Migrating and nonmigrating semidiurnal tides in the upper atmosphere excited by tropospheric latent heat release



[1] We overview the results of a series of global-scale wave model (GSWM) calculations we designed to quantify the mesospheric and lower thermospheric migrating and nonmigrating semidiurnal tidal response to large-scale tropospheric latent heat release associated with deep tropical convection. Our semidiurnal tidal forcing is based on a 7-year database of global cloud imagery that is also characterized herein. The combined responses of the migrating and nonmigrating components are sufficiently large to modulate the radiatively excited migrating semidiurnal tide in the upper atmosphere during every month of the year. This modulation produces longitudinal tidal variability that may be important to the interpretation of both ground-based and satellite-borne semidiurnal tidal diagnostics.

1. Introduction

[2] Atmospheric solar tides are global-scale waves with periods that are harmonics of a solar day. These waves are excited in a variety of ways, including the absorption of solar radiation, large-scale latent heat release, nonlinear interactions between particular sets of global-scale waves, interactions between tides and gravity waves, and the gravitational pull of the Sun. The solar semidiurnal tides are the subset of waves with 12-hour periods that are further characterized by the number of perturbation maxima or minima along a latitude circle, that is, the zonal wave number. By definition, the migrating semidiurnal tide propagates with the apparent motion of the Sun when observed from the ground. Thus it is a westward propagating zonal wave number 2 (W2) perturbation. All other 12-hour global perturbations are nonmigrating semidiurnal tides. These include an eastward propagating wave number 2 (E2) and a standing (S0) perturbation. Throughout this report, we employ this nomenclature to distinguish between the westward propagating (Ws) and eastward propagating (Es) semidiurnal tidal components with characteristic zonal wave number, s. We focus on those components of semidiurnal tide that are excited by the latent heat release associated with raindrop formation in deep convective clouds in the tropical troposphere.

[3] In a complementary study of the diurnal tide [Hagan and Forbes, 2002] we recently highlighted previous work on nonmigrating tides that included descriptions of both observational [e.g., Talaat and Lieberman, 1999] and numerical studies. We pointed to a series of review papers and tutorials [Forbes and Garrett, 1979; Kato, 1980; Forbes, 1984; Volland, 1988; Vial, 1989; Vial and Forbes, 1989; Forbes, 1995; Hagan, 2000] wherein nonmigrating tides emerged as important sources of tidal variability in the upper mesosphere and lower thermosphere (MLT). We also described previous efforts to model nonmigrating tides [Kato et al., 1982; Forbes and Groves, 1987; Tsuda and Kato, 1989; Tokioka and Yagai, 1987; Yagai, 1989; Miyahara et al., 1993; Lieberman and Leovy, 1995; Williams and Avery, 1996; Ekanayake et al., 1997; Hagan et al., 1997]. We paid particular attention to those reports that discuss the MLT effects of nonmigrating diurnal tides. We refer the reader to this body of work and to our complementary report [Hagan and Forbes, 2002] for specific details.

[4] Herein, our focus is the semidiurnal tide with an emphasis on its nonmigrating components and their effects in the MLT. In the remainder of this section we discuss the relevant work on this topic to date.

[5] Bernard [1981] was the first to theoretically explore the longitudinal variability of the semidiurnal tide and hence the nonmigrating tidal components. Thereafter, Miyahara et al. [1993] and Miyahara and Miyoshi [1997] used the middle atmosphere circulation model at Kyushu University (MACMKU) to study the effects of nonmigrating semidiurnal tides in the middle and upper atmosphere. Although they reported measurable effects, these authors were unable to confirm their predictions owing to the lack of sufficient global MLT observations.

