric@atmos.umd.edu

1. Introduction

Dynamical diagnosis of the atmospheric circulation places enormous demands on observational datasets, for such diagnosis requires knowledge of both circulation patterns and the forcing functions that generate and maintain them. The time-mean circulation patterns are relatively easy to observe, given their large horizontal scales and simple vertical structures, and datasets currently available from operational forecast centers show fairly good agreement in their amplitude and spatial structure. By comparison, estimates of forcing functions, such as divergence in barotropic diagnosis and diabatic heating in baroclinic diagnosis, are quite difficult to obtain, given their small horizontal scales, complex vertical structures, and connection to poorly observed regions of the atmosphere. Such estimates show only modest agreement among datasets (Trenberth and Olson 1988), and even small differences in the forcing functions can have tremendous consequences for the diagnosis of the associated circulation patterns.

The Hadley cell provides a good example of the kinds of data required for climate diagnostics. The primary circulation features associated with the Hadley cell consist of the zonally symmetric distributions of temperature and zonal wind ū in the Tropics and subtropics, which are robust features of the general circulation. However, to understand how these primary circulation features are maintained and modulated requires an assessment of the divergent circulation given by the time-mean zonally symmetric meridional and vertical velocities ῡ and ω̄, which are among the subtlest features of the general circulation. Further analysis of the divergent circulation leads in turn to consideration of the diabatic heating field, which is both the most obscure and the most fundamental quantity required for the diagnosis of the Hadley cell (Hou and Lindzen 1992).

The Hadley cell also provides a good example of the difference in perspective between climate diagnosticians and the operational forecast centers. The primary goal of data assimilation at the forecast centers is to create initial conditions that result in the best possible short- and medium-range forecasts, rather than to produce, for example, an accurate depiction of the relationship between the Hadley circulation and the subtropical jets. Unlike operational forecast centers, the mission of the Data Assimilation Office (DAO) at NASA’s Goddard Laboratory for Atmospheres is to produce an integrated and dynamically consistent climate dataset for earth science applications. A proper representation of divergent circulations such as the Hadley cell would thus appear to be an important measure of the DAO’s success.

In this study, we compare the 200-mb circulations during recent El Niño (1987/88) and La Niña (1988/89) winters (DJF) as portrayed by data from the Goddard Earth Observing System (GEOS) Data Assimilation System (GEOS-DAS), produced by the DAO, and from the ECMWF uninitialized analyses. The comparison is undertaken to determine whether there are significant differences in the upper-tropospheric dynamics implied by the two datasets, particularly differences related to the mean meridional circulations portrayed by the datasets, and how such differences might be related to the methods used to produce the data.

The decision to base the comparison on two individual seasons rather than a multiseason composite was motivated by our desire to use a diagnostic model to compare the anomaly dynamics in the two datasets. The model is a spectral divergent steady-state barotropic model (Held and Kang 1987; DeWeaver and Nigam 1995), which solves for the rotational flow anomaly between two seasons, given the corresponding anomalies in divergence and transient vorticity fluxes, and a basic state constructed using the average flow for the two periods. Schneider (1988) has shown that when an anomaly model is formulated in this manner, the resulting equation is automatically linear, without neglecting any quadratic terms. Thus, the two-season format allows us to determine the nonlinearly accurate streamfunction response to an observed forcing anomaly. For the sake of consistency, the dynamics of the climatological flow is examined using the average circulation of the same two winters.

The GEOS-DAS dataset is produced using a novel assimilation algorithm, known as the Incremental Analysis Update (IAU) procedure (Bloom et al. 1991), which is designed to reduce “spinup” in evaporation, precipitation, and radiative fields. In this algorithm, analysis increments (i.e., analysis minus model first guess; increments are also called “corrections” in estimation theory) are divided into small fractions and inserted into a model integration in progress at every time step. The observations thus take the form of external forcing functions that, when applied to an atmospheric general circulation model (AGCM), constrain it to remain faithful to the observed atmosphere. Schubert et al. (1995) characterize the assimilation process generically as ∂x/∂t = dynamics + physics + IAU forcing. Since the IAU forcing represents an external, nonphysical source or sink of x, the diagnosis of x becomes physically meaningful only if the IAU forcing is small compared to the other terms in the budget equation.

The present work considers the extent to which the IAU method uses the available observational data to constrain the mean meridional circulation. Specifically, can divergent circulations such as ῡ and ω̄ be assimilated in the time mean using IAU forcing? Is there an alternative forcing scheme that would be better suited to this task? Finally, given that the wintertime ῡ and ω̄ differ substantially between the GEOS-DAS and ECMWF datasets, what effect do these differences have on the anomaly dynamics diagnosed from the datasets?

It would perhaps be unreasonable to expect that an assimilation method in which observed data is introduced gradually in the form of IAU forcing would provide a completely observationally determined picture of the divergent circulations. However, a detailed analysis of the relative importance of model and observations in this kind of assimilation has not been previously published, for the simple reason that no atmospheric dataset of this type has been available before now.

This study is divided into six sections. Section 2 describes the IAU method used to generate the GEOS-DAS dataset. Section 3 compares the GEOS-DAS Hadley cell with its ECMWF counterpart. In section 4 we use a simple f-plane model to examine the response of the zonally symmetric circulation to various types of IAU forcing; this model demonstrates the difficulty of assimilating the Hadley cell using the IAU method. In the context of this idealized model we propose an alternative method for assimilating the Hadley cell that avoids these difficulties by using a potential vorticity (PV)-based approach. We use the barotropic model in section 5 to diagnose the wintertime anomalies in ū and ῡ and in the eddy streamfunction. Conclusions and recommendations follow in section 6.

2. The IAU method

Figure 1 describes the IAU procedure. At the analysis times (0000, 0600, 1200, and 1800 UTC) a three-dimensional, multivariate optimal interpolation scheme (OI) is used to produce an analysis. The analysis is produced using data from a ±3 h window centered on the analysis time and a model first guess provided by a three hour forecast valid at the same time. The model used is the GEOS-1 AGCM (Takacs et al. 1994). The IAU forcing terms are formed by taking the difference between the prognostic variables from the analysis and the corresponding variables from the model first guess, and dividing by the 6-h time interval. IAU forcing terms are applied in the horizontal momentum, temperature, moisture, and surface pressure equations. The model is then restarted three hours prior to the analysis time with the IAU forcing terms included in the prognostic equations, and the integration continues until three hours after the analysis time. The model integration continues for another three hours with the IAU forcing terms set to zero to produce a first guess for the next analysis period. A detailed discussion of the IAU method can be found in Pfaendtner et al. (1995).

The IAU method is similar in spirit to the Newtonian nudging procedure (Davies and Turner 1977; Daley 1991), since both methods avoid initialization shocks by feeding observed data gradually into the model. However, unlike the Newtonian nudging procedure, in which the forcing terms are proportional to the difference between the instantaneous model state and the target fields, the IAU forcings are held constant for the entire 6-h period to which they are applied. Bloom et al. (1996) show that the IAU method effectively removes high-frequency gravity waves produced by dynamical imbalances in the analysis fields. In particular, they claim that the IAU method virtually eliminates data insertion shocks in the precipitation and evaporation fields.

