Offline estimates and tuning of mesospheric gravity-wave forcing using Met Office analyses

Transcription

1 Quarterly Journalof the Royal Meteorological Society Q. J. R. Meteorol. Soc. 140: , April 2014 DOI: /qj.2168 Offline estimates and tuning of mesospheric gravity-wave forcing using Met Office analyses D. J. Long, a *D.R.Jackson b and J. Thuburn a a University of Exeter, UK b Met Office, Exeter, UK *Correspondence to: D. J. Long, University of Exeter, 319 Harrison Building, North Park Road, Exeter, EX4 4QF, UK. dl226@ex.ac.uk The contribution of D. R. Jackson was written in the course of employment at the Met Office, UK and is published with the permission of the Controller of HMSO and the Queen s Printer for Scotland. Estimates of small-scale non-orographic gravity-wave forcing in the mesosphere are investigated using Met Office middle atmospheric analyses. Such estimates are obtained using the ultrasimple spectral parametrization (USSP) gravity-wave scheme, currently employed operationally by the Met Office. A climatology of monthly zonal mean gravitywave forcing from January 2005 December 2010 is presented, along with a discussion of estimated uncertainties and comparison with previous studies. Mesospheric gravity-wave forcing is found to be underestimated, consistent with the known seasonal evolution of extratropical mesospheric temperature biases within the Met Office assimilated dataset. The sensitivity of gravity-wave forcing to various parameters within the USSP scheme is investigated. Subsequent experiments diagnose the temperature response in a freerunning version of the Unified Model when mesospheric gravity-wave forcing is increased through perturbing the energy scalefactor parameter within the USSP scheme and imposing momentum-flux conservation at the model lid. For physically justifiable perturbations to the USSP scheme, significant temperature responses of K are seen for mesospheric polar regions under solstice conditions, highlighting the positive impact such changes could possibly have on known temperature biases within the Met Office assimilated dataset. Key Words: gravity-wave forcing; mesosphere; USSP scheme Received 3 October 2012; Revised 27 February 2013; Accepted 11 March 2013; Published online in Wiley Online Library 19 June Introduction It is well known that the thermal structure and circulation of the middle atmosphere are dynamically forced from its purely radiatively determined state due to momentum deposition from breaking Rossby and gravity waves (Holton and Alexander, 2000). Temperatures in the polar winter upper mesosphere can be 100 K warmer than those based on purely radiative grounds (Shine, 1987). As a significant proportion of the gravitywave spectrum occurs over subgrid length-scales, modern general circulation models (GCMs) must represent their effects through parametrization schemes (Lindzen, 1981; Palmer et al., 1986; McFarlane, 1987; Hines, 1997; Warner and McIntyre, 2001; Scinocca, 2003). Despite widespread and intensive study, the exact amplitudes, phase speeds and mechanisms of gravitywave breaking are still not fully understood, meaning that all parametrization schemes contain free parameters which to some extent are arbitrarily set. Observational studies (Ern et al., 2004, 2005, 2006, 2011) have provided useful constraints on gravitywave characteristics; however, to some extent studies such as these are parametrized estimates due to the numerous assumptions that must be made when using observed quantities to derive related gravity-wave fields. Therefore, considerable uncertainty in the parameters of all gravity-wave schemes still remains due to the inherent difficulty in producing a fully consistent spatial and temporal climatology of gravity-wave characteristics and activity (Fritts and Alexander, 2003). Given relatively weak constraints, parameters of gravity-wave schemes are often tuned within GCMs to reduce climatological biases (Norton and Thuburn, 1999; Scaife et al., 2002). Adopting this approach can often lead to overcompensating ( masking ) for systematic biases caused by other aspects of the GCM and is therefore not necessarily an improvement to the system (Kim et al., 2003). Recently, (Long et al., 2012, hereafter DL12) validated middle atmospheric temperature fields from operational UK Met Office analyses using independent observational satellite data. The results of DL12 showed that analyses from January 2005 December 2010 contain significant temperature biases throughout the mesosphere. Here, both warm and cold biases of 6 14 K are found consistently at all latitudes and seasons in the lower mesosphere, with maximum cold biases of K found in the polar winter lower mesosphere and maximum warm biases c 2013 Royal Meteorological Society

2 1026 D. J. Long et al. of K found in the polar summer upper mesosphere. As detailed in DL12, such temperature biases are primarily caused by inaccurate diabatic heating calculations within the operational Edwards and Slingo (1996) radiation scheme and insufficient adiabatic heating/cooling associated with misrepresentation of the mesospheric mean meridional circulation. Since observational data are only applied below the stratopause in the operational system, data assimilation is unable to correct for such mesospheric biases. Seasonal evolution of such temperature biases in the polar regions of the mesosphere suggests that momentum deposition in the extratropical mesosphere, supplied by the currently operational ultrasimple spectral parametrization (USSP) gravitywave scheme of Warner and McIntyre (2001), is insufficient. As diagnostic fields of modelled gravity-wave forcing are not archived for the assimilated dataset, the initial focus of this work is to support the results of DL12 by obtaining offline estimates of gravity-wave forcing within the assimilated dataset, comparing them with previous modelling and observational studies. Further details of the analysis fields used in the study are given in section 2. The USSP gravity-wave scheme and known deficiencies of the Edwards and Slingo (1996) radiation scheme in the upper mesosphere are introduced in sections 3 and 4, respectively. The offline approach used to estimate gravity-wave forcing is described in section 5. Offline estimate results, along with a comparison against previous observational and