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  • View in gallery

    Daily time series of the global AAM tendency (dotted) and the sum of the global friction and mountain torque (solid) for the period 1 November 1995–1 November 1996. Units are 1019 kg m2 s−2.

  • View in gallery

    Log–log power spectrum with period of global angular momentum tendency (solid), global mountain torque (dotted), and global friction torque (dash–dot) based upon data for the period February 1992 to November 1996. Units are (1018 kg m2 s−2)2 day. The periodogram is smoothed using a five-point moving average in frequency.

  • View in gallery

    Three-year mean variance of zonally integrated mountain torque in 14-day moving windows shown as a function of latitude and time. Units are (1018 kg m2 s−2)2 per degree latitude. Contours are drawn every 0.2, and values greater than or equal 0.6 are shaded.

  • View in gallery

    (a) Boxes defining four midlatitude domains used in the study to compute the regional mountain torque. The Eurasia box and North America boxes are bounded by latitudes 20° and 60°N, and separated by longitudes 20°W and 180°. The Africa and South America boxes are bounded by latitudes 10° and 40°S, and separated by longitudes 0° and 180°. Shading indicates elevation of at least 1000 m from the Rand 1° × 1° topography grid. (b) Contribution to the total high-frequency variance in a latitude band by the two continental regions in that band, as well as total high-frequency band variance. Units are (1019 kg m2 s−2)2.

  • View in gallery

    Daily time series of the mountain torque in the Eurasia region (solid) and North America region (dotted) for the period 1 January 1996 to 31 March 1996. Units are 1019 kg m2 s−2. The bars beneath the time series highlight the three episodes mentioned in the text.

  • View in gallery

    (a) Daily time series of the sum of the mountain torque in the North America and Eurasia regions (solid) and the global atmospheric angular momentum tendency (dotted) for the period 1 January–31 March 1996. (b) Daily time series of global atmospheric angular momentum tendency from NCEP analysis (dash–dot) and inferred from measurements of LOD (solid). Units are 1019 kg m2 s−2.

  • View in gallery

    Geopotential height of the 700-hPa level at 1200 UTC for (a) 8 March, (b) 15 March, and (c) 20 March 1996. Contours are every 6 dam. Highs and lows discussed in the text are indicated by the letters H and L.

  • View in gallery

    Sea level pressure at 1200 UTC for (a) 8 March, (b) 15 March, and (c) 20 March 1996. Contours are every 6 hPa. Highs and lows discussed in the text are indicated by the letters H and L.

  • View in gallery

    (a) Difference in surface pressure between 1200 UTC 15 March and 1200 UTC 8 March 1996 (every 4 hPa contoured, zero line omitted). Positive contours are solid and negative dashed. (b) Same as (a) except between 1200 UTC 20 March and 1200 UTC 15 March. Shading indicates surface elevation of at least 1000 m.

  • View in gallery

    Response function of the high-pass filter used in the study, plotted linearly in frequency but marked in period. The filter contains 43 weights, and a half-power point of 14 days.

  • View in gallery

    The difference in surface pressure (contoured every 1 hPa) for days when the global high-pass AAM tendency is greater than or equal to +1.5 standard deviations and days when the global high-pass AAM tendency is less than or equal to −1.5 standard deviations from the mean for (a) all months, (b) November–April, and (c) May–October. Shading indicates regions of statistical significance at the 95% confidence level as estimated by a Student’s t-test. Positive values are solid and negative values are dashed.

  • View in gallery

    Daily time series of the difference in sea level pressure (solid, units hPa) between Wichita, Kansas (ICT, 37.7°N, 97.4°W), and Portland, Oregon (PDX, 45.6°N, 122.6°W), plotted with (a) mountain torque over North America (dotted, 1018 kg m2 s−2) and (b) global atmospheric angular momentum tendency (dotted, 1018 kg m2 s−2) for the period 1 January–31 March 1996. Note that the curves are plotted with two different scales.

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Regional Sources of Mountain Torque Variability and High-Frequency Fluctuations in Atmospheric Angular Momentum

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  • 1 Atmospheric and Environmental Research, Inc., Cambridge, Massachusetts
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Abstract

The sources of high-frequency (⩽14 day) fluctuations in global atmospheric angular momentum (AAM) are investigated using several years of surface torque and AAM data. The midlatitude mountain torque associated with the Rockies, Himalayas, and Andes is found to be responsible for much of the high-frequency fluctuations in AAM, whereas the mountain torque in the Tropics and polar regions as well as the friction torque play a much lesser role on these timescales. A maximum in the high-frequency mountain torque variance occurs during the cool season of each hemisphere, though the Northern Hemisphere maximum substantially exceeds that of the Southern. This relationship indicates the seasonal role played by each hemisphere in the high-frequency fluctuations of global AAM.

A case study reveals that surface pressure changes near the Rockies and Himalayas produced by mobile synoptic-scale systems as they traversed these mountains contributed to a large fluctuation in mountain torque and a notable high-frequency change in global AAM in mid-March 1996. This event was also marked by a rapid fluctuation in length of day (LOD), independently verifying the direct transfer of angular momentum from the atmosphere to solid earth below. A composite study of the surface pressure patterns present during episodes of high-frequency fluctuations in AAM reveals considerable meridional elongation of the surface pressure systems along the mountain ranges, thus establishing an extensive cross-mountain surface pressure gradient and producing a large torque. The considerable along-mountain extent of these surface pressure systems may help to explain the ability of individual synoptic-scale systems to affect the global AAM. Furthermore, midlatitude synoptic-scale systems tend to be most frequent in the cool season of each hemisphere, consistent with the contemporary maximum in hemispheric high-frequency mountain torque variance.

Corresponding author address: Dr. Haig Iskenderian, Atmospheric and Environmental Research, Inc., 840 Memorial Drive, Cambridge, MA 02139.