Whereas Bloom et al. discuss the benefits of IAU forcing for the high-frequency flow, our primary interest here is in the seasonal-mean IAU forcing, which occurs because of systematic biases in the AGCM. As an example, Schubert et al. (1995) cite the moisture budget in the Tropics: “Thus, for example, if the model prefers to have a drier tropical atmosphere than nature, the observations (IAUs) will systematically add water during the assimilation.” (p. 5)

3. Comparison of the Hadley circulation

Figures 2a and 2b, taken from Schubert et al.’s (1995) 5-yr climatology, show that the DJF ῡ in GEOS-DAS assimilation and ECMWF uninitialized analysis differ by as much as 1.5 m s−1, or by a factor of 2. The difference in ω̄ (not shown) is of the same order. However, the difference in wintertime between GEOS-DAS and ECMWF is less than 3 K throughout most of troposphere, while the corresponding difference in ū does not exceed 2 m s−1. Since the Hadley cell plays an important role in generating the zonal-mean temperature and zonal wind profiles, the two datasets must imply very different dynamics for the zonal-mean circulation.

The GEOS-DAS Hadley circulation is further examined in Fig. 2c, which compares the 200-mb ῡ climatology as portrayed by ECMWF uninitialized analyses and the GEOS–DAS assimilation, analysis, and first guess fields. Here the climatology is constructed from the average of DJF 1987/88 and DJF 1988/89, for reasons stated in the introduction. In keeping with Fig. 2b, the ECMWF ῡ (filled squares) is considerably stronger than any of the other estimates. Comparison of the GEOS–DAS analysis (open squares) and first guess fields (open circles) shows that the model first guess is consistently weaker than the in-house analysis. The GEOS-DAS-assimilated ῡ, shown by the filled circles in Fig. 2c, is very close to its first-guess counterpart. Evidently, the IAU procedure, including the positive IAU forcing in the mean meridional momentum equation, has not succeeded in assimilating the analyzed values of ῡ.

4. A simple model of zonal-mean assimilation

To determine whether there are inherent difficulties in assimilating the Hadley circulation, we consider a hypothetical assimilation carried out using a zonally symmetric f-plane model in log-pressure coordinates (Holton 1992), that is, z = −Hln(p/p0), given by
i1520-0469-54-13-1758-e1
where Q is the diabatic heating, X is the zonal component of drag owing to small-scale eddies, and ( )′ is the departure of ( ) from its longitudinal average, denoted by an overbar. Let us further assume that both the observed atmospheric state and the model first guess are steady [in particular, we assume geostrophic balance in Eq. (2)] so that, for example, (1) can be written
i1520-0469-54-13-1758-eq1
where ( )FG represents the model first guess and ( )A the observed state, or analysis.
In this situation, the assimilation algorithm will integrate Eqs. (1)–(5) for a period, Δt, using the model variables as the initial condition, and subject to additional forcing functions Fu and Fυ in the horizontal momentum equations and FT in the thermodynamic equation. Since the initial state for the integration is a steady solution to the equations without the F, we can think of the assimilation as a set of forced equations for the zonal-mean perturbation variables u, υ, w, T, and ϕ, which are defined by ū = ūM + u, ῡ = ῡM + υ, and so on. The assimilation is then obtained by integrating the following perturbation equations from a state of rest:
i1520-0469-54-13-1758-e6
To simplify the analysis, we have assumed that the diabatic heating Q and momentum dissipation X are independent of the perturbation flow. Also, since only the zonally symmetric flow is assimilated in this example, the eddy flux terms maintain their first-guess values throughout the assimilation process and, thus, do not enter the perturbation equations.

The goal of the assimilation is to produce a perturbation solution that at t = Δt is identical to the difference between the model first guess and analysis, that is, u = δū, υ = δῡ, T = δT̄, where the increment δ( ) = ( )A − ( )FG. Following the GEOS-DAS procedure, the IAU forcings Fu, Fυ, and FT would be given by Fu = δūt, Fυ = δῡ /Δt, and FT = δt. However, as discussed below in section 4c, the assimilation can perhaps be better accomplished using Fu, Fυ, and FT determined from potential vorticity (PV) and divergent circulation considerations.

A detailed solution to (6)–(10) is provided in the appendix. In the following subsections we examine the dynamics of this system qualitatively by considering the perturbation equations for PV and the meridional–vertical mass transport streamfunction (χ), derived from (6)–(10):
i1520-0469-54-13-1758-e11
Here PV is given by the quantity in brackets on the left-hand side of (11) and χ is defined by ρ0w = ∂χ/∂y, ρ0υ = −∂χ/∂z. Since the model represents a single assimilation cycle over which the forcing terms are held constant, the tendency term on the right-hand side of (12) vanishes.

a. Assimilation using thermally balanced Fu and FT

We first consider the response to Fu and FT alone, where Fu and FT are defined by the GEOS-DAS procedure. With this definition, we can represent the forcing terms in (12) by
i1520-0469-54-13-1758-e13
Our assumption that the model and atmospheric circulations are steady implies that both the analysis and first-guess zonal winds are exactly geostrophic, so the rhs of (13) is zero; that is, Fu and FT are thermally balanced. Thus the forcing term in (12) vanishes, and the assimilation proceeds without any meridional circulation. Setting υ = w = 0 in (6) and (8) gives ∂u/∂t = Fu and ∂T/∂t = FT, and when these equations are integrated from a state of rest for a time Δt we obtain u = δū and T = δT̄, a perfect assimilation of ū and T̄.

b. Assimilation of the Hadley circulation using Fυ alone

Having obtained a perfect assimilation of ū and with thermally balanced Fu and FT, we now attempt to assimilate ῡ using external forcing in the meridional momentum equation (Fυ). This piecemeal approach is possible because the perturbation equations are linear and therefore the responses to the forcing terms can be superposed. We first note that Fυ does not appear in (11), so that PV is conserved in this case, and since the model is integrated from a state of rest, PV = 0 throughout the integration. Thus
i1520-0469-54-13-1758-eq2
This expression can be substituted in the divergence equation, formed by taking the meridional derivative of (7), to derive a prognostic equation for ϕ:
i1520-0469-54-13-1758-e14
Equation (14) is exactly the classical Rossby adjustment equation (Rossby 1938), with Fυ playing the role of the initial PV distribution in Rossby’s problem. This equation shows that unlike Fu and FT, which generate a time-mean acceleration of the flow, Fυ generates only a time-mean height perturbation, accompanied by transients.

Figure 3 gives a qualitative description of the dynamics of Fυ forcing. Suppose that Fυ is applied at 200 mb, with the meridional distribution shown in panel a. If we make the approximation (e.g., Holton 1992), true for a single Fourier component, that second derivatives of ϕ are proportional to ϕ but with opposite sign {i.e., ∂/∂z[(ρ0/ N2)∂ϕ/∂z] ∝ −ϕ}, then PV conservation implies that ∂u/∂y ∝ −ϕ, while in (14) we have ∂Fυ /∂y ∝ −ϕ for the steady forced solution. Thus, the perturbation geopotential height will be negative to the south and positive to the north as shown in panel b. From PV conservation, positive height perturbations are associated with positive vorticity, so that the jet (panel c) has roughly the same meridional profile as Fυ. Consequently the forcing results in a westerly jet with positive geopotential height to the north, so that both the Coriolis force (FCO) and the pressure gradient force (FPG) are southward, in opposition to Fυ. Rather than generating a Hadley circulation, the assimilation has produced an antigeostrophic zonal jet, and a steady state is reached when the forces associated with this jet exactly cancel Fυ. Since Fυ is balanced by FPG and FCO, no acceleration of υ occurs. The literature of the GEOS-DAS project often refers to IAU forcings as “additional heat, momentum, moisture, and mass source terms” (Schubert et al. 1993). But in this case, the meridional IAU force does not constitute a momentum source.

