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  • View in gallery

    (a) The 1-h accumulated rainfall (mm) from the convection-permitting simulation for a typical hour (ending 0300 UTC 1 Sep 2011), (b) hourly averaged momentum flux amplitude (Pa) at 15 km above sea level for the same time. (c),(d) As in (a),(b), but with data coarse grained to 440 km.

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    Scatterplot of coarse-grained (440-km resolution) momentum flux amplitude against surface precipitation. The coarse-grained grid is that shown in Figs. 1c,d, and data points are plotted for each hour of the final 20 days of simulation. The straight line fit is calculated using the points shown in black and, hence, excludes surface precipitation values (shown in gray), which were more than two orders of magnitude less than the maximum 4.9 mm h−1.

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    Normalized gravity wave flux at launch level for 4-yr mean (a) January and (b) July. Current scheme (thick black curves), proportional to the square root of total precipitation (thin red curves), proportional to the square root of convective precipitation (dashed–dotted green curves), proportional to convective precipitation (dashed blue curves), and proportional to the square of total precipitation (dotted black curves).

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    Monthly equatorial 5°S–5°N zonal wind for (a) interactive new source experiment, (b) nudged experiment, and (c) control. Contour intervals at 10 m s−1; dashed contours represent negative (westward) wind values.

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    Multiyear mean eastward gravity wave flux at launch level excited by source (a) annual cycle diagnosed in nudged experiment relative to (b) annual zonal mean, and (c) annual cycle operating in interactive new source experiment relative to (d) annual zonal mean.

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    Probability density functions of absolute momentum fluxes over sea points between 10°S and 10°N in a nudged simulation for January (a) invariant source and (b) new source (note extended scale on the abscissa) and July (c) invariant source and (d) new source.

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    January monthly mean absolute momentum flux differences (new source − invariant source) in nudged experiment for (a) launch height, (b) 30-km height, (c) contribution to 30-km difference because of filtering of source difference, and (d) contribution to 30-km difference because of different filtering.

  • View in gallery

    As in Fig. 7, but for July.

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    Percentage difference in zonal mean absolute momentum flux from nudged experiment between new source and invariant source, normalized to invariant source for (a) January and (b) July.

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    Zonal mean zonal wind for interactive new source experiment for (a) January and (b) July; interactive new source control for (c) January and (d) July; interactive new source − nudged experiment for (e) January and (f) July. Contour intervals at 10 m s−1 (difference plots 5 m s−1 and shaded from 2 m s−1); dashed contours represent negative (westward) wind values.

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    Launch-height monthly mean absolute momentum flux differences (new source − invariant source) in interactive experiment for (a) January and (b) July.

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    Percentage difference in zonal mean absolute momentum flux from the interactive experiment between new source and invariant source, normalized to invariant source for (a) January and (b) July.

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    (left) January and (right) July zonal mean absolute momentum from interactive experiment [new source (solid black) and invariant source (dotted blue)] and from nudged experiment [new source (thin red) and invariant source (dashed–dotted red)] at (top to bottom) 50, 40, 30, and 20 km.

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    Monthly equatorial 5°S–5°N zonal fields from interactive experiment with (a),(c),(e) invariant and (b),(d),(f) new precipitation sources of nonorographic gravity waves. Zonal wind (10 m s−1 contours; negative dashed) overlaid on parameterized vertical flux of (a),(b) westward or (c),(d) eastward horizontal wave pseudomomentum (shading) and (e),(f) net eastward acceleration from parameterized gravity waves.

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Parameterized Gravity Wave Momentum Fluxes from Sources Related to Convection and Large-Scale Precipitation Processes in a Global Atmosphere Model

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  • 1 Met Office, Exeter, United Kingdom
  • | 2 Met Office Hadley Centre, Exeter, United Kingdom
  • | 3 Met Office, Exeter, United Kingdom
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Abstract

Analysis of a high-resolution, convection-permitting simulation of the tropical Indian Ocean has revealed empirical relationships between precipitation and gravity wave vertical momentum flux on grid scales typical of earth system models. Hence, the authors take a rough functional form, whereby the wave flux source spectrum has an amplitude proportional to the square root of total precipitation, to represent gravity wave source strengths in the Met Office global model’s spectral nonorographic scheme. Key advantages of the new source are simplicity and responsiveness to changes in convection processes without dependence upon model-specific details of their representation. Thus, the new source scheme is potentially a straightforward adaptation for a class of spectral gravity wave schemes widely used for current state-of-the-art earth system models. Against an invariant source, the new parameterized source generates launch-level flux amplitudes with greater spatial and temporal variability, producing probability density functions for absolute momentum flux over the ocean that have extended tails of large-amplitude, low-occurrence events. Such distributions appear more realistic in comparison with reported balloon observations. Source intermittency at the launch level affects mean fluxes at higher levels in two ways: directly, as a result of upward propagation of the new source variation, and indirectly, through changes in filtering characteristics that arise from intermittency. Initial assessment of the new scheme in the Met Office global model indicates an improved representation of the quasi-biennial oscillation and sensitivity that offers potential for further impact in the future.

Denotes Open Access content.

Corresponding author address: Andrew Bushell, Met Office, FitzRoy Rd., Exeter, Devon EX1 3PB, United Kingdom. E-mail: andrew.bushell@metoffice.gov.uk

Abstract

Analysis of a high-resolution, convection-permitting simulation of the tropical Indian Ocean has revealed empirical relationships between precipitation and gravity wave vertical momentum flux on grid scales typical of earth system models. Hence, the authors take a rough functional form, whereby the wave flux source spectrum has an amplitude proportional to the square root of total precipitation, to represent gravity wave source strengths in the Met Office global model’s spectral nonorographic scheme. Key advantages of the new source are simplicity and responsiveness to changes in convection processes without dependence upon model-specific details of their representation. Thus, the new source scheme is potentially a straightforward adaptation for a class of spectral gravity wave schemes widely used for current state-of-the-art earth system models. Against an invariant source, the new parameterized source generates launch-level flux amplitudes with greater spatial and temporal variability, producing probability density functions for absolute momentum flux over the ocean that have extended tails of large-amplitude, low-occurrence events. Such distributions appear more realistic in comparison with reported balloon observations. Source intermittency at the launch level affects mean fluxes at higher levels in two ways: directly, as a result of upward propagation of the new source variation, and indirectly, through changes in filtering characteristics that arise from intermittency. Initial assessment of the new scheme in the Met Office global model indicates an improved representation of the quasi-biennial oscillation and sensitivity that offers potential for further impact in the future.

Denotes Open Access content.

Corresponding author address: Andrew Bushell, Met Office, FitzRoy Rd., Exeter, Devon EX1 3PB, United Kingdom. E-mail: andrew.bushell@metoffice.gov.uk

1. Introduction

Atmospheric gravity waves are known to be important in driving and maintaining large-scale circulations of the stratosphere and mesosphere. These waves have horizontal wavelengths ranging from tens of to several hundred kilometers and need to be parameterized because they are not resolved in general circulation models (GCMs). Since Palmer et al. (1986) pioneered the parameterization of gravity waves with orographic sources, using basic fluid dynamical principles, such schemes have emerged in virtually all global models used in climate and weather science (Alexander et al. 2010). Nonorographic gravity wave sources, on the other hand, only became a major issue for climate model parameterization in the last two decades (e.g., Warner and McIntyre 1996; Pawson et al. 2000) as state-of-the-art climate GCMs have extended vertically to the upper mesosphere (see Charlton-Perez et al. 2013, Table 1). In the extratropical upper stratosphere and mesosphere, gravity wave momentum forcing is essential for obtaining the correct dynamic and thermodynamic structures through momentum drag and subsequent adiabatic heating (e.g., Pawson et al. 2000; Austin et al. 2003), while, in the equatorial stratosphere, small-scale nonorographic gravity waves impart a significant forcing to the quasi-biennial oscillation (QBO; Baldwin et al. 2001).

