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  • View in gallery

    Length of day (LOD) regressed onto total global atmospheric angular momentum (TAM) for November–March 1985/86 through 1991/92. Both variables have been bandpass filtered in the 30–70-day band. The abscissa is in days ranging from LOD leading AAM by 25 days (−25) to LOD lagging AAM by 25 days (+25). The ordinate is in milliseconds and represents the LOD value predicted given a one standard deviation value of TAM (=5.0 × 1024 kg m2 s−1).

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    The global relative atmospheric angular momentum (AAM) budget when regressed onto the global relative AAM tendency for leads and lags from −25 to +25 days. The ordinate values are Hadleys (1 Hadley = 1.0 × 1018 kg m2 s−2) and are valid for a one standard deviation of global relative AAM tendency (=8 Hadleys). (a) The observed global relative AAM tendency (heavy solid line), the predicted global relative AAM tendency (dashed line), and the difference (light solid line); (b) the global friction torque (light solid line), the global mountain torque (heavy solid line), and the global Coriolis torque (dashed line).

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    The observed relative AAM anomaly in zonal bands when regressed onto the global relative AAM tendency. The contour interval is 1.0 × 1023 kg m2 s−1, negative contours are dashed, and the zero contour is not shown. Positive values are stippled and negative values are hatched or cross-hatched. The anomalies are valid for a one standard deviation anomaly in global AAM tendency. The abscissa represents leads and lags from −25 to +25 days and the ordinate represents latitude ranging from 60°N to 60°S. The anomalies are spectrally truncated to T12. The global relative AAM anomaly (i.e., the meridional sum of the zonal values for each day) is shown as a curve with values labeled on the left ordinate.

  • View in gallery

    The relative AAM tendency in zonal bands when regressed onto the global relative AAM tendency. The anomalies are valid for a one standard deviation anomaly in global AAM tendency (=8.0 Hadleys). The abscissa represents leads and lags from −25 to +25 days and the ordinate represents latitude ranging from 70°N to 50°S. All fields are spectrally truncated to T12. Two fields are shown in (a): the observed AAM tendency shaded with an interval of 0.1 Hadleys (positive values are stippled and negative values are hatched), and the predicted AAM tendency contoured with an interval of 0.1 Hadleys (positive contours are solid, negative are light solid and the zero contour is not shown). In (b) the budget residual tendency (observed minus predicted) is contoured in the same manner as the predicted relative AAM tendency in (a). All quantities shown are integrals over 2.5° latitude bands centered on the relevant latitude. The shaded values in Fig. 4a along day 0 add up to the one standard deviation (8 Hadleys) of the global AAM tendency.

  • View in gallery

    The zonal relative AAM budget obtained and displayed in the same manner as in Fig. 4. Here, (a) shows the flux convergence of relative AAM (contours) and the total torque (shading). The total torque is given by the sum of the friction, mountain, and Coriolis torques. The contour interval is 0.2 Hadleys, contours start at ±0.1 Hadley, and the zero contour is not shown. Positive contours are solid and negative are dashed. The shading interval is 0.2 Hadleys and shading starts at ±0.1 Hadleys. Positive values are stippled and negative are hatched. The sum of these fields gives the contoured pattern in Fig 4a. The axes of positive and negative tendency are shown with heavy solid and dashed lines respectively. (b) The mountain torque (contours) and the friction torque (shading) separately. Contours and shading are as in (a) except the contour interval for the mountain torque is 0.1 Hadleys.

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    The zonal mean sea level pressure anomalies regressed onto the global relative AAM tendency. The contour interval is 0.1 hPa and negative contours are dashed. The arrows represent the sense of the observed vertically integrated relative AAM anomalies as derived from Fig. 3. Thus an arrow pointing right (left) denotes positive (negative) zonal AAM anomalies. The panel is obtained and displayed as in Fig. 4, except no T12 truncation is performed. The global earth AAM anomaly regressed onto the global relative AAM tendency is shown as a curve with values and units labeled on the left ordinate.

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    Time–longitude plot of OLR anomalies in the 5°N–15°S band with contour interval of 1 W m−2, no zero contour, and negative contours dashed. Values ≤−5 W m−2 are shaded and highlight the axis of the positive convection anomaly. Longitude is labeled at the bottom starting at 0° and day is labeled at the right. The zonal mean OLR (W m−2) as a function of lag is shown at the left. The anomalies were obtained in the same manner as Fig. 4.

  • View in gallery

    The zonal mean flux convergence of zonal momentum at 200 mb obtained and displayed in the same manner as Fig. 5. The contour interval is 0.2 m s−1 day−1 and positive values ≥0.1 m s−1 day−1 are shaded. The fields have been spectrally truncated to T31. (a) The total flux convergence of zonal momentum; (b) the portion of the total flux convergence due to the spatial covariance between 30–70-day filtered 200-mb vector wind perturbations and the November–March climatological 200-mb vector wind; (c) the difference [(a) minus (b)].

  • View in gallery

    The total 200-hPa zonally asymmetric streamfunction for (a) day −4, (b) day +5, and (c) day +16 obtained by regressing wind data at individual grid points onto the global AAM tendency. Wind anomalies were obtained for a 24 Hadley tendency anomaly (see text), and streamfunction anomalies were calculated from the winds. These were added to the November–March climatological streamfunction and the zonal mean was removed from the total to give the final pictures. In the figure positive streamfunction values are shaded, while negative values have dashed contours. The heavy solid contour is the 220 W m−2 OLR contour when the November–March OLR climatology is added to the OLR anomalies corresponding to a 24 Hadley global AAM tendency anomaly. The profiles on the right show the contribution to the zonal mean 200-hPa flux convergence when using regressions of 30–70-day filtered wind perturbations and computing their covariance with the November–March climatological 200-hPa wind. Only the eddy component of the flux convergence is shown. The abscissa values are in units of m s−1 day−1.

  • View in gallery

    Same as Fig. 9 except for the total surface stress vector and outgoing longwave radiation for (a) day −4 and (b) day +18. The contour corresponds to 0.1 N m−2 and the arrow scaling is shown at the lower right. Arrow lengths have been scaled by cosφ.

  • View in gallery

    Longitude–time diagrams as in Fig. 7. Both panels show sea level pressure anomalies in the 2.5°N–2.5°S band with a contour interval of 0.1 hPa and negative contours dashed. In addition, (a) has area-weighted sea level pressure anomalies in the 25°N–85°N band superimposed; positive anomalies are stippled (≥0.2 hPa light, ≥0.4 hPa heavy) and negative anomalies are hatched (≤−0.2 hPa) or cross-hatched (≤−0.4 hPa). Here, (b) has outgoing longwave radiation anomalies in the 5°N–15°S band superimposed; positive values are stippled (≥3 W m−2 light, ≥6 W m−2 heavy) and negative values are hatched (≤−2 W m−2) or cross-hatched (≤−6 W m−2).

  • View in gallery

    Sea level pressure and OLR anomalies at (a) day +6, (b) day +9, (c) day +12, and (d) day +15. The sea level pressure contour interval is 0.1 hPa and negative values are dashed. Negative OLR values (positive deep convection anomalies) have heavy stippling and positive OLR values (negative convection anomalies) have light stippling.

  • View in gallery

    Schematic height–latitude diagrams depicting various aspects of the zonal mean flow evolution during the global AAM oscillation: (a) day −10, (b) day −4, and (c) day +6. The thin lines with arrowheads show anomalous zonal mean mass circulations. The encircled dots and x’s depict westerly and easterly zonal wind anomalies respectively. A double circle signifies a maximum for the zonal wind anomaly at that time. The arrows at upper levels show the direction of anomalous momentum transports, while the encircled +’s signify a positive zonal wind tendency due to the transports. The bottom curve depicts the sea level pressure anomaly during the AAM cycle. See text for further discussion.