While the derivation of (14) depends on our assumption of constant f, the steady, antigeostrophic character of the solution depends only on the conservation of PV. If we relax the assumption of constant f, the perturbation PV is no longer constant but changes due to planetary vorticity advection: ∂PV/∂t = −υβ, where β = ∂f/∂y. We note that the mean meridional circulation equation (12) used to obtain υ is derived without taking any meridional derivatives of f and is thus valid even if f varies. Since a steady Fυ forcing does not generate a meridional circulation in (12), υ and hence the PV source (−υβ) are both zero. Thus, even if f varies, the antigeostrophic relationship between u and ϕ outlined in Fig. 3 still holds.

In this section we have offered our explanation of the results shown in Fig. 2. The simple model derived here suggests that while the GEOS assimilation procedure (i.e., thermally balanced Fu and FT, together with Fυ) has no difficulty assimilating zonal-mean zonal wind and temperature fields, it is unable to assimilate the Hadley circulation through direct forcing. In the next section, we explore the possibility of an indirect assimilation of the Hadley circulation using unbalanced forcing functions derived from the PV and meridional circulation increments.

c. Proposed assimilation using unbalanced Fu and FT

Let us now consider an assimilation of the same increments (thermally balanced δū and δT̄, and δῡ) in which the forcing functions Fu and FT are not necessarily obtained directly from δū and δ but are any two functions that correctly assimilate the PV increment δ(PV), which is given by
i1520-0469-54-13-1758-eq3
Equation (11) shows that perturbation PV increases linearly during the assimilation and that a perfect PV assimilation is achieved when t = Δt, provided that
i1520-0469-54-13-1758-e15
The derivation in the appendix shows that the geopotential height response consists of a geostrophically balanced component that increases linearly with time, accompanied by transients. Since this secular geostrophic component contains all the PV added to the system during the assimilation, a perfect assimilation of PV implies a perfect assimilation of the geopotential height, given that the PV increment being assimilated is obtained from thermally balanced δū and δT̄.

Figure 4 depicts the extreme cases where the PV forcing is added exclusively to either (a) the momentum equation or (b) the thermodynamic equation. In (a), a positive Fu, denoted by the arrowhead symbol (⊚) on the left, accelerates a positive u at the upper level [for convenience, the symbols for Fu and FCO are depicted above and below u in (a) and (b), although these forces are, in fact, collocated with u]. Since Fu is applied only at the upper level, we can take f ∂Fu /∂z > 0 in (12), and under the approximation that second derivatives of χ are proportional to χ but with opposite sign, we can expect χ < 0. This thermally indirect meridional–vertical circulation, induced by the Coriolis force acting on u, generates a perturbation height field ϕ, which is in geostrophic balance with u. In (b), a positive (negative) FT is applied to the south (north) of the desired jet enhancement. The model is hydrostatically balanced, so the thermal forcing by FT generates upper-level height perturbations of the same sign. Since we have ∂FT/∂y < 0 in (12), a meridional–vertical circulation develops with χ > 0, and the Coriolis force acts on this thermally direct circulation to produce a positive jet perturbation u, in geostrophic balance with ϕ.

The above discussion shows that to correctly assimilate δū and δ we have only to constrain Fu and FT so that the PV they add to the system over the period Δt is equal to δ(PV). We are then at liberty to select Fu and FT such that the thermal imbalance between them produces a steady meridional circulation that is equal to the meridional circulation increment δχ̄ (which can be obtained from δῡ using the continuity equation and appropriate boundary conditions). The additional constraint on Fu and FT is obtained by requiring the steady linear operator on the lhs of (12) to operate on the known δχ̄:
i1520-0469-54-13-1758-e16
Thus for this model, we can solve (15) and (16) to obtain forcing functions Fu and FT, which correctly assimilate the three increments δū, δT̄, and δῡ.

The assimilation process outlined above can be understood in terms of classic geostrophic adjustment theory: Fu and FT add PV to the system, and if this PV input is not in geostrophically balanced form, a meridional circulation arises that adjusts the thermal and mechanical components of PV (i.e., the mass and velocity fields) so that the response is in geostrophic (or thermal wind) balance. The primary circulation, consisting of the balanced u and T fields, is the same regardless of whether PV is added to the system in thermal or mechanical form. However, the steady secondary circulation, consisting of υ and w, depends entirely on the relative contributions of Fu and FT to the PV source. If PV is added to the system primarily in thermal (mechanical) form, so that the FT (Fu) term is the dominant term on the rhs of (12), the mean meridional circulation will be thermally direct (indirect).

As an example, consider the case in which the model first guess and observed atmosphere have the same thermally balanced ū and fields in the northern subtropics, but the corresponding meridional circulation is weaker in the model than in the observations, so that δ(PV) = 0 but δχ̄ > 0. In that case, as shown in Fig. 5, the proposed assimilation scheme would enhance the model’s meridional circulation by generating positive (negative) FT forcing to the south (north). However, as shown in Fig. 4b, such FT forcing has the unintended consequence of generating a positive upper-level geostrophic jet at the center of the domain. To prevent this unwanted increase in PV, the scheme generates a negative Fu forcing, which removes the momentum added to the jet by FT.

In short, the assimilation scheme proposed here constructs Fu and FT so that they not only constitute the correct PV input, but the thermal imbalance between them produces a mean meridional circulation equal to the meridional circulation increment to be assimilated. By comparison, the GEOS-DAS procedure assimilates the geostrophic circulation (ū and ) independently of the divergent meridional circulation since u and T are assimilated using thermally balanced forcing functions that do not generate any divergent circulation. While this strategy succeeds in assimilating the geostrophic circulation, the corresponding attempt to assimilate the divergent circulation independently, through direct Fυ forcing, does not.

5. Barotropic diagnosis of wintertime circulation anomalies

The circulation differences between the winters discussed here contain large anomalies of the mean meridional circulation and both the zonal-mean and eddy components of the rotational flow. Such anomalies are to be expected, since the winters were chosen to represent opposite phases of El Niño. These winters also represent opposite phases of the zonal index, defined by Ting et al. (1996), which is associated with large stationary wave anomalies (Ting et al. 1996) and, as we will show, large-scale ῡ anomalies. Given that substantial anomalies of ῡ and the rotational flow coexist in our case study, we wish to assess the implications of ῡ discrepancies between the datasets for the maintenance of the rotational flow anomalies. For this purpose, we use a barotropic model. The model is applied at the 200-mb level, where the divergent outflow accompanying deep tropical heating is most pronounced. It is also near the level of maximum midlatitude ῡ anomalies for this case.

a. The barotropic anomaly model

The seasonal-mean 200-mb flow, including both zonal-mean and eddy components, is assumed to satisfy the steady-state divergent vorticity equation (Held and Kang 1987; DeWeaver and Nigam 1995):
i1520-0469-54-13-1758-e17
where Vψ and Vχ denote rotational and divergent components of the wind field, ζ is the vorticity, and ( )′ is the departure of ( ) from its seasonal average, which is represented by an overbar. The vertical vorticity advection, tilting, and seasonally averaged tendency terms were found to make negligible contributions to the anomaly solutions in both datasets and, hence, are neglected in (17). When applied to GEOS assimilated data, (17) includes an additional IAU forcing term on the rhs.
Using (17), we can form an equation for the difference in circulation between two seasons by applying the equation in each season and taking the difference. Defining anomaly and climatology by ( )a = {( )season 1 − ( )season 2} and ( )c = {( )season 1 + ( )season 2}/2, we can write
i1520-0469-54-13-1758-e18
As Schneider (1988) pointed out, this equation is automatically linear, without neglecting any terms or making further approximations. Thus, although the model is posed as a linear matrix equation, the anomaly solution is nonlinearly accurate. Using (18), we can view the rotational flow anomaly as the steady response to external forcing provided by the anomalies in subseasonal vorticity transients and seasonal-mean divergent flow. By linearity, the rotational flow anomaly can be further decomposed into individual responses to the components of any decomposition of the forcing, such as zonal mean and eddy parts, or regional components.