Many GCMs fail to simulate the QBO, the tropical stratosphere’s most prominent mode of variability, without a parameterization of the upward transport and deposition of momentum by subgrid-scale nonorographic gravity waves (e.g., as triggered by convection). With appropriately tuned parameterizations (e.g., Scaife et al. 2000; Giorgetta et al. 2002; Scaife et al. 2002; Giorgetta et al. 2006; Bushell et al. 2010), model QBOs often have realistic mean periods and amplitudes but underrepresent intercycle variations. Typically, this is because the parameterized nonorographic gravity waves tend to be launched at every model grid point with a prescribed strength that is time invariant and independent of other model prognostic variables. Nonorographic gravity wave parameterizations that can overcome the limitation in many current GCMs of restricted source variability and increase intermittency of the gravity wave forcing potentially may create more realistic model behavior and improved QBOs (e.g., Kim et al. 2013; Richter et al. 2010).

In general, geographical distributions of parameterized gravity wave momentum fluxes in current climate models compare reasonably well with observations, but a few gross morphological features, such as very small fluxes in summer high latitudes or secondary maxima over summer continents near 20°, are not well captured (Geller et al. 2013, 2015). Although global patterns are strongly shaped by filtering of upward-propagating waves, a more direct contributor to these model deficiencies is the absence of (physically based) spatially and temporally varying sources for parameterized nonorographic gravity waves. Meteorologically interactive sources also enable a feedback pathway, in response to changes in climate, for the parameterized gravity waves, which are known (e.g., Butchart 2014) to contribute significantly to driving trends in the stratospheric Brewer–Dobson circulation. As convection is a major source of gravity waves in the tropical atmosphere, parameterizations that represent the link between gravity waves and convective activity offer potential to improve the physical realism of climate and earth system models (ESMs).

With designs based on a combination of linear theory, mesoscale simulations of convection, and simplified heating simulations, several recently developed gravity wave schemes link convective gravity wave source characteristics with GCM convection parameterization schemes (Richter et al. 2010; Choi and Chun 2011, and references therein). Such links between sources and physical generation processes depend on internal details of their respective models’ convective parameterization schemes. These details are relatively poorly constrained by observations, and there exist a number of known biases, such as in the convective heating profile (Del Genio et al. 2012). Consequently, parameterized gravity waves in these schemes depend strongly upon assumptions about the convective heating scale and distribution, which can break down as model resolutions descend into the gray zone near the resolved convection scale. Given a paucity of observational constraints and the many current uncertainties over the schemes’ performance and impact, this approach also seems somewhat complex, [e.g., the Choi and Chun (2011) scheme requires four model fields and eight variables, five from the convective scheme]. In contrast, the stochastic, multiwave scheme of Lott and Guez (2013) identifies total precipitation as a useful proxy for column-integrated latent heat release that avoids any explicit dependence on vertical structure or unresolved convective motions, as would be represented through specific assumptions and details particular to individual convection parameterizations. Nevertheless, biases in their model convection scheme that impact on convective precipitation can still affect the resultant parameterized gravity waves.

In global configurations of the Met Office Unified Model (MetUM; see section 2), the spectral nonorographic gravity wave scheme’s framework supports some aspects that are theoretically well understood (e.g., propagation) and others, kept as simple as possible, that use a more empirical methodology to bridge current knowledge gaps. In this spirit, added complexity, though inevitable when multiple meteorologically sensitive sources replace a single global invariant source, should be kept to a minimum. Central to our strategy for parameterizing convective sources is the analysis of a convection-permitting, limited-area configuration of the MetUM to diagnose empirical relationships (section 3) between grid-scale gravity wave momentum fluxes and other model variables that can underpin a new source representation. Total precipitation stands out as a quantity that is easily extracted from models and also from observations and/or reanalysis datasets. Moreover, the direct connection between precipitation and vertically integrated latent heat flux gives any correlation with gravity wave sources a sound physical basis. Global adoption of the empirical relationship is consistent with our philosophy of taking the simplest source description appropriate to current knowledge. And the blurred distinction between model convective and large-scale precipitation, to some extent, justifies an association of all significant precipitation events with gravity wave generation. However, an obvious consequence, which future investigations might challenge with observations and refine, is that precipitation due to further moist physical processes outside convection regions will also promote gravity wave sources. Generation of resolved gravity waves in midlatitude frontal regions has indeed been identified in global NWP simulations (e.g., Griffiths and Reeder 1996; Reeder and Griffiths 1996; Shutts and Vosper 2011), but the extent to which these arise from embedded convection-like events, or from additional sources that require a more general consideration of the frontal dynamics, remains open to debate.

Section 4 compares momentum fluxes parameterized by this new source with those obtained using the current prescribed (invariant) source of nonorographic gravity waves in nudged simulations of the global model, where the large-scale winds and temperatures are relaxed toward reanalyses. This experimental arrangement constrains the background winds that filter upward-propagating fluxes to a realistic structure that favors equally both new and invariant sources when characterizing and assessing the global momentum flux distributions generated by them. In the freely evolving simulations, differences between the two ultimately lead to winds diverging toward their own distinct climatological structures. The morphology of momentum fluxes parameterized with the new source in the free-running model is presented in section 5, and some comparison is made with published data from observations. Further discussion and concluding remarks, including some consideration of initial sensitivity tests, are in section 6.

2. The MetUM

From its inception over 20 years ago, the MetUM has been developed as a general-purpose atmosphere model for use in numerical weather prediction and global or regional climate research and applications (Walters et al. 2014). The model dynamical core employs a semi-implicit, semi-Lagrangian formulation to solve nonhydrostatic, fully compressible deep-atmosphere equations of motion (Davies et al. 2005) and includes a comprehensive set of state-of-the-art parameterizations to represent subgrid-scale physical processes [again, see Walters et al. (2014) for details]. MetUM global and limited-area configurations are available with a wide variety of horizontal resolutions, and all current standard global configurations extend to the stratosphere and mesosphere with upper boundaries at or near 85 km. The aim here is to improve the nonorographic gravity wave parameterization included in these global configurations (detailed in section 2a) by modifying the current invariant source specification for momentum fluxes at a launch level in the lower troposphere to capture sources from regions where moist processes, primarily tropical convection, are active. Hence, to identify empirically the physical relationship between momentum fluxes and their sources, a convection-permitting, limited-area version of the model is also used (section 2b).

a. Global configuration

The MetUM global configuration used here has 85 vertical levels from the surface to 85 km (~0.01 hPa), with level spacings below 700 m at 18 km, rising to 2645 m at 50 km (upper stratosphere) and 5900 m at the top. It has a latitude–longitude resolution of 1.25° by 1.875° (on an Arakawa C grid) and a 20-min time step. Because of computational cost constraints, a typical choice of global MetUM resolution will require parameterizations for both convective and large-scale precipitation. Convective precipitation is treated by a mass flux scheme based originally on Gregory and Rowntree (1990) but with further developments, including detrainment (Derbyshire et al. 2011). MetUM precipitation in the tropics is predominantly convective. The separate large-scale precipitation scheme operates when grid-scale mean specific humidities approach saturation (Walters et al. 2014). In all current MetUM standard global versions, nonorographic gravity wave activity on scales smaller than the model resolution is represented by the ultrasimple spectral parameterization [USSP; developed originally by Warner and McIntyre (1996, 1999, 2001)]. The USSP treats a spectrum of gravity waves in four azimuth directions (west, north, east, and south), with a modification for use in the MetUM to launch unsaturated spectra from a level close to the surface (Scaife et al. 2000). A key advantage of the scheme is its simplicity, which allows wave generation, conservative upward wave propagation (with implicit handling of wave–wave interactions), and dissipation by critical-level filtering and wave saturation all to be treated without excessive computational costs. The simplicity is also evident in the small number of parameters used, which is appropriate, given the limited number of observational constraints available. Wave reflection is not modeled, as the midfrequency approximation to the dispersion equation assumed for conservative propagation implies hydrostatic wave dynamics with no Coriolis rotation (Warner and McIntyre 2001), but its effect on wave spectrum amplitude is, to some extent, reproduced by launching with amplitudes below the saturated value. Momentum deposition occurs whenever the launch spectra, transformed as they propagate upward, exceed a locally evaluated universal saturation spectrum and lose flux instantly to unspecified nonlinear processes that erode the spectrum shape to match the saturated form. The deposited momentum is then converted into an equivalent force on the local (resolved) horizontal winds.