  • View in gallery

    Fig. B1. The zonal mean flux convergence of zonal momentum at 200 mb obtained and displayed in the same manner as Fig. 8. The contour interval is 0.2 m s−1 day−1 and positive values ≥0.1 m s−1 day−1 are shaded. The fields are shown at their full 2.5°N × 2.5°S resolution. (a) The flux convergence of zonal momentum due to the covariance between perturbation and climatological zonally asymmetric eddies; (b) the flux convergence of zonal momentum due to covariance between perturbation and climatological zonal means; and (c) the momentum transports due to covariance between perturbation and climatological zonal means; that is, the meridional derivative of (c) gives (b).

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The Dynamics of Intraseasonal Atmospheric Angular Momentum Oscillations

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  • 1 Climate Diagnostics Center, National Oceanic and Atmospheric Administration/Environmental Research Laboratory, Boulder, Colorado
  • | 2 Aeronomy Laboratory, National Oceanic and Atmospheric Administration/Environmental Research Laboratory, Boulder, Colorado
  • | 3 University of Colorado/Cooperative Institute for Research in Environmental Science, Boulder, Colorado
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Abstract

The global and zonal atmospheric angular momentum (AAM) budget is computed from seven years of National Centers for Environmental Prediction data and a composite budget of intraseasonal (30–70 day) variations during northern winter is constructed. Regressions on the global AAM tendency are used to produce maps of outgoing longwave radiation, 200-hPa wind, surface stress, and sea level pressure during the composite AAM cycle. The primary synoptic features and surface torques that contribute to the AAM changes are described.

In the global budget, the friction and mountain torques contribute about equally to the AAM tendency. The friction torque peaks in phase with subtropical surface easterly wind anomalies in both hemispheres. The mountain torque peaks when anomalies in the midlatitude Northern Hemisphere and subtropical Southern Hemisphere are weak but of the same sign.

The picture is different for the zonal mean budget, in which the meridional convergence of the northward relative angular momentum transport and the friction torque are the dominant terms. During the global AAM cycle, zonal AAM anomalies move poleward from the equator to the subtropics primarily in response to momentum transports. These transports are associated with the spatial covariance of the filtered (30–70 day) perturbations with the climatological upper-tropospheric flow. The zonally asymmetric portion of these perturbations develop when convection begins over the Indian Ocean and maximize when convection weakens over the western Pacific Ocean. The 30–70-day zonal mean friction torque results from 1) the surface winds induced by the upper-tropospheric momentum sources and sinks and 2) the direct surface wind response to warm pool convection anomalies.

The signal in relative AAM is complemented by one in “Earth” AAM associated with meridional redistributions of atmospheric mass. This meridional redistribution occurs preferentially over the Asian land mass and is linked with the 30–70-day eastward moving convective signal. It is preceded by a surface Kelvin-like wave in the equatorial Pacific atmosphere that propagates eastward from the western Pacific region to the South American topography and then moves poleward as an edge wave along the Andes. This produces a mountain torque on the Andes, which also causes the regional and global AAM to change.

Corresponding author address: Dr. Klaus M. Weickmann, Climate Diagnostics Center, NOAA/ERL, 325 Broadway, Boulder, CO 80303.

Email: kmw@cdc.noaa.gov

Abstract

The global and zonal atmospheric angular momentum (AAM) budget is computed from seven years of National Centers for Environmental Prediction data and a composite budget of intraseasonal (30–70 day) variations during northern winter is constructed. Regressions on the global AAM tendency are used to produce maps of outgoing longwave radiation, 200-hPa wind, surface stress, and sea level pressure during the composite AAM cycle. The primary synoptic features and surface torques that contribute to the AAM changes are described.

In the global budget, the friction and mountain torques contribute about equally to the AAM tendency. The friction torque peaks in phase with subtropical surface easterly wind anomalies in both hemispheres. The mountain torque peaks when anomalies in the midlatitude Northern Hemisphere and subtropical Southern Hemisphere are weak but of the same sign.

The picture is different for the zonal mean budget, in which the meridional convergence of the northward relative angular momentum transport and the friction torque are the dominant terms. During the global AAM cycle, zonal AAM anomalies move poleward from the equator to the subtropics primarily in response to momentum transports. These transports are associated with the spatial covariance of the filtered (30–70 day) perturbations with the climatological upper-tropospheric flow. The zonally asymmetric portion of these perturbations develop when convection begins over the Indian Ocean and maximize when convection weakens over the western Pacific Ocean. The 30–70-day zonal mean friction torque results from 1) the surface winds induced by the upper-tropospheric momentum sources and sinks and 2) the direct surface wind response to warm pool convection anomalies.

The signal in relative AAM is complemented by one in “Earth” AAM associated with meridional redistributions of atmospheric mass. This meridional redistribution occurs preferentially over the Asian land mass and is linked with the 30–70-day eastward moving convective signal. It is preceded by a surface Kelvin-like wave in the equatorial Pacific atmosphere that propagates eastward from the western Pacific region to the South American topography and then moves poleward as an edge wave along the Andes. This produces a mountain torque on the Andes, which also causes the regional and global AAM to change.

Corresponding author address: Dr. Klaus M. Weickmann, Climate Diagnostics Center, NOAA/ERL, 325 Broadway, Boulder, CO 80303.

Email: kmw@cdc.noaa.gov

1. Introduction

Tropical convection over the Indo–Pacific warm pool flares up approximately every 50 days, developing first over the Indian Ocean and then moving eastward to the central Pacific Ocean. This variability is part of the so-called Madden–Julian oscillation (MJO) first discovered and described by Madden and Julian (1971, 1972) Langley et al. (1981) noted a similar 50-day timescale in the earth’s length of day (LOD) and Madden (1987, 1988) suggested that Pacific Ocean friction torques associated with convective fluctuations over the Indo–Pacific warm pool were primarily responsible for the LOD and atmospheric angular momentum (AAM) changes. The link between global AAM and tropical convection was verified by Weickmann et al. (1992), who concluded that mountain torques must also contribute to the AAM changes, at least during northern winter.

In this study we focus on the exchange of angular momentum between the atmosphere and solid earth within a specific intraseasonal (30–70 day) time band and seek to balance the AAM budget knowing that the estimate of the global AAM tendency is reliable (Rosen and Salstein 1983; Rosen et al. 1990; Hide and Dickey 1991). Angular momentum exchange between the earth and atmosphere occurs through normal and tangential stresses at the interface, which are referred to as mountain and friction torques, respectively. The relative contribution of the mountain and friction torque to the total torque is dependent on the timescale (Rosen 1993). On synoptic scales the mountain torque is much larger than the friction torque (Swinbank 1985) and this dominance continues out to at least 20-day fluctuations (Madden and Speth 1995). Within the timescale of interest here, the two contribute about equally to the global torque, while in the zonal budget the friction torque is larger.

Prior to this study, the global AAM budget has been primarily examined in individual cases during northern winter. Weickmann and Sardeshmukh (1994, hereafter referred to as WS) investigated AAM fluctuations during the 1984/85 northern winter and found that the global friction torque preceded the mountain torque, and the two together contributed about equally to the AAM changes. Madden and Speth (1995) reported a similar phasing, although in their 1987–88 cases the mountain torque was much larger. Also, the mountain torque in the WS case came primarily from the Himalayas, while the Madden and Speth torque came primarily from the Rocky Mountains. These discrepancies could result from differences among individual cases and from differences in time averaging (11 day versus ∼3 day). A composite approach and a 30–70-day bandpass filter is used here to help focus on the coherent, reproducible behavior in the frequency band of interest.

Three goals of this investigation into intraseasonal AAM oscillations can be summarized as follows (see also WS):

  1. which torques dominate?

  2. where do they occur?

  3. what determines their timing and spatial distribution?

Resolving the first two issues requires accurate data, while the third involves an understanding of the atmospheric dynamics that produces the torques, including the role of angular momentum transports. A complete discussion of the various dynamical processes that can produce a global friction and mountain torque is given in WS and will not be repeated here. Instead, some dynamical issues regarding alternative views of intraseasonal AAM changes will be briefly reviewed.