[6] Until very recently there was little observational evidence of nonmigrating semidiurnal tides in the MLT. One notable exception is the W1 component which was extensively investigated during the last decade using ground-based MLT wind measurements made at South Pole [e.g., Hernandez et al., 1993; Forbes et al., 1995, 1999; Portnyagin et al., 1998]. Complementary modeling studies [Miyahara et al., 1999; Angelats i Coll and Forbes, 2002; Yamashita et al., 2003] suggest that the W1 semidiurnal tidal winds over South Pole are largely due to the nonlinear interaction between the migrating semidiurnal tide and a wave number 1 stationary planetary wave at lower altitudes. These modelers also reported on the W3 semidiurnal tide, the other by-product of the interaction. Angelats i Coll and Forbes [2002] also provided an observational perspective on the global structure of both components because their report included correlative analyses of upper atmosphere research satellite (UARS) wind measurements. Their work complements the recent results of A. H. Manson et al. (Global distributions of diurnal and semidiurnal tides: Observations from HRDI-UARS of the MLT region, submitted to Journal of Geophysical Research, 2002), who quantified the longitudinal variability of the semidiurnal tide in the MLT using UARS wind data. Diagnostics of the zonally symmetric, or S0, density and temperature perturbations with 12-hour periods at high latitudes in both hemispheres [e.g., Hernandez et al., 1993; Oznovich et al., 1997; Walterscheid and Sivjee, 2001] constitute another notable body of observational evidence of nonmigrating semidiurnal tidal effects in the MLT.

[7] In a previous tidal investigation, Forbes et al. [1997] forced GSWM with migrating diurnal and semidiurnal latent heating rates and reported MLT temperature and wind responses of 5–10°K and 10–20 m/s, respectively. They based the heating rates on annually averaged global cloud imagery (GCI) measurements made over a 7-year period. Forbes et al. [1997] also demonstrated that GCI is a viable proxy for rainfall rate with a correlative analysis of rain gauge data. We report herein on monthly averaged migrating and nonmigrating semidiurnal heating rates derived from the same 7-year GCI database [Forbes et al., 1997] and the GSWM tidal responses to these monthly rates. We describe the GSWM and the latent heating rates in the following section. Subsequently, we overview the monthly variable GSWM responses with representative semidiurnal solutions for December, March, June, and October. Before concluding, we assess the importance of the tropospheric latent heat source to the semidiurnal tide in the MLT and discuss the implications for future observational and numerical studies of atmospheric tides.

2. The GSWM

2.1. Model Overview

[8] The GSWM is a two-dimensional, linearized, steady state numerical tidal and planetary wave model which extends from the ground to the thermosphere [Hagan et al., 1993, 1995, 1999, 2001; http://www.hao.ucar.edu/public/research/tiso/gswm/gswm.html]. The GSWM tidal and planetary wave predictions are solutions to the linearized and extended Navier-Stokes equations for perturbation fields with characteristic zonal wave numbers and periodicities that are specified along with the zonal mean background atmosphere. Mean zonal (meridional) winds are included (neglected). The most recent version of the model, hereafter GSWM-00, was a simple extension to GSWM-98 [Hagan et al., 1999] and produced monthly variable migrating tidal responses to the absorption of solar radiation throughout the atmosphere. Most of the GSWM-98 model inputs and parameterizations vary inherently with month and were also used in GSWM-00 calculations. The exceptions were the seasonally variable GSWM-98 tropospheric radiative heating rates [Hagan, 1996] and the effective Rayleigh friction coefficients that account for gravity wave drag on the diurnal tide [Hagan et al., 1999]. These were linearly interpolated for monthly GSWM-00 calculations. For the GSWM calculations that we report herein we replaced the GSWM-00 tidal forcing functions with the parameterization that is described in the following section and implemented the remaining GSWM-00 schemes and inputs. We further characterize the GSWM-00 background atmosphere and dissipative schemes in the paragraphs below.

[9] From the ground to the upper thermosphere GSWM-00 background temperatures and densities are specified by MSISE90 [Hedin, 1991]. Below ∼20 km the background winds are from the semiempirical model of Groves [1985, 1987], but the strato-mesospheric jets and mesopause region winds are based upon Upper Atmosphere Research Satellite (UARS) High Resolution Doppler Interferometer (HRDI) climatologies [Hagan et al., 1999]. Above ∼125 km, zonal mean zonal winds are from HWM93 [Hedin et al., 1991, 1996].

[10] Tidal dissipation occurs throughout the atmosphere and may be attributable to ion drag, molecular and eddy viscosity and conductivity, and radiative damping. GSWM-00 molecular conductivity and viscosity as well as ion drag and Newtonian cooling parameterizations of radiative damping are discussed by Hagan et al. [1993]. GSWM-00 employs a monthly climatology of eddy diffusion coefficients, Kzz, and explicitly calculates the divergences of the associated heat and momentum fluxes in the model [cf. Forbes, 1982]. Kzz account for the effects of turbulence generated by gravity waves as they become unstable and finally break in the upper mesosphere and lower thermosphere (MLT) along with other related mixing phenomena. The GSWM-00 Kzz are based on the results calculated by Garcia and Solomon [1985] as detailed by Hagan et al. [1995]. GSWM-00 also includes a monthly variable effective Rayleigh friction coefficient [cf. Miyahara and Forbes, 1991] to account for gravity wave drag on the diurnal tide [Hagan et al., 1999]. We refer the reader to the reports cited above along with references therein for additional details regarding tidal dissipation processes and parameterizations in GSWM.