Given their simplicity, the USSP and similar spectral nonorographic gravity wave parameterizations (e.g., Scinocca 2003) represent remarkably well the propagation and momentum deposition by subgrid-scale waves and much of their influence on the general circulation of the stratosphere and mesosphere (Scaife et al. 2000, 2002; Scinocca 2003; Warner et al. 2005). Importantly, as these aspects of the parameterization are physically based, albeit rather generally, it was decided to retain them while improving the physical basis of the source representation used in the MetUM (see section 6 for further discussion). Hence, the approach is still spectral, rather than an alternative ensemble of monochromatic waves (Lott and Guez 2013; Lott et al. 2012; Eckermann 2011). The focus here is to improve the parameterization’s physical basis by replacing the time-invariant, spatially homogeneous total vertical flux of horizontal wave pseudomomentum imposed at the launch level (Scaife et al. 2002) with parameterized values based on empirical results obtained from a convection-permitting model configuration.

b. Convection-permitting configuration

A MetUM configuration similar to that used operationally at the Met Office for U.K.-area, short-range weather prediction (see Holloway et al. 2012, for details) is designed with convection-permitting 2.2-km horizontal resolution (on an Arakawa C grid) to run without a subgrid convection parameterization. A three-dimensional Smagorinsky turbulence option, found to be beneficial for the tropical region selected (see section 3), replaces the global model boundary layer scheme. A vertical grid was chosen with 118 levels, 45 in the lowest 7 km of the atmosphere, to match the current operational U.K.-area configuration. Improved resolution in the lower troposphere was maintained through to the stratosphere with slowly increasing layer thicknesses restricted to 500 m at 18 km, rising to 1800 m at 50 km and a maximum of 3100 m on the model upper boundary at 78 km. A sponge layer (i.e., vertical velocity damping) was used from 40 km up to 78 km, and dynamical core settings (including a 10-s short time step and fully three-dimensional potential temperature advection) were chosen to optimize the representation of gravity waves (Webster et al. 2008).

3. Convectively generated gravity waves

a. Simulations and diagnostics

Tropical convection-permitting simulations [configured as per extended Cascade; Holloway et al. (2012)] were conducted over a broad region including most of the Indian Ocean (e.g., see Fig. 1). This large Indian Ocean domain encompasses a wide range of tropical meteorology and is considered representative of the tropics in general.

Fig. 1.
Fig. 1.

(a) The 1-h accumulated rainfall (mm) from the convection-permitting simulation for a typical hour (ending 0300 UTC 1 Sep 2011), (b) hourly averaged momentum flux amplitude (Pa) at 15 km above sea level for the same time. (c),(d) As in (a),(b), but with data coarse grained to 440 km.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

The 2.2-km resolution model is run nested within a global configuration that provides time-evolving lateral boundary conditions (LBCs) at each time step by linear interpolation in time between hourly output flow fields. Both nested and global models were initialized using the MetUM operational global model analysis valid at 0000 UTC 18 August 2011. The models were integrated for 21 days, with the 2.2-km model free running, while the global model was run for 6 h and then reinitialized with the next operational analysis, to keep the 2.2-km LBCs realistic.1 Spurious noise generation at the reinitialization time is prevented by use of the same flow fields forecast at time T + 6 h from the previous global model cycle (i.e., valid at the new analysis time) to calculate LBCs for both the hour prior to and the hour after reinitialization; this avoids interpolation between LBCs derived from different analyses.

Diagnostics to calculate the model gravity wave field were output from the 2.2-km model every 2 min for the 21 days simulated. Thus, the zonal, meridional, and vertical flow components, potential temperature, and density (u, υ, w, θ, ρ) were output on geometric height levels, as described in the appendix; and a double coarse-graining procedure was applied. First, a high-pass filter [taking deviations from a coarse-grained average , which represents a climate model grid resolution] was used to define perturbation fields and compute momentum flux τ. Second (see the appendix for details), we applied further averaging over 1 h and an adjustable outer spatial scale.

b. Empirical relationships for momentum fluxes

Preliminary assessment of the high-resolution simulations detected the expanding ripple signature of convectively forced gravity waves in a range of parameters, including diabatic and latent heating, outgoing longwave radiation, total precipitation, and vertical velocity. It was decided to focus just on total precipitation P as a basic quantity that is readily available from all global models, irrespective of which convective parameterization is used, and from the convection-permitting simulation without a subgrid scheme. Examples of convection, both isolated [O(10) km] and organized [O(100) km], are readily seen in a snapshot of hourly averaged surface precipitation on the high-resolution model grid (Fig. 1a), which also illustrates the nested model domain. The associated magnitudes of vertical flux of horizontal (zonal and meridional) momentum |τ| are shown at the 15-km level (Fig. 1b) because it lies closest to the cloud tops associated with explicit deep convection and, hence, depicts the convectively generated gravity wave source field most clearly. At lower levels, |τ| includes significant in-cloud fluxes, whereas, at higher levels, horizontal propagation of the wave field makes the wave sources harder to identify.

Many regions of significant momentum flux at 15 km, though covering larger areas, are associated with regions of significant surface precipitation (Fig. 1a), thereby confirming the relatively robust total precipitation as a suitable model proxy for gravity wave generation by active moist processes. In this experiment, any distinction between strong precipitation caused by motions associated with resolved-scale convection, as opposed to more general convergence that might be classified large scale, is at best arbitrary. In addition, waves detected at 15 km may arise from many sources, including orography, that are not expected to show the same correlation with precipitation. Larger areal extents for features seen in the momentum flux field compared to corresponding features in the precipitation field are expected for two reasons. First, convective dynamical activity normally has a broader extent than the peak updrafts that produce high precipitation. Second, gravity waves will propagate some distance horizontally from the source [Fig. 7 in Hankinson et al. (2014) shows horizontal ray-tracing estimates with horizontal propagation of order 300 km]. Figures 1c and 1d show the coarse-grained fields for, respectively, surface precipitation and , also at a height of 15 km. Regions with trace precipitation (<0.01 mm h−1), such as the southern Indian Ocean (cf. Fig. 1a), show large areas with negligible flux amplitudes (Fig. 1d). However, from the log–log scatterplot of coarse-grain-averaged (440-km resolution) momentum flux amplitude versus precipitation (Fig. 2), it appears that these values, at least one order of magnitude smaller than the values associated with high local rainfall, might actually represent some form of background field [resulting from a mixture of sources; Fritts and Alexander (2003)] that is present even in the zero rainfall limit. Nonetheless, because of the exponential decrease in density with altitude, even small background levels of at 15 km can induce major accelerations of the mean flow if they break in the mesosphere after propagating upward without significant filtering by the intervening stratospheric winds.

Fig. 2.
Fig. 2.

