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The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.
The contribution of these authors was written in the course of their employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.
The accuracy of Met Office middle atmospheric analyses is investigated via direct validation against observational temperature data from two independent satellite instruments. A climatology of monthly zonal mean temperature biases from January 2005 to December 2010 is presented. For analyses produced before October 2009 there is a consistent cold bias of ∼30–40 K in the polar winter lower mesosphere, suggestive that gravity wave forcing in this region is too weak. Such cold biases are accompanied by smaller-magnitude cold biases in the opposing summer hemisphere, most likely associated with compensating warm biases from an insufficient gravity wave-driven circulation and cold biases resulting from deficiencies in radiative heating due to the operational ozone climatology. For analyses produced after October 2009, where the model lid was raised to include the upper mesosphere, cold biases in the winter lower mesosphere are reduced. However, systematic warm biases of ∼40–60 K in the summer upper mesosphere again suggest that gravity wave forcing within the operational system is underestimated. The absence of cold biases in the winter upper mesosphere also suggests that radiative errors contribute significantly in this region.
Since September 1991 daily analyses of global temperature, wind and geopotential height have been produced by the Met Office middle atmospheric data assimilation system. At the heart of this operational system is a global middle atmospheric configuration of the Met Office's Unified Model (UM) (Cullen, 1993). These daily analyses are used to populate the stratospheric assimilated dataset, which has been extensively used in numerous areas of research (Randel and Wu, 1999; Schoeberl, 2004; Manney et al., 2005b; Polavarapu et al., 2005). Despite such widespread use, little has been published on the quality of the stratospheric assimilated dataset. Previous work compared Met Office analyses produced in the 1990s with similar global middle atmospheric analysis datasets from elsewhere (Schöllhammer et al., 2003; Randel et al., 2004; Manney et al., 2005a). The present work focuses on Met Office middle atmospheric analyses produced from January 2005 to December 2010. Analyses are validated using independent observational data from the Earth Observing System Microwave Limb Sounder (EOS MLS) and the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) experiments, following the approach used in Jackson (2007). For this novel approach, the spatial coverage of the observational data allows analyses errors to be determined over a near pole-to-pole range of latitudes. Unlike previous studies we focus on monthly zonal mean biases using a climatology over the above years to diagnose any systematic biases in the dataset, with the aim of attributing them to specific aspects of the operational system.
Section 2 describes the evolution of the UM and the stratospheric assimilated dataset from January 2005 to December 2010. Section 3 introduces the EOS MLS and SABER datasets. The competing influence of both radiative and dynamical heating, which principally determine the thermal structure of the middle atmosphere, are discussed in section 4. Section 5 details the method employed for analysis validation, while resulting temperature biases for the L50 and L70 models are discussed in sections 6 and 7, respectively. Conclusions and discussion are given in section 8.
2. Evolution of Unified Model and stratospheric assimilated dataset
Since the last evaluation of the middle atmospheric configuration of the UM by Jackson et al. (2001) the following significant changes have been made to the operational system used to populate the stratospheric assimilated dataset.
On 10 October 2003 the dynamical core of the UM was upgraded to the non-hydrostatic fully compressible deep atmosphere formulation (White et al., 2005) incorporating a semi-Lagrangian advection scheme (Davies et al., 2005). Accompanying this upgrade was the introduction of a normalized height-based vertical coordinate using a staggered Charney–Phillips grid (Staniforth et al., 2004), which incorporated a 50-level vertical grid configuration from the surface to the lower mesosphere at ∼63 km. The operational system during this time used a three-dimensional variational (3D-Var) data assimilation scheme (Lorenc et al., 2000) formulated with an incremental approach (Courtier et al., 1994). Here the 3D-Var approach involves minimizing a cost function describing the distance between model forecasts, initial background guess (previous analyses) of the atmospheric state and observational data within a 6 h window centred over the current analyses time. As such, all observations are treated as if they occurred directly at the analyses time, creating smoother assimilation of data between regions that have different observations. The 3D-Var approach also allows the use of additional observational information, such as temperature radiances, obtained directly from original satellite measurements (Andersson et al., 1994).