The link between global AAM and tropical convection on intraseasonal timescales has already been cited; however, the fundamental causes of the tropical convective variability itself remain unresolved. Some observational features are consistent with frictional Kelvin wave–CISK (conditional instability of the second kind) (Wang 1988; Salby et al. 1994) although other ideas abound. Whatever its cause, a discrete, intraseasonal convective signal (Salby and Hendon 1994) could produce an AAM oscillation through either its zonally symmetric or asymmetric component (or both). Weickmann and Sardeshmukh (1994) argue for the latter and a dominant role for 30–70-day eddy perturbations, while Hendon (1995) argues for an important contribution from zonal mean convective forcing. We will return to this issue in the discussion section.

An alternate view of the intraseasonal AAM changes is provided by Jin and Ghil (1990), who show that a tilted-trough vacillation interacting with Northern Hemisphere topography can produce ∼40 day timescales in a simple barotropic model. Marcus et al. (1994, 1996) show that this vacillation also occurs in a more complex general circulation model even though the model has only weak tropical convective variability. A small extratropical AAM oscillation occurring at about 40 days is also observed in global AAM (Dickey et al. 1991), which in our study is likely to be obscured by the much larger, apparently tropically forced oscillation. Marcus et al. (1996) have postulated that the tilted troughs that force the extratropical intraseasonal mountain torques may also excite 30–70-day tropical convection anomalies, in which case the vacillating troughs should be evident in our results.

Weickmann and Sardeshmukh (1994) extended previous work on the atmospheric angular momentum budget by examining the zonal budget and emphasized the important role played by the transports induced by 30–70-day wind perturbations. This paper follows a similiar outline to WS except that a composite budget is described and interpreted. After presenting the data and analysis technique in sections 2 and 3, the composite global and zonal AAM budgets are detailed in sections 4 and 5, respectively. Synoptic features of the composite global AAM cycle are examined in section 6. This includes tropical convection, zonal mean momentum transport, surface stress, and atmospheric mass anomalies. The role of the November–March basic state in the zonal mean momentum transports is also illustrated. In section 7 we return to the questions posed above and present conclusions.

2. Data and computations

Our primary dataset consists of daily (average of 00 and 12 Z) National Centers for Environmental Prediction (NCEP) analyses of the vector wind on 12 pressure surfaces for the period December 1984–December 1992. A surface pressure field was derived by interpolating geopotential height to a 2.5° × 2.5° orography (Mayer 1988). Vertical integrals of the relative AAM tendency and the meridional divergence of the relative AAM transport were computed using a numerical scheme similar to that described by Williamson et al. (1987). Unlike WS, a zonal surface stress was computed using a drag coefficient (cD) of 1.5 × 10−3 over the ocean and 6.5 × 10−3 over land. The land value was obtained by linear regression as detailed in appendix A.

Daily outgoing longwave radiation (OLR) observed by the National Oceanic and Atmospheric Administration’s operational polar orbiting satellites is used to provide information on variations in deep convection within the Tropics. The OLR dataset also has 2.5° × 2.5° resolution and the daily mean is an average of day and night observations. To simplify the discussion and avoid confusion, we will use the terminology positive and negative convection anomaly when referring to negative and positive OLR anomalies, respectively.

The total specific AAM is given by the sum of relative and “Earth” components,
mmemraua
where Ω is the earth’s angular velocity, u is the zonal wind, a is the earth’s radius, and φ is latitude. The relative part mr is determined by the zonal wind and the earth part me by the distribution of atmospheric mass. Note that the global integral of me is much greater than that of mr; however, its time variation turns out to be smaller than that of mr. The vertically and zonally integrated budget equations for mr and me are (see WS)
i1520-0469-54-11-1445-e2
while the global equations become
i1520-0469-54-11-1445-e4
In Eqs. (2)–(5) vertical, zonal, and meridional integrals are indicated by the brackets { }, [ ], and 〈 〉, respectively. Thus the global integral of a quantity A is written as
i1520-0469-54-11-1445-e6
where dμ = cosϕ dϕ. The symbols in (2)–(6): V = υ cosφ where υ is the meridional wind, f is the Coriolis parameter 2Ω sinφ = 2Ωμ, Φs is surface geopotential, ps is surface pressure, and τs is zonal surface stress. In the following, we will also use the symbols τC, τM, and τF, respectively, when referring to the three global quantities on the right-hand side of (4).

Integrals were computed within 2.5° latitude strips by multiplying the terms in (2) and (3) by a cosφΔφ. This allows both the zonal and global integrals to be described in units of Hadleys (1 Hadley = 1.0 × 1018 kg m2 s−2). Anomalies for all terms and variables were defined and determined as departures from the first three harmonics of the mean annual cycle.

A quantity that is difficult to estimate for the AAM budget is the Coriolis torque τC (=〈 fa[{V}]〉 in the global budget). We determine the zonal integral of the Coriolis torque indirectly as in WS by integrating the observed surface pressure tendency with latitude. Here, τC was then determined by summing the zonal integrals over all latitudes. There are a number of other sources of error that impact the budget calculations, including variations in observation density, finite difference approximation, vertical interpolation, etc. Some of these are discussed in WS.

3. Regression analysis technique

All the fields shown in this paper, with the exception of Fig. 1, are determined by regressing a specific variable against the 30–70-day filtered time series of the global relative AAM tendency (〈[{mr}]〉). The technique used is similar to that in Kiladis and Weickmann (1992) and Hendon and Salby (1994); the latter give a compact description of it in the frequency domain. The regression is carried out at each grid point and for each variable out to lags of ±25 days; this gives 51 daily maps to examine and provides valuable time resolution of the composite AAM cycle. The evolution is first described through the use of time–latitude diagrams and then by depicting certain phases from the lagged fields.

All data are filtered with a 30–70-day Lanzcos filter as in Kiladis and Weickmann (1992). The filtering operation leaves the seven November–March periods of 1985/86 through 1991/92 available for determining the regressions. For statistical significance testing, a nominal period of 50 days for an AAM oscillation would give three per winter or 21 total oscillations in the period of record. This number would also be a conservative estimate of the degrees of freedom for estimating local statistical significance so that a correlation coefficient of 2 × 1/(21)1/2 = 0.44 would represent the 95% confidence level. In the synoptic wind maps we plot a wind vector if the correlation with u or υ is >0.25, which is the 70% level.

Regressions onto the global relative AAM tendency are carried out at each grid point for both the filtered AAM budget anomalies and other selected anomaly fields. The global and zonal integrals are determined by summing the regressed components of the budget over the appropriate grid points.

4. Global AAM budget

The total global AAM (TAM) is given by the sum of the wind and pressure terms in (1) and is related to independent measurements of LOD. The regression of LOD on the TAM is shown in Fig. 1. The two time series are highly correlated (0.9 at zero lag), and for a one standard deviation anomaly in filtered TAM, LOD is predicted to change ∼0.1 millisecond. This is consistent with previous studies that related LOD and AAM changes on various timescales (Rosen and Salstein 1983). The lagged regressions indicate there is a slight lead of 2 days by LOD of TAM. However, the relatively small number of degrees of freedom available for the correlations lead to some uncertainty in the values and thus we assume that the two time series are essentially in phase [see also errors bars on phase in Rosen et al. (1990)].

The main features of the global relative AAM budget (4) are shown in Fig. 2. The observed relative AAM tendency (Fig. 2a) peaks at day 0 and reaches minima around days −21 and +22. This oscillatory behavior is partially due to the 30–70-day time filtering but it is also present in less highly filtered data (e.g., 10–150 day filtered, not shown). The predicted tendency (sum of the global Coriolis, friction, and mountain torques) is shifted in phase and has an rms error over the 51 days of 2.4 Hadleys when compared with the observed global tendency. Later we show that the main contributor to the observed minus the predicted global tendency (i.e., the budget residual) is the Southern Hemisphere subtropics.

The individual torques are shown in Fig. 2b. Consistent with the case study of WS, the friction torque (τF) peaks about 10 days before the mountain torque (τM) and together these contribute about equally to the global tendency. The friction torque is somewhat larger, although we note that the global residual in Fig. 2a is almost exactly in phase with the mountain torque. Thus one way to better balance the global budget would be to approximately double the magnitude of the mountain torque. In fact, we suspect that poor representation of the Andes mountains by the 2.5° orography used in this study may contribute to a large part of the global residual.