Scatterplot of coarse-grained (440-km resolution) momentum flux amplitude against surface precipitation. The coarse-grained grid is that shown in Figs. 1c,d, and data points are plotted for each hour of the final 20 days of simulation. The straight line fit is calculated using the points shown in black and, hence, excludes surface precipitation values (shown in gray), which were more than two orders of magnitude less than the maximum 4.9 mm h−1.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

In the scatterplot, high rainfall values extending above the background field show an approximate power-law dependence of on precipitation with the form (Fig. 2), as indicated by the straight line, which represents a best fit to the high rainfall data when α = 0.64. From supplementary analysis, the result was essentially unchanged for data preselected on either sea-only or land-only locations, but the exponent α may range between 0.2 and 0.8, depending upon the arbitrary outer spatial scale of the coarse-graining procedure, upon the geometric height level for which was calculated, and upon the range of surface precipitation values that are included. Significantly, this relatively weak power-law dependence in the model results is broadly consistent with the latest observational studies (Hankinson et al. 2014).

The most likely reason for a relatively weak power-law dependence is a systematic dependence of P on the scale of the convection, which effectively reduces the wave-making efficiency for higher P values. Interestingly, in these simulations, variations in the amount of wave generation do not appear strongly related to variations in the intensity of individual convective events, nor to their number density within the coarse-grain-averaged regions. A linear dependence on local intensity of convection would lead to an alternative power law of the form . Conversely, if the intensity of convective events remained roughly unaltered but the number density varied, the expected form of power-law dependence would be . It is possible that the model underrepresents these particular variations or that the Indian Ocean region where the high-resolution experiment is located, though extensive, is still too small to be sufficiently representative of the full range of variability. But in the absence, noted in the introduction, of observational constraints on gravity wave momentum fluxes sufficient to narrow these uncertainties, the single variable P was considered appropriate for parameterizing this source of gravity waves in the MetUM.

c. A source of parameterized gravity waves for the MetUM

A new source is defined with launch amplitudes scaled by , as a computationally efficient approximation to the power law obtained from the convection-permitting simulations. However, interpretation of the relationship between momentum fluxes at 15 km and the altitude or possible anisotropy of the gravity wave sources is much more ambiguous from these results. Recent work by Geller et al. (2015) implies a strong role of filtering between source locations and observed distributions at altitudes in the tropical lower stratosphere, which supports previous findings (Warner et al. 2005) that the USSP scheme was able to reproduce qualitatively the observed anisotropy in midlatitude pseudomomentum fluxes at ~16 km by launching isotropic fluxes from (time invariant) sources placed in the MetUM planetary boundary layer. Thus, it was decided initially to retain the isotropic, low-altitude aspects for the new source, which carries advantages of both simplifying comparison with the invariant source and ensuring momentum conservation, in the sense that the momentum deposited near where waves are generated, in the troposphere, is equal and opposite to that subsequently deposited when they propagate further upward into the stratosphere and mesosphere. In combination with an opaque upper-boundary condition, inclusion of this parameterization thus has zero impact on net momentum conservation in the MetUM.

Large-scale and convective precipitation processes in GCMs tend to operate in a compensating manner where, if the convection scheme underestimates precipitation, grid-scale mean specific humidity will be higher, increasing the likelihood of large-scale precipitation, and vice versa. Total precipitation is thus a more consistent measure than its individual components when comparing across regions, between resolutions, or against datasets from reanalyses and observations. In general, MetUM precipitation distributions reproduce many features seen in observed climatologies [Walters et al. (2014, Figs. 8 and 9)] and, even when the new source parameterization is included and interacting freely, the global MetUM is still in reasonable agreement (not shown) with a total precipitation climatology derived from satellite and rain gauge measurements. Hence, there is some confidence that gravity wave pseudomomentum fluxes launched by the new parameterized source will emanate from MetUM precipitation events at the correct locations and times.

Zonal mean distributions of nonorographic gravity waves launched by the USSP scheme with the current invariant source in a free-running global MetUM simulation (Fig. 3) are compared with alternative launch-level fluxes diagnosed consistently from spatially varying precipitation rates updated on each 20-min time step of this control experiment. January and July zonal means of the launch-level vertical flux of horizontal pseudomomentum for the current source are specified by an invariant amplitude parameter scaled by density at the launch level to create fluxes which vary weakly with variations in local orography (e.g., over the high Antarctic Continent). These act as references for source schemes in which the launch amplitude is proportional to the square or to the square root of total precipitation and to convective precipitation or its square root. Each zonal mean flux distribution has been normalized by the point maximum detected from its respective monthly mean versus latitude (Hovmöller) distribution over the 4-yr simulation.

Fig. 3.
Fig. 3.

Normalized gravity wave flux at launch level for 4-yr mean (a) January and (b) July. Current scheme (thick black curves), proportional to the square root of total precipitation (thin red curves), proportional to the square root of convective precipitation (dashed–dotted green curves), proportional to convective precipitation (dashed blue curves), and proportional to the square of total precipitation (dotted black curves).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

The invariant source flux distribution launched at 3.8 km is not a like match with previous model results (cf. Geller et al. 2013, Fig. 2) because propagation up to 20 km modifies the distribution considerably (shown in section 5). However, two qualitative findings from the Geller et al. (2013) comparison against observation data can carry down to the present source level: namely, that agreement with observations would be improved were (i) the invariant source (Fig. 3) tapered to very low values poleward of 80° and (ii) its amplitude in the region of 20° in the summer hemisphere somewhat enhanced relative to neighboring latitudes. The source proportional to convective precipitation (blue dashed line) peaks very strongly in the tropics to the summer side of the equator and drops to zero poleward of about 70°. Using the square root of convective precipitation enhances the normalized source strength in the tropical summer peak but by a reduced amount relative to secondary midlatitude peaks around 50° (35°) in the summer (winter) hemisphere (green dashed–dotted line). Trials of an alternative convection source of gravity waves for the MetUM (Kim et al. 2013) detected similar peaks outside the tropics. Kim et al. (2013) also found it necessary to retain a reduced proportion of the invariant source, notably, poleward of 60°, where convective activity in the MetUM tails off rapidly, as a residual contribution to the momentum budget by other (unidentified) gravity wave sources. The simplest assumption, gravity wave amplitude scaled linearly with precipitation, would give a launch-level flux (black dotted line) that is even more focused on strongly convecting regions.

The proposed new source form, proportional to the square root of total precipitation (red thin line), retains the summer convection peak that improves upon the invariant source but gives even more relative weighting to the midlatitude peaks, especially at winter storm-track latitudes. Measured against the above criteria for a better latitudinal distribution, the new source appears to improve upon the invariant source, and it reduces relative to the invariant source at the poles, although, unlike the other sources, it does not taper entirely to zero. As should be emphasized, the empirical relation between precipitation and source fluxes does have a physical basis, despite a complete theoretical explanation having proven elusive, that derives from use of resolved fields from a physical high-resolution model. Within the Indian Ocean domain, the use of total precipitation to capture convective gravity wave sources with realistic large-scale spatial and temporal variation achieves a primary aim for the new source flux and opens a route to further development.

Progress beyond the single invariant source demands a balance between synthetic development of individual, leading-order sources that can act in combination and its analytic counterpart, whereby the collective impact required to satisfy relatively tight constraints of model momentum budgets and large-scale wind structures is decomposed into known and residual contributions. The new source scaling factor was thus initially estimated to match the annual mean contribution over 75°N–75°S from the current invariant isotropic source, with which MetUM simulations are able to reproduce QBO signals that have periods in the observed range and polar night jets of the correct strength, at least for current climate (Scaife et al. 2000, 2002; Warner et al. 2005; Bushell et al. 2010). Monthly equatorial 5°S–5°N mean zonal winds over the period 1989–2001 confirm the reliability of this estimate (Fig. 4). A simulation with the new source operating in a fully interactive capacity (Fig. 4a) has a mean westward (eastward) phase partial period of 15.3 (12.2) months at the 30-hPa pressure level, compared with partial periods for the invariant source control experiment (Fig. 4c) of 15.3 (12.4) months. These values lie within the variability of a simulation where winds were nudged toward reanalysis (details in section 4), which has a 15.5-month mean westward phase and 11.5-month mean eastward phase partial period (Fig. 4b).