Email: haig@aer.com

Abstract

The sources of high-frequency (⩽14 day) fluctuations in global atmospheric angular momentum (AAM) are investigated using several years of surface torque and AAM data. The midlatitude mountain torque associated with the Rockies, Himalayas, and Andes is found to be responsible for much of the high-frequency fluctuations in AAM, whereas the mountain torque in the Tropics and polar regions as well as the friction torque play a much lesser role on these timescales. A maximum in the high-frequency mountain torque variance occurs during the cool season of each hemisphere, though the Northern Hemisphere maximum substantially exceeds that of the Southern. This relationship indicates the seasonal role played by each hemisphere in the high-frequency fluctuations of global AAM.

A case study reveals that surface pressure changes near the Rockies and Himalayas produced by mobile synoptic-scale systems as they traversed these mountains contributed to a large fluctuation in mountain torque and a notable high-frequency change in global AAM in mid-March 1996. This event was also marked by a rapid fluctuation in length of day (LOD), independently verifying the direct transfer of angular momentum from the atmosphere to solid earth below. A composite study of the surface pressure patterns present during episodes of high-frequency fluctuations in AAM reveals considerable meridional elongation of the surface pressure systems along the mountain ranges, thus establishing an extensive cross-mountain surface pressure gradient and producing a large torque. The considerable along-mountain extent of these surface pressure systems may help to explain the ability of individual synoptic-scale systems to affect the global AAM. Furthermore, midlatitude synoptic-scale systems tend to be most frequent in the cool season of each hemisphere, consistent with the contemporary maximum in hemispheric high-frequency mountain torque variance.

Corresponding author address: Dr. Haig Iskenderian, Atmospheric and Environmental Research, Inc., 840 Memorial Drive, Cambridge, MA 02139.

Email: haig@aer.com

1. Introduction

Because of its conservative properties, atmospheric angular momentum (AAM) is often used to study the variations of the general circulation on timescales of days to years. Starr (1948) noted that the exchange of angular momentum across the atmosphere’s lower interface is achieved by two independent mechanisms: friction torque and mountain torque. The friction torque is a result of the tangential stress placed upon the earth’s surface by the horizontal wind. The mountain torque arises from differences in surface pressure across the eastern and western faces of topographic features.

Several earlier studies of the mountain torque considered its contributions to variations in AAM from the time- or zonally averaged perspective. White (1949) computed the mountain torque in 5° latitude bands in the Northern Hemisphere for a single month and noted that, averaged over the 1-month period, the mountain torque was of the same order of magnitude as the friction torque, and therefore the mountain torque could not be neglected in the angular momentum budget of the earth–atmosphere system. White further found that the Northern Hemisphere mountain torque during this month was dominated by surface pressure differences across the Rockies and Himalayas. Newton (1971) studied the mountain torque in both hemispheres and noted that on the seasonal timescale the mountain torque, while weaker than the friction torque, played a significant role in the angular momentum budget.

On synoptic to submonthly timescales, the mountain torque is typically much larger than its monthly or seasonal average. Wei and Schaack (1984) demonstrated, using First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) data from 1979, that such differences can be nearly one order of magnitude. Swinbank (1985) noted that there was a close connection between these high-frequency fluctuations in mountain torque and the changes in AAM during the FGGE period, which led him to suggest that on timescales of about a week, the mountain torque dominated the angular momentum exchange. On the basis of such studies, Rosen (1993) concluded that the friction torque typically dominates the changes in AAM on timescales of months, whereas on timescales shorter than several weeks the mountain torque is the dominant mechanism.

Some case studies have isolated particular instances in which momentum exchange was affected by mountain torque on submonthly time scales. Rosen et al. (1984) noted a rapid increase in global AAM during January 1983, a period that coincided with the height of the 1982–83 El Niño–Southern Oscillation (ENSO) episode, and speculated that the changes in AAM were due to the mountain torque. Wolf and Smith (1987) followed by studying AAM changes during that strong ENSO event, suggesting that the mountain torque was produced by an eastward surface pressure gradient across the Rockies established by a midcontinent high pressure center to the east of the Rockies and a sequence of eastern Pacific cyclones to the west of the mountains. Salstein and Rosen (1994) investigated a 6-day period in July and August 1992 during which there was a rapid oscillation in global AAM. They found that the mountain torque in the Southern Hemisphere was largely responsible for the rapid fluctuation in AAM, in association with a change in the zonal pressure gradient across the Andes due to a strong winter anticyclone that traversed the mountains. Recently, Czarnetzki (1997) identified mountain torque fluctuations with several cyclones in the lee of the Rockies using a high-resolution regional model.

These earlier case studies indicate that on synoptic timescales, surface pressure systems in the vicinity of major mountain ranges may alter the global AAM through the mountain torque. These studies also suggest that specific geographic locations such as the Rockies, Himalayas, and the Andes may be particularly influential as regions of AAM transfer. By using a longer time series of surface torque and AAM data than previously available, we will attempt to generalize these results by determining the regional sources of the mountain torque that typically lead to high-frequency AAM fluctuations. Then the features in the general circulation that are responsible for these fluctuations will be identified. Thus it is hoped that this study will help advance a more complete picture of the angular momentum balance of the earth–atmosphere system on high frequencies.

2. Definitions and data sources

The global atmospheric angular momentum about the earth’s axis can be expressed as
MrMΩ
where
i1520-0493-126-6-1681-e2
is the entire atmosphere’s angular momentum associated with its motion relative to the rotating solid earth, a is the earth’s radius, g is acceleration due to gravity, u is zonal wind, and the integral is performed over all latitudes ϕ, longitudes λ, and pressures p. The angular momentum associated with the rotation of the atmosphere’s mass is
i1520-0493-126-6-1681-e3
where Ω is the mean rotation rate of the earth and ps the surface pressure (Rosen 1993).
The conservation of angular momentum states that changes in AAM are related to the surface torque by the relationship
i1520-0493-126-6-1681-e4
where the mountain torque (Tm) and friction torque (Tf) are defined through the following relationships (White 1991):
i1520-0493-126-6-1681-e5
Here, τ is surface stress and H indicates the height of the sloping topography.