2.2. GSWM Tidal Forcing Due to Tropospheric Latent Heat Release

[11] In this section we overview our GSWM parameterization of tidal forcing due to latent heat release that is based on 3-hourly measurements of satellite cloud images made during 1988 to 1994. In our previous report on the diurnal tide [Hagan and Forbes, 2002] we described our approach in detail. Herein, we discuss the characteristics of the semidiurnal component after we briefly summarize our assumptions and methodology. We refer the reader to Hagan and Forbes [2002] and references therein for additional details.

[12] We use satellite GCI and the relationship between infrared brightness temperatures and the fractional coverage of the clouds on a 2.5° latitude by longitude grid between 40°S and 40°N to deduce 3-hourly monthly averaged rainfall rates. Cloud brightness temperatures are cold when the cloud tops are high and tropical tropospheric convection is deep [Arkin and Xie, 1994; Janowiak and Arkin, 1991], and deep convective activity is a proxy for latent heat release associated with raindrop formation. We then harmonically decompose the rainfall rates to determine the mean, diurnal, and semidiurnal components. We subsequently Fourier fit the harmonics at each latitude to quantify the 13 zonal wave number (E6 to W6) perturbations of monthly rainfall rate [Hendon and Woodberry, 1993; Williams and Avery, 1996].

[13] Figure 1 illustrates a map of the January semidiurnal harmonic of monthly averaged rainfall rates between 30°S and 30°N along with our 13-zonal wave number fit to these data. Many of the features of these semidiurnal components are similar to their diurnal counterparts which we previously illustrated [Hagan and Forbes, 2002]. One notable difference is the magnitude of the semidiurnal rainfall rates which is ∼35% smaller than the diurnal component. Thus the associated semidiurnal tidal forcing is weaker than the diurnal forcing. We cannot deduce anything about the comparative efficiency with which the upward propagating components of the semidiurnal forcing are excited without considering the tidal vertical wavelengths and the depth of the latent heating. We pursue such a discussion after we describe some of the features seen in Figure 1 that are also common to the diurnal rainfall component.

Figure 1.

Contour maps of the semidiurnal component of rainfall rate (mm/day) deduced from the 7-year GCI measurements made during the months of January (top) and the reconstructed 13 zonal wave number fits (bottom) to these data. See text for details.

[14] Semidiurnal rainfall rates between 50 and 90°E are linear interpolations across a gap in the GCI coverage. During January rainfall rates are strongest in the tropical Southern Hemisphere and over the continents. Similar patterns characterize the remaining 11 months (not illustrated), but the locations of rainfall maxima move across the equator with the seasonal migration of the intertropical convergence zone (ITCZ).

[15] Only the gross features of the semidiurnal rainfall rate are evident in the reconstructed wave number fit (Figure 1), so this fit is smooth and comparatively weaker than the observations in regions where there is significant mesoscale variability. For example, the semidiurnal rainfall rate exceeds 2.2 mm/day in localized regions over Indonesia, Northern Australia, and the southern Pacific (∼90–200°E), but the reconstructed fit to these data maximizes at ∼1 mm/day. Further, the weak and patchy precipitation features in the Northern Hemisphere (e.g., poleward of 10°N) are absent from the reconstructed fit. In contrast, strong diurnal rainfall rate measurements (>2.2 mm/day) over large regions of southern Africa and South America are also evident in the reconstructed fit.

[16] We base our GSWM tidal forcing parameterization on the deconstructed wave number fit to the semidiurnal rainfall rates (Figure 1), but we exclude the artifacts of rainfall near 30°N and 90 to 110°E because they cannot be associated with deep tropical convection. We invoke an exponential tail-off poleward of 40° and deduce the latitudinal variation of the GSWM semidiurnal tidal forcing for each of the 13 zonal wave numbers. Despite the absence of any tidal forcing at middle to high latitudes, it is reasonable to expect a global response aloft because tides are global-scale waves. That is, the comparatively localized forcing projects onto horizontal expansion functions that extend from pole to pole, well beyond the region of excitation. Further, tides are Doppler shifted by the mean winds. These effects are particularly pronounced for tidal components with large zonal wave numbers.

