Abstract

The global mountain (τM ) and frictional (τF ) torques are lag correlated within the intraseasonal band, with τF leading τM. The correlation accounts for 20%–45% of their variance. Two basic feedbacks contribute to the relationship. First, the mountain torque forces global atmospheric angular momentum (AAM) anomalies and the frictional torque damps them; thus, F/dt ∝ −τM. Second, frictional torque anomalies are associated with high-latitude sea level pressure (SLP) anomalies, which contribute to subsequent mountain torque anomalies; thus, M/dtτF. These feedbacks help determine the growth and decay of global AAM anomalies on intraseasonal timescales.

The low-frequency intraseasonal aspect of the relationship is studied for northern winter through lag regressions on τF. The linear Madden–Julian oscillation signal is first removed from τF to focus the analysis on midlatitude dynamical processes. The decorrelation timescale of τF is similar to that of teleconnection patterns and zonal index cycles, and these familiar circulation features play a prominent role in the regressed circulation anomalies.

The results show that an episode of interaction between the torques is initiated by an amplified transport of zonal mean–zonal momentum across 35°N. This drives a dipole pattern of zonal mean–zonal wind anomalies near 25° and 50°N, and associated SLP anomalies. The SLP anomalies at higher latitudes play an important role in the subsequent evolution. Regionally, the momentum transport is linked with large-scale eddies over the east Pacific and Atlantic Oceans that have an equivalent barotropic vertical structure. As these eddies persist/amplify, baroclinic wave trains disperse downstream over North American and east Asian topography. The wave trains interact with the preexisting, high-latitude SLP anomalies and drive them southward, east of the mountains. This initiates a large monopole mountain torque anomaly in the 20°–50°N latitude band. The wave trains associated with the mountain torque produce additional momentum flux convergence anomalies that 1) maintain the zonal wind anomalies forced by the original momentum transport anomalies and 2) help drive a global frictional torque anomaly that counteracts the mountain torque. Global AAM anomalies grow and decay over a 2-week period, on average.

Over the Pacific–North American region, the wave trains evolve into the Pacific–North American (PNA) pattern whose surface wind anomalies produce a large portion of the compensating frictional torque anomaly. Case studies from two recent northern winters illustrate the interaction.

1. Introduction

During northern winter, global mountain torque (τM ) anomalies are produced by synoptic-scale wave trains that disperse energy across Asian and North American topography (Iskendarian and Salstein 1998; Weickmann et al. 2000, hereafter WRP). The wave trains tap preexisting, high-latitude sea level pressure (SLP) anomalies and drive them southward, east of the mountains, as the wave trains' centers amplify aloft. On average, these events are short-lived and typically produce modest but detectable global atmospheric angular momentum (AAM) anomalies. Both relative and earth AAM contribute to the total AAM anomaly.

The mountain torque anomaly is associated with an anomalous upper-level momentum transport into adjacent latitude bands. More angular momentum is transported into the 20°–30°N band, where the local relative AAM anomaly appears. The anomaly rapidly becomes equivalent barotropic and leads to a global frictional torque that damps the local and global AAM anomalies. An anomalous mass redistribution also accompanies the mountain torque and acts to geostrophically balance the surface zonal wind anomalies that develop in the 20°–30°N band. Midlatitude eddies provide the physical link between the mountain and frictional torque.

No such simple picture yet exists for the global frictional torque (τF ). Previous investigations of this torque have concentrated on the component linked with the quasi-oscillatory Madden–Julian oscillation (MJO). Yet, this accounts for only a small portion of the total variance of the torque. The purpose of this investigation is to present the characteristic global, zonal, and regional anomalies associated with global frictional torque anomalies and to develop a composite picture of the torque in the manner described above for the mountain torque.

Previous investigations of the relationship between global AAM and its torques by WRP and by Egger and Hoinka (2002, hereafter EH) allow us to anticipate some of the results:

  1. The global frictional torque has a 6-day decorrelation timescale, suggesting that it is linked with teleconnection patterns and zonal index variations, which have similar decorrelation timescales. Removal of the linear MJO signal does not alter the decorrelation timescale of τF.

  2. In the intraseasonal band 20%–45% of the variance of the friction and mountain torque is lag correlated. The torques are in quadrature and the friction torque leads the mountain torque. Thus, regressions on either torque will find a lag relationship with the other.

  3. Approximately 25% of the frictional torque's anomalous variance acts to damp global AAM anomalies. This means that friction torque anomalies tend to be out of phase with AAM anomalies. (EH show that this cannot occur on average on an aquaplanet.) By contrast, mountain torque anomalies provide the primary forcing of global AAM in the intraseasonal band; that is, they lead global AAM anomalies.

Additional insight on points 2 and 3 is provided by a simple Markov model used by WRH and EH to model the relationship between global AAM and the torques. In the model, a portion of the frictional torque is assumed to damp AAM anomalies while the remainder of the frictional torque and all of the mountain torque forces AAM stochastically. The model captures a portion of the feedback between the torques and confirms that it exists, on average, because of damping by the frictional torque. A typical sequence for generation and decay of a positive total global AAM (MTOT) anomaly is as follows: (τM > 0) ⇒ (dMTOT/dt > 0 and F/dt < 0) ⇒ (MTOT > 0 and τF < 0) ⇒ (dMTOT/dt < 0) ⇒ (MTOT ∼ 0). The strength of the relationship between the torques is determined by the damping timescale of τF on MTOT; that is, F/dtατM, where α = −1/30 days [see Eq. (4.2) in EH]. With the 30-day damping timescale used in the model (obtained through linear regression), the relation accounts for 5%–20% of the torques' variance compared with 20%–45% for the observations.