The other component of the global TAM tendency, the pressure term or 〈[{me }]〉t, is equivalent to minus the globally-integrated Coriolis torque [τC, see Eq. (5)]. In Fig. 2b, τC is the dashed line and is about eight times smaller than the tendency of relative AAM. The peak negative τC at day +5 means that the globally integrated flow is equatorward, which would act to decrease the relative AAM but increase the earth AAM by converging atmospheric mass into tropical regions. This implies a mass redistribution between the extratropics and the Tropics that will be examined in more detail later.

5. Zonal AAM budget

a. Relative component

In the previous section, the composite global AAM tendency anomaly was displayed and compared to the global friction and mountain torques. It will also prove useful to have a picture of the composite zonal and global AAM anomalies themselves when regressed onto the global AAM tendency. These are shown in Fig. 3 as a function of lag. The zonal AAM anomalies originate in equatorial regions and move poleward. The global AAM curve, which is shifted by one-quarter cycle compared to the heavy solid curve in Fig. 2a, peaks when the poleward moving AAM anomalies are at 10°N and 15°S. The poleward movement is a well-known feature of the AAM cycle on intraseasonal timescales (Anderson and Rosen 1983) and will be discussed further below.

The accuracy of our zonal budget calculation can be assessed in Fig. 4a where the observed relative AAM tendency is compared to the “predicted” tendency [i.e., the sum of the torques and transports on the right-hand side of (2)]; the difference as a function of lag and latitude is shown in Fig. 4b. As a reminder, the fields were obtained by regressing the relative AAM tendency, the convergence of relative AAM transport, and the torques at individual grid points onto the global relative AAM tendency time series followed by zonal integration. The largest tendencies (Fig. 4a) are confined to latitudes equatorward of 30° since the cos2φ area weighting in the integrals weakens the extratropical anomalies considerably. As in AAM itself, a clearly defined poleward movement of relative AAM tendency is evident; for example, peak positive tendencies move from equatorial regions at day −4 to the subtropics of both hemispheres by day +6. There is symmetry about the equator, although the observed tendency is larger in the Northern (winter) Hemisphere.

The tendency predicted by the right-hand side of (2) is seen to correspond well to the observed tendency, especially in the Northern Hemisphere. The largest errors (Fig. 4b) are associated with an underprediction of equatorial tendencies and their movement into the Southern Hemisphere subtropics. Since the budget is well balanced in the Northern Hemisphere, the relation between the flux convergence of relative AAM (i.e., −a−1[{mrV}]μ) and the surface torques can be examined with more confidence there.

Figure 5a shows the total torque and the AAM flux convergence from the zonal AAM budget [see Eq. (2)]. For the climatological winter-mean budget, these two terms are nearly equal and opposite giving practically a zero tendency (e.g., Lorenz 1967; Newton 1971). This is not the case for the composite intraseasonal budget shown in Fig. 5. The sum of the two terms gives the predicted tendency shown in Fig. 4a, which is as large as either of the individual terms.

The flux convergence of relative AAM (contours in Fig. 5a) displays a well-defined poleward movement similar to the AAM tendency in Fig. 4a. The total torque (shading in Fig. 5a) also shows some poleward movement although it is less well defined. The largest torques occur around 20°N and 20°S. The axes of maximum and minimum AAM tendency are displayed on Fig. 5 using heavy solid (positive) and dashed (negative) lines. In equatorial regions, the relative AAM tendency is primarily associated with the flux convergence of AAM, while in the subtropics it comes from a lag between the flux convergence and the torques. The subtropical phase relation is such that an increase of westerly momentum due to transports around 20°N leads a negative torque (i.e., westerly surface flow) by about 10 days. By contrast, farther north near 45°N, the flux convergence also leads the torque but by considerably less, more like 1–3 days. These lags represent an important observational component of the AAM oscillation and should be part of any dynamical explanation of it.

The contribution of the mountain and friction torque to the total is shown in Fig. 5b. A substantial portion of the total torque is associated with surface friction. This quantity also displays some poleward movement that appears to follow the movement of momentum flux convergence. Surprisingly, in view of previous estimates, the largest mountain torque occurs in the Southern Hemisphere in the latitude band of the Andes, with weaker contributions from the midlatitudes of the Northern Hemisphere. Referring back to Fig. 2a, one sees that τM maximizes around day +5 when both regions have the same sign while τF maximizes around day −5 when the Northern Hemisphere subtropical values are largest.

b. “Earth” component

Equation 5 shows that global changes in the earth AAM are caused by vertically and zonally integrated meridional flows that redistribute atmospheric mass across latitude circles. Figure 6 shows the zonal mean sea level pressure anomaly and the globally integrated earth AAM anomaly, both of which have been regressed onto the global relative AAM tendency. As would be expected, the sea level pressure (SLP) anomalies in equatorial regions dominate the global integral since 〈[{me}]〉 is proportional to SLP multiplied by cos3φ.

Arrows superimposed on Fig. 6 show the vertical and zonal integral of the relative AAM anomaly as determined from Fig. 3. Consistent with earlier discussion, the global relative AAM anomaly peaks when the zonal wind anomalies reach 10°N and 15°S at day +11/−11 while the global earth AAM anomaly peaks about 5–7 days later when SLP anomalies maximize near the equator. This contrasts with model results by Marcus et al. (1994) and with regressions based on observed midlatitude mountain torques (not shown). In both of these cases, the global relative AAM leads the global earth AAM by only 1–2 days. We ascribe the longer lag in our study to the fact that large zonal mean zonal wind anomalies originate in the equatorial upper troposphere while zonal mean zonal winds at the surface remain small (<0.1 m s−1, not shown). Thus the relative AAM anomalies start growing well before the earth AAM anomalies. Surface pressure anomalies do not develop until the upper-level zonal winds move off the equator and become more barotropic, leading to meridional pressure gradients that geostrophically balance the strengthening surface winds. By contrast, when zonal mean wind anomalies develop in midlatitudes (e.g., Marcus et al. 1994), geostrophic adjustment proceeds more rapidly.

An added contribution to surface pressure anomalies in equatorial regions may come from tropical convection anomalies (see section 6a below), which maximize over the western Pacific warm pool at about the time of lowest zonal mean equatorial pressure (day −4 in Fig. 6). Of course, the poleward movement of the zonal mean zonal wind and the convection anomalies over the warm pool are closely interrelated phenomena. More will be said about this later.

There are also interesting regional features associated with the mass redistribution between the extratropics and the Tropics. The change in sign of zonal mean tropical pressure anomalies at day −15 and day +6 occurs in conjunction with an equatorial Kelvin wave that rapidly propagates across the Pacific. The generation of this wave front coincides with a transition in the tropical convection anomalies; however, the persistent pressure anomalies that build in behind the wave also signal a larger-scale mass redistribution. We illustrate these features in section 6d.

6. Synoptic features during the AAM cycle

a. Tropical convection

The results from the zonal and global AAM budget raise a number of issues concerning the forcing of the AAM changes and how they relate to the torques. In this section we examine the global synoptic evolution of several key variables within the context of the zonal and global AAM budget. Since modulation of convective activity over the November–March oceanic warm pool contributes to the AAM changes, the convective signal accompanying the global AAM variations is examined first.

Figure 7 shows a time–longitude plot of the tropical OLR anomaly in the band between 5°N and 15°S obtained by regressing the outgoing longwave radiation onto the global relative AAM tendency. The familiar features of the MJO during northern winter (e.g., Knutson and Weickmann 1987; Kiladis and Weickmann 1992) are seen. Eastward propagation starts near Africa, progresses over the Indo–Pacific warm pool, and eventually extends past the date line. When compared to a Hovmöller diagram produced using an OLR average from 5°N to 15°S and 140° to 160°E as a base point for regression (e.g., Kiladis and Weickmann 1992, their Fig. 7a), the propagation in Fig. 7 is somewhat more regular and continues more strongly past the dateline giving a large anomaly center at 155°W. However, the magnitudes of the anomalies in the two figures are very similiar, suggesting that most eastward moving convective events in this time band are associated with a fluctuation in AAM. This implies that zonally asymmetric forcing of the circulation plays an important role in the AAM budget, as discussed in WS.