[17] Figure 2 illustrates the monthly variability of this latitude variation at low latitudes for four select wave numbers: the W2 (migrating), E2, W6, and W1 components of semidiurnal rainfall. The semidiurnal W2, E2, and W6 rainfall rates can be explained in simple terms that involve the semidiurnal harmonic of the absorption of solar energy and its subsequent conversion to deep convection which differs over continental and maritime locations [e.g., Bergman, 1997]. Specifically, the 12-hour harmonic of energy absorption (i.e., the W2 component) is modulated at the surface by the dominant zonal wave number 4 in topography [Yagai, 1989] at low latitudes. This modulation produces the E2 and W6 components [Forbes et al., 2003]:

display math

where λ is longitude, t is UT hours, and Ω is 2π/24 hours. Wave number 1 is the second most important topographic component in the equatorial region. In a similar manner the modulation of W2 solar heating gives rise to the W1 and W3 semidiurnal rainfall rate components.

Figure 2.

Contours of the westward propagating wave number 2 (upper left), eastward propagating wave number 2 (upper right), westward propagating wave number 6 (lower left), and westward propagating wave number 1 (lower right) components of tropical semidiurnal rainfall rate (mm/day) as a function of month and latitude.

[18] The migration of the semidiurnal rainfall with the ITCZ that we described above is evident in the seasonal variations of the components illustrated in Figure 2 as well as those that are not shown in this report. Even though interhemispheric asymmetries occur throughout the year, the associated semidiurnal heating rates are more symmetric about the equator near equinox than they are near solstice. This behavior is especially apparent in the W1 and W6 rates. The rainfall rates and thus the tidal forcing are stronger during austral summer than they are in boreal summer. The migrating component of semidiurnal rainfall is the most significant with maximum amplitudes at 10°S that exceed 1 mm/day during January and February (Figure 2). Complementary E2 rates during this period are up to 60% as large as the W2 but the E2 semidiurnal rainfall maximum is about 5 degrees further south (near 15°S). There is another burst of equally strong E2 activity, which moves from the equator to 10°S during October and November. These E2 signatures are comparable to the near equatorial W2 rates at these times. There are also equatorial peaks in the W6 component of semidiurnal rainfall in March, April, May, September, and October, but these never approach the magnitude of the W2 activity there. In contrast, W1 rates are strong (>0.4 mm/day) well into the southern extratropics during austral summer when they are comparable to the migrating component near 20°S. The W6 and W1 rainfall rates exemplify most of the remaining components in that their monthly amplitude maxima range between about 0.2 and 0.4 mm/day (Figure 2). The E4, E5, and E6 rainfall rates are exceptions with comparatively negligible rainfall rates of at most 0.2 mm/day (not illustrated). There are also notable differences between the W6 and W1 responses: differences in month-to-month amplitude variations, hemispheric symmetry, and latitudinal extent of the component contribution. We find similar differences between these and the remaining components (not illustrated).

[19] Next, we overview our assumptions regarding the depth and the vertical structure of the latent heating associated with the convective activity inferred from the GCI measurements. We refer the reader to the detailed discussion and illustration given by Hagan and Forbes [2002] for additional details. Specifically, we assume

display math

to specify the depth and the vertical structure of tropospheric latent heating. Equation (2) was initially developed by Hong and Wang [1980] for altitude, z (km), and 1.0 mm/day = 5.34 mW/kg. J(z) peaks at 6.5 km, but it can only be associated with deep convective activity since the heating extends throughout the troposphere, from the surface up to an altitude that is consistent with the global-mean tropopause (∼15 km). Our GCI rainfall determinations inherently include elements of the so-called stratiform precipitation which forms in comparatively narrow layers in the tropical troposphere [Houze, 1997]. Thus we reduced the monthly rainfall rates by 25% to exclude stratiform precipitation effects from our GSWM tidal forcing scheme in keeping with the discussion put forth by Houze [1997]. The depth of the heating specified by equation (2) suggests that semidiurnal tidal components with vertical wavelengths of ∼25–30 km (i.e., twice the depth of the heating) should be most readily excited by this forcing function [e.g., Garcia and Salby, 1987].