Model solutions presented here are obtained from a spectral version of the model truncated rhomboidally at wavenumber 15 (R15), with Rayleigh damping r = (5 days)−1 and biharmonic viscosity ν = 1016 m4 s−1. ECMWF data were available on a 2.5° × 2.5° latitude–longitude grid, while GEOS-DAS winds and transients were obtained from a 2° × 2.5° latitude–longitude grid. Vorticity transients are calculated from twice-daily ECMWF analyses and from 6-h GEOS-DAS assimilated data so that all the available data is used. The model was solved in all cases for both zonal-mean and eddy components of the rotational flow anomaly.

b. Diagnosis of zonal-mean anomalies

Figure 6 shows the 200-mb anomalies in ū and ῡ between the 1987/88 (El Niño, positive zonal index) and 1988/89 (La Niña, negative zonal index) winters (DJF). As in the climatological case, the ECMWF analyzed and GEOS-DAS assimilated ū fields agree quite well (panel a), while the corresponding ῡ fields (panel b) show significant differences. The most dramatic difference in ῡ occurs near 30°N, where ECMWF shows positive anomalies in excess of 35 cm s−1, while the GEOS-DAS anomalies are less than 5 cm s−1 in magnitude and generally negative. Panel (c) compares anomalous ῡ profiles from the GEOS-DAS analysis (open circles), first guess (filled circles), and assimilation (line) between 20° and 40°N. From this figure it is clear that the assimilation is not responding in any direct way to the IAU forcing in the meridional momentum equation; at 30°N, where the IAU forcing is strongest, the first guess and assimilation values are practically the same. Figures 6b and 6c are thus quite consistent with Fig. 2c.

In the ECMWF analysis, the collocation of midlatitude ū and ῡ anomalies strongly suggests that the ū anomaly is maintained at least in part by Coriolis deflection acting on the ῡ anomaly. But the ū anomaly in the GEOS-DAS data is clearly maintained by other processes. Using a steady barotropic anomaly model, we examine this important difference in the anomaly dynamics implied by the two datasets. Figure 7 shows the ū anomaly produced by solving (18) using data from GEOS-DAS (a) and ECMWF (b). The solid line shows the target ūa for each dataset, while the open circles show the response to all forcings and the filled circles show the response to ῡa alone. For both datasets, the solutions show considerable departures from the target fields in northern high latitudes and in the Southern Hemisphere; however, the two solutions verify better from the subtropics to 50°N. In the ECMWF case, the agreement between the open and filled circles indicates that ῡa does, in fact, maintain ūa in these latitudes, in sharp contrast to the GEOS–DAS diagnosis, in which the response to ῡa is exactly out of phase with both the observed and simulated midlatitude ūa.

The zonal-mean zonal momentum equation corresponding to (18) can be written
i1520-0469-54-13-1758-e19
where a represents the forcing of ūa by anomalous stationary eddies (included in the model operator) and transients. The ECMWF simulation suggests that the dominant midlatitude balance in (19) is between Coriolis torque acting on ῡa and momentum dissipation. However, the lack of correspondence in the Tropics and midlatitudes between the open and filled circles in Fig. 7a shows that this balance plays a minor role in the GEOS-DAS case. The crosses in Fig. 7a show the response to anomalous IAU vorticity forcing: the response to IAU forcing is generally large in amplitude and in northern midlatitudes it contributes significantly to the observed ūa. Furthermore, Fig. 7c shows that the GEOS-DAS transient forcing produces a response that is considerably stronger than its ECMWF counterpart and, for reasons unknown to us, accounts quite well for the observed ūa.
Our inability to simulate the observed ūa using GEOS-assimilated data is somewhat puzzling since the assimilation is intended to produce dynamically consistent data, which are known exactly on a regular grid. One possible explanation is that dissipation plays a minor role in the upper-tropospheric zonal-mean zonal momentum budget of the assimilation (19). Scaling with model parameters suggests that the advection term on the lhs of (19) is roughly one-fifth of the friction term. Moreover, ῡc has several nodes in the domain, so if mechanical dissipation were supplied as an external forcing on the rhs of (19), the linear operator on the lhs would be singular and could not be inverted to determine ūa. Thus, if momentum dissipation is of secondary importance in (19), the ū anomaly may be undiagnosable. As Lorenz (1967) puts it,

It is sometimes stated that the strong upper-level westerly winds are maintained by a convergence of the horizontal transport of angular momentum. In a sense this statement is true; there is convergence of the horizontal transport where the westerlies reach their maximum. Yet there is no simple relation through which the westerly wind speed may be deduced from the field of angular momentum transport.

Since in the long run any convergence of the horizontal or vertical transport of angular momentum must be balanced by turbulent friction, the time-averaged field of friction may be deduced from the field of angular momentum transport. The westerly-wind field may therefore be deduced from the angular momentum transport field only to the extent that it may be deduced from the field of friction.

The role and representation of dissipation in the upper troposphere are contentious issues. Although the next version of the GEOS assimilation will be produced using a gravity-wave drag parameterization, the version examined here was generated without such effects. While it is quite possible that the midlatitude ῡ anomaly in the ECMWF data is an overestimate, the corresponding GEOS-DAS anomaly is almost certainly an underestimate since the IAU scheme lacks the ability to correct the first guess estimate of ῡ based on its own analysis.

c. Influence of ῡ anomalies on the stationary wave simulation

In the previous section, we used the barotropic model (18) to show that, at least according to the ECMWF analyses, a dynamical relationship exists between ῡa and the zonal-mean rotational flow anomaly, or ūa. Here we attempt to determine whether ῡa has any dynamical influence on the barotropic simulation of the corresponding eddy rotational anomalies. In this model, ῡa can provide direct forcing to the eddy rotational flow anomaly through the terms ζcῡa/∂y and ῡaζc/∂y. Furthermore, since the basic state for the barotropic model contains the eddy components of the climatology, the model can produce an eddy response to the zonal-mean forcing given by (ζ̄c + f)∂ῡa/∂y + ῡa∂(ζ̄c + f)/∂y through the eddy correlation terms Vψa· ζc and ·Vcζa. Since the model also produces a zonal-mean response to these forcing terms, the model can be said to represent the dynamical interaction between the zonal-mean and eddy responses ūa and ψa generated by the forcing.