The sense of the mountain torque is such that lower surface pressure on the western side of a north–south-oriented mountain range relative to the eastern side (i.e., an eastward surface pressure gradient across the mountains) results in a positive torque on the atmosphere. Therefore, lower pressure on the western slopes relative to the eastern slopes of a mountain range tends to increase AAM through the mountain torque. In the case of the friction torque, an easterly surface wind will be indicated by τ > 0 and a positive friction torque tending to increase AAM.

The torque and AAM data in this study were prepared by White (1991) using the National Centers for Environmental Prediction (NCEP) operational analysis system (Kanamitsu 1989). The calculations were based upon the initialized analysis on sigma levels, where the highest sigma level is at about 20 hPa. Calculations of mountain torque in (5) rely upon the product of analysis values of surface pressure and the zonal gradient of surface topography whereas friction torque in (6) relies on model-based surface stresses. This study used global integrals of torque and AAM, both of which were produced four times daily (0000, 0600, 1200, and 1800 UTC) for the period of February 1992–November 1996. Torque data on a 1° × 1° grid used to compute the global integrals were also available four times daily but were limited to the period April 1993–November 1996. To focus on regional patterns, we also used 1° × 1° gridded surface pressure data, available for the period April 1994–November 1996. The gridded fields and global integrals were daily averaged for this study and centered upon 0900 UTC, the mean time of the four synoptic hours for a given calendar date. Because the mountain torque is an instantaneous value and the friction torque is a 6-h average, slightly different averaging techniques were used for the two torques to maintain the 0900 UTC central time.

In section 3c, we identify a case of a pronounced high-frequency fluctuation in global AAM. To relate this fluctuation in global AAM to synoptic-scale surface and upper-air features, sea level pressure and 700-hPa geopotential height fields produced by the NCEP operational analysis system for the period of March 1996 were obtained from the National Center for Atmospheric Research (NCAR). These data were available twice daily on a 2.5° × 2.5° grid. The length of day (LOD) time series used was the Jet Propulsion Laboratory’s (JPL) Kalman-filtered time series [after Gross (1996)], which combines earth rotation estimates from several space–geodetic techniques. These LOD data are available once daily at 0000 UTC from September 1978 to February 1997.

3. Sources of high-frequency mountain torque variance

The overall quality of the NCEP dataset can be judged in part by its ability to relate the sum of the globally integrated surface torques to the AAM tendency, or equivalently, to satisfy (4). Figure 1 shows daily values of this balance for a 1-yr subset of the global torque and AAM tendency time series, both of which are in reasonably good agreement on all timescales considered here. A low-frequency oscillation is apparent in both the torque and AAM tendency, with minima in January and July. Such a prolonged minimum in January is somewhat unusual, with the negative torque leading to a profound decrease in AAM around that time (not shown). Superimposed upon the low-frequency signal are submonthly fluctuations in AAM tendency, and these are also well captured by the sum of the two torques. In fact, for the entire time period (February 1992–November 1996) the correlation between the series is 0.86, indicating that this balance is well represented in the NCEP dataset. The lack of complete agreement arises because mountain torque is calculated from the surface pressure and topography fields, whereas friction torque is calculated from physical parameterizations of the forecast model (Salstein and Rosen 1994). To place the rapid fluctuations in perspective, such surface torques typically produce an angular momentum change equivalent to about 10% of the mean value of Mr, as deduced from Fig. 2 of Rosen and Salstein (1983).

To assess the relative importance of mountain and friction torques to the high-frequency changes in AAM, a power spectrum of the terms in the global AAM budget [Eq. (4)] was computed. To do so we calculated the power spectral density of the angular momentum tendency and torque terms at a bandwidth of 0.0036 day−1 during the interval February 1992 to November 1996. It is clear from the resulting spectrum in Fig. 2 that although the levels in the power in the mountain and friction torques are generally comparable on timescales longer than about a 15 days, mountain torque substantially dominates friction torque on shorter timescales. At these highest frequencies, the power in the mountain torque is nearly equivalent to that in the global angular momentum tendency, a fact that is also evident from examination of a series in the time domain, such as Fig. 1 of Salstein et al. (1996). Furthermore, this strong dominance of the mountain torque is consistent with the results of Madden and Speth (1995), who found that on timescales of 5–20 days, it is more closely related to changes in AAM than is the friction torque. Thus, for purposes of studying rapid fluctuations in AAM shorter than 2 weeks, we will focus upon the characteristics of mountain torque alone and we can safely neglect further consideration of the friction torque.

The presence of known major spectral peaks in Fig. 2, though at lower frequencies than is our present focus, gives us additional confidence in the general utility of the NCEP torque series used here. For example, there are spectral peaks in the current series in both mountain and friction torque at about 360, 180, and 33 days. These peaks have been previously identified in AAM by Eubanks et al. (1985) and others. The peaks near 360 and 180 days are a result of the strong annual and semiannual oscillation of AAM, respectively (Rosen and Salstein 1985), and that at 33 days is likely related to the mechanism identified by Madden and Julian (1971). Although it is a tropical oscillation often identified with fluctuations across the Pacific Ocean, this Madden–Julian oscillation is also associated with changes in AAM (Anderson and Rosen 1983; Weickmann et al. 1997).