[20] In accordance with classical tidal theory [e.g., Chapman and Lindzen, 1970] each of the wave number components of semidiurnal rainfall can also be quantified in terms of a Hough mode expansion series. Hough modes are either symmetric or antisymmetric about the equator and each mode has a characteristic wavelength. Thus in this formulation the efficacy of the semidiurnal tidal excitation that results from the latent heating associated with raindrop formation will depend both on the depth of the heating and on the projection of its latitudinal structure onto a given mode. Many of the migrating and nonmigrating semidiurnal tides have major upward propagating wave number components with such vertical wavelengths, so it is reasonable to expect that deep convective activity in the tropical troposphere generates global scale waves that propagate into the middle and upper atmosphere during every month of the year. The E2 semidiurnal tide is a notable exception. The infinite and 183-km vertical wavelengths of its gravest symmetric and antisymmetric modes, respectively, are too large for these waves to be efficiently excited by latent heat release in deep convective clouds. Thus we do not expect strong signatures of the E2 semidiurnal tide in the MLT in spite of its prominent role in our GCI analysis results (Figure 2). We report on the results of our GSWM calculations that confirm this conjecture and investigate the associated nonmigrating semidiurnal tides that along with the monthly variable zonal mean zonal winds and dissipation, modulate the behavior of the migrating component in the following section.

3. Results

[21] We calculated the semidiurnal tidal response for each of 13 zonal wave numbers (W6 to E6) and for every month of the year using the GSWM-00 background atmosphere and tidal dissipation schemes along with the tidal forcing described above. Owing to space limitations it is impossible for us to discuss the entire set of 156 calculations. We therefore present representative results for December, March, June, and October and focus on the components that produced MLT temperature or horizontal wind perturbations in excess of 5°K and 5 m/s, respectively. The GSWM responses for 10 of the 13 semidiurnal components that we investigated meet these criteria but not during every month or at all latitudes. The comparatively weak E4, E5, and E6 responses do not, and because they produce no measurable MLT effects, we omit their further discussion. Hereafter, we refer to the MLT results that excede 5°K or 5 m/s as the major component solutions.

3.1. Latitudinal Variations of Select Major Component Responses

[22] Figure 3 illustrates the latitude variation of the GSWM major semidiurnal zonal wind amplitudes at 115 km during December, March, June, and October. Figure 4 illustrates the complementary temperature amplitudes at 124 km. The W2 response to tropospheric latent heating persistently exceeds our major component threshold amplitudes and dominates the GSWM middle to high-latitude semidiurnal response with a couple of notable exceptions. There is a strong W1 wind amplitude that peaks at the North Pole during southern summer (Figure 3) and an S0 semidiurnal temperature maximum at South Pole during northern summer (Figure 4). The associated S0 zonal wind response is comparable to the W2 during June (Figure 3) when the associated S0 meridional wind exceeds the W2 amplitude between ∼45 and 85°S (not illustrated). The W6 semidiurnal tide is the other persistent major component solution. This component dominates the equatorial and low-latitude temperature and zonal wind responses to semidiurnal latent heating, but the W6 meridional amplitudes are negligible throughout the year. The remaining major component responses that we illustrate include the W3, W4, and E3 semidiurnal tides. Their contributions to the MLT response are comparatively intermittent, while the low-latitude W5 amplitudes are significant throughout most of the year with the exception of boreal summer (Figures 3 and 4). The GSWM meridional wind response also includes a significant E1 component during October and an E2 component during March (not illustrated).

Figure 3.

The latitude structure of GSWM semidiurnal zonal wind amplitudes (m/s) at 115 km during December (top), March (second), June (third), and October (bottom) for the W2 (solid curve), W6 (dashed curve), W5 (thick dot-dashed curve), S0 (thick dotted curve), W1 (thick triple dot-dashed curve), W3 (thin dot-dashed curve), and E3 (thin dashed curve) component solutions excited by tropospheric latent heat release. See text for details.

Figure 4.

Same as Figure 3, except for semidiurnal temperature amplitudes (°K) at 124 km and the additional W4 (thin dotted curve) component solution.

[23] We interpret the behavior of the largest W2, W6, W1, and S0 semidiurnal tides (Figures 3 and 4) in light of the gravest Hough modes associated with these components. The S0 Hough function and the W1 Hough wind expansion functions peak at the poles where the associated functions for all the remaining components approach zero. Thus we expect S0 temperature, density and vertical velocity perturbations, and W1 horizontal wind perturbations to dominate the semidiurnal tidal response at polar latitudes. Additionally, the latitude structure of the W6 expansion functions based on classical theory are reminiscent of those of a Kelvin wave with temperature and zonal wind peaks at the equator and negligible meridional wind amplitudes at all latitudes.