modelling studies of mesospheric gravity-wave forcing, are given in Section 6. The secondary focus concentrates on improving the representation of the mesosphere within the Met Office assimilated dataset. The offline approach can be used to test the sensitivity of gravity-wave forcing to perturbations of free parameters contained within the USSP scheme. Both observational and theoretical constraints on available USSP free parameters and the results of selected forcing sensitivity studies are detailed in section 7. Following such sensitivity studies, numerical experiments with the Met Office Unified Model (UM) were performed with various perturbed parameter values of the USSP gravity-wave scheme. Full details of the experimental design, along with results detailing the impact perturbed USSP parameters have on mesopheric temperatures within the UM, are detailed in section 8. Finally, conclusions are given in section Analysis description The daily analyses of global temperature, wind and geopotential height used in this work are identical to those in DL12, and range from 1 January December Analyses were produced daily at 1200 UTC by the Met Office middle atmospheric data assimilation system using the global configuration of the UM (Cullen and Davies, 1991). From January 2005 February 2006, analyses were produced using three-dimensional variational (3D-Var) data assimilation (Lorenc et al., 2000) on a 50-level vertical grid configuration of the UM from the surface to the lower mesosphere at 63 km. Here the horizontal resolution was 2.5 latitude 3.75 longitude. From March 2006, the 3D-Var assimilation scheme was upgraded to the currently operational four-dimensional variational (4D- Var) formulation (Rawlins et al., 2007). During this upgrade, the horizontal resolution of the middle atmosphere UM was refined to latitude longitude, while the previous vertical resolution and model domain were retained. After November 2009, analyses were produced using a 70-level configuration of the UM with model lid at 80 km. The horizontal resolution of the 70-level model was initially identical to the previous 50-level configuration, however in March 2010 it was further refined to latitude longitude. For brevity, analyses from January 2005 November 2009 shall be referred to as L50 and those from November 2009 December 2010 as L70. It should be noted that, while the assimilated analyses are produced on model levels, both L50 and L70 analyses used in this study are archived on pressure levels that have 6 intervals per decade change in pressure. Archived analysis fields have a standard horizontal resolution of 2.5 latitude 3.75 longitude. Further details of the analyses used in this study can be found in DL12 and Long (2011). 3. USSP gravity-wave scheme Small-scale non-orographic gravity waves, which dominate the dynamical forcing of the mesosphere (Holton, 1983), are represented within the UM using the USSP scheme. The USSP scheme uses the spectral approach to gravity-wave parametrization (Fritts and Alexander, 2003). Here, gravity-wave forcing is determined from the vertical divergence of momentum flux deposited locally into the background mean flow through an erosion of an initial spectrum of gravity waves launched in the troposphere as it propagates vertically through an atmosphere with varying density, static stability and background wind. The USSP scheme is based on the full three-dimensional scheme described by Warner and McIntyre (1996), where the wave energy spectrum at the launch level is identical to the empirical form used by Fritts and Vanzandt (1993). As detailed in Bushell et al. (2007) and Warner and McIntyre (2001), the launch momentum flux spectrum is determined from the spectral characteristics of the launch energy spectrum and the vertical component of group velocity for gravity waves in terms of the magnitude of vertical wave number m only. Here the vertical component of group velocity for gravity waves is described by the mid-frequency approximation, N 2 ˆω 2 f 2,where ˆω is the intrinsic frequency (that relative to the background flow), N is the buoyancy frequency and f is the Coriolis parameter. Following Fritts and Lu (1993), the launch momentum flux spectrum can be further approximated by idealized spectral shapes, separating the spectrum into two distinct parts defined by power laws of m, which can be integrated analytically. Here, small and large vertical wave numbers have a power-law dependence m s and m t respectively. Small m values range between a cut-off value of m min and m,wherem corresponds to the m value with maximum wave energy and is known as the characteristic wave number. Large m values range between m and infinity. The values of (s, t) are empirical constants, which, alongside a scale factor C l0, define the total energy flux of the full three-dimensional spectrum (Bushell et al., 2007) and thus the momentum flux at the launch level within the USSP scheme. Note that the scale factor C l0 depends on an energy scale factor β and p, the power-law dependence for the intrinsic frequency spectrum ˆω, which are both used in defining the full three-dimensional spectrum (Fritts and Vanzandt, 1993). The UM uses a normalized height-based vertical coordinate (η) on a staggered Charney Phillips grid (Staniforth et al., 2004). The momentum flux spectrum, which is homogeneous and isotropic in four azimuthal directions, is launched at the model level which is closest to the value of η = (Bushell et al., 2007), resulting in a launch level close to Earth s surface in the lower troposphere. For the L50 analyses, this typically results in a launch altitude of 2800 m, while differences in vertical grid configurations results in a launch altitude of 3500 m for the L70 model (Long, 2011). Note that the launch level of η = is hard-wired into the UM and is therefore not a freely adjustable parameter. The initial launch momentum flux spectrum is conservatively propagated in the vertical, with wave number m components being refracted by changes in density, static stability and background vertical wind shear. For each vertical level, the magnitude of momentum-flux deposition, i.e. erosion of the launch spectrum, is calculated by determining which spectral elements exceed a specified saturation spectrum or chopping function. As detailed in Warner and McIntyre (2001), the chopping function has a spectral shape identical to that of the launch spectrum at asymptotically large vertical wave numbers. Here the shape of the chopping function is based on empirical