Such zonal-eddy interactions may seem unlikely, since the winters in this study represent opposite phases of El Niño, and El Niño-related stationary waves are not generally thought to interact directly with the El Niño-related zonal-mean anomalies (Hoerling et al. 1995). However, Fig. 6a shows a strong opposition between the ū anomalies at 35° and 55°N, indicative of a large departure of the zonal index defined by Ting et al. (1996; see also Branstator 1984), who show evidence for dynamical coupling between the zonal-mean and eddy anomalies associated with this index. Moreover, the stationary waves associated with the zonal index in their study share some common features with the eddy streamfunction anomalies shown here.

In this section, we present the eddy streamfunction simulations produced using ECMWF and GEOS-DAS data and show that these simulations are in fact influenced by the corresponding ῡ anomalies. We then use linear regression to show that, for flow perturbations associated with this index, there is observational evidence for the relationship between the anomalies of ῡ and the eddy streamfunction, which our model suggests.

Figure 8 shows the eddy components of the anomaly simulations using GEOS-DAS and ECMWF data. The top panels show the actual 200-mb streamfunction (Ψ200) anomalies, which agree closely between the two datasets. The middle panels show the simulations produced using global divergence, vorticity transients, and additional IAU vorticity forcing in the GEOS-DAS case. Both simulations capture the gross features of the anomalies, including the four-celled wave pattern in the central/eastern Pacific, the ridge over eastern Canada, and the trough over the Gulf of Mexico. However, the simulations also have serious flaws, both in phase and amplitude. In the GEOS-DAS case, the central/eastern Pacific wave pattern is weak. The ECMWF simulation, on the other hand, exhibits exaggerated amplitudes for most features, particularly in high latitudes.

To determine the impact of the ῡ anomalies on the eddy simulations, we exchanged the ῡa fields used to force the model and repeated the simulations. The bottom left panel shows the GEOS-DAS simulation with ῡa taken from the ECMWF data, while the bottom right panel shows the ECMWF simulation with the GEOS-DAS ῡ anomaly. While the simulations are qualitatively similar to those in the middle panels, there are some significant modifications. In the GEOS-DAS case, the exchange of ῡ anomalies causes substantial strengthening of all the major features of the Northern Hemisphere, including a threefold increase in the strength of the northern equatorial anticyclone in the Pacific and the trough over the Aleutian gulf. In addition, the trough over the Gulf of Mexico becomes a local minimum distinct from the North Atlantic trough. All of these features cause the GEOS simulation to better resemble the ECMWF simulation shown in Fig. 8d. Conversely, the ECMWF simulation using the GEOS ῡa shows weakening of the Northern Hemisphere features, including the northern equatorial anticyclone, which is now divided into two distinct maxima, and the Aleutian trough.

Defining the zonal index as ū (35°N) − ū (55°N), we find a difference of 7.4 m s−1 between the winters considered here, a large value compared to the standard deviation of 2.7 m s−1 for this index reported by Ting et al To determine whether the eddy streamfunction anomalies considered here, including those which show sensitivity to the zonal-mean divergence anomalies, are related to the large zonal index difference, we regressed the 200-mb streamfunction against the normalized zonal index. For this analysis, we used monthly averages of the ECMWF uninitialized analyses for the 35 winter months (DJF) from January 1985 to February 1996. The resulting covariant eddy streamfunction pattern, shown in Fig. 9a, has some notable similarities with the streamfunction anomalies shown in Figs. 8a and 8b, including ridges over Greenland, the tropical Atlantic, and central Asia, and troughs over the Gulf of Mexico, the North Atlantic, and the Arabian peninsula. It is also of interest to note that the streamfunction pattern contains large amplitudes south of 20°N. These tropical teleconnections were not reported by Ting et al., who based their statistics on NCEP’s (Formerly National Meteorological Center) 500-mb height analyses for 1947–94, which are only available from 20° to 90°N. The height perturbations would not, in any event, have large amplitudes near the equator.

Further comparison of Fig. 9a and Figs. 8e and 8f shows that some of the features of the simulations that are sensitive to ῡa are also prominent in the zonal index composite, including the Aleutian low and the features over central Europe and the Arabian peninsula. If the dynamical relationship between ῡa and these streamfunction anomalies is indeed characteristic of zonal index fluctuations, we would expect to see ῡ anomalies associated with the zonal index that are consistent with those shown in Fig. 6b. Figure 9b shows that there is a ῡ maximum at 200 mb associated with the zonal index, although this maximum is rather small and shallow compared to the high-latitude maximum.

The covariant ū pattern in Fig. 9c shows a 200-mb maximum at 30°N, collocated with the local ῡ maximum, indicating that, just as in our case study, the Coriolis torque generated by the ῡ anomaly is acting to maintain the ū anomaly. In high latitudes, near 60°N, the ῡ anomaly acts to limit ū. This out of phase relationship between ū and ῡ is also present in our case study (see Figs. 6a and 6b). Figure 9b also shows that the ῡ anomalies associated with the zonal index are by no means confined to the extratropics: the largest negative anomaly occurs at 400 mb at 10°N, near the central latitude of the wintertime Hadley circulation.

The results of this section suggest that large-scale anomalies of the mean meridional circulation play a role in the dynamics of stationary waves associated with the zonal index. Our results thus emphasize the importance of accurately representing the mean meridional circulation during episodes of zonal index fluctuation.

6. Discussion

In this study we have compared climatological and anomalous features represented by the ECMWF’s uninitialized analyses—a widely used dataset in climate diagnostics—with their counterparts in the dataset produced by GEOS-DAS, which NASA will use to assimilate data from its planned earth observing satellite missions. The comparison is undertaken to determine whether there are significant differences in the large-scale upper-tropospheric dynamics implied by the two datasets and whether these differences can be related to the methods used in producing the data. Although the two datasets show a high degree of similarity in their depictions of the zonal-mean and eddy components of the rotational flow, there are substantial differences in the mean meridional circulations.

We find the GEOS-assimilated Hadley circulation (200-mb ῡ) during the winters 1987/88 and 1988/89 to be weak not only with respect to the ECMWF analyses, but also compared to the in-house analyses; in fact, the assimilated 200-mb ῡ is nearly indistinguishable from the GEOS first-guess field. Likewise, the ῡ anomalies in these winters are substantially weaker between 20° and 40°N than their ECMWF counterparts.

To understand why ῡ is so little influenced by the time-mean IAU forcing in the GEOS scheme, we explore the assimilation of the Hadley circulation using a simple zonally symmetric model. Our analysis suggests that

  • Use of thermally balanced IAU forcing in the zonal momentum (Fu = δūt) and thermodynamic equations (FT = δt, with δū in thermal wind balance with δ) leads to perfect assimilation of ū and T̄.

  • IAU forcing in the mean meridional momentum equation (Fυ = δῡt) does not lead to any enhancement of the mean meridional circulation. Rather, the meridional IAU forcing generates an antigeostrophic response, in which the Coriolis (−fu) and pressure gradient forces do not balance each other, but instead act in concert to oppose the applied forcing.