a. Zonally integrated mountain torque variance

As a first step toward isolating the regions responsible for the high-frequency fluctuations in global AAM, we determine which latitude bands contain the most mountain torque variance at frequencies shorter than 2 weeks. To do so, we integrated the gridded mountain torque fields around a belt of constant latitude using the relationship
i1520-0493-126-6-1681-e7
which yields the zonally integrated mountain torque per degree latitude. Then the temporal variance of 〈Tm〉 was computed in 14-day moving windows centered on every day in the period April 1993–April 1996. This calculation effectively provided a time series of high-frequency mountain torque variance in each latitude band without the need to digitally filter the series first. (The variance was also computed using data that were first high-pass filtered, and the results were quantitatively similar, giving us confidence in the ability of the 14-day moving window to remove lower-frequency oscillations). The calendar dates for the 3-yr period were then averaged to yield a time average of the zonally integrated mountain torque variance in each latitude band. The mean annual cycle at different latitudes is shown in a Hovmöller diagram in Fig. 3. The high-frequency variance displays maxima in the midlatitudes of the Northern and Southern Hemispheres along 40°N and 25°S, respectively. Further, each hemisphere has a relative maximum in its cool season, with the maximum in the Northern exceeding that of the Southern Hemisphere. The polar regions contain significantly less variance, although they do have peaks during their respective cool seasons near such high features as the Antarctic and the lands bordering the Arctic Ocean. The high-frequency variance in the Tropics is negligible.
The latitude bands that contain the largest variance at high frequencies contain several major mountain ranges, and we wish to assess the relative contribution of the continental regions containing these individual ranges to the total torque variance in the latitude band. For simplicity we divided the latitude bands into two regions (A and B), so that, for example, the contribution from the two regions to the total variance in that band is given by the relationship
To define the boundaries of the regions, we selected two regions in each midlatitude band that broadly contained the major mountain ranges of the midlatitudes (Fig. 4a). The northern and southern boundaries of the regions were chosen to contain the main areas of variance shown in Fig. 3. The eastern and western boundaries were chosen to separate the major mountain ranges such as the Rockies, Himalayas, Andes, and the mountains of southern Africa. For convenience, we have included Australia and Africa within the same Southern Hemisphere region. Furthermore, it was desirable that the eastern and western boundaries lie at sea level to yield a more accurate computation of the area-averaged mountain torque (Wei and Schaack 1984).

Next, the gridded mountain torque was summed within the areas of each of the four regions of the two midlatitude bands. Then the three terms in (8) were computed in 14-day moving windows for the two latitude bands (20°–60°N and 10°–40°S). The contributions from the four broad continental regions to the total mountain torque variance in each band are illustrated in Fig. 4b. Eurasia and North America contribute about equally to the total variance in the Northern Hemisphere midlatitude band. At times an individual region dominates the total in the band; a striking example of this behavior occurred over Eurasia in February 1996. In the Southern Hemisphere, the Andes are primarily responsible for the high-frequency fluctuations in that hemisphere’s mountain torque, with less contribution from Africa. The variance in the Southern Hemisphere is generally of less magnitude than in the Northern, as previously noted in Fig. 3, and the largest such variance occurs in each hemisphere’s cool season.

Figure 4b also shows that the period of January–March 1996 exhibited considerable variance in Northern Hemisphere mountain torque. The fluctuations during this period significantly exceeded the two earlier Northern Hemisphere cool seasons. In particular, there was a significant event of a large mountain torque fluctuation in each of the three calendar months. The time series of the mountain torque in the two Northern Hemisphere midlatitude regions for the period 1 January 1996–31 March 1996 (Fig. 5) reveals the details of the three notable events. In early January 1996, both regions experienced a significant increase and then decrease in mountain torque. Second, during mid-February, the mountain torque across Eurasia decreased greatly, then increased sharply, but was partly offset by a weaker fluctuation in the opposite sense in the North America region. Third, in mid-March, both regions experienced a decrease and then a sharp increase in mountain torque at about the same time.

The combined effect of the North America and Eurasia mountain torque in the midlatitudes demonstrates the important contributions of these regions to the global AAM tendency during early 1996 (Fig. 6a). Throughout this period, the AAM tendency was well represented by the sum of the mountain torque in the two regions of the Northern Hemisphere midlatitudes, with this regional mountain torque correlating with global AAM tendency at r = 0.74, and therefore explaining more than half (55%) of the variance in the global AAM tendency during this period. Mountain torque in these regions does not fully explain the global AAM tendency because the friction torque and mountain torque produced elsewhere of course need to be considered. Throughout the period, the global friction torque was significantly weaker than the mountain torque even during the mid-March case when a lower-amplitude fluctuation of the friction torque occurred (not shown), similar in phase to the Northern Hemisphere midlatitude mountain torque, but with about one-third the amplitude. The mountain torque from the other regions was also less than the mountain torque in the Northern Hemisphere midlatitude region by about a factor of 3.

Although global high-frequency AAM fluctuations may be affected by the mountain torques in a single midlatitude region (Fig. 5), such as in the 8–16 February Eurasian episode, when the sense of the torque over Eurasia and North America is similar, such as during 3–10 January and 8–20 March 1996, the impact upon the global AAM tendency is dramatic. For the entire time series, however, the mountain torque in these two regions is poorly correlated, suggesting that the spectacular events of large fluctuations in AAM tendency brought about by coincident events are not the rule.

Since the angular momentum of the earth–atmosphere system is conserved on the timescales considered here, but for minor interactions with the ocean (Ponte 1990), AAM fluctuations are often associated with small but measurable changes in the rotation rate of the solid earth reckoned as changes in the LOD (Rosen and Salstein 1983), as follows:
k
where AAM* = Mr + 0.7MΩ (Barnes et al. 1983) incorporates a small adjustment on the MΩ contribution to account for the response of the nonrigid solid earth to changes in the mass of the overlying atmosphere. Here, k = 1.68 × 10−29, ΔLOD is in units of seconds, AAM* is in kilogram square meters per second, and the changes are relative to a reference state appropriate for each quantity. Alternatively, we can relate daily changes of AAM* to daily changes in LOD through
i1520-0493-126-6-1681-e10
which states that an increase in AAM leads to an increase in LOD, and a decrease in AAM results in a shorter day.

We wish to investigate the extent to which the high-frequency fluctuations in AAM tendency shown here are reflected in LOD tendency, given the limits of dataset inaccuracy. Relationship (10) is generally valid for early 1996 (Fig. 6b), and is particularly good during the early January and mid-March events. Given the strong relationship between the global AAM tendency and the Northern Hemisphere mountain torque shown in Fig. 6a, this result suggests that this torque was largely responsible for the rapid fluctuations in LOD as a result of the exchange of angular momentum between the atmosphere and solid earth. This connection between the mountain torque and LOD is especially good during events of large high-frequency mountain torque variance.

b. A case study of a strong mountain torque fluctuation

The rapid fluctuations in the Northern Hemisphere midlatitude mountain torque shown in Fig. 6a are, by definition of the mountain torque [Eq. (5)], a result of changes in surface pressure on the eastern and western sides of the sloping topography. A case study is presented to establish the relevant synoptics which produce the high-frequency fluctuations mountain torque and global AAM tendency in the dramatic event of mid-March 1996. We have chosen the 700-hPa geopotential fields as representative of the flow aloft and relate the synoptic-scale upper-air features to the surface pressure changes in the vicinity of the mountains. Findings from the early January and mid-February cases were broadly consistent with those presented for the March case.