Apparently, an additional feedback occurs in the observations, namely, M/dtτF. There are two possibilities. First, a positive τF implies net easterly surface wind stress anomalies over the globe. If these winds occur over the mountains, the associated surface pressure anomalies would produce positive mountain torque anomalies. For example, in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis, there is a correlation of −0.79 between the North American mountain torque and the zonal wind anomaly averaged over elevations above 500 m. Second, a positive τF also implies something about the distribution of SLP anomalies. In the right location, they could lead to a positive mountain torque anomaly. Figure 6d of WRP shows a positive frictional torque anomaly prior to day 0, primarily due to easterly zonal wind anomalies at 50°N. These are accompanied by positive SLP anomalies over the polar cap that, when “tapped” by a passing synoptic-scale wave train, result in a positive mountain torque anomaly. A feedback due to the SLP anomalies appears to be more likely than one due directly to the wind anomalies. Since surface zonal wind anomalies tend to be out of phase with mountain torque anomalies, the latter would give τMτF, not M/dtτF.

To summarize, the combination of these two feedbacks, one due to τF's damping component and the other to the torques' stochastic component, should result in a prominent τM < 0 → τF > 0 → τM > 0 sequence (or vice versa) when regressing onto the global frictional torque.

As in WRP, the primary analysis will use regressions of global and zonal integrals of the vertically integrated total angular momentum budget onto the frictional torque as a function of lag. The explicit dynamics in this reduced system are the vertical and zonal mean momentum and mass transport. In general, zonal mean mass and momentum are continually redistributed within the atmosphere, particularly during zonal index variations. We will show that global frictional torque events comprise a subset of zonal index variations during which an additional momentum source/sink due to the mountain torque becomes involved. Regionally, the development of the Pacific–North American (PNA) teleconnection pattern (Wallace and Gutzler 1981) plays a prominent role in the link between the mountain and frictional torque.

In the next section, the time evolution of global AAM and its torques are contrasted by regressing onto various indices of global AAM tendency, including the frictional torque. Evidence for a link with zonal index variations is presented. Section 3 reviews the evolution of circulation anomalies associated with mountain torques over Asian and North American topography. These appear in modified form later, in lag regressions with the global frictional torque. Section 4 illustrates the vertically and zonally integrated variations associated with the stochastic frictional torque and further develops the role of zonal index variations and momentum transports. The synoptic evolution that accompanies the frictional torque during northern winter is also presented in section 4. The primary centers of action are in the extratropics and regionally involve the PNA teleconnection pattern. Section 5 contains case studies of two frictional torque events, one during the 1997/98 and the other during the 2000/01 northern winter. Discussion and conclusions are presented in section 6.

2. Global intraseasonal atmospheric angular momentum variations

Atmospheric angular momentum is defined by

 
m = me + mr = (Ωa cosϕ + u)a cosϕ,
(1)

where me and mr are earth and relative AAM, respectively. The conservation equations governing local and global AAM are derived in Weickmann and Sardeshmukh (1994). For global AAM,

 
formula

For vertically and zonally integrated AAM,

 
formula

Vertical and zonal integrals are indicated by the brackets { } and [ ], respectively. Thus, the vertical and zonal integral of a quantity A is written as

 
formula

The symbols in (2)–(7) have their usual meanings: 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 not consider the gravity wave drag torque τG since, as presently formulated, it has a negative impact on the AAM budget (Huang et al. 1999). The symbols τM, τF, and τC refer to the global integral of the mountain, friction, and coriolis torques, while MTOT, MR, and ME refer to the global integrals of m, mr, and me. Calculations are based on the NCEP–NCAR reanalysis data (Kalnay et. al. 1996). A 192 × 94 Gaussian grid is used to compute global and zonal integrals, and a 144 × 72 equally spaced grid is used to plot synoptic maps.

Figure 1 summarizes the lag relationship among MTOT, τF, τM, and [{m}] for various global indices. The results are for 16 (1979–95) northern winter seasons (November–March), and similar relations are found when using a different set of 16 winters (1962–78; not shown). The figure is obtained by using lagged linear regression onto an index of (a) the daily global MR tendency, (b) the daily MR tendency but filtered for 30–70 days, (c) the daily MR tendency but filtered for <30 days, (d) the daily global mountain torque, and (e) the daily global frictional torque. All these indices are time tendencies, and thus the MTOT curve is always increasing around day 0.

Fig. 1.

The MTOT (solid curve), τM (long dashed curve), τF (short dashed curve), and [{m}] (contours) anomalies, obtained by lag regressions onto various indices using 16 northern winter (Nov–Mar) seasons. The indices used are (a) the daily MR tendency, (b) the daily MR tendency filtered to retain 30–70-day periods, (c) the daily MR tendency filtered to retain <30 day periods, (d) the daily τM, and (e) the daily τF. The anomalies are for a one standard deviation value of an index. The left ordinate labels are torque units in Hadleys (1 Hadley = 1.0 × 1018 kg m2 s−2), and the right labels are AAM units (1 unit = 1.0 × 1024 kg m2 s−1). For the contours, the right labels also represent latitude/10, i.e., 6 = 60°N, etc. The contour and shading interval is 0.1 × 1024 kg m2 s−1 (the value corresponds to a vertical and zonal mean zonal wind anomaly of 0.3 m s−1 at 30°N). The contours start at 0.05 × 1024 kg m2 s−1 in (c) and (d). The abscissa is lag where negative (positive) values mean that the regressed quantity leads (lags) the index

Fig. 1.

The MTOT (solid curve), τM (long dashed curve), τF (short dashed curve), and [{m}] (contours) anomalies, obtained by lag regressions onto various indices using 16 northern winter (Nov–Mar) seasons. The indices used are (a) the daily MR tendency, (b) the daily MR tendency filtered to retain 30–70-day periods, (c) the daily MR tendency filtered to retain <30 day periods, (d) the daily τM, and (e) the daily τF. The anomalies are for a one standard deviation value of an index. The left ordinate labels are torque units in Hadleys (1 Hadley = 1.0 × 1018 kg m2 s−2), and the right labels are AAM units (1 unit = 1.0 × 1024 kg m2 s−1). For the contours, the right labels also represent latitude/10, i.e., 6 = 60°N, etc. The contour and shading interval is 0.1 × 1024 kg m2 s−1 (the value corresponds to a vertical and zonal mean zonal wind anomaly of 0.3 m s−1 at 30°N). The contours start at 0.05 × 1024 kg m2 s−1 in (c) and (d). The abscissa is lag where negative (positive) values mean that the regressed quantity leads (lags) the index

Three features stand out in Figs. 1a–e: 1) MTOT anomalies are nearly out of phase with τF anomalies, 2) MTOT anomalies lag τM anomalies, and 3) τF anomalies lead τM anomalies. These relationships are consistent with the forcing/damping role assigned to τM/τF in the introduction, but also display the effects of the other postulated feedback between the distribution of mass anomalies (linked to the frictional torque) and the mountain torque. The latter contributes to the nonzero τF in Fig. 1d before day 0 and the nonzero τM in Fig. 1e after day 0. At periods much longer than the 30-day damping timescale (e.g., interannual variability), the quadrature relation between the torques approaches an out-of-phase one (see WRP). This implies a near balance of AAM anomalies, with the surface stress torque acting to weaken them and the mountain torque acting to maintain them.