  • Only unbalanced forcing in the zonal momentum and thermodynamic equations can enhance the mean meridional circulation in the time mean. For this simple model, we propose an assimilation strategy in which thermally unbalanced forcing functions Fu and FT are constructed using constraints imposed by the potential vorticity (δPV) and meridional circulation (δχ̄) assimilation targets. These Fu and FT yield a correct assimilation of PV, and for the steady geostrophic flow considered here, a correct assimilation of PV implies a correct assimilation of ū and T̄. At the same time, the thermal imbalance between Fu and FT produces a mean meridional circulation equal to the meridional circulation increment to be assimilated. Our approach is, of course, limited by the availability of accurate observations of the divergent flow. Sardeshmukh (1993) has proposed a method for inferring the divergent flow from the better known rotational flow: in our case, this would be equivalent to solving (1′) for ῡA. However, the determination of ῡA from (1′) depends on the mechanical dissipation XA, which cannot be determined from observations.

The GEOS-DAS literature invites comparison between IAU forcing and the physical parameterizations used in the assimilating model (Schubert et al. 1995). The atmospheric motions considered above are generally thought to result from a process of adjustment, in which physical processes introduce PV into the system in thermal and mechanical form, and secondary circulations arise that exchange these forms until a geostrophically balanced distribution is achieved. In our view, forcing functions constructed from δPV and δχ̄ in this manner constitute corrections to model physics rather than model dynamics and could thus be helpful in providing estimates of physical processes such as diabatic heating and mechanical dissipation in the real atmosphere. The determination of these forcing terms from the observed circulation is a problem of considerable interest in climate diagnostics (e.g., Sardeshmukh 1993; Nigam 1994): in some cases observationally based estimates are preferred to estimates provided by forecast models, which are subject to the uncertainties of their parameterization schemes.

Differences in mean meridional circulation are important for the diagnosis of wintertime rotational flow anomalies. The ECMWF analyses suggest that the midlatitude ū anomaly considered here is maintained against dissipation by Coriolis torque acting on the associated ῡ anomaly. In the GEOS-DAS data, the mechanisms that maintain the ū anomaly are not clear, although transients and IAU forcing appear to make some contribution. The anomalous ῡ also has an influence on the barotropic simulation of the eddy streamfunction anomalies. Moreover, most of the eddy streamfunction features, which are sensitive to ῡ in our model, appear in a composite eddy streamfunction field produced by regression against a zonal index given by ū (35°N) − ū (55°N). In ECMWF analyses, ῡ, too, shows substantial anomalies covariant with the zonal index, including the midlatitude anomaly discussed above. This statistical evidence thus supports the idea that the dynamical relationship between the anomalies of ῡ and the eddy rotational flow found in our case study is typical of zonal index variations.

Our demonstration of the pitfalls of assimilating the divergent circulation through direct forcing strictly applies only to steady zonally symmetric flow on an f-plane. However, there are reasons to believe that the same difficulties arise in a more general context. Figure 10 shows the extent of assimilation of the El Niño-related tropical divergence anomaly in the GEOS-DAS dataset. The top panel shows that the divergence anomalies in the GEOS analyses are stronger than their first-guess counterparts: comparison of Fig. 10a and 10c shows that the analyzed equatorial divergence anomaly is about 20% stronger, while the accompanying subtropical subsidence is stronger by as much as 50%. Despite the strong IAU forcing implied by these divergence differences, Fig. 10b indicates that the assimilated divergence differs little from the first-guess field.

The stated goal of the GEOS-DAS project is to provide a dataset for use in climate diagnostics. For this purpose an accurate representation of the mean meridional circulation, constrained by the available observations, is as important as the representation of the large-scale primary circulation features, which may already be well represented by existing datasets. Thus we believe that the development and refinement of a PV-based assimilation scheme such as the one proposed above should be a priority in future assimilation system development.

Acknowledgments

This work was supported by DOE/OER/CHAMMP Grant DEFG02-95ER 62022 to Professor Ferdinand Baer and NSF Grant ATM9316278 and NOAA Grant NA46GP0194 to Sumant Nigam, both at the University of Maryland.

The authors would like to thank Ferdinand Baer and Ming Cai for helpful discussions.

REFERENCES

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  • Branstator, G., 1984: The relationship between zonal mean flow and quasi-stationary waves in the midtroposphere. J. Atmos. Sci.,41, 2163–2178.

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  • DeWeaver, E., and S. Nigam, 1995: Influence of mountain ranges on the mid-latitude atmospheric response to El Niño events. Nature,378, 706–708.

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  • ——, C.-K. Park, C.-Y. Wu, W. Higgins, Y. Kondratyeva, A. Molod, L. L. Takacs, M. Seablom, and R. Rood, 1995: A multiyear assimilation with the GEOS-1 system: Overview and results. NASA Tech. Memo. 104606, Vol. 6, 183 pp. [Available from Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Takacs, L. L., A. Molod, and T. Wang, 1994: Documentation of the Goddard Earth Observing System (GEOS) General Circulation Model—Version 1. NASA Tech. Memo. No 104606, Vol. 1, 100 pp. [Available from Goddard Space Flight Center, Greenbelt, MD 20771.].

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APPENDIX

Analytical Solution of (6)–(10) for General Fu and FT

Since the IAU forcing to Eq. (11) is steady, and the perturbation equations are integrated from a state of rest, we can integrate (11) to get
i1520-0469-54-13-1758-ea1
where FPV is given by (15). We can then take ∂/∂y(7) and substitute from (8) and (10) to obtain
i1520-0469-54-13-1758-ea2
The forcing term in (A2) vanishes since FT is steady; substituting for ∂u/∂y from (A1) then yields
i1520-0469-54-13-1758-ea3
The solution to (A3) consists of a free component, ϕ0, which satisfies ((A3) with no forcing, and a forced component, ϕ1 = *(y, z), where ϕ* satisfies
i1520-0469-54-13-1758-ea4

To determine the variables u1, υ1, and w1 corresponding to the forced solution ϕ1, we use the hydrostatic equation to find T1 = tT*(y, z), which is the applied in the thermodynamic equation to obtain w1: w1 = (R/N2H)[FTT*]. This equation shows that w1 is steady; the continuity equation then implies that υ1 is also steady, which from (7) also implies that u1 is in geostrophic balance with ϕ1. Equations (6) and (8) can then be combined using the thermal wind relationship to show that υ1 and w1 are the steady forced solution to (12).

To determine the initial conditions for the free components w0 and υ0 corresponding to ϕ0, we note that since the system is integrated from a state of rest, we must have υ0 (t = 0) = −υ1, w0 (t = 0) = −w1. Since ϕ0 is the solution to the unforced system, the initial condition for w0 can be substituted in (8) to find an initial condition for ∂ϕ0/∂t:
i1520-0469-54-13-1758-eq4

Fig. 1.
Fig. 1.

Schematic of the IAU scheme employed in the GEOS assimilation system. The short upper arrows indicate the forecasts that produce a first guess at the analysis times. Once the analysis is performed, the AGCM is restarted three hours prior to the analysis time and run for 6 h forced by the constant IAU forcing functions defined in the text (from Pfaendtner et al. 1995).

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 2.
Fig. 2.

Zonal-mean meridional wind (ῡ) for northern winter (DJF) determined from GEOS-DAS and ECMWF data. Five-year climatology (1990–95) of the GEOS assimilation (a) and ECMWF uninitialized analyses (b), taken from Schubert et al. (1995). Contour interval is 0.5 m s−1, and negative values are shaded. Top level is 30 mb. (c) 200-mb ῡ climatology for the winters 1987/88 and 1988/89 as depicted by the ECMWF analyses (filled squares), the GEOS analysis (open squares), and first guess (open circles) fields used to produce the assimilation, and the assimilation itself (filled circles).