The previous Edwards and Slingo (1996) radiation scheme and Gregory etal. (1998) orographic gravity wave drag (GWD) scheme were retained in the new UM version; however, a physically more realistic representation of non-orographic gravity waves was obtained by introducing the Ultra Simple Spectral Parametrization (USSP) scheme of Warner and McIntyre (2001). As for all GWD schemes the USSP has several free parameters which to some degree are arbitrarily set (Fritts and Alexander, 2003). The standard values of these parameters, used in all subsequent UM versions and detailed in Bushell et al. (2007), were chosen to achieve a quasi-biennial oscillation signal in the model which was realistic (Scaife et al., 2000, 2002); they are not tuned specifically for estimating extratropical gravity wave forcing. As detailed in Long (2011), the USSP scheme calculates forcing from estimated vertical momentum flux profiles. Approaching the model lid remaining values of momentum flux are allowed to leave the model domain, known as the ‘transparent' lid condition. While such a transparent lid condition is theoretically undesirable, it was employed in the 50-level model (and retained in the 70-level configuration detailed below) for issues relating to numerical stability (Scaife et al., 2002). The 50-level model version at this date had a horizontal resolution of 2.5° latitude × 3.75° longitude.
On 14 March 2006 the 3D-Var assimilation scheme was upgraded to the currently operational four-dimensional variational (4D-Var) formulation (Rawlins etal., 2007). As for 3D-Var assimilation, the 4D-Var scheme uses observational data from within a 6 h window centred over the current analyses time. However, directly modelling the time evolution of errors between the model forecast, initial background guess and observations using a perturbation forecast model and its adjoint (Lorenc and Payne, 2007) allows observations within the 6 h window to be treated at their correct times. During this upgrade the horizontal resolution of the middle atmosphere UM was refined to 0.375° latitude × 0.5625° longitude, while the previous vertical resolution and model domain were retained. From this date the USSP scheme was removed from the system until 5 December 2006, when it was subsequently reintroduced.
On 10 November 2009 the model lid of the middle atmospheric UM was vertically extended to its currently operational configuration, which resolves the majority of the upper mesosphere. This new configuration now includes 70 model levels ranging from the ground to the model lid at ∼80 km. The 70-level model, compared to the 50-level model, has increased vertical resolution in the lower stratosphere but degraded vertical resolution in the upper stratosphere and mesosphere. 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 0.2343° latitude × 0.3516° longitude.
Along with changes to the model configuration and data assimilation scheme, the choice of temperature observations used in the data assimilation process has also varied. Each day, the Met Office middle atmospheric data assimilation system receives hundreds of thousands of atmospheric observations from various sources, including radiosonde soundings, aircraft observations and satellite soundings from the following experiments: ‘SATEM’ reports from the TIROS Operational Vertical Sounder (TOVS) (Smith et al., 1979) series of polar orbiting satellites operated by the National Oceanic and Atmospheric Administration (NOAA); High Resolution Infrared Radiation Sounder (HIRS) (Koenig, 1980); Advanced TOVS (ATOVS) (Reale et al., 2008) series of satellites NOAA-15, NOAA-16, NOAA-17 and NOAA-19 containing the Advanced Very High Resolution Radiometer (AVHRR) (Cracknell, 1997) and the Advanced Microwave Sounding Unit (AMSU) (Aumann et al., 2003); Atmospheric Infrared Sounder (AIRS) (Aumann et al., 2003); Global Positioning System Radio Occulation (GPSRO) temperature profiles from the CHAllenging Mini-Satellite Payload (CHAMP) (Wickert et al., 2004); the Global navigation satellite systems Radio Occulation Receiver (GRAS) (Loiselet et al., 2000); the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) (Rocken et al., 2000); and the Gravity Recovery and Climate Experiment (GRACE) missions, Special Sensor Microwave Imager/Sounder (SSMIS) (Kunkee et al., 2008) and the Infrared Atmospheric Sounding Interferometer (IASI) (Siméoni etal., 1997). Table 1 details the time-line of observational changes used in creation of the stratospheric assimilated dataset from January 2005 and December 2010.
Table 1. Summary of changes made to data assimilation scheme and assimilated observations from January 2005 to December 2010.
Bugged airs radiance data added
Airs Radiance Bugged Fixed
GPSRO CHAMP/GRACE data
GPSRO CHAMP withdrawn
GPSRO COSMIC data added
IASI radiance data added
GPRSO GRAS data added
NOAA-19 data added
SSMIS data added
Analyses produced by different configurations of the UM will be referred to according to the number of vertical model levels used in the model. Hence analyses from 1 January 2005 to 10 November 2009 will be referred to as L50 and those from 10 November 2009 to 31 December 2010 as L70.