The zonal mean OLR anomaly is also shown in Fig. 7 as a function of lag. The largest implied zonal mean convective forcing of the circulation occurs on day −15 (strong) and day +6 (weak) when opposite phases of the anomalous convection peak over the eastern Indian Ocean (Hendon 1995). The maximum positive AAM tendency, however, occurs on day 0 after a positive convection anomaly (i.e., a negative OLR anomaly) has passed through the region of strongest base state convection, which in November–March extends over Indonesia and the oceanic warm pool from about 80° to 150°E.

b. Winds and meridional transports at 200 hPa

The AAM flux convergence shows a coherent poleward movement in Fig. 5a and in this section we examine the processes responsible for this signal. The zonal mean momentum transport at any instant may be subdivided as follows:
ūῡūυuῡuυ
where u and υ are both decomposed into a time mean and a perturbation (e.g., u = ū + u′) and the square brackets [ ] now denote a zonal mean. These calculations are performed with daily data, so these unfiltered perturbations represent all fluctuations with periods >2 days. When considering a particular frequency band (e.g., 30–70 days), (7) shows that the filtered cross-product anomaly is in general not given by the covariance between the 30–70 day filtered u and υ perturbations alone. Nonlinear interactions among different frequency bands (the [uυ′] term) as well as the spatial covariance between the base state and filtered perturbations (the linear [ūυ′] and [uῡ] terms) also contribute.

Using wind data at 200 hPa for the period December 1984–December 1994, daily momentum flux and momentum flux convergence anomalies were determined by removing the annual mean and the first three annual harmonics. This was done separately for u, υ, and the product uυ. The anomalies were then filtered and regressed onto the global relative AAM tendency just as the vertically integrated results in the previous section. The same seven winters from November–March of 1985/86 through 1991/92 were used for generating the figures shown below.

Figure 8a shows the filtered zonal mean momentum flux convergence at 200 hPa as a function of lag, which should be compared with the vertical and zonal integral of the AAM flux convergence shown as contours in Fig. 5a. Despite the fact that the 200-hPa curves are not spectrally truncated to T12, the two resemble each other closely equatorward of ∼35°. In midlatitudes the 200-mb momentum transport is not a good indicator of the vertically integrated transport since maxima differ by about 7 days between Figs. 5a and 8a. Below we will focus primarily on the tropical and subtropical transports.

Figure 8b shows the portion of the total flux convergence given by the covariance between the evolving 30–70 day perturbations and a fixed November–March basic state {i.e., the sum of the [ūυ′] and [uῡ] terms in (7)}. Clearly, a major portion of the composite flux convergence within the Tropics and subtropics is captured by these terms; the covariance of 30–70 day u and υ wind perturbations is very small (not shown). Figure 8c shows the difference between Figs. 8a and 8b and has largest values in northern middle and high latitudes. These can be produced by a variety of processes, but further calculations reveal that at 200 mb low-frequency transient eddies (>10 days) whose momentum transport has a 30–70 day component are responsible. This result does not necessarily apply to the vertically integrated transports in midlatitudes, which could still include a high-frequency eddy component.

An additional issue of interest regarding the transports in Fig. 8a is the relative contribution of zonal eddy versus zonal mean anomalies. Recall that both the perturbations and the climatology have zonal mean components; thus we are curious whether the poleward movement is mainly due to processes such as advection of zonal mean perturbations by the climatological zonal mean Hadley cell or whether interaction between the zonally asymmetric eddies themselves can produce a poleward movement. The breakdown is described in appendix B and shows approximately equal contributions to the zonal mean transport from zonal mean versus eddy processes. Interestingly, the eddies produce equatorially symmetric momentum sources and sinks that then shift poleward into both hemispheres, whereas the zonal means produce an equatorially asymmetric component that moves across the equator into the Northern Hemisphere.

We now seek to determine how the 30–70-day zonal eddies modulate the wintertime stationary waves to give the flux convergence anomalies shown in Fig. 8b. Figure 9 is a map sequence showing the 30–70-day 200-hPa eddy streamfunction added to the November–March climatological eddy streamfunction for three selected days during the composite AAM oscillation. Likewise the shading shows OLR values <220 W/m2 when 30–70 day OLR anomalies are added to the November–March mean OLR. The curves on the right depict the anomalous, zonal mean, 200-hPa eddy flux convergence derived as in Fig. 8b, but retaining only zonal waves 1–4. The days depicted (−4, +5, +16) include the time of maximum (day −4) and minimum (day +16) convection over the oceanic warm pool. During this time the curves on the right depict momentum sources moving from equatorial regions into the subtropics of both hemispheres (following the “+” symbols on right curves). For illustrative purposes the anomalies used for the maps are for a typical value of the global AAM tendency in unfiltered data (∼24 Hadleys), while those for the curves are still for a 1σ value of 30–70-day filtered global AAM tendency (∼8 Hadleys).

In all three maps the climatological eddies are still recognizable. Twin anticylones occur in the subtropical Eastern Hemisphere and twin cyclones in the subtropical Western Hemisphere. The eddies are strong in the Northern Hemisphere extratropics and weak in the Southern Hemisphere. The area of deep convection over Indonesia is much more extensive on day −4 than day +16, when it increases over South America and Africa.

We now examine the differences in the total eddy pattern and how these can account for the flux convergence anomalies shown in the curves on the right. First, comparing Fig. 9a with 9c shows a better defined and more amplified eddy pattern at the time of strong convection over Indonesia. The eddy anomaly pattern itself (not shown) consists of anomalous twin anticyclones over the Eastern Hemisphere and downstream cyclones over the Western Hemisphere at day −4 and the reverse at day +16. The anomalies in momentum transport are due to subtle variations in the tilt of the total wave pattern, particularly in the regions highlighted with heavy arrows in Fig. 9. These anomalies contribute to a strengthened “climatological” momentum sink in the subtropics when the total eddy pattern is amplified (day −4) and a weaker sink when the eddy pattern is weak (day +16). Day +5 represents a transition period when positive flux convergence anomalies move farther poleward from ∼10° to ∼15° although it is difficult to see the specific features that contribute to this movement in the Fig. 9b map.

These results indicate that as convection anomalies move through the warm pool the associated perturbations of the circulation produce a total zonally asymmetric eddy field whose evolving tilts give rise to a symmetric poleward movement of flux convergence anomalies. An equatorially asymmetric portion is introduced by the covariance of zonal mean perturbations with the zonal mean climatology. In the Northern Hemisphere midlatitudes, an eddy portion is produced by nonlinear interaction, which at 200 mb is dominated by low-frequency (>10 day) waves.

c. Surface wind stress

Previously, Fig. 5 showed that there is a different phase lag between the vertically integrated flux convergence of momentum and the surface frictional torque at different latitudes. In the subtropics positive friction torque anomalies lag negative flux convergence anomalies by about 8–10 days; at 45°N the lag is much less. If the flux convergence of momentum is represented as an oscillatory forcing and the mountain torque is assumed to be zero, such phase differences between the forcing and response (friction torque) are understandable (see appendix C). The difference depends on an effective drag coefficient (proportional to [us]/fN) that is a strong function of latitude. However, the nonzero mountain torque, as well as presumed zonal mean convective forcing, produces discrepancies from such a simple theory. Nevertheless, a large portion of the friction torque is probably being forced by the poleward moving transports that reach maxima at day −14 and day +9 in the subtropics. We will return to this topic in the discussion section.

Figure 10 shows the pattern of total surface stress for day −4 and day +18 when the friction torque anomalies in the subtropics are at their extrema. Two regions stand out with regard to the subtropical zonal stress variations, the Pacific Ocean and the Atlantic Ocean–African region. The patterns show that the subtropical frictional torque signal is nearly a zonally symmetric one and not just confined to the Pacific basin. The large wind signal in the Atlantic–African sector is opposite to what might be expected given the inferred convection anomalies in this sector; this suggests that the upper-tropospheric zonal mean transports are an important forcing for the low-level zonal and meridional wind.