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 3.
Fig. 3.

Schematic illustration of the response of the f-plane model to steady forcing in the zonal-mean meridional momentum equation (Fυ). As discussed in section 4b, Fυ is a proxy for the forcing used by the GEOS-DAS IAU procedure to assimilate ῡ. (a) Idealized profile of Fυ that would occur if the first guess ῡ were weaker that the analyzed ῡ at 200 mb in the Tropics and subtropics. The forcing in (a) gives rise to zonal-mean perturbations in geopotential height ϕ (b) and zonal wind u (c). The pressure gradient force FPG associated with ϕ and Coriolis force FCO associated with u are both in opposition to Fυ, as shown by the arrows, and these forces prevent Fυ from accelerating ῡ.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 4.
Fig. 4.

Response of the idealized zonal-mean assimilation system to mechanical and thermal IAU forcing. Each panel shows the external IAU forcing and the Coriolis force FCO induced by it, together with the response in u, ϕ, and χ, depicted by the arrowhead (⊚), dotted curve, and solid oriented contour, respectively. In (a), a positive IAU forcing Fu is applied to the zonal-mean zonal momentum equation, resulting in an acceleration of the upper-level jet. The Coriolis force FCO associated with this jet enhancement drives a thermally indirect circulation, depicted by the oriented streamfunction contour, that brings the height field ϕ into geostrophic balance with u (although FCO and Fu are shown above and below u, these forces are collocated with u in both panels). In (b), a positive IAU forcing FT is applied to the thermodynamic equation, resulting in a height perturbation ϕ. The pressure gradient force associated with ϕ drives a thermally direct circulation, and FCO acts on this circulation to produce a perturbation jet u. While Fu and FT produce the same u and ϕ, they generate opposite meridional–vertical circulations.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 5.
Fig. 5.

Example of proposed IAU forcing functions, using the schematic conventions of Fig. 4. In this case, the model first guess and analysis have the same thermally balanced zonal-mean temperature and zonal wind fields, so that the PV increment to be assimilated is zero. However, the steady meridional–vertical circulation is weaker in the model than in the analysis, so that δχ̄ > 0. The proposed scheme generates a positive (negative) FT to the south (north) to enhance χ, together with a negative Fu, which counteracts the acceleration of u caused by the Coriolis force acting on the meridional–vertical circulation.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 6.
Fig. 6.

The 200-mb zonal-mean zonal and meridional wind (ū and ῡ) anomalies from ECMWF analyses and GEOS assimilation: (a) ū anomaly from ECMWF uninitialized analyses (open circles) and GEOS assimilation (filled circles), (b) ῡ anomaly from ECMWF analyses (open circles) and GEOS assimilation (filled circles), and (c) midlatitude (20–40°N) ῡ anomaly from GEOS assimilation (line). GEOS analyses (open circles), and GEOS first guess (filled circles).

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 7.
Fig. 7.

Barotropic diagnosis of 200-mb zonal-mean zonal wind anomalies (ūa) of Fig. 6a from ECMWF analyses and GEOS assimilation. (a) Barotropic anomaly model (section 5a) response with basic state and forcing terms taken from the GEOS assimilation. The panel shows the assimilated ūa at R15 resolution (solid line); the ūa simulation produced by forcing the model with the anomalies in divergent wind, vorticity transients, and IAU vorticity forcing (open circles); the model response to forcing by the assimilated zonal-mean divergent wind anomaly (ῡa) shown in Fig. 6b (filled circles); and the response to IAU vorticity forcing alone (crosses). (b) Response of the model with basic state and forcing terms taken from ECMWF analyses. The panel shows the analyzed ūa at R15 resolution (solid line), the ūa simulation produced by forcing the model with the anomalies in divergent wind and vorticity transients (open circles), and the response to forcing by the ECMWF-analyzed ῡa depicted in Fig. 6b (filled circles). (c) Response to forcing by vorticity transients alone, with transients and basic state taken from the ECMWF analyses (open circles) and the GEOS assimilation (filled circles). The solid line shows the GEOS-assimilated ūa at R15 resolution.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 8.
Fig. 8.

Barotropic diagnosis of 200-mb eddy streamfunction anomalies between the winters (DJF) of 1987/88 and 1988/89 from ECMWF analyses and the GEOS assimilation. The top panels show the eddy streamfunction anomalies taken from GEOS (a) and ECMWF (b) data, while the middle panels show the corresponding simulations produced using basic state and forcing terms from the GEOS assimilation (c) and ECMWF analyses (d). Both simulations are forced by anomalies in divergence and vorticity transients, and the GEOS simulation includes additional IAU vorticity forcing. Bottom panels show the model response when the ῡ anomalies are exchanged in the forcing terms used to produce the simulations in the middle panels; for example, (e) is the response using GEOS data except for ῡa, which is taken from ECMWF. Contour interval is 3 × 106 m2 s−1, and values greater (less) than ±6 × 106 m2 s−1 are heavily (lightly) shaded. Zero contours are suppressed.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 9.
Fig. 9.

Anomalies of ū, ῡ, and 200-mb eddy streamfunction covariant with the zonal index. The top panel shows the 200-mb eddy streamfunction with a contour interval of 1 × 106 m2 s−1, dark (light) shading for values greater (less) than ±2 × 106 m2 s−1, and zero contour suppressed. The middle panel shows the ῡ anomaly contoured at 3 cm s−1, and dark (light) shading for values in excess of 3 cm s−1, while the bottom panel shows ū contoured at 0.5 m s−1 with dark (light) shading for values in excess of 0.5 m s−1. Zero contours are shown in (b) and (c).

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Fig. 10.
Fig. 10.

Differences between El Niño-related divergence anomalies (DJF 1987/88 − DJF 1988/89) taken from the GEOS analysis, first guess, and assimilation datasets at R15 resolution. (a) Difference between divergence anomalies taken from the GEOS analysis and first guess datasets. (b) Difference between divergence anomalies taken from the GEOS assimilation and first guess datasets. (c) Divergence anomaly from the GEOS assimilation. In (a) and (b), contour interval is 2 × 10−7 s−1, with dark (light) shading for positive (negative) values in excess of 2 × 10−7 s−1. In (c), contour interval is 6 × 10−7 s−1, with dark (light) shading for positive (negative) values in excess of 6 × 10−7 s−1. Zero contours are suppressed in all panels.

Citation: Journal of the Atmospheric Sciences 54, 13; 10.1175/1520-0469(1997)054<1758:DOZMFA>2.0.CO;2

Save
  • Bloom, S. C., L. L. Takacs, and E. Brin, 1991: A scheme to incorporate analysis increments gradually in the GLA assimilation system. Preprints, Ninth Conf. on Numerical Weather Prediction, Denver, CO, Amer. Meteor. Soc., 110–112.

  • ——, ——, A. M. DaSilva, and D. Ledvina, 1996: Data assimilation using incremental analysis updates. Mon. Wea. Rev.,124, 1256–1271.

  • Branstator, G., 1984: The relationship between zonal mean flow and quasi-stationary waves in the midtroposphere. J. Atmos. Sci.,41, 2163–2178.

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Davies, H., and R. Turner, 1977: Updating prediction models by dynamic relaxation: An examination of the technique. Quart. J. Roy. Meteor. Soc.,103, 225–245.