While the Met Office middle atmospheric data assimilation system produces four analyses each day, one for each 6 h window of observational data, only analyses produced at 1200 UTC are archived and available for scientific study. It should also be noted that, while the stratospheric assimilated analyses are produced on model levels, both L50 and L70 analyses are archived on pressure levels which have six intervals per decade change in pressure. The archived analyses also have a standard horizontal resolution of 2.5° latitude × 3.75° longitude. The temporal range of data considered in this work is from 1 January 2005 to 31 December 2010, allowing a detailed assessment of the most recently produced stratospheric assimilated analyses. We consider validating analyses in this range as we can assess the impact of significant changes to the operational system, e.g. the increased vertical domain which occurred in November 2009. Furthermore, we are restricted by the spatial coverage of observational temperature datasets since 1991. While temperature profiles are available through the 1990s from the HALogen Occultation Experiment (HALOE) instrument (Russell et al., 1993), latitudinal coverage is too poor for effectively validating global analyses. From 1992 to 1994 temperature profiles with sufficient spatial coverage are available from the Upper Atmosphere Research Satellite (UARS) MLS instrument (Livesey etal., 2003). Validation of analyses using UARS MLS data during this period (not shown) reveals that temperature biases in the upper stratosphere and lower mesosphere have similar magnitudes to those discussed in section 6. However, as detailed in Long (2011), allowing for possible biases between the UARS MLS and EOS MLS instruments, analysis errors in this region between 1992 and 1994 are ∼2–10 K colder than those seen from 2005 to 2009 (detailed below). Full details of the above validation results are presented in Long (2011), which notes that the above difference in temperature biases are most likely attributed to the previous (Ingram, 1990) radiation scheme being replaced by the currently operational (Edwards and Slingo, 1996) scheme.
3. Observational datasets
3.1. EOS MLS dataset
The EOS MLS experiment is one of four instruments on board the National Aeronautics and Space Administration (NASA) Aura satellite. The vertical coverage for temperature is from ∼5 km to ∼90 km, ranging from the upper troposphere into the upper mesosphere, with a vertical resolution of 4 km at 10 hPa, 8 km at 1 hPa, 9 km at 0.1 hPa and 14 km at 0.01 hPa. The latitude coverage of the EOS MLS temperature data is from 82°S to 82°N. Full technical details of the EOS MLS instrument can be seen in Filipiak (1999). Here we use the second publicly released (version v2.2) EOS MLS temperature data (Livesey et al., 2007), which has been validated by Schwartz et al. (2008) using correlative temperature data from four independent satellite instruments (excluding SABER) and the global radiosonde network (Durre et al., 2006). The results of this validation, summarized in Figure 26 of Schwartz et al. (2008), show that global biases of the EOS MLS temperature data with respect to the correlative data are less than 2 K in the upper stratosphere, from 0 to +3 K at the stratopause and from −5 to 0 K in the lower and upper mesosphere.
3.2. SABER dataset
The SABER experiment is one of four instruments on board NASA's Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite. The SABER instrument has two modes of viewing: north and south. In north viewing mode the tangent point locations of the vertical scans vary from 83°N to 52°S. This mode occurs for 60–63 days, after which a yaw manoeuvre turns the instrument to its south viewing mode, where the tangent point locations of the vertical scans vary from 83°S to 52°N. The south viewing mode again occurs for 60–63 days, after which the viewing sequence is repeated. This results in only latitudes from 52°N to 52°S having continuous coverage. The SABER temperature data have a high vertical resolution of ∼2 km throughout its vertical range from ∼10 to 110 km. Full technical details of the SABER instrument can be seen in Russell et al. (1999). For this study we use version 1.07 of SABER temperature data, which has been extensively validated by Remsberg etal. (2008) using correlative temperature data from four independent satellite instruments (excluding EOS MLS), along with falling spheres measurements and Rayleigh lidar temperature soundings. The results of this study show that global biases of the SABER temperature data with respect to the correlative data are from −5 to +2 K in the upper stratosphere, from −5 to 0 K at the stratopause and lower mesosphere, and from −5 to +9 K in the upper mesosphere.
4. Radiative versus dynamical heating
To first order the thermal structure of the upper stratosphere and mesosphere is radiatively determined. In the short-wave region diabatic heating is primarily due to ozone, while in the long-wave diabatic cooling is primarily due to carbon dioxide (Gille and Russell, 1984; Kiehl and Solomon, 1986). Throughout most of the middle atmosphere radiative cooling is in the global mean balanced by radiative heating (Holton, 2004). The temperature distribution determined entirely by this net radiative transfer is referred to as the ‘radiative equilibrium’ temperature (Shine, 1987). Since carbon dioxide is relatively well mixed, the vertical temperature structure of the middle atmosphere is predominantly determined by the strength of solar heating due to ozone.