The meridional component of the stress in Fig. 10 represents the lower branch of a strong (Fig. 10a) versus weak (Fig. 10b) zonal mean Hadley cell that oscillates in phase with convection anomalies over the Indo–Pacific warm pool (i.e., positive convection anomalies imply equatorward meridional surface winds). Over the Pacific Ocean, the low-level convergence anomalies are initiated by a surface pressure wave that moves eastward along the equator at ∼40 m s−1. The wave is part of a global mass redistribution that will be described next.

d. Atmospheric mass

In Fig. 6, the latitudinal contributions to the global mass redistribution accompanying the AAM cycle were described. The sign of the global anomaly was mostly determined by the tropical surface pressure anomalies, since these have the largest impact on the atmosphere’s moment of inertia. The figure showed that an exchange of mass between the Tropics and extratropics is related to the poleward shift and vertical deepening of zonal mean zonal wind anomalies.

Figure 11a shows the relation between SLP anomalies along the equator and SLP anomalies averaged over latitudes between 25° and 85°N. The Hovmöller diagram suggests that a mass exchange occurs preferentially across the Asian continent and a sequence of SLP maps confirms this inference (not shown). For example, at day 0 the shaded regions show pressure anomalies building up over extratropical Asia with maxima along 60°E and 120°E. Simultaneously, the contours show pressure increasing over the equatorial Indian and then the western Pacific Ocean before they finally shift eastward to the South America coast at roughly the speed of an equatorial Kelvin wave (40 m s−1). The bulk of this surface pressure pulse stops where it encounters the topography of the Andes at 80°W.

In Fig. 11b, the equatorial SLP anomalies are shown with OLR anomalies averaged between 5°N and 15°S superimposed. As convection anomalies develop over the warm pool, they are accompanied by dynamically consistent SLP anomalies; that is, positive convection anomalies coincide with negative pressure anomalies and vice versa. The pressure pulse itself seems to be excited as convection anomalies are changing sign over the equatorial western Pacific Ocean. However, as shown previously, these same convection anomalies also help produce momentum transports that force zonal mean zonal wind anomalies. These anomalies propagate poleward and eventually penetrate to the surface requiring a redistribution of surface pressure fields.

Figure 12 maps the evolution of the OLR and SLP anomalies for a sequence from day +6 to day +15. In this sequence a suppressed convective signal is being rapidly established northeast of New Guinea (∼150°E), although convection anomalies east of the dateline are changing only slowly. The pressure pulse appears as contours of positive pressure perturbation moving eastward across the Pacific along, and decaying away from, the equator. After encountering the Andes, the perturbation then moves poleward into both hemispheres along the west coast of the Americas, although some throughflow is evident near Panama. The horizontal structure and phase speed of this signal is characteristic of a Kelvin wave (Milliff and Madden 1996; Bantzer and Wallace 1996) that is initially trapped along the equator and then along the western topographic boundary of the Andes. The buildup and reversal of the strong pressure gradient along the Andes associated with positive and negative phases of the Kelvin wave impulses give rise to the bulk of the mountain torque along 20°S in Fig. 5b.

The buildup of mass seen behind the Kelvin wave front is partly due to geostrophic adjustment processes associated with the developing subtropical surface wind anomalies. Thus both a local transition in convection and the subtropical response to convection likely combine to produce the observed tropical surface mass evolution.

7. Discussion and conclusions

Three questions were posed in the introduction to which we can now provide some answers.

First, as found in case studies, both the friction and mountain torque contribute to the exchange of angular momentum between the atmosphere and the solid earth for the specific intraseasonal 30–70 day band considered here. The relative breakdown between the torques, however, remains uncertain since the global budget errors are still significant. The zonal budget tells us these errors are primarily in the Southern Hemisphere, and we suspect they are largely in τM since the steep slopes of the Andes Mountains may be misrepresented by the 2.5° × 2.5° orography used to estimate τM here. However, errors in the observed surface wind field in the Southern Hemisphere, and thus in τF, cannot be discounted.

Second, the regional character of the torques is fairly well determined, including their longitudinal structure and their timing within the AAM oscillation. A surprising result is the large mountain torque around the Andes that surpasses the Northern Hemisphere midlatitude mountain torques by a factor of ∼2 or more (see Fig. 5b). The torque is apparently due to the combination of a Rossby wave train arcing through the Southern Hemisphere (not shown) and mass fluctuations on the west side of the South American cordillera. The latter are initiated by the surface pressure signal of an atmospheric Kelvin wave. In the Northern Hemisphere, a complementary Rossby wave train arcs over North America, providing some mountain torque via its surface component while surface pressure fluctuations east of the Himalayas also contribute. There is little evidence that the composited mountain torque is linked with the tilted trough vacillation studied by Marcus et al. (1994, 1996). Instead, Rossby wave trains emanating from the Tropics and mass redistributions between high and low latitudes centered around topographic features appear important. We note that this view of the Northern Hemisphere mountain torque is valid for 30–70-day filtered data. The mountain torque is more prominent in less highly filtered composites, as will be shown in a future study.

The friction torque in the subtropics dominates the global torque and consists of a regional convectively driven component over the Pacific Ocean (e.g., Madden 1988) and a remote component that is especially strong over the Atlantic Ocean–African region. The friction torque is weaker in the Southern Hemisphere subtropics and appears to come primarily from Australia, the east Pacific, and South America. In general, the land friction torque contributes substantially to the total and would imply zero time lag between the total AAM and LOD variations. However, the large ocean stresses over the eastern Pacific and the Atlantic could contribute to a nonzero lag as the oceanic stress is communicated to the ocean basin boundaries (Ponte 1990).

Finally, the budgets have provided clues on the important dynamical mechanisms governing the global and zonal 30–70-day AAM cycle during northern winter. To focus this discussion, a schematic in Fig. 13 depicts the evolution of zonal mean circulation anomalies during the composite AAM cycle. The vertical structure of the anomalies in Fig. 13 is inferred from regressions of the 200-mb and surface zonal mean wind and wind divergence onto the global AAM tendency. A budget of the primary terms of the 200-mb zonal mean zonal wind was also examined.

The schematic starts at day −10 with an enhanced Hadley cell that coincides with positive convection anomalies over the entire Indo–Pacific warm pool (see Fig. 7). This is also the time of minimum 〈[{mr}]〉 as deep easterly anomalies occur in tropical/subtropical regions. This relationship between the mass circulation and zonal wind anomalies was also found by Kang and Lau (1994), who speculated that eddy transports may play an important role in the evolution of intraseasonal zonal mean flow anomalies. Day −10 is the time of maximum 200-mb momentum flux divergence at 20°, largely the result of eddy transports.

The way the enhanced Hadley cell develops can be seen by tracing the evolution from Fig. 13a to its opposite phase in Fig. 13c. At day −10 (Fig. 13a), a momentum source due to the processes described in section 6b is developing in equatorial regions. Just off the equator, the momentum source results in a shallow upper-level indirect mass circulation as the atmosphere adjusts to the source. At day −4 (Fig. 13b), the Hadley cell is still strong with maximum surface wind convergence, maximum frictional torque, and minimum 〈[{me}]〉. Largest positive convection anomalies now coincide with the region of maximum climatological convection during November–March (110–170°E). At this stage, a momentum sink due to transports still exists near 20°; however, the strong Hadley cell is no longer merely adjusting to the sink. Instead, positive zonal mean convective forcing may be important and forces a weakening of easterly wind anomalies in the upper subtropics via the Coriolis torque.

In the Tropics, the transport-induced momentum sources continue to move away from the equator, and the accompanying reverse Hadley cell in the upper troposphere intensifies and penetrates farther downward, away from the source. The vertical structure of the anomalous mass circulation at 10° latitude is now complicated with a convection- and transport-driven direct cell being replaced by a transport-induced indirect cell.

By day +6 (Fig. 13c), convection is being suppressed over the Indian Ocean and is weakening over the western Pacific Ocean. Maximum 200-mb westerly anomalies are now located over the equator with only weak pressure gradients and zonal wind anomalies at low levels. The momentum source associated with momentum fluxes is continuing poleward and its accompanying indirect mass circulation is penetrating to the surface. A Kelvin wave front is starting eastward from the western Pacific heralding a mass increase (decrease) in equatorial (midlatitude) regions.