3 Tuning of Mesospheric Forcing 1027 knowledge, i.e., regardless of the physical mechanisms responsible for gravity-wave breaking, the large m part of the spectrum tends to a ceiling m t (Warner and McIntyre, 1996). Following the details of McLandress and Scinocca (2005), the chopping function and large m part of the launch spectrum may be related through the non-dimensional constant C, allowing normalization of each spectrum to be specified independently. Hence, although at large m both the launch and saturated spectrums share the same power-law dependence, they need not be equivalent, i.e. it is not necessary for the large m components of the initial spectrum to be saturated at the launch level. However, for this study, as for the operational USSP scheme and the previous studies of Warner and McIntyre (1996, 2001) and Scinocca (2002, 2003), we define the large m components of the launch spectrum to be equivalent to the chopping function, i.e. C = 1. It should be noted that the launch spectrum represents the sole source of momentum flux within the USSP scheme, i.e. there is no further generation of non-orographic gravity waves above the launch level. Alongside the non-orographic USSP scheme, orographic gravity-wave forcing is also represented using the Gregory et al. (1998) parametrization; above 20 hpa this orographic scheme is switched off. Over our period of interest, analyses are generated with both gravity-wave schemes being run simultaneously but uncoupled to each other. In addition to parametrized gravity wave sources, the relatively high spatial resolution of the UM versions considered here have the potential to resolve a significant proportion of the gravity-wave spectrum explicitly. The operational UM employs the technique of offcentring (time-weighting) parameters within the semi-implicit time integration scheme, placing more weight on values at future time steps. This approach has been shown by Shutts and Vosper (2011) to suppress any resolved gravity wave motion very effectively within the operational L70 model if a sufficiently long time step (15 min) is employed, thereby reducing the risk of parametrizations double-counting the resolved gravity-wave spectrum. In an ideal situation, the model vertical domain would extend to an altitude where all of the initial launch momentum flux has been eroded. In practice, there are often significant amounts of momentum flux remaining at the model lid and one of two options is allowed. The first option is a transparent lid condition, where the remaining momentum flux is allowed to propagate freely through the model lid. The second option is an opaque lid condition, where all remaining momentum flux is confined to the model domain by requiring that the momentum flux value at the model lid is zero. Since the launch momentum flux is isotropic in each azimuthal direction, the net momentum flux introduced at the launch level is zero. Therefore, the opaque lid condition is theoretically preferred as it prevents any anisotropy of momentum flux leaving the model lid and consequently results in momentum being conserved throughout the model domain. Momentum conservation has been shown by Shepherd and Shaw (2004) to avoid any spurious influence of radiative perturbations in the mesosphere on the atmosphere below through gravity-wave drag feedbacks. Such feedbacks predominantly have an important impact over seasonal time-scales and hence do not constrain the choice of model lid condition for numerical weather prediction forecasts. However, since above 1.0 hpa the UM is essentially free-running and no observational data are assimilated, it is possible that the choice of lid condition could significantly impact the model s representation of the mesosphere. Nevertheless, as noted by Scaife et al. (2002), if modelled gravity waves approaching the model lid contain significant amounts of momentum flux then the requirement of depositing all momentum at this level can lead to model instability. For this reason, the transparent lid condition was applied in creation of the L50 analyses, where, due to the altitude of the model domain being located in the lower mesosphere, large portions of the gravity-wave spectrum are unsaturated and carry significant values of momentum flux. Table 1. Summary of freely adjustable parameters in the USSP gravity-wave scheme, with given standard values. Name Description Standard value p Intrinsic frequency spectrum 5/3 power index β Energy scale factor m Characteristic vertical wave 2π/(4300) m 1 number at launch level φ Angle of azimuthal sector π/2 m min Minimum vertical wavenumber 2π/( )m 1 s Low vertical wavenumber spectrum 1 power index t High vertical wavenumber spectrum 3 power index C l0 Launch spectrum scale factor s 2 C Saturation normalization constant 1 Lid Momentum flux lid condition Transparent It should be noted that the transparent lid condition was also applied in creation of the L70 analyses. All of the freely adjustable parameters within the USSP scheme have the capacity to affect the magnitude of gravity-wave forcing produced (Ern et al., 2005, 2006; Warner and McIntyre, 1996, 1997, 1999, 2001). A summary of all parameters available for tuning the USSP scheme to produce different forcing values, along with standard values used in the UM since the scheme was introduced in October 2003, is given in Table 1. It should be noted that, along with large-scale momentum forcing, gravity-wave breaking is also known to cause localized small-scale mixing (Fritts and Werne, 2000), which, through turbulent dissipation and diffusion, may result in both direct heating and cooling of the atmosphere (Becker and Schmitz, 2002; Becker, 2004). While direct heating from gravity-wave breaking is known to make a significant contribution to the overall heating budget of the upper mesophere (above 65 km), such terms are currently not represented within the operational version of the USSP scheme. 