Fig. 4.
Fig. 4.

Monthly equatorial 5°S–5°N zonal wind for (a) interactive new source experiment, (b) nudged experiment, and (c) control. Contour intervals at 10 m s−1; dashed contours represent negative (westward) wind values.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

Unlike the invariant source, however, the new source is sensitive to variation in the total precipitation both geographically (instantaneously across latitude and longitude) and from one model time step to the next, providing intermittency in the short term, seasonal variation, and ultimately an ability to respond to secular changes in precipitation caused by a changing climate. With the tuning described here, the new source strength in Pa is
eq1
compared to the invariant source strength of
eq2
where ρ(zL) is the density at launch altitude zL (set at 3825 m for both schemes); P(λ, ϕ, t) (kg m−2 s−1) is the total precipitation at longitude λ, latitude ϕ, and time t; and Pbase is a threshold value that herein equates to 0.1 mm day−1. The invariant and local source strength values will thus match for a precipitation rate ~0.77 mm day−1 (0.03 mm h−1), which for expected density values gives a source amplitude of ~1.68 mPa per azimuth direction (4 in total). The sensitivity of the MetUM’s climatology to rescaled launch amplitudes is considered further in section 6.

4. Assessment of momentum flux characteristics

An issue with comparing fluxes from the new and invariant sources is that free-running simulations deviate toward their own characteristic wind climatologies, with the result that changes in vertical structure feed back on the momentum deposition and, hence, the flux profile. An experimental arrangement that provided the same realistic background winds when assessing characteristics of upward-propagating momentum flux from both new and invariant sources, favoring both equally, took the standard MetUM atmosphere-only global configuration and nudged (Telford et al. 2008) over the height range 1–65 km toward temperature and wind conditions from the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) for the period 1988–2008. Sea surface temperature and sea ice distributions derived from observations for the same period were prescribed at the lower boundary. Nonorographic gravity wave tendencies were supplied by the standard, invariant source scheme, which deposited momentum as it would in a free-running simulation, though nudging constrained the background wind structure to remain close to that observed. The propagation and filtering of parameterized momentum fluxes from the new sources were also calculated within the same simulation, but the associated momentum deposition did not feed back on the model evolution.

For a launch-level gravity wave flux based on the new source relation ( in Fig. 3) the multiyear mean annual cycle anomaly from the zonal and annual mean demonstrates the seasonality at different latitudes (Fig. 5). The new source in the nudged simulation peaks at 3.15 mPa in January just south of the equator, where its seasonal maximum (Fig. 5a) and the zonal annual mean maximum (Fig. 5b) coincide; mainly because of precipitation resulting from convective activity in the intertropical convergence zone (ITCZ). Although the precipitation itself is not constrained directly in the nudged simulation, the constrained winds inevitably converge in a similar manner to the reanalysis. Hence, the precipitation distribution in the nudged run exhibits characteristics of the ERA climatology (not shown), such as a local minimum in the equatorial zone, which are distinct from those of the equivalent free-running MetUM or observation-derived climatologies. Differences in latitudinal distributions and seasonality of source fluxes in the nudged (Figs. 5a,b) and interactive simulation described in the next section (Figs. 5c,d) arise mainly from these characteristic differences, rather than any feedback on total precipitation as the interactive source impacts model wind fields. This highlights sensitivity to the accuracy of the model’s moist processes that can emerge when sources of nonorographic gravity waves are related to precipitation. The invariant source weighting by density results in a weak variation (two standard deviations are 7% of the 1.68-mPa global mean) that is greatest (−14%) over the high-altitude South Pole. The new source has a similar global mean value of 1.67 mPa in the nudged simulation, but the latitudinal variation in its annual mean has a standard deviation that is 24% of the global value, and the seasonal cycle, based on zonal and monthly mean data, has a peak-to-peak range of 85% relative to the global value, with maximum seasonal variation in the tropics and midlatitude storm-track regions.

Fig. 5.
Fig. 5.

Multiyear mean eastward gravity wave flux at launch level excited by source (a) annual cycle diagnosed in nudged experiment relative to (b) annual zonal mean, and (c) annual cycle operating in interactive new source experiment relative to (d) annual zonal mean.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

Another measure used to compare the relative intermittency of fluxes from the two sources is the absolute momentum flux (Geller et al. 2013), which combines the vertical flux of horizontal momentum from unresolved gravity waves represented by both orographic and nonorographic parameterization schemes in a manner that facilitates validation against observations. Instantaneous values of absolute momentum flux are captured at every sea point between 10°S and 10°N (thus removing the orographic gravity wave component) on every hour over the months of January and July 1989. The data are aggregated to build up momentum flux probability density functions (PDFs) that represent the statistical likelihood of encountering fluxes of particular magnitudes at selected height levels between 13 and 30 km (Fig. 6). At the launch level, the invariant nonorographic gravity wave source distribution is almost a delta function about the 1.68-mPa mean value described above, which sums over the four USSP azimuths described in section 2a to an absolute momentum flux of 6.72 mPa. At higher levels (Fig. 6a), the PDFs are generated by erosion of the original source spectrum as momentum is deposited, increasing the probability of progressively lower flux amplitudes below the launch limit. A consequence of launching the invariant source with subsaturation amplitudes is that the dominant deposition mechanism for the USSP scheme in the troposphere and lower stratosphere is critical line filtering of the Doppler-shifted spectrum as wind shear is encountered. In the PDFs, this behavior manifests as clustering at multiples of the 1.68-mPa single azimuth amplitude as shifts in wind direction with altitude lead to rapid reduction of the available momentum flux.

Fig. 6.
Fig. 6.

Probability density functions of absolute momentum fluxes over sea points between 10°S and 10°N in a nudged simulation for January (a) invariant source and (b) new source (note extended scale on the abscissa) and July (c) invariant source and (d) new source.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

The most noticeable difference in the PDFs from the new source (Fig. 6b) is the extensive tail of high fluxes with low-occurrence frequency that reach up to 56.4 mPa for the 13-km-altitude distribution. These better resemble data derived from 19-km balloon observations (e.g., Fig. 3 in Hertzog et al. 2012), though note that for observations the distinction between orographic and nonorographic waves is ambiguous. In place of a delta function at launch level, the PDF flux dependence for the new source is determined by the spatial and temporal distribution of total precipitation events. The form of PDFs at higher levels will again emerge from erosion of the launch flux spectrum, but even at 30 km, the January 14.2-mPa maximum flux for the new scheme PDF is a factor of 4 greater than the 3.6-mPa maximum for the invariant scheme. The ratio at launch (56.4: 6.6 mPa) shows that, though both encounter identical winds, the larger-amplitude new source spectra are filtered much more strongly. This may be understood by considering that, even at launch, the spectra for the high flux tail may be close to local saturation, at which point the dominant mechanism for momentum deposition shifts to the constraint applied by wave breaking upon the growth of wave amplitudes in reducing density with altitude, which is independent of the wind direction. Minor changes in the invariant source spectra between January and July (Fig. 6c) reflect the impact of seasonal differences in wind patterns on upward propagation of the launch-level flux. For the new source, the maximum amplitude at 13 km in July (Fig. 6d) remains very similar to its January value, but the mean increases from 5.2 to 6.1 mPa. Comparison of this 0.9-mPa difference with the absolute momentum range of 5.8 mPa for the seasonal cycle amplitude of fluxes at the 3.8-km launch height provides further evidence of the damping effect of filtering on variations in the upward-propagating wave spectra.