For the oscillation during mid-March 1996, Fig. 6a shows that relative maxima in Northern Hemisphere mountain torque occur on 8 March and 20 March, and a relative minimum occurs on 15 March. Figure 7 displays the 700-hPa geopotential height field at these three times. On 1200 UTC 8 March (Fig. 7a), there is a high pressure ridge along the Rockies with a low pressure trough over the eastern Pacific. Over the Himalayas, a ridge along 100°E extends northward from a center at 30° to 70°N into Siberia. A trough extends southward along 60°E from a center near 70°N. On 1200 UTC 15 March (Fig. 7b), the ridge previously positioned over the Rockies has now been replaced by a trough that extends southwestward from the central United States to over extreme northwestern Mexico, and a second trough is located over British Columbia. A ridge is now present over the eastern Pacific. The ridge previously positioned over the Himalayas at 100°E has now been replaced by a trough that extends from 60°N into eastern China, and a ridge centered at 60°N, 50°E extends southward to 40°N, a region previously occupied by a trough. Thus the midlatitude upper-air pattern around the two mountain ranges has reversed during the 7-day period. Inspection of the 700-hPa charts during intermediate times (not shown) reveals that these troughs and ridges can be traced back to the west several days prior, and hence they represent mobile synoptic-scale disturbances in the westerlies. On 1200 UTC 20 March (Fig. 7c), a ridge is once again positioned over the Rockies, and a trough is now over the eastern Pacific, largely repeating the synoptic-scale pattern of 12 days earlier (Fig. 7a). Over Eurasia, both the trough over eastern China and the ridge to the west of the Himalayas have weakened considerably during the 5-day period.

Figure 8 shows the reflections of the upper-air troughs and ridges in the sea level pressure field, a measure of synoptic activity near the surface. On 8 March (Fig. 8a), there is a strong high pressure system to the east of the Rockies that extends from about 60° to 20°N, located slightly downstream of the upper ridge in Fig. 7a. Low pressure is situated to the west of the Rockies over the eastern Pacific beneath the trough aloft. Over Eurasia, there is high pressure over northern China that extends from 70° to 20°N into the East China Sea and positioned just downstream of the upper ridge, and a low pressure trough to the west of the Himalayas along 60°E extends from 80° to 40°N, and is located beneath the upper trough. These sea level pressure systems show considerable meridional elongation, particularly the high pressure on the eastern sides of the Rockies and Himalayas.

On 15 March (Fig. 8b), the sea level pressure patterns across the Rockies and Himalayas have reversed from the prior time (Fig. 8a). Over North America, there is a low pressure center east of the Rockies at 55°N, 110°W, and a low pressure trough extends into eastern Mexico. High pressure is located over the eastern Pacific. Both the high and low pressure systems are positioned slightly downstream of their associated upper-level ridge and trough, respectively. Low pressure is positioned over eastern China near 35°N, 105°E, with a strong high pressure system to the west centered near 60°N, 50°E, positioned beneath an upper trough and ridge, respectively. On 20 March (Fig. 8c), a high pressure system once again extends along the eastern slopes of the Rockies all the way equatorward into Central America, which, combined with the low pressure over the eastern Pacific, yields a sea level pressure pattern across the Rockies similar to 8 March (Fig. 8a). Over Eurasia, the pressures directly to the west of the Himalayas have risen slightly as the high previously positioned at 60°N has moved south, while those to the east have risen substantially as the low previously situated over eastern China has tracked away from the region.

The changes in surface pressure in the vicinity of the mountains, which is directly responsible for the mountain torque fluctuations, are shown in Fig. 9. For the period of decreasing Northern Hemisphere mountain torque (and global AAM tendency) between 1200 UTC 8 March and 1200 UTC 15 March previously shown in Fig. 6a, Fig. 9a illustrates that there are substantial surface pressure rises on the western sides of the mountains and falls on the eastern sides. This succession increases the westward surface pressure gradient across both mountain ranges, and decreases the mountain torque in both midlatitude regions (Fig. 5), which helps to produce a significant decrease in global AAM tendency (Fig. 6a). During the increase in mountain torque between 15 and 20 March, there are surface pressure rises on the eastern side of the Rockies and falls on the western side (Fig. 9b). Over Eurasia, the surface pressure rises more on the eastern side of the Himalayas relative to the western side. This sequence of surface pressure changes increases the eastward pressure gradient across both mountain ranges, increases the local mountain torque (Fig. 5), and helps increase the global AAM tendency (Fig. 6a). Thus, the spectacular oscillation of global AAM tendency of mid-March 1996 appears to be responding to the mountain torque in the Northern Hemisphere produced by the substantial simultaneous local surface pressure changes in the vicinity of both the Rockies and Himalayas associated with synoptic-scale features of the general circulation.

c. Composite pressure patterns that produce large AAM changes

The case study illustrated the strong relationship between surface pressure gradients produced by mobile synoptic-scale systems, the mountain torque they produce, and the high-frequency fluctuations in global AAM. We now wish to determine if the pressure patterns responsible for the rapid changes in mountain torque and AAM shown in that strong case were characteristic of those associated with other high-frequency changes in AAM. We also wish to determine the pressure patterns associated with mountain torque fluctuations in other regions of the globe.