4. Edwards Slingo radiation scheme Radiative transfer within the L50 and L70 model configurations is calculated using the Edwards and Slingo (1996) scheme, incorporating all major radiatively active gaseous species in the both short- and long-wavelength spectral bands. A major feature of this radiation scheme is the use of pre-processed spectral files containing physical information such as the number of radiatively active species used, irradiance values of the incident solar spectrum, gaseous absorption coefficients and details of the k fit for gaseous transmissions (Edwards et al., 2004). The spectral files used in the L50 and L70 model configurations are based on those from the Hadley Center Global Environment Model (HadGEM1) detailed in Davies et al. (2005), with minor changes to the representation of atmospheric aerosols. Both these spectral files and the Edwards and Slingo (1996) scheme were initially optimized to represent the troposphere accurately; the spectral files are known to be inherently inaccurate in the upper mesospheric region (J. Manners, 2010, personal communication). Furthermore, the Edwards and Slingo (1996) scheme is based on the assumption that local thermodynamic equilibrium (LTE) holds throughout the model domain. A brief description of the LTE condition and its implications when calculating mesospheric heating rates are given below. Below 65 km, the density of the atmosphere is great enough that we may assume that the redistribution of absorbed solar energy is determined almost entirely by collisions between molecules and is instantaneously available to be converted to heat (thermally realized) and subsequently lost (entirely) through thermal emissions; this is known as LTE. Above 65 km, the density decrease results in the mean free path of molecules

4 1028 D. J. Long et al. increasing and collisions becoming sufficiently infrequent that, following the absorption of solar radiation, additional processes, such as re-emission directly to space or transfer between different energy level states, can reduce the amount of infrared energy converted to heat, known as non-lte conditions (Fomichev, 2009). Above 65 km, there is solar radiative heating from ozone and molecular oxygen, together with heating by CO 2 absorption in the near-infrared µm bands (Lopez-Puertas et al., 1990). There is also radiative cooling in the long-wave, chiefly from the 15-µm CO 2, 9.6-µm O 3 and infrared H 2 O bands (though note that in the uppermost mesosphere the 9.6-µm O 3 heats, rather than cools, the atmosphere). The impact of non-lte is as follows. Between 65 and 85 km, non-lte conditions can result in a 25% and 15% reduction in heating from ozone and molecular oxygen respectively (Fomichev and Shved, 1988; Mlynczak and Solomon, 1993) and heating in the near infrared µm bands can be overestimated by 3 6 times (Fomichev et al., 2004) if non-lte effects are not included. Inclusion of non-lte effects also results in a reduction of cooling from the 15-µmCO 2 band, though significant impacts are typically only seen in regions above 80 km (Fomichev, 2009). It has been noted (Bushell, 2005; Long et al., 2012) that deficiencies in the spectral files of the Edwards and Slingo (1996) radiation scheme used in middle atmospheric configurations of the UM contribute to warm temperature biases in the upper stratosphere and lower mesosphere. It is also expected that upper mesospheric heating rates calculated with the Edwards and Slingo (1996) radiation scheme will contain significant biases, since they do not include the impact of non-lte conditions discussed above. Additional biases in the upper mesosphere are also expected, since the direct heating associated with exothermic chemical reactions is also not represented and can exceed direct heating from solar radiation between 70 and 90 km (Mlynczak and Solomon, 1993). It is therefore possible that any tuning of the USSP scheme to remove systematic biases could be not only compensating for a misrepresented mesospheric circulation but also missing radiative physical processes. However, since the gravity-wave tuning we apply is intended to reduce cold (warm) biases of the winter (summer) polar upper mesosphere, which are characteristic of an excessively weak mean meridional circulation, there is a strong chance that any positive impact with such regions represents a genuine model improvement. 5. Offline experimental design As noted above, model fields of gravity-wave drag are not archived for the stratospheric assimilated dataset. However, it is possible to obtain estimates of gravity-wave drag within the model by applying the USSP scheme offline to the temperature and wind fields of both the L50 and L70 analyses. Unless stated, all offline estimates in this study were obtained using the standard USSP parameter values detailed in Table 1 with a transparent model lid. Since the temperature and wind fields used in the offline calculations are from the daily analyses at 1200 UTC, the results are essentially for single time steps of the forecast model integration at this particular time. The largest source of discrepancy between model and offline fields is expected to arise from the difference in altitudes of the initial launch spectrum. Previous studies of Ern et al. (2005, 2006) have shown that the momentum flux and gravity-wave distributions of the stratosphere, obtained using the USSP scheme, are sensitive to the launch altitude of the initial momentum flux spectrum and in fact the appropriate choice of launch level is open for debate (Fritts and Alexander, 2003). Here, differences in the above fields could occur due to the differences in wave filtering by tropospheric jets. All results presented in this study have been obtained using a momentum flux launch level of 681 hpa. Under solstice conditions, where maximum magnitudes of gravity-wave forcing occur in the extratropical mesosphere, the launch level of the offline estimates is typically m higher than the L50 model launch level of 2800 m. For the L70 offline estimates, again under solstice conditions, the launch level is typically m lower than the model launch level of 3500 m. Therefore, as fully detailed in Long (2011), offline estimates most likely underestimate (overestimate) westward (eastward) forcing for the L50 analyses and overestimate (underestimate) westward (eastward) for the L70 analyses; however, the magnitude of this inaccuracy is generally less than 10% of the calculated values. 