In this model of the AAM oscillation, the movement of local convection anomalies across the Indo–Pacific warm pool is taken as a given consequence of the MJO. The convection anomalies produce asymmetric circulation anomalies that start to grow over the equatorial Indian Ocean and eventually spread throughout the globe. Within the November–March basic state, these circulation anomalies modulate the transport of momentum into and out of the subtropics and also produce a poleward movement of the zonal mean zonal wind anomaly. The zonal mean atmospheric response to the pattern of momentum transport (i.e., as function of latitude) and the direct surface wind response to the convection produce a global friction torque.

There are a number of unresolved issues in this picture of intraseasonal AAM oscillations. A complete dynamical explanation must also consider feedbacks between the surface torque and the convection and between the zonal mean flow and the asymmetric waves. The role of zonal mean convective forcing, the synoptics of the midlatitude eddy transports, and the role of mountain torques (e.g., Madden and Speth 1995) also require clarification. However, a fundamental question is to what extent the evolving eddy transports equatorward of 35° alone determine the primary features of the global AAM oscillation. This issue could be further investigated with a simple numerical model that is forced with an oscillating source, includes a zonally varying base state, and parameterizes the link between upper-level transports and the low-level flow.

The observed budget provides a contrast with similar studies of intraseasonal AAM variations using an aquaplanet general circulation model (Feldstein and Lee 1995) and a simple baroclinic model (Itoh 1994). In those studies, the simpler basic state (Feldstein and Lee 1995) and simpler specification of forcing (Itoh 1994) could mean that different physical processes than those important here are contributing to the terms in the AAM budget, particularly where the transports are concerned. Probably as a result, neither study simulates the poleward movement of AAM anomalies seen in the observations.

In conclusion, it appears that AAM transports are an important component of the MJO–AAM link and that filtered upper-tropospheric wind anomalies evolving on a zonally varying climatological flow produce the bulk of these transports. This process makes the MJO–AAM link linear and enables a sensible, nearly complete description of the oscillation using composite and linear regression techniques. By way of contrast, identifying the synoptic features that contribute to the nonlinear transports in northern midlatitudes (Fig. 8c) requires more sophisticated diagnostic analysis.

Acknowledgments

We thank Joan Hart for performing the calculations and producing the figures. Craig Anderson helped with Fig. 13. Conversations with Brian Hoskins, Michiko Masutani, and colleagues at CDC were helpful and appreciated. The useful comments of two reviewers helped focus and shorten the final manuscript.

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APPENDIX A

Estimation of Land Drag Coefficient

The results of WS were reproduced for the period 1 December 1984–6 February 1985. (Recall that WS used actual stresses derived from a one-time step prediction of a general circulation model, whereas in this paper a bulk method based on analyzed surface winds is used.) The primary discrepancy appeared in the friction torque and was largest in the latitude bands containing substantial land area (not shown). This was further investigated by comparing a subset of our global friction and mountain torque time series with a 391-day set prepared by White (1992). White used surface pressure fields from initialized sigma analyses and surface stresses from the last three hours of a six-hour National Meteorological Center (NMC, now NCEP) model forecast that was the first guess for the analyses. The effect of gravity wave drag was included in White’s surface stress but not in ours. Surprisingly, after removing the 391-day mean the mountain torques agreed almost perfectly (temporal correlation = 0.97), while the frictional torque contained more significant discrepancies (correlation = 0.83). This led us to suspect that our original calculation that assumed the same constant drag coefficient over land and ocean was too simple.

Land values for cDl were adjusted to 6.5 × 10−3, obtained by minimizing the mean square difference in the variance over the 391 days between a) the NMC global friction torque (τNMC) minus the ocean values with cDo = 1.5 × 10−3 and b) the land stress, that is,
τNMC−3PocDlPl
where Pl = Σ u(u2 + υ2)1/2 over all land points and Po = Σ u(u2 + υ2)1/2 over all ocean points. Although the global balance is slightly better with a cDl = 6.5 × 10−3, discrepancies still exist. It is obviously not possible to model the complex surface friction effects with only two numbers, one for the ocean and the other for land. The more closely balanced budget achieved for the seasonal cycle of global relative AAM when using the friction torque as computed by White supports this interpretation (not shown). Nevertheless, the small Northern Hemisphere AAM budget residuals in Fig. 4b suggest that our simple formulation is adequate for the purposes of this paper.

APPENDIX B

Flux Convergence of Momentum: Zonal Eddy versus Zonal Mean Perturbations

The breakdown of the total flux convergence (i.e., Fig. 8a) due to eddy and zonal mean perturbations is shown in Fig. B1. Both components contribute about equally to the total transport, although the eddy component (Fig. B1a) produces equatorially symmetric sources and sinks of momentum while the zonal mean component (Fig. B1b) produces asymmetric ones. The synoptic structures responsible for the eddy transports were described in the main body of the paper. The processes responsible for the zonal mean flux convergence in Fig. B1b can be inferred from Fig. B1c, which shows the transports (not the flux convergence) due to the zonal mean flow. The pertubation zonal mean zonal wind at 200 mb (not shown, but see Fig. 3), together with the climatological Hadley cell, reveals that the transport oscillation along 5°N is associated with the wintertime Hadley cell advecting the perturbation zonal mean zonal wind. Likewise, considering the mass circulation that must accompany the frictional torque shown in Fig. 5b, together with the climatological zonal mean zonal wind, reveals that the transport oscillation along 25°N is associated with a pertubation mass circulation advecting the wintertime zonal mean jet stream. At the present time we view these zonal mean transports as modifying the more fundamental momentum forcing produced by the zonal eddies.

APPENDIX C

On the Time Lag between the Flux Convergence of Momentum and the Friction of Torque

Some insight into the relative phasing of the zonal AAM budget quantities may be gained by approximating (2) for the 30–70 day filtered anomalies as
i1520-0469-54-11-1445-ec1a
where the primes refer to the filtered anomalies, the overbar refers to the November–March climatological mean values, and FT refers to the filtered AAM flux convergence anomalies. For simplicity the Coriolis and mountain torques have been neglected in (C1a). The 30–70 day friction torque has been approximated first as a linearized drag on the surface flow in (C1c) and then as a drag on the vertical and zonal mean AAM anomaly [{mr}] itself in (C1d). (This assumes that [{mr}] is in phase with [τs a cosφ].) The latter is based on the argument given in WS and amounts to assuming that us is proportional to [{mr}]f/N, where N is the Brunt–Väisälä frequency. This makes the effective drag coefficient r proportional to [ūs]f/N, a strong function of latitude. The analysis of Klinker and Sardeshmukh (1992) suggests a midlatitude value of ∼1/(5 days) for r.
If FT at any latitude is viewed as a periodic forcing of [{mr}] at that latitude, at a frequency ω0 ∼ 2π/(50 days), the solution of (Cld) is
mriθFTr2ω201/2
where θ = cos−1{r/(r2 + ω20)1/2} is the phase lag between [{mr}] and FT. According to this analysis, at latitudes where rω0, such as middle and high latitudes, there should be no phase lag between [{mr}] and FT; at latitudes where rω0, such as the Tropics, [{mr}] should lag FT by a quarter cycle, that is, about 12 days, and by a somewhat lower interval in the subtropics. These phase relationships can be seen to hold, at least approximately, in Fig. 5.

Fig. 1.
Fig. 1.

Length of day (LOD) regressed onto total global atmospheric angular momentum (TAM) for November–March 1985/86 through 1991/92. Both variables have been bandpass filtered in the 30–70-day band. The abscissa is in days ranging from LOD leading AAM by 25 days (−25) to LOD lagging AAM by 25 days (+25). The ordinate is in milliseconds and represents the LOD value predicted given a one standard deviation value of TAM (=5.0 × 1024 kg m2 s−1).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 2.
Fig. 2.