Figures 1a–1e provide insight into phenomena that dominate the forcing of AAM anomalies on intraseasonal timescales:

  • Figure 1a. Regression on the daily MR tendency shows the important role of the MJO in intraseasonal AAM variations. Well-known MJO features include [{m}] anomalies that start on the equator and move poleward to the subtropics and global curves that all contain a ∼50 day quasi oscillation. However, the figure also indicates the presence of other timescales (e.g., in the τM curve) and hints at variability in other regions (e.g., in northern midlatitudes in [{m}]).

  • Figure 1b. Regression on the 30–70-day MR tendency shows the MJO behavior more explicitly. For example, a “cleaner” poleward propagation signal comes out. Weickmann and Sardeshmukh (1994) and Weickmann et al. (1997) investigated the AAM budget in this time band, while Weickmann et al. (2000) cautioned against interpreting all of the AAM variability in the 30–70-day band as due to the MJO.

  • Figure 1c. Regression on the <30 day MR tendency captures the remainder of the variability in Fig. 1a. The mountain torque is the most prominent feature, but all curves also show evidence for a weak quasi-oscillation at about 20 days. Lott et al. (2003a,b, manuscripts submitted to J. Atmos. Sci.) investigated 15–30-day oscillations of the mountain torque, including the associated synoptic structures. Ghil and Robertson (2002) summarized modeling and observational work on fluctuations around this period.

  • Figure 1d. Regression on the daily mountain torque shows a strong but short-lived signal that forces MTOT. It has a decorrelation timescale of 1–2 days and its global signature is also seen in Figs. 1a and 1c. Salstein and Rosen (1994), Iskenderian and Salstein (1998), and Weickmann et al. (2000) investigated its behavior. More than 80% of the variance of MTOT is forced by τM for periods <30 days.

  • Figure 1e. Regression on the daily frictional torque recovers the ∼6 day decorrelation timescale, and shows larger zonal and global anomalies than for τM. There is evidence for MJO-like features in [{m}] that are also seen in Figs. 1a and 1b. A stronger zonal signal is present at 50°N, which is suggestive of zonal-index-like behavior. In contrast to Fig. 1d, the largest zonal anomalies occur before day 0. This attests to the damping role played by the frictional torque in anomalous AAM variations.

There is a considerable mixture of temporal variability evident in the various panels of Fig. 1, including synoptic-scale, zonal index cycles and the MJO. Ultimately, we are interested in how these phenomena interact to produce individual cases of intraseasonal AAM variation. An intermediate goal in this investigation is to determine the processes responsible for driving the global frictional torque. Clearly, the MJO is one of these; but are there other, perhaps extratropical processes, that also contribute? Are zonal index cycles and teleconnection patterns important local components of τF variations? The likely answer is yes since the τF lag autocorrelation function has a decorrelation timescale similar to those of these phenomena. In the rest of the paper, the MJO component is linearly removed from τF to help highlight these other types of variability.

3. Stochastic mountain torque

Before presenting the results for the frictional torque, some general aspects of mountain torque variability are discussed. Since this paper deals with global integrals or integrals over a continental mountain complex, monopole zonal mean anomalies of the mountain torque are emphasized. By way of contrast, the November–March seasonal mean mountain torque has a dipole meridional structure with negative values north of ∼37°N and positive values to the south. Held et al. (2002) discuss the stationary waves produced by flow over Northern Hemisphere topography that give rise to the seasonal mountain torque.

The preferred meridional structure of zonal mountain torque anomalies is determined by an empirical orthogonal function (EOF) analysis of daily anomalies during November–March. EOF 1 (not shown) has a monopole structure between 20° and 60°N and accounts for 33% of the zonal variance over the globe. EOF 2 (not shown) has a dipole, seasonal-like structure and accounts for 16% of the variance. Both EOF coefficients have a decay timescale of ∼1.8 days, but the spectrum of EOF 1 deviates from the red-noise background in the 3–15-day band, whereas the spectrum of EOF 2 deviates in the >20 day band. The implication is that EOF 2 is responding to modulation of the seasonal stationary waves, whereas EOF 1 is responding to upstream synoptic developments and associated downstream energy dispersion. The latter is apparently more important for anomalous global AAM variations than the former.

WRP showed regression results for the global mountain torque that involve the same sign anomaly over both Asian and North American topography. Regressing on EOF 1 gives similar results. In Fig. 2 we present regression results for the mountain torque when summed separately over the Europe–Asian and North American regions.

Fig. 2.

Regressions of 250-hPa streamfunction (contours) and SLP (shading) anomalies onto (left) the Asia/Europe mountain torque (summed over the region 18°–65°N, 20°W–180°) and (right) the North American mountain torque (summed over the region 18°–65°N, 180°–20°W). The anomalies are for a one standard deviation value of an index. The first three panels in each column show the local regressions at days −3, 0, and +3. The contour interval is 1.0 × 106 m2 s−1. The last panel shows the zonal integral of the mountain torque for each day [day −3 (A), day 0 (B), day +3 (C)] summed over the longitudes defined above. The abscissa labels are Hadleys (1 H = vertical and zonal mean zonal wind tendency of 0.2 m s−1 day−1 at 30°N), and the ordinate labels are north latitude. The shading of SLP anomalies in the top six panels is as follows: white is <−1.0 hPa, red is −1.0 to −0.5 hPa, light red is −0.5 to 0 hPa, gray is 0 to 0.5 hPa, dark blue is 0.5 to 1.0 hPa, light blue is >1.0 hPa

Fig. 2.

