#### 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, K_{zz}, and explicitly calculates the divergences of the associated heat and momentum fluxes in the model [cf. *Forbes*, 1982]. K_{zz} 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 K_{zz} 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.

[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]:

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.

[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

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.