To focus on high-frequency fluctuations in AAM, the time series of global AAM tendency was now first high-pass filtered using a Lanczos filter (Duchon 1979) containing 43 weights and a half-power point of 14 days. The response function of this reasonably sharp filter is shown in Fig. 10. We next prepared composites of surface pressure based upon phases of the high-pass-filtered AAM tendency. The first sample was defined by days when the global high-pass AAM tendency (AȦM) was greater than or equal to +1.5 standard deviations (σ) from the mean, and the second by days when AȦM ⩽ −1.5σ. We then created a composite of surface pressure for these days, called here times when AAM was strongly increasing and strongly decreasing, and the difference in the composite pressure fields of the two samples provides a good indication of the surface pressure patterns present during opposite phases of high-frequency fluctuations in AAM tendency. Given the seasonality of high-frequency mountain torque variance (Figs. 3, 4), composites were formed separately for all months, for the Northern Hemisphere cool season (November–April), and for the Southern Hemisphere cool season (May–October). The composites span the period of April 1994–November 1996.

Figure 11a shows the difference in composite surface pressure between days when AAM is strongly increasing and AAM is strongly decreasing. There are 65 and 72 days in these increasing AAM and decreasing AAM composites, respectively. The surface pressure patterns during the opposite extremes of the AAM tendency have a considerable cross-mountain component near the Rockies, Himalayas, and Andes, indicating the importance of these mountain ranges to high-frequency fluctuations in global AȦM through the mountain torque. Lesser surface pressure gradients exist across Greenland, the Alps, and southern Africa. The net effect of these surface pressure patterns is to create an eastward-directed pressure gradient across the mountains which, through Eq. (5), is consistent with the production of a positive mountain torque and positive AAM tendency.

The composite difference in surface pressure for strongly increasing AAM and strongly decreasing AAM days for the Northern Hemisphere cool season is shown in Fig. 11b. There are 32 and 35 days in these composites, respectively. The patterns have stronger centers in the Northern Hemisphere than in the Southern Hemisphere. Most pronounced are the eastward surface pressure gradients across the Rockies and Himalayas, although there is also an eastward pressure gradient across Greenland and an indication of an eastward pressure gradient across the Alps. The high pressure to the east of the Rockies is centered in the midwestern United States, and extends the large distance from southern Canada to Central America. The low pressure to the west of the Rockies is centered off the coast of British Columbia, and it extends poleward to Alaska and equatorward to northern Mexico. In the Eurasia region, there is relatively high pressure over eastern China and low pressure to the west of the Himalayas. The high pressure extends well poleward into the northeastern portion of the Asian continent. Such a pressure pattern resembles that responsible for the rapid increase in mountain torque and AAM tendency during the case study of mid-March 1996 discussed above (Fig. 9b). In the Southern Hemisphere, relatively high pressure exists on the eastern side of the Andes and across southern Africa.

A similar composite is shown for the Southern Hemisphere cool season (May–October) in Fig. 11c. There are 33 and 37 days in the strongly increasing AAM and strongly decreasing AAM composites, respectively. The pressure differences across the Northern Hemisphere mountains are greatly diminished while the pressure differences across the Southern Hemisphere mountains are better defined, in agreement with our previous results regarding the seasonal nature of the contributions from the two hemispheres to the high-frequency mountain torque variance. The most notable pattern is situated across the Andes with relatively high pressure centered over Argentina, extending poleward and equatorward along the eastern slopes of the Andes, similar to the configuration of the anticyclone discussed in a case study of a rapid fluctuation in AAM by Salstein and Rosen (1994). Low pressure is situated on the western side of the Andes, creating a significant eastward pressure gradient across the mountains. As in Fig. 11b, there is high pressure to the east of southern Africa and low pressure to the west.

Two other features in the composites are worth mentioning. First, the composite pressure systems have significant meridional elongation along the eastern slopes of all three major mountain ranges, particularly during the cool seasons. This meridional elongation in the lee of the mountains was previously noted in the case study (Fig. 8) and creates a zonal pressure gradient across the topography of considerable north–south extent. The result is a significant local contribution to the global mountain torque. Additionally, the equatorward extension of the surface pressure features may be important because for a given topography, a larger mountain torque is produced from a fixed pressure gradient at a lower (compared to a higher) latitude due to the influence of the distance to the earth’s axis of rotation upon the torque [Eq. (5)]. Thus, these synoptic-scale meridionally elongated pressure systems appear to have a significant impact upon the changes in global AAM on timescales of less than 2 weeks.

Second, the locations of the centers of surface pressure differences in Fig. 11 are relatively invariant with respect to season. There is some poleward movement of the surface pressure centers from the cool season to the warm season, but for the most part the cool season patterns are simply amplifications of those during the warm season. This relationship indicates that the regions responsible for the high-frequency fluctuations in AAM tendency are nearly invariant, being tied to the earth’s topography, and that only their relative importance changes with season. This result also suggests that by knowing the surface pressure in localized regions, one can obtain considerable information about high-frequency changes in the regional mountain torque and global AAM.

The localized nature of the results in Fig. 11 suggest that a meaningful index of regional mountain torque and high-frequency changes in global AAM can be derived from only a small subset of surface pressure data. For example, two stations were chosen, Wichita, Kansas (ICT, 37.7°N, 97.4°W), and Portland, Oregon (PDX, 45.6°N, 122.6°W), that lie near the centers of the surface pressure differences in Fig. 11a that straddle the Rockies. The sea level pressure observations from synoptic hours (0000, 0600, 1200, and 1800 UTC) were daily averaged to be centered at 0900 UTC in the same manner as the torque data. The difference in daily averaged pressure between the two stations is plotted along with the mountain torque in the North America region for the period of January–March 1996 (Fig. 12a). The two time series correlate very well (r = 0.81), indicating that the pressure difference between these two points is a very good indicator of the sense of the mountain torque across the entire North America region.

The sea level pressure difference between these two stations is now plotted with the global AAM tendency in Fig 12b. Changes in sea level pressure difference between these two stations coincide fairly well with the global AAM tendency (r = 0.67), and thus a considerable amount of information regarding the global AAM tendency during this 3-month period can be gathered simply by knowing the sea level pressure difference between these two North American stations. Future work will focus upon testing the robustness of this relationship between local pressure differences and global AAM for a longer time series and for other regions of the globe, such as in the vicinity of the Himalayas and Andes.