Regressions of 250-hPa streamfunction (contours) and SLP (shading) anomalies onto (left) the Asia/Europe mountain torque (summed over the region 18°–65°N, 20°W–180°) and (right) the North American mountain torque (summed over the region 18°–65°N, 180°–20°W). The anomalies are for a one standard deviation value of an index. The first three panels in each column show the local regressions at days −3, 0, and +3. The contour interval is 1.0 × 106 m2 s−1. The last panel shows the zonal integral of the mountain torque for each day [day −3 (A), day 0 (B), day +3 (C)] summed over the longitudes defined above. The abscissa labels are Hadleys (1 H = vertical and zonal mean zonal wind tendency of 0.2 m s−1 day−1 at 30°N), and the ordinate labels are north latitude. The shading of SLP anomalies in the top six panels is as follows: white is <−1.0 hPa, red is −1.0 to −0.5 hPa, light red is −0.5 to 0 hPa, gray is 0 to 0.5 hPa, dark blue is 0.5 to 1.0 hPa, light blue is >1.0 hPa

In both regions, there is easterly anomalous flow at day −3, south of preexisting positive SLP anomalies at high latitudes. This is followed at day 0 by an amplification of circulation anomalies upstream of the mountains and then at day +3 by energy dispersion downstream. Individual centers within the wave trains move at 10 m s−1, while energy propagates eastward at 25 m s−1. The wave trains show a mixture of equivalent barotropic and baroclinic vertical structures, with the latter more prominent upstream and the former more prominent over and downstream of the topography. In terms of synoptic evolution, the Asian sector (left-hand panels) displays a more compact, mobile wave train, while the North American sector (right-hand panels) has a more complicated evolution, probably a result of the different time-mean flow in the two regions. Consistent with EOF 1, the meridional profiles of the mountain torque at day 0 have a single maximum, around 30°N for the Europe–Asian region and 40°N for the North American continent.

4. Stochastic frictional torque

Quantitative budget studies of AAM are feasible with current global assimilated datasets such as the NCEP–NCAR reanalysis to be used here. The results with these data show a good balance for global integrals and intraseasonal variations, and during northern winter/spring. The budgets get much worse when gravity wave drag is included, if zonal integrals are considered, and during summer/fall seasons. The zonal and global budgets are determined by computing lagged regressions on the global frictional torque with the MJO removed. The MJO was removed by regressing the frictional torque onto the first two EOFs of outgoing longwave radiation (see WRP) and then subtracting this estimate from the original series; that is,

 
τintF(t) = τF(t) − [b*1c1(t) + b*2c2(t)],
(8)

where b1, b2 are the regression coefficients and c1, c2 are the EOF time series.

The regressions are performed on 16 winter (November–March) periods from 1979/80 through 1994/95. The 150-day mean anomaly was removed from each segment to minimize contamination of the results by interannual variations. All anomalies are then reconstructed or “predicted” based on a one-sigma anomaly in the index. The index, τintF, is used throughout the remainder of the paper to define the internal or stochastic frictional torque.

a. Global and zonal budget

The regression results in this section are presented using a combined global–zonal format so that the contribution of zonal integrals to the global integral can be easily seen. Local statistical significance of the correlation coefficient is shown with shading and is determined as described in WRP. A two-sided 98% significance level is used with a null hypothesis of zero correlation.

Figure 3a shows the total AAM anomalies when regressed on τintF. Compared with the regression on τF (Fig. 1e), [{m}] anomalies have a more pronounced zonal index structure, with larger values at 50° and 20°N but smaller values near the equator. An apparent poleward-propagating signal remains. The time-lagged MTOT and [{m}] anomalies show intensification around day −12, largest anomalies at day −2, and rapid decay thereafter.

Fig. 3.

Zonal (contours) and global integral (curves) anomalies obtained by lag regression onto τintF (see text). (a) Total AAM: contour interval is 0.1 × 1024 kg m2 s−1, and left ordinate labels are for the global curve in AAM units (1 unit = 1.0 × 1024 kg m2 s−1). (b) Earth AAM: same as in (a). (c) Relative AAM tendency: contour interval is 0.1 Hadley, starting at +0.2 and −0.2 Hadleys, left ordinate labels are in Hadleys. (d) The sum of the terms in the relative AAM budget (frictional torque + mountain torque + Coriolis torque + flux convergence of relative AAM); contours/labels are same as in (c). In (a), (b), (c), the heavy (light) shading highlights negative (positive) zonal anomalies that pass a 98% local significance test. Regressions were performed for lags from −25 days (variable leads frictional torque) to +25 days (variable lags). The right ordinate labels are latitude for the zonal contours

Fig. 3.

Zonal (contours) and global integral (curves) anomalies obtained by lag regression onto τintF (see text). (a) Total AAM: contour interval is 0.1 × 1024 kg m2 s−1, and left ordinate labels are for the global curve in AAM units (1 unit = 1.0 × 1024 kg m2 s−1). (b) Earth AAM: same as in (a). (c) Relative AAM tendency: contour interval is 0.1 Hadley, starting at +0.2 and −0.2 Hadleys, left ordinate labels are in Hadleys. (d) The sum of the terms in the relative AAM budget (frictional torque + mountain torque + Coriolis torque + flux convergence of relative AAM); contours/labels are same as in (c). In (a), (b), (c), the heavy (light) shading highlights negative (positive) zonal anomalies that pass a 98% local significance test. Regressions were performed for lags from −25 days (variable leads frictional torque) to +25 days (variable lags). The right ordinate labels are latitude for the zonal contours

Figure 3b shows the surface mass anomalies that accompany the vertically integrated wind anomaly. Both ME and [{me}] make significant contributions to the total anomalies. Initially (day −12), positive [{me}] anomalies near 40°N support westerly surface flow anomalies near 50°N and easterly flow anomalies in the subtropics. Subsequently, falling surface pressures in the Tropics support stronger easterly flow anomalies in the subtropics. Negative ME anomalies are largest around day 0, when tropical pressure anomalies are negative. The regional contribution to these changes is examined later.