6. Offline estimates for the L50 and L70 analyses Figure 1 details the offline monthly zonal mean zonal forcing obtained from the L50 and L70 analyses averaged over each December, March, June and September for the following periods: (a) January 2005 February 2006, (b) March 2006 October 2009 and (c) November 2009 December These periods are identical to those used in the validation study of DL12, and were chosen to highlight the impact that major changes to the operational system have on temperature biases of the stratospheric assimilated dataset. In all cases, the majority of forcing occurs in the upper levels of the model domain, with magnitudes greater than 10 m s 1 day 1 generally restricted to the mesosphere above 0.4 hpa. The extratropical mesospheric forcing detailed in Figure 1 is consistent with previous studies, where the zonal direction of gravity-wave forcing above regions of maximum zonal wind contours (known as the mesospheric jets ) opposes the seasonal direction of the zonal mean flow in each hemisphere (Andrews et al., 1987; Holton and Alexander, 2000; Randel et al., 2004) L50 results From Figure 1(a) and (b), we find that under summer solstice conditions maximum values of forcing are similar for each hemisphere, with magnitudes of m s 1 day 1 between 0.2 and 0.1 hpa. For the winter months, the westward forcing of the southern hemisphere is generally greater than the eastward forcing seen in the opposing summer hemisphere, with typical values of m s 1 day 1, while northern hemisphere values are comparable to opposing summer magnitudes. These distributions and magnitudes of offline forcing in the lower mesosphere are qualitatively similar to those obtained by Scaife et al. (2002), placing confidence in the results of the offline calculations L70 results From Figure 1(c) we find that the magnitudes of forcing supplied at and below 0.1 hpa are similar to those seen in the L50 analyses for each season. Above 0.1 hpa, the L70 forcing in the extratropical mesosphere increases until reaching maximum magnitudes between 0.02 and 0.01 hpa. Here, the summer months of both hemispheres have two distinct regions of maximum forcing in the upper mesosphere, occurring at subtropical latitudes of and extratropical latitudes of For the southern hemisphere summer months, maximum forcing occurs at extratropical latitudes during December with magnitudes of m s 1 day 1. Similar magnitudes are also seen in the northern hemisphere summer month of June, however here maximum values occur at tropical latitudes. For the winter season of both hemispheres, the magnitudes of forcing seen at tropical latitudes are smaller than those seen in the opposing tropical summer hemisphere. Winter-season maximum values generally occur at extratropical latitudes of For the northern hemisphere winter season, maximum forcing of m s 1 day 1 occurs during December. For

5 Tuning of Mesospheric Forcing 1029 (a) DEC MAR JUN SEP (b) ms 2 day 1 (c) Figure 1. Offline monthly zonal mean zonal gravity-wave drag values averaged over each December, March, June and September from (a) January 2005 February 2006 (L50), (b) March 2006 October 2009 (L50) and (c) November 2009 December 2010 (L70). Drag values have a contour interval of 5 m s 1 day 1 with negative values dashed. the southern hemisphere winter season, maximum forcing of m s 1 day 1 is seen during June Comparison with previous studies Previous estimates of gravity-wave forcing in the mesosphere have been performed using a variety of approaches including momentum-balance studies (Hamilton, 1983; Smith and Lyjak, 1985; Gille et al., 1987; Marks, 1989; Shine, 1989; Huang and Smith, 1991), modelling studies where gravity-wave breaking is parametrized (Lindzen, 1981; Holton, 1982, 1983; Garcia and Solomon, 1985; Huang and Smith, 1991; Fritts and Lu, 1993; Alexander and Dunkerton, 1999; Fomichev et al., 2002; Yang et al., 2006; Richter et al., 2008, 2010; Becker and McLandress, 2009; Orr et al., 2010), inverse data-assimilation techniques (Pulido and Thuburn, 2005, 2006, 2008) and high-resolution modelling (Hamilton et al., 1999; Kawatani et al., 2010; Sato et al., 2012; Watanabe et al., 2008). In addition, observational studies of momentum flux from which gravity-wave forcing can be inferred have also been conducted by Fritts and Yuan (1989), Jiang et al. (2006), Nakamura et al. (1996), Reid and Vincent (1987), Tsuda et al. (1990, 2000) and Ern et al. (2011). A review of each technique can be found in Fritts and Alexander (2003). A summary of maximum extratropical mesospheric gravity-wave forcing, under solstice conditions, detailed in the above studies is given in Table 2. In the lower mesosphere, gravity-wave forcing from momentum balance, high-resolution modelling and data-assimilation methods are generally consistent with each other. Here, maximum forcing ranges from m s 1 day 1 and 5 50ms 1 day 1 in the southern and northern winter seasons respectively and from m s 1 day 1 for both summer hemispheres. Observational studies and parametrization respectively produce larger forcing values in the southern and northern winter lower mesosphere, compared with the above values; however, it should be noted that all approaches have high uncertainty. In the upper mesosphere, the majority of studies are based on the parametrization of gravity-wave forcing. Here, maximum forcing is generally larger than other methods (Fritts and Alexander, 2003) and ranges from m s 1 day 1 depending on season. Again uncertainty in these results is relatively large due to the limited accuracy of observational data