4. Discussion

This study has shown that high-frequency fluctuations in global AAM result primarily from the mountain torque in the midlatitudes of both hemispheres due to changes in surface pressure across the major mountain ranges (Rockies, Himalayas, and Andes) accompanying synoptic-scale systems. A case study was presented to provide an example of the relevant synoptics associated with a rapid modulation of local mountain torque and global AAM. Our results have also indicated that each hemisphere has a maximum in high-frequency mountain torque variance in its cool season.

It is likely, then, that the seasonal dependence of high-frequency mountain torque variance is directly related to the frequency of occurrence of midlatitude synoptic-scale cyclones and anticyclones near the Rockies, Himalayas, and Andes. In support of this conjecture, synoptic climatology studies indicate that in the Northern Hemisphere, there is a cool season maximum in the frequency of midlatitude cyclones and anticyclones in the vicinity of the Rockies and Himalayas (Petterssen 1956; Whittaker and Horn 1984; Zishka and Smith 1980). In the Southern Hemisphere, Sinclair (1994, 1996) found a cool-season maximum of both anticyclone and cyclone frequency in the region of South Africa. To the east of the Andes, there is a maximum of anticyclone frequency in cool season, while cyclones in the vicinity of the Andes are prevalent year-round (Jones and Simmonds 1994; Sinclair 1996; Taljaard 1967). The decrease in cyclone and anticyclone activity from the cool to the warm season is a result of a weakening of the tropospheric meridional temperature gradient and a poleward shift of the upper-level storm track. Thus the seasonal changes in high-frequency mountain torque variance found here are consistent with the alteration in synoptic-scale activity from the cool to the warm season of both hemispheres.

The case study and composite study also show considerable meridional elongation of the surface pressure patterns that are associated with strong high-frequency fluctuations in AAM, and this elongation is particularly evident on the lee side of the mountain ranges. For high pressure systems, the meridional elongation is characteristic of synoptic-scale events called “cold surges” which are associated with marked equatorward penetration of cold air. Cold surges are observed most often during the cool season in the lee of the Rockies (DiMego et al. 1976; Henry 1979), Himalayas (Murakami and Nakamura 1983), and Andes (Hamilton and Tarifa 1978). The equatorward progression of the cold surges is believed to be a result of the interaction between the synoptic-scale flow and the sloping topography (Colle and Mass 1995). In the case of low pressure, westerly airflow over topography often leads to meridionally elongated surface troughs in the lee of the topographic barrier (Hess and Wagner 1948; Newton 1956). Thus, the meridionally elongated structure of the pressure systems observed in this study is consistent with those synoptic-scale features observed in the vicinity of the mountains. These synoptic-scale features may, by virtue of their meridionally extensive cross-mountain pressure gradient, result in considerable high-frequency fluctuations of mountain torque and, therefore, AAM tendency. Indeed, such elongated patterns have been shown to produce mountain torques for an individual mountain range (Czarnetzki 1997).

It is also suggested in this study that the large fluctuations in global AAM tendency during early 1996 were reflected in the measurements of changes in the length of day, and that the mountain torque is the primary mechanism by which angular momentum is exchanged between the atmosphere and solid earth on these short timescales. Previous studies (Rosen et al. 1984; Salstein and Rosen 1994; Wolf and Smith 1987) also identify this relationship between AAM and LOD for isolated cases of high-frequency fluctuations in AAM. When viewed over a longer time series, however, high-frequency fluctuations in LOD are poorly related to fluctuations in AAM (Rosen et al. 1990), and the lack of agreement is attributed to declining signal-to-measurement noise ratios of both data types (Dickey et al. 1992). It is also possible that the poor relationship is produced by the inclusion of many smaller, poorly measured events while large-amplitude episodes of AAM fluctuations are indeed detectable.

To test this hypothesis, we return to the time series of high-pass-filtered AAM tendency and we calculate a number of correlation coefficients between daily changes in LOD and AAM, based on the strength of the daily AAM changes. For the entire time series, such a correlation is 0.39. If we select only those days when |AȦM| ≥ 1.5σ the correlation increases to 0.59, and for days when |AȦM| ≥ 2.0σ, the correlation grows further to 0.71. These results indicate that for the cases of sufficiently strong high-frequency fluctuations in AAM, the exchange in angular momentum between the solid earth and atmosphere through the mountain torque is reasonably well captured by the current analysis systems and LOD observing networks.

5. Conclusions

This study sought to identify the relative role of the mountain versus friction torque to the high-frequency (⩽14 day) fluctuations in global AAM tendency, isolate the regions responsible for these fluctuations, and suggest a mechanism in the global circulation responsible for the high-frequency fluctuations. We find that the mountain torque is much more important than the friction torque in the global balance of atmospheric angular momentum on high frequencies. On timescales greater than about three weeks, however, the friction torque begins to play a more significant role. The midlatitudes of both hemispheres are primarily responsible for the high-frequency fluctuations in mountain torque and global AAM.

To identify the mechanism responsible for the high-frequency fluctuations, first a case study was performed during an extraordinary fluctuation in mountain torque and AAM tendency in mid-March 1996. The case study revealed that the mountain torque fluctuations were a result of changes in the surface pressure gradient across a wide north–south extent of both the Rockies and Himalayas, brought about by migratory synoptic-scale weather systems as they traversed these mountain ranges. The resulting regional mountain torque then impacted the global AAM on synoptic timescales, and caused a coincident fluctuation in LOD. This result is consistent with those of previous case studies involving high-frequency fluctuations in AAM.