Figures 3c and 3d show observed and computed tendencies of MR and [{mr}]. Comparing the two illustrates the budget imbalance. The observed [{mr}]t (Fig. 3c) shows a north–south dipole pattern in the Northern Hemisphere at day −10, followed by positive tendencies in the Tropics at day −4 that decelerate the tropical easterly flow anomalies. At the same time (day −4), tendencies are weak elsewhere so that negative and positive [{mr}] anomalies persist near 25° and 50°N, respectively (see Fig. 3a). The computed [{mr}]t (Fig. 3d) is given by the sum of the momentum flux convergence and the Coriolis, friction, and mountain torques. Comparison of the curves in Figs. 3c and 3d shows that the MR budget is well balanced, but the computed [{mr}]t has large errors, although approximately the correct pattern.

There is evidence that the observed frictional torque may be to blame for the errors. The zonal budget residual arises because the observed transports are considerably larger than the sum of the torques, which is dominated by [τs cosϕ]. Ponte et al. (2002) found errors in the surface wind field over the oceans that contribute to a similar zonal budget residual on seasonal timescales. Moreover, the use of 6-h predictions of the surface stress field to obtain the “observed” frictional torque could introduce additional systematic model errors. This zonal imbalance is an important unresolved issue for observed AAM variability.

Figure 4 shows the individual terms of the relative AAM budget: (a) the frictional torque, (b) the flux convergence of [{mr}], (c) the mountain torque, and (d) the Coriolis torque. The global curves shown in Fig. 4a cause the MTOT variation seen in Fig. 3a. The negative τM anomaly (dotted curve) drives MTOT to larger negative values, and the positive τintF anomaly (solid curve) brings it back toward zero. The quadrature relation between the torques is clear. For the reasons discussed in the introduction, negative anomalies in τM are linked with F/dt > 0 and positive anomalies in τF with M/dt > 0. In the MR budget, τC (Fig. 4d) partially compensates τM so that the mass redistribution associated with τM appears in the ME budget [see (3) and (4)].

Fig. 4.

Zonal (contours) and global integral (curves) anomalies obtained by lag regression onto τintF (see text). (a) Frictional torque: contour interval is 0.1 Hadleys; the global mountain torque curve is also shown (dashed curve). (b) The flux convergence of relative AAM: contour interval is 0.2 Hadleys. (c) The mountain torque: same as in (a), except the 0.05-Hadley contour is included. (d) The Coriolis torque is the same as in (a). Note that the contour interval in (b) is twice that in (a), (c), and (d). In (a), (b), (c), (d), the heavy (light) shading highlights negative (positive) zonal anomalies that pass a 98% local significance test. The left ordinate labels are Hadleys for the global curves and the right ordinate labels are latitudes for the zonal contours

Fig. 4.

Zonal (contours) and global integral (curves) anomalies obtained by lag regression onto τintF (see text). (a) Frictional torque: contour interval is 0.1 Hadleys; the global mountain torque curve is also shown (dashed curve). (b) The flux convergence of relative AAM: contour interval is 0.2 Hadleys. (c) The mountain torque: same as in (a), except the 0.05-Hadley contour is included. (d) The Coriolis torque is the same as in (a). Note that the contour interval in (b) is twice that in (a), (c), and (d). In (a), (b), (c), (d), the heavy (light) shading highlights negative (positive) zonal anomalies that pass a 98% local significance test. The left ordinate labels are Hadleys for the global curves and the right ordinate labels are latitudes for the zonal contours

The zonal integrals in Fig. 4 provide a first glimpse into the role of atmospheric dynamics in τintF variations. The relative momentum flux convergence (Fig. 4b) implies a northward transport of momentum across ∼35°N, early in the composite evolution, that strengthens at day −10. This drives an anomaly pattern of surface westerly flow at 50°N and easterly flow at 20°N (Fig. 4a; ∼day −10), much like during a typical zonal index cycle. The high-latitude surface westerly flow anomalies coincide with a weak negative mountain torque anomaly but also imply negative SLP anomalies at high latitudes. This sets the stage for an interaction between the preexisting SLP anomalies and a wave train that culminates in a large monopole mountain torque anomaly at day −5 (Fig. 4c), which is apparently not typical of most zonal index cycles.

Two dynamical signals are then observed in the flux convergence term (Fig. 4b). First, a positive tendency develops near 5°N that is partially responsible for the observed positive [{mr}]t seen previously in Fig. 3c. As noted earlier, this weakens the easterly flow anomalies in the Tropics and, combined with the persistent anomaly near 25°N, gives the impression of poleward propagation in [{mr}]. Second, a strengthened momentum sink develops in the subtropics between 15° and 30°N (Fig. 4b, days −3 to +4). Coinciding with this (primarily) upper-level momentum sink, positive frictional torque anomalies extend deeper into the subtropics after day 0 (Fig. 4a). As a result, the frictional torque anomalies persist and help to counteract the AAM anomalies produced by the negative mountain torque. The processes responsible for these zonal mean signals require further investigation but probably involve transient eddy–mean flow interactions.

These composite relationships are not surprising and are physically plausible, but the accompanying temporal correlations, while statistically significant, are small when using daily data. A good illustration is the link between momentum transports across 35°N and the global frictional torque 10 days later. In daily data, these variables have a lag correlation of 0.2. The small signal emphasizes the large amount of noise present in daily data and the small transitional probabilities inherent in evolution described in Fig. 4.

b. Synoptic patterns and time evolution

Figure 5 presents the 250-hPa vector wind and SLP anomaly patterns for selected leads/lags when regressed onto τintF. Wind vectors are plotted wherever the u or υ component passes a two-sided 98% significance test on its correlation with τintF. The evolution of the zonal mean flow anomalies discussed earlier should be evident in these regional fields.