Simulated momentum flux climatology

At the 3.8-km launch level in the nudged experiment, there is strong spatial variation in the geographic distribution of multiyear mean January absolute momentum flux differences between the new and invariant source (Fig. 7a). This variation is attributable entirely to the nonorographic gravity wave sources, as the contributions to this diagnostic from the orographic component cancel exactly. As expected, the largest increases due to the new source occur in the ITCZ (18.2-mPa maximum) and in the winter storm tracks of the northern Atlantic and Pacific Oceans, but, overall, the global mean difference for January gives a 0.25-mPa flux reduction. July distributions of absolute momentum flux (Fig. 8a) show similar differences between the initial sources in the ITCZ region, where the 20.0-mPa maximum is slightly higher than for January. As increases over the Southern Ocean are much more extensive than for the Northern Hemisphere storm tracks in January, the global mean difference is actually a 0.22-mPa increase with the new source. This counterbalances the January decrease and leads to near-zero differences in the global annual mean flux, as required by experimental design.

Fig. 7.
Fig. 7.

January monthly mean absolute momentum flux differences (new source − invariant source) in nudged experiment for (a) launch height, (b) 30-km height, (c) contribution to 30-km difference because of filtering of source difference, and (d) contribution to 30-km difference because of different filtering.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

Fig. 8.
Fig. 8.

As in Fig. 7, but for July.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

The same anomalies are calculated at a height of 30 km, after flux filtered by the subtropical jets has propagated into the stratosphere (Fig. 7b). Variations in the time mean flux anomalies at 30 km arise from a combination of geographic variability and temporal intermittency and would replicate exactly those at the launch level if the propagation were fully conservative. In general, however, variation in the source anomaly each time step is modified in two ways: directly, as filtering applied equally (given identical background wind fields) to the new and invariant source fluxes damps the upward-propagating spatial anomaly, and indirectly, through changes in time mean filtering characteristics that apply in the new and invariant source cases. If the initial difference in time mean source flux [S] in Fig. 7a is
eq3
and the filtering is expressed as a fraction f such that the time mean flux at 30 km equals (1 − f)[S], the difference at 30 km may be quantified as
eq4

Geographic variations in Fig. 7b are thus a sum of variations at the launch level due to the new source anomalies ΔS, and to modifications, respectively direct and indirect, as described above. The direct term −fInvΔS, appears as a damping of the source anomaly due to time mean filtering of propagating waves between the launch level and 30 km (Fig. 7c). The indirect term represents the impact of changes in filtering characteristics on the new source relative to the invariant, which primarily arise from intermittency (Fig. 7d). In most regions, direct damping dominates the indirect filtering changes. Even though both source propagation calculations see identical nudged wind structures, the filtering characteristics can differ between the two cases because spectra with different amplitudes, as a result of intermittency of the new source, are impacted differently by the local saturation spectrum. This is especially true once the threshold is exceeded beyond which amplitude limitation replaces critical line filtering as the dominant filtering mechanism. Setting aside possible uncertainties over the choice of saturation spectrum used by the USSP scheme, filtering is most effective where the wave spectrum exceeds local saturation by the largest amount and wave momentum deposition into the mean flow is consequently largest. Hence, the new source scheme has a key characteristic that, in a region where the invariant source is replaced by an intermittent source that is instantaneously larger but has a time mean of comparable magnitude, the filtering fraction will, in general, rise substantially, and deposition will occur at lower altitudes, increasing drag in the lower stratosphere. As a result, the indirect filtering term is negative at most locations, leading to a global mean value of −0.34 mPa that accounts for most of the global mean difference between the flux at launch level and 30 km, whereas the direct damping term dominates locally.

In the ITCZ region, with a 3.68-mPa anomaly maximum at 30 km, filtering reduces the effects of the largest launch-level differences, primarily through direct damping of the source variation (Fig. 7c), although the largest negative changes in filtering also collocate to this region. Polar and subtropical subsidence regions, where the new source flux was reduced at launch, lose differentiation less rapidly with height, leading to a shift in magnitude relative to the tropics between the launch level and 30 km that a narrower range of shading exaggerates (Fig. 7b). This shift also explains a further reduction in global mean flux difference (−0.59 mPa) relative to that at launch. A similar change in distribution of the anomalies on ascending to 30 km is seen in July (Fig. 8b), though the relative shift between poles and tropics is less marked, with the global mean value dropping to a reduction of 0.36 mPa and the range again substantially reduced. As July winds around the strong Southern Hemisphere polar vortex are eastward over the entire atmosphere depth, eastward nonorographic gravity wave fluxes are strongly filtered, but the westward component can propagate up to the mesopause; hence, at 30 km, the source variation damping term (Fig. 8c) is weakened south of 45°S. Meanwhile, the change in filtering term contributes a 0.40-mPa reduction in the global mean (Fig. 8d). A local increase in subtropical subsidence regions arises because suppressed precipitation in these regions leads to very low values of source flux with the new parameterization and correspondingly reduced levels of filtering upon propagation upward.

Relative differences in vertical propagation of zonal mean absolute momentum fluxes can be tracked on ascent from the troposphere, where values from the new source are enhanced relative to the invariant source (Fig. 9: positive shading) across the high-precipitation tropical convection zones and at latitudes covering the winter hemisphere storm tracks. As filtering of the new source is more effective because of the intermittency effect discussed earlier, the enhancement in these regions reduces with height (most rapidly where the initial enhancement was largest), and by 40 km in the July winter vortex region (70°–50°S) or 16 km in the tropics it disappears altogether. This implies that both spectra are reduced to the local saturation, losing all memory of the launch-level sources, with the result that even a very sophisticated scheme might perform no better than a simple invariant source. In the dry, low-precipitation, subtropical subsidence and polar regions, where the new source produces less flux at launch (negative shading), the intermittency effect still operates on the new source, causing the greatest percentage reductions in the lower stratosphere circa 28 km. Above 28 km, invariant and new source fluxes are each progressively eroded by filtering until near the mesopause, around 80 km (~1 Pa), the relative difference signal again converges to zero.

Fig. 9.
Fig. 9.

Percentage difference in zonal mean absolute momentum flux from nudged experiment between new source and invariant source, normalized to invariant source for (a) January and (b) July.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

5. Impact on evolution of a free-running model

The nudged configuration allows assessment under realistic background wind conditions as to where differences in the location of momentum deposition might arise when the new source is introduced. Nudging proved a useful tool for isolating effects upon the upward-propagating gravity waves of changes in sources from changes in filtering, most especially in circumstances where changes in the gravity wave momentum flux impacted primarily upon the steady-state mean climate of the MetUM. However, only a free-running simulation permits the study of aspects such as the impact of spatial and temporal variation in the gravity wave sources upon MetUM variability or feedback of flux intermittency upon evolution of the precipitation field. Hence, for an initial exploration (as prelude to more detailed study), a further 12-yr atmosphere-only experiment was set up in which the new source fluxes interacted with the freely evolving mean flow. For comparison, momentum fluxes as parameterized by the standard invariant scheme were calculated simultaneously, solely for diagnosis of their propagation and filtering.

a. Mean state

January and July (Figs. 10a,b) height–latitude zonal mean zonal winds with the new interactive source parameterization maintain jet structures with minor differences against the invariant source control (Figs. 10c,d). In the mesosphere (above 1 hPa) the difference pattern is consistent with slightly reduced drag at most latitudes (not shown) from persistently reduced deposition at the highest altitudes. Comparison against winds from the nudged simulation suggests a tendency for the equatorward curvature of the winter hemisphere vortex core with height to be somewhat weaker than in the reanalysis (Figs. 10e,f). As previously reported (e.g., Fig. 1 in Butchart et al. 2011) this problem, identified with insufficient deposition of gravity wave momentum in the upper stratosphere, is common to many GCM simulations, including the MetUM control.

Fig. 10.
Fig. 10.