[24] The other notable features of the GSWM semidiurnal results illustrated in Figures 3 and 4 are the expected zonal mean wind effects on the W2 component. That is, the strong strato-mesospheric eastward jets (not illustrated) retard the W2 tidal propagation in the winter hemisphere, and the MLT response is comparatively stronger in the summer hemisphere because the eastward winds Doppler shift the W2 tide to higher frequency rendering dissipation less effective. The W2 response is comparatively more symmetric about the equator during equinox when the mean winds are weaker and more symmetric (not illustrated). There is also evidence of mean wind effects on other major component responses in the equatorial asymmetry that migrates with season.

3.2. Altitudinal Variations of Select Major Component Responses

[25] Figure 5 illustrates profiles of zonal wind amplitudes and phases for the major component semidiurnal latent heating responses at 21°S along with the GSWM-00 migrating semidiurnal radiative response at 21°S during December, March, June, and October. Figure 6 illustrates the complementary temperature amplitudes and phases at 6°S. Throughout the year semidiurnal amplitudes remain small below 90–100 km at most locations which renders the associated phases meaningless. There are notable general exceptions at high latitudes (not illustrated) that are also evident in select zonal wind perturbations in March and October. In the remainder of this section we discuss the illustrated profiles in more detail in order to overview the salient features of the comparative low and middle latitude semidiurnal latent and radiative heat responses calculated with GSWM.

Figure 5.

MLT profiles of semidiurnal zonal wind amplitudes (left column) and phases (right column) at 21°S during December (top row), March (second row), June (third row), and October (bottom row). GSWM-00 migrating semidiurnal radiative responses (open circles) are plotted with the W2 (solid curve and filled circles), W6 (dashed curve), and W5 (dot-dashed curve) component solutions excited by tropospheric latent heat release. See text for details.

Figure 6.

Same as Figure 5, except for semidiurnal temperature amplitudes (°K) and phases (UT hour of maximum amplitude at 0° longitude) at 6°S and the additional W4 (thin dotted curve) component.

[26] The peak latent heat responses are smaller than the migrating radiative responses throughout the year, but the former peaks frequently occur below the latter so there are MLT locations where the migrating tidal winds excited by the absorption of solar radiation throughout the atmosphere do not dominate the semidiurnal response. For example, at 21°S the W6 zonal wind amplitudes maximize at ∼15 m/s and exceed the GSWM-00 W2 amplitudes between ∼100 and 110 km during March (Figure 5). The W6 component also dominates the semidiurnal zonal wind response near 100 km at this location during June. The W6 and GSWM-00 W2 perturbations are in phase at 0° longitude during both months (Figure 5), so these waves are also phase coherent at ±90° longitude and at 180° longitude.

[27] The profiles of GSWM semidiurnal temperature perturbations near the equator (Figure 6) are notably different. Semidiurnal temperatures above 100 km are dominated by the migrating radiative response at all altitudes and throughout the year. There is a persistent W6 semidiurnal temperature and a significant W5 component during equinox. The W2 temperature response to latent heat is also significant except during October. Temperature perturbations generally peak between 120 and 125 km, some 10 km above the location of the maximum horizontal wind perturbations. The phase progression of the W2 GSWM-00 semidiurnal temperature is markedly different from the major component responses due to latent heat, which suggests that these waves combine in different ways as a function of altitude. We present evidence of the aggregate effects of the latent heat response on the migrating semidiurnal tide that is excited by absorption of solar radiation in the following section.

3.3. Total GSWM Semidiurnal Tidal Response

[28] Even though the GSWM nonmigrating tidal responses that we calculated for individual wave numbers are generally smaller than the GSWM-00 migrating semidiurnal tide, their aggregate effects significantly modulate the latter and establish measurable longitudinal variability. Further, these aggregate effects vary with both latitude and altitude as suggested by the results presented in sections 3.1 and 3.2. In this section we present evidence of the aggregate tropospheric latent heating effects at select altitudes. We also illustrate how these tidal responses modulate the dominant GSWM-00 tide excited by the absorption of solar radiation. We present results for March which are representative of equinox conditions when the nonmigrating components are comparatively more important than they are during solstice.