Fig. 5.

Lag regressions of 250-hPa vector wind (arrows) and SLP (shading) anomalies onto τintF (see text) for lags on (a) day −10, (b) day −6, (c) day −2, and (d) day +4. An arrow is plotted wherever the u or v component at a grid point passes a 98% two-sided significance test. SLP anomalies greater than (less than) 0.5 hPa (−0.5 Pa) are blue (red)

Fig. 5.

Lag regressions of 250-hPa vector wind (arrows) and SLP (shading) anomalies onto τintF (see text) for lags on (a) day −10, (b) day −6, (c) day −2, and (d) day +4. An arrow is plotted wherever the u or v component at a grid point passes a 98% two-sided significance test. SLP anomalies greater than (less than) 0.5 hPa (−0.5 Pa) are blue (red)

At day −10 (Fig. 5a), a ring of 250-hPa anticyclones is evident around the midlatitudes of the Northern Hemisphere. The ring coincides with the axis of the mean wintertime jet stream and indicates a northward-shifted jet, consistent with anomalous zonal mean momentum transports across 35°N. By day −6 (Fig. 5b), wave trains develop on this poleward-shifted westerly flow, first across Northern Asia and then, by day −2 (Fig. 5c), across North America. While these wave trains resemble the patterns shown in Fig. 2 (with opposite sign), the individual eddies are more zonally elongated over the east Pacific and less mobile over north Asia. The synoptic evolution shows 1) energy dispersion from a North Atlantic equivalent barotropic anomaly (day −10) across northern Asia and into the Pacific Ocean, and 2) growth of an east Pacific equivalent barotropic anomaly (days −10 to −6) and then energy dispersion across North America and into the Atlantic Ocean. The latter leads to a PNA-type teleconnection pattern at day −2 and beyond.

These developments are accompanied by the anomalous zonal mean flux convergence of momentum discussed earlier. The effect of the zonal mean westerly acceleration in the Tropics can be seen by comparing day −6 (Fig. 5c) with day +4 (Fig. 5d). At the same time, a strong momentum sink at 25°N maintains easterly anomalies in the PNA region (day −2; Fig. 5c) and drives a positive frictional torque (day 0; Fig. 4a), presumably through a zonal mean mass circulation. Although nonlinear transient-eddy fluxes dominate the zonal mean flux convergence anomalies (not shown), the regional anomalies could be driven by a different dynamical process.

The evolution of the SLP anomalies (shading in Fig. 5) complements those at 250 hPa and provides information on the vertical structure of anomalies and, indirectly, on the surface wind anomalies. We have already noted the equivalent barotropic structure of the anomalies over the midlatitude oceans at day −10 and beyond. To the north of positive SLP anomalies (Fig. 5a), negative SLP anomalies stretch from east Asia across the North Pacific to the North Atlantic Ocean, consistent with the westerly flow anomalies at 50°N. The pressure anomalies provide a regional illustration of the lag relation between τF and τM discussed earlier. During day −6 to day −2 (Figs. 5b,c), they are “tapped” by the developing wave trains and driven southward, east of east Asian and North American topography, giving a negative mountain torque. As the PNA-like pattern develops at day −2, negative SLP anomalies also develop over the equatorial tropical Pacific in support of the stronger easterly flow along ∼25°N that gives a positive frictional torque.

Before examining two cases of τintF variation in the next section, the suggestion that the PNA pattern is involved in the synoptic evolution is investigated. First, a daily index of the PNA pattern was derived using the centers of action defined by Barnston and Livezey (1987; see http://www.cdc.noaa.gov/map/wx/indices.shtml). Next, a daily time series of projection coefficients was computed by projecting the total 250-hPa streamfunction anomolies onto the regressed 250-hPa streamfunction anomolies at day −2 (Fig. 5c). Temporal correlations were then determined, again using the method described in WRP to test for statistical significance. The PNA index is correlated with τintF at −0.32 and with the projection time series at −0.65. Both are significant at >99%, confirming the relation with the PNA pattern.

5. Case studies: 1997/98 and 2000/01

Two cases are presented that illustrate the regression results of the preceding section. One involves a strengthening and then weakening of positive global AAM anomalies during the 1997/98 El Niño, and the other a strengthening and then weakening of negative AAM anomalies during the weak 2000/01 La Niña. An MJO was present in the more recent case, but, on average, this tropical phenomenon does not have a simple linear relationship with midlatitude mountain torques (see WRP). For each case, global and zonal mean anomalies of AAM and its torques are shown. These are complemented by a set of maps that illustrate 1) the preexisting SLP anomalies, 2) the SLP anomalies that give the mountain torque, and 3) the surface zonal wind anomalies that give the frictional torque.

a. January–February 1998

Figure 6 shows the time evolution of [{m}] and MTOT anomalies during January–February 1998. The zonal winds are already anomalous westerly in the subtropics in early January 1998, consistent with the ongoing El Niño. Positive MTOT anomalies are near one sigma (Fig. 6b). Around 18 January 1998, an intensification of anomalous southward momentum transports occurs at around 40°N (not shown) and leads to a strengthening and tightening of zonal mean zonal wind anomalies (Fig. 6a). This date corresponds to day −10 in the regressions. Thereafter, MTOT increases, reaches a maximum positive value on 6 February 1998, and then declines rapidly until mid-February 1998.

Fig. 6.

The total AAM anomalies for 1 Jan–28 Feb 1998: (a) zonal integrals, shading interval is 0.5 × 1024 kg m2 s−1 and (b) global integral, ordinate labels are ×1025 kg m2 s−1. Data in (a) are smoothed with a 5-day running mean, (b) is unsmoothed daily data

Fig. 6.