Zonal mean zonal wind for interactive new source experiment for (a) January and (b) July; interactive new source control for (c) January and (d) July; interactive new source − nudged experiment for (e) January and (f) July. Contour intervals at 10 m s−1 (difference plots 5 m s−1 and shaded from 2 m s−1); dashed contours represent negative (westward) wind values.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

Changes in the tropics between the ΔS launch-level mean absolute momentum flux anomalies for the interactive simulation in January and July (Figs. 11a,b) and the equivalent nudged simulation data (Figs. 7 and 8) are consistent with differences between their respective precipitation distributions, as discussed in section 4. Midlatitude peak differences at the launch level also appear to be systematically lower for the interactive run, but the filtering terms change relatively little (not shown) between the nudged and interactive simulations. Hence, differences in the two sets of flux anomalies between latitudes 30° and 60° retain a similar signal at 30 km to those noted for the launch level. The patterns of launch-level anomalies from the interactive simulation and their upward propagation can again be tracked (Fig. 12) and compared with the nudged simulation (Fig. 9), which further illustrates that the distribution at launch is altered, albeit within the broad envelope of enhanced values (positive shading) in the high-precipitation tropical ITCZ and midlatitude storm-track regions. Note that the enhancement signal generally propagates higher in the nudged simulation, where the new source has no impact on the flow evolution, than in the interactive simulation, where the changes in momentum flux are allowed to feed back.

Fig. 11.
Fig. 11.

Launch-height monthly mean absolute momentum flux differences (new source − invariant source) in interactive experiment for (a) January and (b) July.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

Fig. 12.
Fig. 12.

Percentage difference in zonal mean absolute momentum flux from the interactive experiment between new source and invariant source, normalized to invariant source for (a) January and (b) July.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

A direct comparison of the propagation and filtering of absolute momentum fluxes at altitudes 20, 30, 40, and 50 km is made with zonal mean distributions for January (Fig. 13, left panels) and July (Fig. 13, right panels) from both the new source [interactive simulation (black line) and nudged (thin red line)] and the invariant source [interactive simulation (dotted blue line) and nudged (dashed–dotted red line)]. This alternative to Fig. 12 also allows comparison with a previously published assessment of model absolute momentum fluxes (Fig. 2 in Geller et al. 2013) against results derived from observation datasets (Fig. 1 in Geller et al. 2013). Among the models presented in Geller et al. (2013) was an earlier version of the MetUM, and it is reassuring that the invariant source behavior is sufficiently independent of model version to produce latitudinal distributions that are strikingly similar in either context. Latitudes where the new and invariant sources perform very similarly at 20 km (e.g., round 50° to 60° in winter hemispheres) are likely to be dominated by orographic gravity wave activity that affects each identically. More importantly, when the new source replaces the invariant, the flux reductions seen here at 20 km over the polar regions (of over 50% for Antarctica) improve agreement with observations presented in Geller et al. (2013). Differences between new source fluxes from the nudged and interactive run are consistent with those described above and are still evident as high as 50 km, although damped by filtering. Where the new source has enhanced values relative to the invariant, they have by 30 km in each case largely been eroded back to the invariant source values. Thus, at higher altitudes, the main differences left are the more slowly eroded reductions against the invariant source. At 20 km in the vicinity of 20° in the summer hemisphere, the new source distribution is more peaked than the invariant, caused less by enhancement in the ITCZ than by reduced fluxes in the subsidence regions on either side. Latitude–longitude plots (not shown) of these fluxes show that introducing the new source enhances the peaks over land (improving agreement with Geller et al. 2015) and suggest that the combination of a convective precipitation source and filtering between 3.8 and 20 km may account for much of the spatial variation in their tropical absolute momentum flux distributions. However, this should not detract from the role of other sources (e.g., frontal and jet emission) that may dominate at different times or locations.

Fig. 13.
Fig. 13.

(left) January and (right) July zonal mean absolute momentum from interactive experiment [new source (solid black) and invariant source (dotted blue)] and from nudged experiment [new source (thin red) and invariant source (dashed–dotted red)] at (top to bottom) 50, 40, 30, and 20 km.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

b. Variability

All three simulations have similar mean QBO periods (Fig. 4), consistent with the choice of time mean parameterized flux amplitudes. However, closer inspection of the QBO signal at 30 hPa (not shown) reveals more-regular individual periods in the control (free-running invariant source) than in the nudged simulation, used here as a proxy for reality by virtue of its constrained wind flows. Several studies have identified variability from real-world sources that are not represented in models [e.g., caused by dynamical interactions with ozone (Butchart et al. 2003) or injections of stratospheric aerosols (Aquila et al. 2014)]. And it has long been recognized that steady, low-level gravity wave forcing by an invariant source requires gravity wave filtering to account for much of the variability seen in the lower stratosphere (Warner et al. 2005; Hertzog et al. 2012). When strong geographical and seasonal variations in the launch-level fluxes (Fig. 5) are able to propagate upward, an interactive source can introduce desirable additional variability into the middle atmosphere. Lott and Guez (2013) report similar impacts. The interactive source simulation offers a promising initial indication of stronger stalling in the westward phase during the 1991–92 winter, for instance, but a longer experiment is required to determine whether this improvement is statistically significant. The QBO westward peak amplitudes at 30 hPa are weaker by 4–8 m s−1 in the control than in the nudged “reality,” while eastward peak amplitudes are mostly stronger by 2–5 m s−1. When the interactive sources are introduced, the eastward peak values reduce to match the nudged values much more closely, but little impact is seen on westward peak amplitudes, resulting in an overall reduction of amplitude relative to the control that is beneficial.

Modest improvement is also evident in the 1-hPa semiannual oscillation (SAO) in monthly zonal mean zonal wind against a plausible nudged simulation result, which has April (October) eastward peaks with wind strengths 28.7 (13.7) m s−1; marked asymmetry between the two seasons supports a strong annual component. Eastward peak values of 7.3 (0.3) m s−1 for the interactive simulation improve upon the control values of 2.5 (3.0) m s−1 and show stronger asymmetry, but large biases still remain. An SAO signal with low sensitivity to changing gravity wave sources might imply that unresolved gravity waves are simply not the biggest contributors to more realistic zonal mean wind differences. Indeed, Fig. 9 implies that relative differences above 40 km (~30 hPa) in the tropics are largely filtered out, but this result might be sensitive to a change in saturation assumption.

Zonal mean zonal wind contours from the interactive simulation are replicated for reference on each time series of monthly equatorial (5°S–5°N) mean upward-propagating flux of horizontal pseudomomentum (Figs. 14a–d, shaded) and emphasize the importance of critical-level filtering, where sharp gradients in upward-propagating fluxes denote momentum deposition that impacts the mean flow. For example, the descending transition to westward winds around 20 km during 1992 is a barrier to the westward fluxes (Figs. 14a,b) but transparent to eastward fluxes (Figs. 14c,d). Below 10 km, the most visible difference is a strong annual cycle for the interactive source (Figs. 14b,d) that is absent with the standard invariant source (Figs. 14a,c). Gravity wave momentum deposition in the QBO is concentrated into narrow shear zones in advance of the descending zero-wind line, where the resulting acceleration draws the shear zone downward (Figs. 14e,f). The degree of similarity between the two source cases is emphasized by this test because use of the same background wind fields ensures that critical levels seen by both are collocated. Nevertheless, they differ from equivalent nudged experiment results, where larger fluxes propagated through the lower stratosphere to the 20–30-km height range within which interaction with the QBO occurs. The acceleration bands were broader than for the interactive simulation, where the zonal wind vertical structure can respond to deposited gravity wave momentum. Choices to retain the same launch level (3825 m) for both sources and the same values for calculating the saturation spectrum also have the effect of limiting differences between the two as erosion of fluxes from both sources to the local saturation form at a given level leaves them thereafter appearing much more alike. Thus, differences in the distributions are more prominent when low precipitation activity (e.g., Figs. 14c,d in second half of 1991) yields reduced launch fluxes relative to the invariant source and there is no flux to propagate higher. The impact of source changes is, however, sensitive to choices made for these other aspects of the parameterization.