The global relative atmospheric angular momentum (AAM) budget when regressed onto the global relative AAM tendency for leads and lags from −25 to +25 days. The ordinate values are Hadleys (1 Hadley = 1.0 × 1018 kg m2 s−2) and are valid for a one standard deviation of global relative AAM tendency (=8 Hadleys). (a) The observed global relative AAM tendency (heavy solid line), the predicted global relative AAM tendency (dashed line), and the difference (light solid line); (b) the global friction torque (light solid line), the global mountain torque (heavy solid line), and the global Coriolis torque (dashed line).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 3.
Fig. 3.

The observed relative AAM anomaly in zonal bands when regressed onto the global relative AAM tendency. The contour interval is 1.0 × 1023 kg m2 s−1, negative contours are dashed, and the zero contour is not shown. Positive values are stippled and negative values are hatched or cross-hatched. The anomalies are valid for a one standard deviation anomaly in global AAM tendency. The abscissa represents leads and lags from −25 to +25 days and the ordinate represents latitude ranging from 60°N to 60°S. The anomalies are spectrally truncated to T12. The global relative AAM anomaly (i.e., the meridional sum of the zonal values for each day) is shown as a curve with values labeled on the left ordinate.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 4.
Fig. 4.

The relative AAM tendency in zonal bands when regressed onto the global relative AAM tendency. The anomalies are valid for a one standard deviation anomaly in global AAM tendency (=8.0 Hadleys). The abscissa represents leads and lags from −25 to +25 days and the ordinate represents latitude ranging from 70°N to 50°S. All fields are spectrally truncated to T12. Two fields are shown in (a): the observed AAM tendency shaded with an interval of 0.1 Hadleys (positive values are stippled and negative values are hatched), and the predicted AAM tendency contoured with an interval of 0.1 Hadleys (positive contours are solid, negative are light solid and the zero contour is not shown). In (b) the budget residual tendency (observed minus predicted) is contoured in the same manner as the predicted relative AAM tendency in (a). All quantities shown are integrals over 2.5° latitude bands centered on the relevant latitude. The shaded values in Fig. 4a along day 0 add up to the one standard deviation (8 Hadleys) of the global AAM tendency.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 5.
Fig. 5.

The zonal relative AAM budget obtained and displayed in the same manner as in Fig. 4. Here, (a) shows the flux convergence of relative AAM (contours) and the total torque (shading). The total torque is given by the sum of the friction, mountain, and Coriolis torques. The contour interval is 0.2 Hadleys, contours start at ±0.1 Hadley, and the zero contour is not shown. Positive contours are solid and negative are dashed. The shading interval is 0.2 Hadleys and shading starts at ±0.1 Hadleys. Positive values are stippled and negative are hatched. The sum of these fields gives the contoured pattern in Fig 4a. The axes of positive and negative tendency are shown with heavy solid and dashed lines respectively. (b) The mountain torque (contours) and the friction torque (shading) separately. Contours and shading are as in (a) except the contour interval for the mountain torque is 0.1 Hadleys.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 6.
Fig. 6.

The zonal mean sea level pressure anomalies regressed onto the global relative AAM tendency. The contour interval is 0.1 hPa and negative contours are dashed. The arrows represent the sense of the observed vertically integrated relative AAM anomalies as derived from Fig. 3. Thus an arrow pointing right (left) denotes positive (negative) zonal AAM anomalies. The panel is obtained and displayed as in Fig. 4, except no T12 truncation is performed. The global earth AAM anomaly regressed onto the global relative AAM tendency is shown as a curve with values and units labeled on the left ordinate.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 7.
Fig. 7.

Time–longitude plot of OLR anomalies in the 5°N–15°S band with contour interval of 1 W m−2, no zero contour, and negative contours dashed. Values ≤−5 W m−2 are shaded and highlight the axis of the positive convection anomaly. Longitude is labeled at the bottom starting at 0° and day is labeled at the right. The zonal mean OLR (W m−2) as a function of lag is shown at the left. The anomalies were obtained in the same manner as Fig. 4.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 8.
Fig. 8.

The zonal mean flux convergence of zonal momentum at 200 mb obtained and displayed in the same manner as Fig. 5. The contour interval is 0.2 m s−1 day−1 and positive values ≥0.1 m s−1 day−1 are shaded. The fields have been spectrally truncated to T31. (a) The total flux convergence of zonal momentum; (b) the portion of the total flux convergence due to the spatial covariance between 30–70-day filtered 200-mb vector wind perturbations and the November–March climatological 200-mb vector wind; (c) the difference [(a) minus (b)].

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 9.
Fig. 9.

The total 200-hPa zonally asymmetric streamfunction for (a) day −4, (b) day +5, and (c) day +16 obtained by regressing wind data at individual grid points onto the global AAM tendency. Wind anomalies were obtained for a 24 Hadley tendency anomaly (see text), and streamfunction anomalies were calculated from the winds. These were added to the November–March climatological streamfunction and the zonal mean was removed from the total to give the final pictures. In the figure positive streamfunction values are shaded, while negative values have dashed contours. The heavy solid contour is the 220 W m−2 OLR contour when the November–March OLR climatology is added to the OLR anomalies corresponding to a 24 Hadley global AAM tendency anomaly. The profiles on the right show the contribution to the zonal mean 200-hPa flux convergence when using regressions of 30–70-day filtered wind perturbations and computing their covariance with the November–March climatological 200-hPa wind. Only the eddy component of the flux convergence is shown. The abscissa values are in units of m s−1 day−1.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 10.
Fig. 10.

Same as Fig. 9 except for the total surface stress vector and outgoing longwave radiation for (a) day −4 and (b) day +18. The contour corresponds to 0.1 N m−2 and the arrow scaling is shown at the lower right. Arrow lengths have been scaled by cosφ.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 11.
Fig. 11.

Longitude–time diagrams as in Fig. 7. Both panels show sea level pressure anomalies in the 2.5°N–2.5°S band with a contour interval of 0.1 hPa and negative contours dashed. In addition, (a) has area-weighted sea level pressure anomalies in the 25°N–85°N band superimposed; positive anomalies are stippled (≥0.2 hPa light, ≥0.4 hPa heavy) and negative anomalies are hatched (≤−0.2 hPa) or cross-hatched (≤−0.4 hPa). Here, (b) has outgoing longwave radiation anomalies in the 5°N–15°S band superimposed; positive values are stippled (≥3 W m−2 light, ≥6 W m−2 heavy) and negative values are hatched (≤−2 W m−2) or cross-hatched (≤−6 W m−2).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 12.
Fig. 12.

Sea level pressure and OLR anomalies at (a) day +6, (b) day +9, (c) day +12, and (d) day +15. The sea level pressure contour interval is 0.1 hPa and negative values are dashed. Negative OLR values (positive deep convection anomalies) have heavy stippling and positive OLR values (negative convection anomalies) have light stippling.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

Fig. 13.
Fig. 13.

Schematic height–latitude diagrams depicting various aspects of the zonal mean flow evolution during the global AAM oscillation: (a) day −10, (b) day −4, and (c) day +6. The thin lines with arrowheads show anomalous zonal mean mass circulations. The encircled dots and x’s depict westerly and easterly zonal wind anomalies respectively. A double circle signifies a maximum for the zonal wind anomaly at that time. The arrows at upper levels show the direction of anomalous momentum transports, while the encircled +’s signify a positive zonal wind tendency due to the transports. The bottom curve depicts the sea level pressure anomaly during the AAM cycle. See text for further discussion.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

i1520-0469-54-11-1445-f14

Fig. B1. The zonal mean flux convergence of zonal momentum at 200 mb obtained and displayed in the same manner as Fig. 8. The contour interval is 0.2 m s−1 day−1 and positive values ≥0.1 m s−1 day−1 are shaded. The fields are shown at their full 2.5°N × 2.5°S resolution. (a) The flux convergence of zonal momentum due to the covariance between perturbation and climatological zonally asymmetric eddies; (b) the flux convergence of zonal momentum due to covariance between perturbation and climatological zonal means; and (c) the momentum transports due to covariance between perturbation and climatological zonal means; that is, the meridional derivative of (c) gives (b).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2

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