The total AAM anomalies for 1 Jan–28 Feb 1998: (a) zonal integrals, shading interval is 0.5 × 1024 kg m2 s−1 and (b) global integral, ordinate labels are ×1025 kg m2 s−1. Data in (a) are smoothed with a 5-day running mean, (b) is unsmoothed daily data

Figure 7 shows the same time period, but for the mountain and frictional torque. The τF and τM curves are shown together in Fig. 7b. The persistently positive anomalies of τM from 22 January to 7 February 1998 force the MTOT increase described in Fig. 6. The τM signal is produced by a positive monopole anomaly pattern in the Northern Hemisphere midlatitudes, as seen in Fig. 7a. The monopole occurs after the period of easterly surface flow anomalies (i.e., positive frictional anomalies) around 55°N, which can be seen in Fig. 7c. Large negative anomalies in the frictional torque then develop in the northern subtropics from 27 January to 11 February 1998. The global frictional torque counteracts the mountain torque, driving global AAM back down.

Fig. 7.

For 1 Jan–28 Feb 1998: (a) the zonal mountain torque anomaly, (b) the global mountain torque (heavy solid: 5-day running mean; light solid: daily mean) and frictional torque (medium solid: daily mean) anomalies, and (c) the zonal frictional torque anomaly. The shading interval in (a) and (c) is 0.5 Hadleys; yellow to reds are positive anomalies, green to blues are negative anomalies. The ordinate labels in (b) are ×1019 kg m2 s−2. A 5-day running mean is applied to (a) and (c)

Fig. 7.

For 1 Jan–28 Feb 1998: (a) the zonal mountain torque anomaly, (b) the global mountain torque (heavy solid: 5-day running mean; light solid: daily mean) and frictional torque (medium solid: daily mean) anomalies, and (c) the zonal frictional torque anomaly. The shading interval in (a) and (c) is 0.5 Hadleys; yellow to reds are positive anomalies, green to blues are negative anomalies. The ordinate labels in (b) are ×1019 kg m2 s−2. A 5-day running mean is applied to (a) and (c)

Figure 8 provides synoptic snapshots of SLP and surface zonal wind anomalies during the case. Figure 8a illustrates the positive SLP anomalies at high latitudes that are a precursor to positive mountain torque anomalies. The SLP anomalies can be inferred from the easterly zonal wind anomalies at 55°N, seen in Fig. 7c, which in turn contribute to a positive τF (Fig. 7b). Figure 8b illustrates the SLP anomalies several days later. The figure was constructed by taking 4 days with a large positive τM anomaly and subtracting 4 days with a negative or zero τM anomaly within the period 20–30 January 1998 (see daily τM time series in Fig. 7b). The result (Fig. 8b) illustrates both the SLP pattern around the east Asian and North American topography and the synoptic-scale wave trains that give a large τM. Figure 8c shows the result of dynamical processes that lead to strong surface westerly wind anomalies at around 30°N and a large, negative frictional torque. The surface signature of the PNA pattern is evident in this field. This case represents the regressions fairly well, although its life cycle is somewhat longer than average.

Fig. 8.

(a) SLP anomalies for 18–23 Jan 1998; (b) SLP anomalies obtained by subtracting the average of 23, 24, 27, and 28 Jan from the average of 20, 21, 25, and 30 Jan 1998; and (c) surface zonal wind anomalies for 1–11 Feb 1998. The shading interval is 2 hPa in (a), (b) and 2 m s−1 in (c), with positive anomalies shaded green to red, and negative anomalies blue to purple

Fig. 8.

(a) SLP anomalies for 18–23 Jan 1998; (b) SLP anomalies obtained by subtracting the average of 23, 24, 27, and 28 Jan from the average of 20, 21, 25, and 30 Jan 1998; and (c) surface zonal wind anomalies for 1–11 Feb 1998. The shading interval is 2 hPa in (a), (b) and 2 m s−1 in (c), with positive anomalies shaded green to red, and negative anomalies blue to purple

b. January–February 2001

In the previous case, the positive mountain torque was relatively persistent, leading to a gradual rise in AAM. In the case of January–February 2001, the negative mountain torque is large, impulsive, and followed by a large opposite-signed τM anomaly. Figure 9 shows the evolution of MTOT and [{m}] anomalies. The preexisting anomalies during most of January 2001 reflect the ongoing La Niña, combined with an index cycle. Their subsequent amplification and decay reflect a τintF variation.

Fig. 9.

Same as Fig. 6, except for 1 Jan–28 Feb 2001

Fig. 9.

Same as Fig. 6, except for 1 Jan–28 Feb 2001

As in the previous case (but with opposite sign), there is an abrupt northward transport of momentum across 35°–40°N centered on 25 January 2001 (not shown). This is equivalent to day −10 in the composite. The effect on [{m}] is subtle, but Fig. 9a shows prevailing negative anomalies along 50°N that then become weakly positive. Thereafter, MTOT anomalies decline rapidly, reach a minimum on 3 February 2001, and then rapidly increase to above zero. The [{m}] anomalies (Fig. 9a) are approximately opposite in sign to the previous case.

Figure 10 shows the mountain and friction torque. The zonal frictional torque (Fig. 10c) shows the midlatitude surface westerly flow anomaly in late January 2001 that is linked with the abrupt change in momentum transports. The strengthened westerly flow implies negative SLP anomalies at high latitudes, which precede a negative mountain torque. Indeed, Fig. 10a shows a monopole mountain torque anomaly that develops in midlatitudes and persists for about 6 days. The global anomaly (Fig. 9b) reaches values near −50 Hadleys (3 sigma). Thereafter, τF anomalies become large positive (Fig. 10b) and drive AAM anomalies back toward zero. The frictional torque anomalies are concentrated south of 35°N (Fig. 10c) and coincide with a negative PNA pattern (not shown). The global curves plotted together in Fig. 10b provide a good illustration of the coherent relation between the torques.

Fig. 10.

Same as Fig. 7, except for 1 Jan–28 Feb 2001. The heavy dots on the global mountain and friction torque curves correspond to the dates shown in Fig. 11 

Fig. 10.

Same as Fig. 7, except for 1 Jan–28 Feb 2001. The heavy dots on the global mountain and friction torque curves correspond to the dates shown in Fig. 11 

The sequence of maps in Fig. 11 again corresponds well with the regressions. Figure 11a shows the negative SLP anomalies at high latitudes that precede the negative τM. Figure 11b shows the pressure difference across the topography of east Asia and North America that gives the negative τM. Figure 11c shows the amplified easterly flow anomalies at the surface that give the positive τF anomalies.