A composite study using a time series of global AAM tendencies and gridded surface pressure showed that the surface pressure gradients in the vicinity of the Rockies, Himalayas, and Andes, and to a lesser extent southern Africa, were routinely associated with significant high-frequency fluctuations in AAM tendency. The pressure differences across the Rockies and Himalayas of the Northern Hemisphere play a major role in the high-frequency fluctuations in AAM tendency during the Northern Hemisphere cool season (November–April), whereas the Andes in the Southern Hemisphere were most important in the Southern Hemisphere cool season (May–October). Further, the composites suggest that as in the case study, the surface pressure systems responsible for the most notable high-frequency fluctuations in global AAM tendency exhibit considerable meridional elongation, particularly on the eastern sides of the topography, which is characteristic of synoptic-scale systems in the lee of mountains. This meridional elongation results in a zonal pressure gradient across the mountains spanning many latitudes, and helps to produce significant local mountain torque fluctuations and hence global AAM fluctuations on synoptic timescales. These relatively large amplitude mountain torque fluctuations were able to produce changes in LOD consistent with an exchange of momentum between the solid earth and atmosphere through the mountain torque.

Lastly, it was suggested that the sea level pressure differences at a limited set of stations can yield considerable information about the mountain torque over a broad continental region and, to a lesser extent, the global AAM tendency. Future work will attempt to more precisely isolate the regions responsible for high-frequency mountain torque variations through the development of a mountain torque index based upon sea level pressure differences from station data. The development of such an index based upon the historical record of sea level pressures may allow for the study of mountain torque and AAM fluctuations over a longer period than is possible from an analysis system alone. Further, in light of the connection between synoptic-scale pressure changes at the surface and disturbances aloft, the dependence of mountain torque variance upon midlatitude flow regimes and upper-level storm track position will be investigated.

Acknowledgments

We wish to thank Glenn White at NCEP who provided us with the torque and AAM data used in this study, Richard Gross at JPL for the LOD data, and Karen Cady-Pereira and Peter Nelson for archiving the data at AER and providing software support. Gratitude is also expressed to Richard D. Rosen for his thoughtful review of the manuscript, and Klaus Weickmann for his comments on the work. Helpful suggestions were also provided by Lance Bosart and Ed Bracken. Our use of the NCAR data archive is acknowledged. Support for this project was provided by NASA Mission to Planet Earth Awards NAGW-2615 and NAS5-32861 and by the NOAA Climate and Global Change Program under Award NA46GP01212E.

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Fig. 1.
Fig. 1.

Daily time series of the global AAM tendency (dotted) and the sum of the global friction and mountain torque (solid) for the period 1 November 1995–1 November 1996. Units are 1019 kg m2 s−2.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 2.
Fig. 2.

Log–log power spectrum with period of global angular momentum tendency (solid), global mountain torque (dotted), and global friction torque (dash–dot) based upon data for the period February 1992 to November 1996. Units are (1018 kg m2 s−2)2 day. The periodogram is smoothed using a five-point moving average in frequency.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 3.
Fig. 3.

Three-year mean variance of zonally integrated mountain torque in 14-day moving windows shown as a function of latitude and time. Units are (1018 kg m2 s−2)2 per degree latitude. Contours are drawn every 0.2, and values greater than or equal 0.6 are shaded.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 4.
Fig. 4.

(a) Boxes defining four midlatitude domains used in the study to compute the regional mountain torque. The Eurasia box and North America boxes are bounded by latitudes 20° and 60°N, and separated by longitudes 20°W and 180°. The Africa and South America boxes are bounded by latitudes 10° and 40°S, and separated by longitudes 0° and 180°. Shading indicates elevation of at least 1000 m from the Rand 1° × 1° topography grid. (b) Contribution to the total high-frequency variance in a latitude band by the two continental regions in that band, as well as total high-frequency band variance. Units are (1019 kg m2 s−2)2.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 5.
Fig. 5.

Daily time series of the mountain torque in the Eurasia region (solid) and North America region (dotted) for the period 1 January 1996 to 31 March 1996. Units are 1019 kg m2 s−2. The bars beneath the time series highlight the three episodes mentioned in the text.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Daily time series of the sum of the mountain torque in the North America and Eurasia regions (solid) and the global atmospheric angular momentum tendency (dotted) for the period 1 January–31 March 1996. (b) Daily time series of global atmospheric angular momentum tendency from NCEP analysis (dash–dot) and inferred from measurements of LOD (solid). Units are 1019 kg m2 s−2.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 7.
Fig. 7.

Geopotential height of the 700-hPa level at 1200 UTC for (a) 8 March, (b) 15 March, and (c) 20 March 1996. Contours are every 6 dam. Highs and lows discussed in the text are indicated by the letters H and L.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 8.
Fig. 8.

Sea level pressure at 1200 UTC for (a) 8 March, (b) 15 March, and (c) 20 March 1996. Contours are every 6 hPa. Highs and lows discussed in the text are indicated by the letters H and L.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 9.
Fig. 9.

(a) Difference in surface pressure between 1200 UTC 15 March and 1200 UTC 8 March 1996 (every 4 hPa contoured, zero line omitted). Positive contours are solid and negative dashed. (b) Same as (a) except between 1200 UTC 20 March and 1200 UTC 15 March. Shading indicates surface elevation of at least 1000 m.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 10.
Fig. 10.

Response function of the high-pass filter used in the study, plotted linearly in frequency but marked in period. The filter contains 43 weights, and a half-power point of 14 days.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 11.
Fig. 11.

The difference in surface pressure (contoured every 1 hPa) for days when the global high-pass AAM tendency is greater than or equal to +1.5 standard deviations and days when the global high-pass AAM tendency is less than or equal to −1.5 standard deviations from the mean for (a) all months, (b) November–April, and (c) May–October. Shading indicates regions of statistical significance at the 95% confidence level as estimated by a Student’s t-test. Positive values are solid and negative values are dashed.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

Fig. 12.
Fig. 12.

Daily time series of the difference in sea level pressure (solid, units hPa) between Wichita, Kansas (ICT, 37.7°N, 97.4°W), and Portland, Oregon (PDX, 45.6°N, 122.6°W), plotted with (a) mountain torque over North America (dotted, 1018 kg m2 s−2) and (b) global atmospheric angular momentum tendency (dotted, 1018 kg m2 s−2) for the period 1 January–31 March 1996. Note that the curves are plotted with two different scales.

Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1681:RSOMTV>2.0.CO;2

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