6 1030 D. J. Long et al. Table 2. Summary of maximum magnitudes in extratropical mesospheric zonal gravity-wave forcing detailed by previous studies under solstice conditions. For each period considered, the gravity-wave forcing opposes the seasonal zonal mean wind. All forcing magnitudes are given in m s 1 day 1. The latitudinal location of each maximum forcing region in degrees is given in parentheses. References marked (*) are momentum-balance studies where the zonal forcing from resolved planetary waves are included within the forcing estimate. For such studies, the planetary forcing is expected to be small except during the northern hemisphere winter season. The results of Orr et al. (2010) are shown when employing the Scinocca (2003) (SO3) or the Hines (1997) (DSP) gravity wave parametrization. The observational results of Ern et al. (2011) are absolute values of gravity-wave forcing described as potential accelerations, since they are rough estimates based on numerous caveats. Lower Mesosphere hpa Method SH Winter SH Summer NH Winter NH Summer Reference Momentum balance 55 (50 60) (30 70) 40 (50 60) (30 70) Marks (1989) 5 25 (50 70) Hamilton (1983) (50 70) (30 40) (60 70) 20 (30 40) Shine (1989)* 25 (60 70) Smith and Lyjak (1985) (40 55) Gille et al. (1987) High resolution (50 70) 10 (30 40) (50 70) (30 40) Watanabe et al. (2008) Observational study 100 (45 65) 40 (45 65) Jiang et al. (2006) Data assimilation (60 65) (20 50) (50 70) (20 50) Pulido and Thuburn (2008) Parametrization modelling 102 (38) Lindzen (1981) Upper Mesosphere hpa Method SH Winter SH Summer NH Winter NH Summer Reference Momentum balance (45 55) (55 65) (30 40) (40 70) Huang and Smith (1991)* High resolution (30 60) (50 60) (50 60) (50 60) Watanabe et al. (2008) Observational study (35) Reid and Vincent (1987) (40 50) (40 50) (50 60) (50 60) Ern et al. (2011) Parametrization modelling 100 (35 55) 100 (45 60) Holton (1983) (β-plane) (β-plane) Holton (1982) (50 60) (50 70) Richter et al. (2010) (45 65) (45 55) (60 70) (40 70) Orr et al. (2010) SO (50 65) (55 70) (50 60) (60 70) Orr et al. (2010) DSP (40 50) (35 45) Huang and Smith (1991) (55 65) (55 70) Fomichev et al. (2002) (50 65) (50 60) (40 70) (45 60) Richter et al. (2008) 100 (40 55) 50 (30 40) Yang et al. (2006) 135 (38) Lindzen (1981) 120 (40) 130 (40) Alexander and Dunkerton (1999) 80 (40) 100 (40) Fritts and Lu (1993) (50 60) (40 60) Becker and McLandress (2009) (50) Medvedev and Klaassen (2000) used to tune certain free parameters in the gravity-wave schemes used. Recently, Ern et al. (2011) have used satellite temperature observations to derive values of absolute momentum flux and hence gravity-wave forcing throughout the upper mesosphere. However, as noted in Ern et al. (2011), these estimates are very rough estimates of absolute values only, where magnitudes of forcing are most likely low biased due to the limited proportion of the gravity-wave spectrum resolved by the satellite instruments. In general, the offline estimates in Figure 1 show that gravitywave forcing in the L50 model is too weak, or at the lower limit, when compared with the previous studies discussed above. This disagreement is less for the summer hemisphere, where the offline values are generally smaller than previous estimates by less than 10 m s 1 day 1. In the winter hemispheres, the disagreement is generally m s 1 day 1 or larger, although, as mentioned above, previous studies are subject to a high degree of uncertainty. The offline estimates in Figure 1 also show that gravity-wave forcing in the L70 model is too weak, or at the lower limit, in both the lower and upper mesosphere when compared with previous studies. It should also be noted that regions of maximum forcing in the L70 model occur at higher altitudes in the mesosphere when compared with previous estimates. Since the error of the offline calculations is estimated to be only 10% of the presented values, we can confidently state that differences between these values and previous estimations of middle atmospheric gravity-wave forcing, accounting for biases in these estimations, are due to deficiencies in the USSP scheme, e.g. values of free parameters or deficiencies caused by employing a transparent lid, and not inaccuracies of the offline calculations. The weak gravity-wave forcing highlighted by the offline results and comparison above and present in both the L50 and L70 models is consistent with the temperature biases noted in DL12. The offline studies therefore place additional confidence in the results of DL12, i.e. that the mean meridional circulation in the mesosphere of both L50 and L70 analyses is underestimated and that gravity-wave forcing supplied by the USSP scheme is insufficient in the extratropical mesosphere. 7. Offline sensitivity studies Based on the results of DL12 and the above offline forcing estimates, it is apparent that small-scale gravity-wave forcing provided by the USSP scheme within the UM is insufficient; such a deficiency contributes significantly to temperature biases in the middle atmosphere. As detailed in section 3, the USSP scheme has several free parameters that can be tuned, within certain limits of both observational and theoretical constraint, to produce changes in gravity-wave forcing. The sensitivity of forcing to certain free parameters can be estimated using the offline approach introduced above. Reasons for the selection of certain free parameters from those detailed in Table 1, along with results from associated offline sensitivity studies, are discussed and presented below Free parameters excluded from sensitivity studies Previous observational studies (Vanzandt, 1982; Smith et al., 1987; Allen and Vincent, 1995; Hertzog et al., 2001) have shown that the power-law dependence for larger vertical wave numbers

7 Tuning of Mesospheric Forcing 1031 (t 3) is highly constrained. Based on observations (Allen and Vincent, 1995; Hertzog et al., 2001; Tsuda and Hocke, 2002), the allowed values of m are also highly constrained and, as shown by Ern et al. (2006), the standard value of m = 2π/(4300) m 1 is currently at the upper limit of such a constraint. The parameter p is fairly well constrained by observations (Cot, 2001; Hertzog and Vial, 2001; Tsuda et al., 2004), with magnitudes capable of varying from 1 2; however, the majority of studies obtain values close to the standard value of p = 5/3. The value of m min was chosen to give energy dissipation rates comparable with observations from Lubken (1992, 1997). While momentum forcing is highly sensitive to the value of m min, as noted in Warner and McIntyre (1999) such sensitivity is only seen higher than 90 km, above the L70 model lid. Gravity-wave forcing is highly sensitive to the choice of launch-spectrum scale factor C l0, which is only loosely constrained. However, this parameter was initially tuned to achieve a realistic quasi-biennial oscillation (QBO) signal. Furthermore, the impact when changing C l0 magnitudes has been studied in detail by Bushell et al. (2010). In addition to the above parameters, the USSP scheme can also launch momentum flux in additional azimuthal directions (currently the four directions