Fig. 11.

(a) SLP anomalies for 22–26 Jan 2001, (b) SLP anomalies for 29–31 Jan 2001, and (c) surface zonal wind anomalies for 6–11 Feb 2001. The shading interval is 2 hPa in (a), (b) and 2 m s−1 in (c), with positive anomalies shaded green to red, and negative anomalies blue to purple

Fig. 11.

(a) SLP anomalies for 22–26 Jan 2001, (b) SLP anomalies for 29–31 Jan 2001, and (c) surface zonal wind anomalies for 6–11 Feb 2001. The shading interval is 2 hPa in (a), (b) and 2 m s−1 in (c), with positive anomalies shaded green to red, and negative anomalies blue to purple

6. Discussion and conclusions

The global frictional torque represents processes with decorrelation timescales similar to zonal index cycles and teleconnection patterns, in a 6–10-day range. By contrast, the global mountain torque is nearly white and is linked with synoptic-scale wave trains that disperse energy eastward over the mountains and into adjacent ocean basins. The torques are lag correlated, and the frictional torque leads the mountain torque. The Markov models of WRP and EH capture the fundamental reason for the relationship between the torques; that is, the mountain torque forces AAM anomalies and the frictional torque damps them. Formally, this implies F/dt ∝ −τM, where the physical link is through atmospheric dynamical processes. An additional feedback between the torques is not part of the simple Markov model. Physically, it relates high-latitude SLP anomalies that accompany the frictional torque with the phase and strength of the subsequent mountain torque. This implies M/dtτF.

The physical relation between the torques was further investigated by regressing global, zonal mean, and local variables onto the internal global frictional torque. The typical τintF life cycle is similar to that described for τM in the introduction. [In fact, several aspects of the τintF life cycle can be recovered by regressing on low-pass (>10 day) filtered τM.] Both cycles display a 4–5-day lag between maximum negative (positive) τM and maximum positive (negative) τF anomalies (e.g., Fig. 4a). However, a τintF event lasts longer and is associated with larger global AAM anomalies. Synoptic structures are also different, as illustrated by comparing Fig. 2 with Fig. 5.

The zonal regressions on τintF (Figs. 3, 4) suggest a link with zonal index fluctuations, which are initiated by stochastic momentum transports across ∼35°N. These produce zonal mean AAM anomalies (Fig. 3a) that project onto the first EOF of zonal AAM anomalies during northern winter. Feldstein (1998, hereafter F98) and Feldstein and Lee (1998) have studied the composite life cycle of this EOF by regressing onto [{mr}] at 22.5°N. They find a simple picture wherein impulsive eddy momentum transports across ∼35°N force AAM anomalies that are then damped by surface friction.

The regression on τintF focuses on a subset of these EOF events, namely, those cases where zonal mean zonal wind anomalies help drive a large or persistent mountain torque over Asia and North America. In contrast to F98, the momentum flux convergence anomalies persist and then strengthen in the τintF regressions. The strengthening appears linked to transient eddy momentum fluxes that accompany the mountain torque.

The regional regressions on τintF (Fig. 5) show a relation with Rossby wave trains and the PNA teleconnection pattern. The Fig. 5a pattern precedes the growth of the PNA pattern and is consistent with patterns found in previous investigations (e.g., Dole and Black 1990). Cash and Lee (2001) and Winkler et al. (2001) confirm that the PNA pattern can be produced by linear growth from an “optimal” pattern of circulation anomalies.

The mechanism of PNA development has been studied by Feldstein (2002), who finds a dominant role for barotropic interactions with the zonally asymmetric climatological flow. In the current study, equivalent barotropic anomalies over the east Pacific and Atlantic Oceans precede the downstream amplification of baroclinic wave train anomalies that produce mountain torques over North American and east Asian topography. This appears to support the Feldstein (2002) result. However, real-time monitoring suggests that, in individual cases, the PNA anomaly has multiple sources for initial growth. The issue may depend on the definition of the growth phase. In Feldstein (2002) and Cash and Lee (2001), the individual PNA centers are already established at their respective initial times. On the other hand, Winkler et al. (2001) and this study find significant precursors before the PNA's centers are established. Consistent with this, Feldstein (20028) notes that “at the earliest stage of the anomaly evolution, the initial disturbance … is excited by transient eddy fluxes.” A similar result is found for the τintF regressions.

The case studies from two recent winters confirm that τintF events are initiated during periods of persistent forcing of the Northern Hemisphere jet stream, much as was found in the regression results. In the 1998 case, El Niño produced a persistent southward momentum transport across 35°N, while in 2001 a weak La Niña/index cycle produced a persistent northward transport across 35°N. In both cases, the existing pattern of zonal wind and global AAM anomalies first amplified because of interactions accompanying the mountain torque and then decayed as the same interactions led to growth of the frictional torque. Although the cases occurred outside of the winters used for regression (1979–95), they fit the composite evolution well. The cases represent extreme events (>2 sigma) in the distribution of τintF anomalies.

There are other aspects of τintF variations that we have not addressed. For example, regressions show a significant tropical and subtropical convective signal (not the MJO) that may play a feedback role in the dynamics that link the mountain and frictional torque. Nevertheless, within the context of global AAM variations, the frictional torque studied in this paper should be viewed as an independent extratropical mode that is intimately tied to the mountain torque. It interacts with other stochastic and oscillatory timescales (e.g., Fig. 1) to produce individual cases of intraseasonal global AAM variability.

Acknowledgments

Discussions with colleagues at the CDC are much appreciated, particularly Cecile Penland and Matt Newman. The comments of Steven Feldstein and two anonymous reviewers helped improve the manuscript.

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Footnotes

Corresponding author address: Klaus Weickmann, NOAA–CIRES Climate Diagnostics Center, R/CDC1, 325 Broadway, Boulder, CO 80303-3328. Email: Klaus.Weickmann@noaa.gov