Fig. 14.
Fig. 14.

Monthly equatorial 5°S–5°N zonal fields from interactive experiment with (a),(c),(e) invariant and (b),(d),(f) new precipitation sources of nonorographic gravity waves. Zonal wind (10 m s−1 contours; negative dashed) overlaid on parameterized vertical flux of (a),(b) westward or (c),(d) eastward horizontal wave pseudomomentum (shading) and (e),(f) net eastward acceleration from parameterized gravity waves.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-15-0022.1

6. Discussion and conclusions

A new meteorologically sensitive source scheme for nonorographic gravity waves has been developed for the MetUM within the USSP scheme conceptual framework (Warner and McIntyre 1996) that improves upon the present invariant source by introducing total precipitation as a proxy for a vertically integrated latent heat release source. This qualitatively produces large-scale spatial and temporal variation consistent with observational constraints. Coarse-grain-averaged output from a convection-permitting, limited-area MetUM configuration has been used to diagnose an empirical relationship between total precipitation and gravity wave momentum fluxes, measured on grid scales typical of earth system models (section 3a). A relationship of the form , approximated to , was adopted as a basis for the simple new source launch flux parameterization to replace the current invariant source. Although the Indian Ocean region represents a broad domain for the convection-permitting simulation, it is clearly possible that similar analyses of regions elsewhere on the globe (extratropical, for instance) might yield a different relationship form or reveal dependences on variable combinations that would not be apparent from a single study case. Nevertheless, our findings are consistent with recent tropical warm pool results reported by Hankinson et al. (2014) for the Timor Sea.

The remarkable success of invariant source gravity wave schemes implies that they produce zonal and annual mean momentum budget contributions which are appropriate for maintenance of realistic values for key measurands, such as the QBO period. Hence, the new source’s amplitude scaling parameter was chosen such that its multiannual near-global mean launch flux matched the equivalent for the invariant isotropic source. The similarity of QBO periods from the interactive new source and invariant control simulations provides evidence that mean period values are primarily determined by large-scale mean fluxes, supplied by the new source at the launch level, rather than the increased variation in flux amplitudes both geographically and over time. PDFs of the new source absolute momentum flux exhibit an extended tail of large-amplitude, low-occurrence events, which improves comparison with data from balloon observations. QBO variability, which is underpredicted in MetUM simulations with the current invariant source, may plausibly be enhanced by this added source variability, but longer experiments are needed to assess this impact.

An experimental configuration in which temperature and wind conditions over the height range 1–65 km were nudged toward those from a reanalysis (section 4) proved useful for assessing the immediate impact of replacing the previous invariant source. Source intermittency at the launch level impacts fluxes at higher levels in two ways: directly, because of upward propagation of the new source variation, and indirectly, through changes in filtering characteristics. Hence, in agreement with Lott and Guez (2013), when the invariant source is replaced by an intermittent source that is instantaneously larger but has a time mean of comparable magnitude, the filtering fraction will rise substantially, and deposition will occur at lower altitudes, increasing drag in the lower stratosphere.

The new source is the first of possibly several [a complete prescription might include frontal activity (de la Cámara and Lott 2015; Plougonven and Snyder 2007; Charron and Manzini 2002) or jets (Fritts et al. 2006; Uccellini and Koch 1987)] and fulfils a primary aim to represent the impact of tropical convection on gravity waves. The new source embraces a broader connection to active moist processes, and their associated latent heat release, that generate high precipitation rates globally. With little direct observational evidence to support a detailed specification of individual wave amplitudes, the spectral distribution is retained in preference to discrete multiwave alternatives (Richter et al. 2010; Choi and Chun 2011; Eckermann 2011; Lott et al. 2012). Besides additional sources, we note other key aspects of the scheme that offer potential for improved performance within ESMs and deserve further comment:

  • Rescaled amplitude of source or saturation spectrum: Increased source amplitudes tend to increase filtering efficiency, with impacts mostly in the lower stratosphere, where gravity waves interact with the QBO or extratropical jets. Independently increasing the saturation spectrum amplitude tends to reduce the filtering differences, which might offer a route for addressing systematic biases in the SAO. The challenge is to explore how interactions with locally and intermittently large-amplitude wave packets might permit enhanced flux propagation yet still remain consistent with the well-established universal spectrum paradigm for larger spatial scales and longer mean periods.
  • Residual flux: The new source flux is scaled by that for the arbitrary precipitation rate threshold (0.1 mm day−1), below which it is set to zero. In fact, the high-resolution analysis (section 3) would support a nonzero residual flux in the presence of vanishingly low precipitation. By analogy with the original argument for employing an invariant source, such a background might arise from extra sources for gravity waves or neglect of their horizontal propagation.
  • Launch-level height and directionality: In sensitivity tests, raising the source launch height above the standard 3825 m had a complex impact on filtering effectiveness relative to the invariant source because of the dependence on relative amplitudes of the source and local saturation spectrum at the launch level; wind shear between the launch level and altitudes above; and whether the launch level lay above or below regions where large amounts of momentum flux are deposited (e.g., jets). Introduction of a source launched at variable heights toward cloud-top or tropopause levels would force a departure from the current momentum-conserving assumption that launch fluxes in each azimuthal direction should be isotropic. Thus, a mechanism for representing directionality and balancing the momentum budget in the gravity wave source regions would also be required.

In summary, the new scheme achieves more realistic spatial and temporal variability than with the previous invariant source scheme and gains the ability within an earth system model to respond to future climate scenario increases in total precipitation with an increase in nonorographic gravity wave fluxes that are launched from the troposphere. This ability to represent a link between gravity waves and convective activity offers potential to improve the physical realism of climate and earth system models that can seldom afford the resolutions required for them to represent the global momentum budget without a contribution from parameterized subgrid buoyancy waves.

Acknowledgments

This work was supported by the European Commission’s 7th Framework Programme, under Grant Agreement 282672; the EMBRACE project; and the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA1101). Cascade is a U.K. funded by the Natural Environment Research Council. The authors express their gratitude to Albert Hertzog, Francois Lott, Riwal Plougonven, and the two reviewers for useful scientific discussions and/or comments on the manuscript.

APPENDIX

Coarse Graining of High-Resolution Model Output

A double coarse-graining procedure forms the basis for analysis of the high-resolution model data. First, we define an inner scale (taken here as 110 km) and filter perturbations relative to that scale (larger scales are attributed to the large-scale flow). Second, for representativeness, we average over an adjustable outer scale, ranging from 110 km to the full high-resolution model domain, to give a mean magnitude of the vertical flux of horizontal (zonal and meridional) momentum for similarly averaged rainfall.

Specifically, (at geometric height levels 5, 10, 15, …, 40 km)

  1. Raw ρ, u, υ, and w fields are sampled from the 2.2-km model every 2 min.
  2. At each time, local means are computed by area averaging on the inner scale. Perturbations are defined as , etc.
  3. Perturbations u′, υ′, and w′ and momentum flux magnitudes |τ| = ρ|(uw′, υw′)| are computed at each point on the 2.2-km grid.
  4. Momentum flux magnitudes |τ| and associated rainfall rates P are time averaged over 1 h and spatially averaged over the outer scale to give and .

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1

For technical reasons, the global configuration of the MetUM used for these simulations and the concomitant nested model had a slightly older version of the dynamical core than that used in the other global simulations presented in this paper, although care was taken to choose parameter options that restricted the differences. Some changes in the behavior of resolved waves are to be expected, most noticeably at scales close to the configuration grid resolution. Because of the clear separation of these scales in the 2.2-km model and in the earth system models for which the parameterization of unresolved gravity waves is developed, these differences are judged not to affect the paper’s main conclusions.

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