north, west, south and east are used) via decreasing φ. However, this approach will increase the computational expense of the scheme and, as shown by Warner and McIntyre (1996), results in relatively small differences in the magnitude of gravity-wave forcing. As noted in McLandress and Scinocca (2005), increasing the value of C can increases the height at which momentum flux is deposited and thus may increase the peak values of gravity-wave forcing seen at upper model levels; however, its operational value is hard-wired into the formulation of the USSP used by the UM and is not freely adjustable. Based on the above constraints, the number of azimuthal sectors and the values of t, p, m, C l0, m min and C are not suitable parameters for tuning the USSP scheme to produce additional forcing in the extratropical mesosphere Free parameters suitable for use in sensitivity studies Within the USSP scheme, the energy scale factor β for the launch spectrum is directly proportional to the amount of gravity-wave momentum flux at all altitude levels. Hence variation in β scales the magnitude of deposited momentum flux and derived gravitywave forcing, without changing the overall distribution. From theoretical assumptions, the value of β is 10 1 (Warner and McIntyre, 1996; Fritts and Alexander, 2003), with an uncertainty factor of 2. The power law s is the least well-constrained free parameter, theoretically or by observation (Fritts and Alexander, 2003), as corresponding vertical wavelengths are too large to be resolved practically. This part of the gravity-wave spectrum corresponds to deep gravity waves, which are believed to carry significant proportions of the momentum flux spectrum into the mesosphere. Since β and s are both weakly constrained, they are ideal candidates to use for tuning the USSP scheme to produce additional forcing in the extratropical mesosphere. Therefore, the sensitivity of gravity-wave forcing to perturbing both of these parameters is investigated. In addition to these two parameters, the impact on forcing when using an opaque lid condition is also examined. Approaching 0.01 hpa, the momentum flux modelled by the USSP scheme has significant (non-zero) values in the L70 analyses (Long, 2011). Therefore, based on the downward control argument of Haynes et al. (1991), when applying the opaque lid condition a proportion of the momentum forcing that would occur above the model lid (thus influencing the atmosphere below) is retained within the model domain. It is therefore expected that an opaque lid will result in increased forcing compared with the standard transparent condition Sensitivity study results Offline sensitivity studies were performed by comparing forcing values obtained using perturbed parameter values against those obtained using standard values, when the USSP scheme was applied to L70 analyses fields of June Since the energy scale factor simply scales the magnitude of forcing produced by the USSP scheme, perturbed values of β were increased and varied from Previous studies (Ern et al., 2006) have shown that variation of s from its standard value primarily results in differences in the vertical distribution of the gravity-wave forcing produced rather than changes in magnitude. Therefore, perturbations that both increase and decrease the standard value of s, ranging from , were investigated. To apply conservation of momentum throughout the model domain, the transparent lid was simply switched to the opaque lid condition. Experiments for each parameter were run independently, i.e. with the remaining two parameters fixed at their standard values. Previous experimental results of Hitchman et al. (1989), Garcia and Boville (1994), Hamilton (1995), Orr et al. (2010) have shown that an increase in forcing of the order 10 m s 1 day 1 in the upper mesosphere will provide a significant strengthening of the mesospheric meridional circulation and hence temperature responses in the polar regions of the mesospheric winter and summer hemispheres. Restricting the increase of gravity-wave forcing to these values is justified, since the resulting magnitude of total forcing within the L70 analyses would not exceed previous estimates discussed in section 6.3. Results from the sensitivity studies (selected results shown in Figure 2) reveal that increasing β increased the drag seen in each hemisphere as expected. From Figure 2(a) we find that a value of β = 0.14 results in increases of forcing of up to m s 1 day 1 in the winter upper mesosphere and 8 12ms 1 day 1 in the summer upper mesosphere. Using a value ofβ = 0.14 is therefore physically reasonable, considering the high level of uncertainty in all estimates of mesospheric gravity-wave forcing. From Figure 2(b) we also find that using a perturbed value of s = 0.6 also produces an increase of the westward winter forcing and eastward summer forcing in the respective hemispheres. Here magnitudes of forcing increases are 6 8ms 1 day 1,evenfor large perturbations from standard values. Sensitivity studies when applying an opaque lid condition (not shown) resulted in an increased gravity-wave forcing of 8 12ms 1 day 1 in each hemisphere. However, forcing increases were confined to the uppermost pressure level at the model lid. Full details of the above results can be found in Long (2011). Since the magnitude of forcing changes when varying s (even for large perturbations) is relatively small, it was subsequently dropped from further investigation involving full UM integrations. Instead we concentrate on diagnosing the impact on the mesospheric circulation and temperatures when applying a value of β = 0.14 and an opaque lid condition, via the UM experiments detailed in the following section. 8. Unified Model experiments The following experiments were designed to investigate the impact that increased gravity-wave forcing may have on extratropical mesospheric temperatures within the UM. Under solstice conditions, model forecasts obtained when applying an energy scale factor of β = 0.14, an opaque lid with a standard-value energy scale factor and those obtained when using an opaque model lid combined with an increase in energy factor of β = 0.14 are compared with a control run, which uses the transparent lid condition and standard free parameter values. For brevity, the above experiments shall be referred to as the β, opaque, β-opaque and control forecasts respectively. The magnitude and