  • DeWeaver, E., and S. Nigam, 1995: Influence of mountain ranges on the mid-latitude atmospheric response to El Niño events. Nature,378, 706–708.

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  • Fig. 1.

    Schematic of the IAU scheme employed in the GEOS assimilation system. The short upper arrows indicate the forecasts that produce a first guess at the analysis times. Once the analysis is performed, the AGCM is restarted three hours prior to the analysis time and run for 6 h forced by the constant IAU forcing functions defined in the text (from Pfaendtner et al. 1995).

  • Fig. 2.

    Zonal-mean meridional wind (ῡ) for northern winter (DJF) determined from GEOS-DAS and ECMWF data. Five-year climatology (1990–95) of the GEOS assimilation (a) and ECMWF uninitialized analyses (b), taken from Schubert et al. (1995). Contour interval is 0.5 m s−1, and negative values are shaded. Top level is 30 mb. (c) 200-mb ῡ climatology for the winters 1987/88 and 1988/89 as depicted by the ECMWF analyses (filled squares), the GEOS analysis (open squares), and first guess (open circles) fields used to produce the assimilation, and the assimilation itself (filled circles).

  • Fig. 3.

    Schematic illustration of the response of the f-plane model to steady forcing in the zonal-mean meridional momentum equation (Fυ). As discussed in section 4b, Fυ is a proxy for the forcing used by the GEOS-DAS IAU procedure to assimilate ῡ. (a) Idealized profile of Fυ that would occur if the first guess ῡ were weaker that the analyzed ῡ at 200 mb in the Tropics and subtropics. The forcing in (a) gives rise to zonal-mean perturbations in geopotential height ϕ (b) and zonal wind u (c). The pressure gradient force FPG associated with ϕ and Coriolis force FCO associated with u are both in opposition to Fυ, as shown by the arrows, and these forces prevent Fυ from accelerating ῡ.

  • Fig. 4.

    Response of the idealized zonal-mean assimilation system to mechanical and thermal IAU forcing. Each panel shows the external IAU forcing and the Coriolis force FCO induced by it, together with the response in u, ϕ, and χ, depicted by the arrowhead (⊚), dotted curve, and solid oriented contour, respectively. In (a), a positive IAU forcing Fu is applied to the zonal-mean zonal momentum equation, resulting in an acceleration of the upper-level jet. The Coriolis force FCO associated with this jet enhancement drives a thermally indirect circulation, depicted by the oriented streamfunction contour, that brings the height field ϕ into geostrophic balance with u (although FCO and Fu are shown above and below u, these forces are collocated with u in both panels). In (b), a positive IAU forcing FT is applied to the thermodynamic equation, resulting in a height perturbation ϕ. The pressure gradient force associated with ϕ drives a thermally direct circulation, and FCO acts on this circulation to produce a perturbation jet u. While Fu and FT produce the same u and ϕ, they generate opposite meridional–vertical circulations.

  • Fig. 5.

    Example of proposed IAU forcing functions, using the schematic conventions of Fig. 4. In this case, the model first guess and analysis have the same thermally balanced zonal-mean temperature and zonal wind fields, so that the PV increment to be assimilated is zero. However, the steady meridional–vertical circulation is weaker in the model than in the analysis, so that δχ̄ > 0. The proposed scheme generates a positive (negative) FT to the south (north) to enhance χ, together with a negative Fu, which counteracts the acceleration of u caused by the Coriolis force acting on the meridional–vertical circulation.

  • Fig. 6.

    The 200-mb zonal-mean zonal and meridional wind (ū and ῡ) anomalies from ECMWF analyses and GEOS assimilation: (a) ū anomaly from ECMWF uninitialized analyses (open circles) and GEOS assimilation (filled circles), (b) ῡ anomaly from ECMWF analyses (open circles) and GEOS assimilation (filled circles), and (c) midlatitude (20–40°N) ῡ anomaly from GEOS assimilation (line). GEOS analyses (open circles), and GEOS first guess (filled circles).

  • Fig. 7.

    Barotropic diagnosis of 200-mb zonal-mean zonal wind anomalies (ūa) of Fig. 6a from ECMWF analyses and GEOS assimilation. (a) Barotropic anomaly model (section 5a) response with basic state and forcing terms taken from the GEOS assimilation. The panel shows the assimilated ūa at R15 resolution (solid line); the ūa simulation produced by forcing the model with the anomalies in divergent wind, vorticity transients, and IAU vorticity forcing (open circles); the model response to forcing by the assimilated zonal-mean divergent wind anomaly (ῡa) shown in Fig. 6b (filled circles); and the response to IAU vorticity forcing alone (crosses). (b) Response of the model with basic state and forcing terms taken from ECMWF analyses. The panel shows the analyzed ūa at R15 resolution (solid line), the ūa simulation produced by forcing the model with the anomalies in divergent wind and vorticity transients (open circles), and the response to forcing by the ECMWF-analyzed ῡa depicted in Fig. 6b (filled circles). (c) Response to forcing by vorticity transients alone, with transients and basic state taken from the ECMWF analyses (open circles) and the GEOS assimilation (filled circles). The solid line shows the GEOS-assimilated ūa at R15 resolution.

  • Fig. 8.

    Barotropic diagnosis of 200-mb eddy streamfunction anomalies between the winters (DJF) of 1987/88 and 1988/89 from ECMWF analyses and the GEOS assimilation. The top panels show the eddy streamfunction anomalies taken from GEOS (a) and ECMWF (b) data, while the middle panels show the corresponding simulations produced using basic state and forcing terms from the GEOS assimilation (c) and ECMWF analyses (d). Both simulations are forced by anomalies in divergence and vorticity transients, and the GEOS simulation includes additional IAU vorticity forcing. Bottom panels show the model response when the ῡ anomalies are exchanged in the forcing terms used to produce the simulations in the middle panels; for example, (e) is the response using GEOS data except for ῡa, which is taken from ECMWF. Contour interval is 3 × 106 m2 s−1, and values greater (less) than ±6 × 106 m2 s−1 are heavily (lightly) shaded. Zero contours are suppressed.

  • Fig. 9.

    Anomalies of ū, ῡ, and 200-mb eddy streamfunction covariant with the zonal index. The top panel shows the 200-mb eddy streamfunction with a contour interval of 1 × 106 m2 s−1, dark (light) shading for values greater (less) than ±2 × 106 m2 s−1, and zero contour suppressed. The middle panel shows the ῡ anomaly contoured at 3 cm s−1, and dark (light) shading for values in excess of 3 cm s−1, while the bottom panel shows ū contoured at 0.5 m s−1 with dark (light) shading for values in excess of 0.5 m s−1. Zero contours are shown in (b) and (c).

  • Fig. 10.

    Differences between El Niño-related divergence anomalies (DJF 1987/88 − DJF 1988/89) taken from the GEOS analysis, first guess, and assimilation datasets at R15 resolution. (a) Difference between divergence anomalies taken from the GEOS analysis and first guess datasets. (b) Difference between divergence anomalies taken from the GEOS assimilation and first guess datasets. (c) Divergence anomaly from the GEOS assimilation. In (a) and (b), contour interval is 2 × 10−7 s−1, with dark (light) shading for positive (negative) values in excess of 2 × 10−7 s−1. In (c), contour interval is 6 × 10−7 s−1, with dark (light) shading for positive (negative) values in excess of 6 × 10−7 s−1. Zero contours are suppressed in all panels.

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