[29] Figure 7 illustrates longitude versus latitude maps of the March horizontal wind amplitudes due to the total GSWM response at 115 km to semidiurnal tropospheric latent heating. We combined the 10 major component responses described above (i.e., W6 to E3) to quantify the variability of the semidiurnal tide at this altitude. Both the zonal and meridional wind perturbations exceed 20 m/s at low to middle latitudes in the Southern Hemisphere, but the horizontal wind component peaks are not collocated. There are also regions where the meridional perturbations exceed 20 m/s at low Northern Hemispheric latitudes. Because the zonal and meridional perturbations associated with the nonmigrating tides are very different, we anticipate the pronounced differences in these maps. Some differences are due to the comparative importance of the zonal and meridional major component responses. Other differences are attributable to the latitude structure of the major component responses that are common to both wind fields.

Figure 7.

Contour maps of semidiurnal zonal (top) and meridional (bottom) wind amplitude (m/s) at 115 km that are attributable to the combined effects of the W6, W5, W4, W3, W2, W1, S0, E1, E2, and E3 components excited by tropospheric latent heat release.

[30] Figure 8 shows the modulation of the March GSWM-00 longitude versus latitude semidiurnal wind response when it is combined with the results illustrated in Figure 7. The ∼20 m/s longitudinal variations in the semidiurnal zonal wind amplitude are as large or even larger than the GSWM-00 response near 115 km (e.g., Figure 5). Although the aggregate meridional wind amplitudes due to latent heating are comparable in magnitude to the zonal response (Figure 7), the GSWM-00 meridional response exceeds 25 m/s at low latitudes (not illustrated). Thus the modulation of the latter by the former is not as pronounced. Similar modulations characterize both horizontal wind responses at middle and high latitudes in the Southern Hemisphere during March (Figure 8) where the GSWM-00 response also exceeds the semidiurnal winds generated by latent heat release. In contrast, there is little to no longitudinal variability in the semidiurnal wind amplitudes at middle to high Northern Hemispheric latitudes (Figure 8) where the aggregate response to latent heating is 10 m/s or less (Figure 7).

Figure 8.

Contour maps of semidiurnal zonal (top) and meridional (bottom) wind amplitude (m/s) at 115 km when the GSWM-00 W2 solutions are combined with the results illustrated in Figure 7.

[31] Figures 9 and 10 illustrate maps of temperature amplitude at 124 km that are associated with the aggregate latent heat response and the modulation of the GSWM-00 results by that response, respectively. As with the wind perturbations described above, the latent heating effects on semidiurnal temperature amplitude are most pronounced at the equator and low latitudes where they exceed 35°K near 60° and 90°E (Figure 9). Even though the amplitudes in these regions are comparable, the associated phases are different (not illustrated). Thus the semidiurnal temperature amplitudes at these locations are different when the latent heat response is combined with the GSWM semidiurnal temperatures that are excited by absorption of solar radiation (Figure 10). Specifically, the 60°E latent heat response is in phase with the GSWM-00 temperature perturbation and the combined amplitude is ∼100°K, while these components are out of phase at 90°E and the combined response is ∼50°K. Thus any attempt to interpret the variability of the semidiurnal tide in the MLT requires careful attention to its phase structure.

Figure 9.

Same as Figure 7, except for semidiurnal temperature amplitude (°K) at 124 km.

Figure 10.

Same as Figure 8, except for semidiurnal temperature amplitude (°K) at 124 km.

4. Discussion

[32] The GSWM calculations highlighted herein confirm that the semidiurnal tide in the MLT is affected by latent heat release associated with raindrop formation in deep convective clouds in the tropical troposphere. Further, the measurable longitudinal variability associated with the GSWM nonmigrating component results varies with atmospheric field and from month to month. The subset of results that we illustrate and describe in detail demonstrates that the tropospheric latent heating effects on the semidiurnal tide are most profound above ∼100 km and during equinox when the migrating component excited by the absorption of solar radiation is comparatively weaker than it is during solstice. Strong wave number 4 signatures over the tropics above ∼110 km during equinox are particularly noteworthy (e.g., Figures 8 and 10). This amplitude structure may be anticipated because the W2 and W6 components are most significant and the longitude variation due to the sum of two waves with a common frequency, σ, is given by

display math

where A(λ) = (A12 + A22 + 2A1A2cos[(s1s2) λ − (φ1 − φ2)])1/2 for component amplitudes, A1 and A2, phases, φ1 and φ2, and zonal wave numbers, s1 and s2 (after Angelats i Coll and Forbes [2002]).