8 1032 D. J. Long et al. (a) (b) ms 2 day 1 Figure 2. Offline USSP parameter sensitivity studies detailing the difference in monthly zonal mean gravity-wave forcing for June 2010 when applying perturbed values of (a) β = 0.14 and (b) s = 0.6 compared with standard parameter values. Both panels show the change in gravity-wave forcing (perturbed minus control values of Figure 1). Drag values have contour interval of 5 m s 1 day 1, with negative values dashed. distribution of gravity-wave forcing and temperature responses for all experiments are described below. All of the experiments were performed using a free-running forecast version of the Unified Model, i.e. no data-assimilation cycle included. This approach is justified, as the currently operational Met Office system only assimilates data up to the stratopause, i.e. is a free-running model throughout the mesosphere. All experiments were performed using an 85 level configuration (hereafter L85) of the UM that has a model lid at 85 km, 5 km higher than the L70 model, and a horizontal resolution of latitude longitude. It should be noted that the L85 configuration has noticeably enhanced resolution throughout the middle atmosphere compared with the L70 model (Long, 2011). The L85 configuration was chosen, as the increased vertical resolution has been shown to reduce stratospheric biases for forecasts over days (S. Mahmood, 2010, personal communication), consistent with the results of Marshall and Scaife (2010) and Roff et al. (2011), who compare forecasts using the Hadley Center global environmental model (HadGEM1) with varying vertical resolution throughout the stratosphere. The L85 model is the currently preferred configuration for Met Office global seasonal and climate forecasting models. Furthermore, it is anticipated that the operational global analyses will soon be upgraded to the L85 vertical grid configuration. Model forecasts were initialized using European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses (Gobiet et al., 2005) for 1 June and 1 December A spin-up time of one month was employed to evolve the biases present in the initial conditions to those more characteristic of the Met Office Unified Model. It is well known that model forecasts over days are unable to predict the occurrence of sudden stratospheric warmings effectively. Since a major sudden stratospheric warming occurred in the northern hemisphere during the latter half of January 2009, over 50 days from the start of our model integrations, it is unlikely such an event will be accurately represented in our integrations, resulting in large temperature differences between experiments in the northern hemisphere over this period. While these differences are an interesting topic of study on their own, we are not concerned with such phenomena here. Therefore, to allow a cleaner comparison of temperature responses between the southern (where for our period of study no sudden stratospheric warming occurred) and northern hemispheres, model fields are analysed from 1 July 2008 and 1 January 2009 for a two-week period Control experiment and natural variability The control-run integrations employed the Li and Shine ozone climatology (Li and Shine, 1995) and identical solar spectrum and spectral files used in the operational Edwards Slingo radiation scheme. Figure 3 details the zonal mean temperature biases and zonal mean zonal gravity-wave drag of the control run averaged from 1 14 July 2008 and January Here, temperature biases are with respect to observational retrievals from the Earth Observing System Microwave Limb Sounder (EOS MLS). Also shown are the standard deviations of middle atmospheric temperatures from the EOS MLS instrument averaged over six years from for the first 14 days of January and July. We are primarily concerned with responses of the UM experiments compared with the control run and how these responses could possibly impact the operational analyses. However, it is possible that the magnitude and distribution of responses are influenced by the initial state of the control-run fields or affected by differences between the model configurations, i.e. assimilation of data or vertical resolution. Thus, in order to assess qualitatively the response that different UM experiments may possibly have on the operational analyses, it is first necessary to compare the temperature biases of the control run against those of the L70 analyses. From Figure 3 we find in the upper stratosphere and lower to middle mesosphere that control-run temperatures in the subtropics and midlatitudes have warm and cold biases from hpa and hpa respectively. These biases are characteristic of the operational L70 analyses and have magnitudes comparable with those detailed for identical seasons in DL12. However, in the upper mesosphere there are more significant differences between the temperature biases of the control run and those found in the L70 analyses, most noticeable at polar latitudes of each hemisphere. Upper mesospheric polar temperature biases seen during both winter hemispheres of the control run are 8 24 K warmer than those typical of the operational L70 analyses. As fully detailed in Long (2011), differences in gravity-wave forcing of these regions contribute to these discrepancies. When comparing offline estimates in Figure 1(c) and Long (2011) with those from Figure 3(a), we find that gravity-wave forcing is stronger in the controlrun winter upper mesosphere compared with L70 analyses, most noticeable in the southern hemisphere where differences are m s 1 day 1. Stronger forcing of the control-run winter upper mesosphere results in an increase in the poleward meanmeridional mass flux, downward circulation at high latitudes and the associated adiabatic warming of this region (Andrews et al., 1987; Holton and Alexander, 2000). Differences between control-run and L70 upper mesospheric gravity-wave forcing during the winter seasons are most likely caused by differences in stratospheric temperature and wind fields, where L70 analyses are highly constrained through data assimilation compared with the free-running control experiment. From Figure 3(b), we find that for the control run there are stratospheric warm biases of K from during winter seasons, which are