[33] Despite the complexity of the variability of the GSWM solutions that we describe herein, our calculations are not definitive in that we only account for one plausible source of nonmigrating semidiurnal tides. For example, our GSWM W1 horizontal wind perturbations at high northern latitudes during southern summer complement those for high southern summer latitudes that were recently reported by Yamashita et al. [2003]. In their interpretive numerical experiment they reproduced the high southern latitude signatures of the MACMKU W1 semidiurnal winds with a primitive model that accounted for the nonmigrating tidal source generated at low altitudes by the nonlinear interaction between a stationary wave number 1 planetary wave and the migrating semidiurnal tide. These results produced no measurable Northern Hemispheric effects during southern summer. In contrast, our results provide only evidence of the latter and suggest that this response is directly attributable to tropospheric latent heating.

[34] As middle and upper atmospheric general circulation models (GCMs) become increasingly robust, mechanistic models such as GSWM provide insight into the underlying physics governing their MLT tidal dynamics. Our GSWM solutions can also be effectively used as lower boundary conditions in GCMs without realistic tropospheres so that they can properly account for nonmigrating tidal effects that are generated below the model domain. Finally, when combined with GSWM-00 results our nonmigrating tides can be used to interpret both ground based and satellite borne semidiurnal tidal measurements. In carrying out any such interpretation careful consideration must also be given to the geomagnetic activity conditions that prevailed when the observations were made. Our results for the combined semidiurnal GSWM-00 and latent heating responses can only account for upward propagating tidal variability effects and not for distortions in tidal structure that accompany solar storms. Further, the GSWM solutions described herein are only valid at altitudes below ∼130 km where we can neglect the semidiurnal tidal component that is generated in situ by the absorption of extreme ultraviolet radiation [Hagan et al., 2001].

5. Summary and Conclusion

[35] We used 7 years of global cloud imagery data representing geographical locations of deep convective activity to parameterize monthly variable semidiurnal tropospheric latent heating rates. We subsequently used these data in a series of GSWM calculations to explore the effects of the associated migrating and nonmigrating semidiurnal tidal signatures aloft. We quantified select results which vary from month to month and produce measurable semidiurnal amplitude variations in the upper atmosphere that are in excess of 20 m/s and 35°K and modulate the migrating semidiurnal tide excited by the absorption of solar radiation. We conclude that it may be important to consider tidal variability due to the tropospheric latent heat source when comparing correlative MLT tidal diagnostics like those measured by CEDAR instruments on the ground and by the TIMED satellite. The semidiurnal results that we report herein complement similar findings for the diurnal tide [Hagan and Forbes, 2002], but they differ from the diurnal responses in three important ways. First, the semidiurnal tide propagates well into the lower thermosphere, some 10–15 km higher than the diurnal tide. Second, comparatively more nonmigrating semidiurnal components propagate into the upper atmosphere, so the semidiurnal response aloft is more complicated than that of the diurnal tide. There are nonmigrating semidiurnal tidal effects at all latitudes, while the diurnal responses are confined to low and middle latitudes. Finally, the month-to-month variations in the upper atmospheric diurnal and semidiurnal tides excited by tropospheric latent heat release are different. For all of these reasons, it is impossible to infer the response of one harmonic by examining the behavior of the other. It is reasonable to expect year-to-year variability in the tropospheric tidal forcing of both the diurnal and semidiurnal tides associated with deep convective activity in the tropics. This variability may in turn produce year-to-year variations in upper atmospheric dynamics, but these effects are beyond the purview of our current investigation.


[36] We thank Jens Oberheide for comments on an early draft of this manuscript and Xiaoli Zhang for the tabulations of monthly tidal heating rates and for her assistance in the preparation of Figures 1 and 2. The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation (NSF). M. Hagan acknowledges the support of the NSF CEDAR program, the National Aeronautics and Space Administration (NASA) Sun-Earth Connections Theory Program, and grant S-S-10105X to NCAR. J. Forbes acknowledges support from the NSF through grant ATM-0097829 to the University of Colorado.

[37] Shadia Rifai Habbal thanks Neil F. Arnold and another referee for their assistance in evaluating this paper.