For solstice months the seasonal variation of the zonal mean winds (Fleming etal., 1990; Randel et al., 2004) ‘filters' vertical-propagating gravity waves, resulting in angular-momentum deposition primarily decelerating the zonal mean flow in each hemisphere of the upper mesosphere. Through an associated Coriolis torque such zonal wind changes induce a meridional mass flux towards polar regions of each hemisphere. The resulting solstice circulation in the mesosphere is a single cell with meridional drift from the summer to winter hemispheres (Holton and Alexander, 2000). Via mass conservation the above meridional circulation results in ascending/descending motion at polar latitudes of the summer/winter hemispheres, resulting in adiabatic cooling/heating, forcing mesospheric temperature to be perturbed from their radiatively determined values.
For equinox months the relatively weak (eastward in both hemispheres) stratospheric zonal winds result in weak westward gravity wave forcing in the upper mesosphere, creating a two-cell circulation with rising vertical motion at tropical latitudes and sinking vertical motion at both polar regions. Adiabatic heating/cooling from such a circulation results in tropical temperatures being below and polar temperatures above their radiatively determined values in the upper mesosphere during equinox seasons.
In the time-mean, when zonal wind tendencies vanish, the thermal structure of the extratropical middle atmosphere is therefore determined by momentum deposition, vertical mass flux and diabatic heating. Owing to its relaxational nature diabatic heating acts like a ‘spring’ against any adiabatic heating from dynamical motions (Fels, 1985). Hence, in the middle atmosphere, it is angular-momentum deposition which determines the magnitude and distributions of perturbations from the purely radiatively determined state (Shepherd, 2000). Accurate predictions of middle atmospheric temperatures therefore require both realistic representations of diabatic heating and perturbations from this radiative determined state, through a mean-meridional circulation primarily driven by dynamical forcing and secondarily from differential diabatic heating due to the annual solar cycle (Shine, 1987).
5. Validation method
For each of the daily analyses, the range of vertical temperature profiles used for validation was restricted to a 3 h window either side of 1200 UTC. For each observational profile in this temporal range (typically ∼900 per day), temperature values from the corresponding analysis grid region were horizontally averaged to the profile location. These horizontally averaged analysis values were then vertically interpolated to the nearest profile pressure level, with the differences between analyses and observed values binned according to latitude and pressure. The latitude bins have intervals of 5°, while the pressure bins have six intervals per decade change in pressure. The resulting differences (analyses–observations) were then averaged over each month to obtain monthly zonal mean temperature biases.
It should be noted that the retrieval algorithm used to generate EOS MLS data operates in a two-dimensional manner using the averaging kernel approach (Rodgers, 2000). The use of such averaging kernels results in a relatively coarse vertical resolution, compared to SABER data, and a degree of vertical smoothing. Therefore, when validating analyses using EOS MLS data, vertically interpolating model fields to the nearest observational profile pressure level could introduce large errors, particularly for regions with strong vertical temperature gradients such as the stratopause. An appropriate test to ascertain whether such errors would impact the validation results when using EOS MLS data is to diagnose the magnitude of vertical smoothing when the above averaging kernels are applied to analysis fields. Such a test was performed by applying the one-dimensional vertical averaging kernels (available at http://mls.jpl.nasa.gov/data/ak/) to L70 vertical temperature fields at 70° north for each month of 2010. Differences between these ‘smoothed’ profiles and those obtained using the validation method above were obtained and zonally averaged over each month. The results (not shown) showed that the largest impact of smoothing the analyses profiles does occur in the stratopause region; however, differences between temperature profiles are typically less than ∼1 K. It is therefore unlikely that the vertical smoothing of EOS MLS data has a large impact on the validation results detailed below.
6. L50 analysis temperature bias
Figures 1 and 2 detail the zonal mean temperature biases of the L50 analyses, versus EOS MLS and SABER data, respectively, averaged over each December, March, June and September for the following periods: (a) January 2005 to February 2006; and (b) March 2006 to October 2009. Such periods were chosen to highlight the impact that major changes to the operational system, as discussed in section 2 and summarized in Table 2, have on L50 temperature biases. Here we find that differences between the EOS MLS and SABER validation results generally have magnitudes smaller than 6 K. Temperature biases with respect to EOS MLS data are consistently ∼2–6 K colder than those using SABER data across all latitudes approaching the stratopause (∼1.0 hPa), and consistently ∼2–6 K warmer across all latitudes from ∼0.8 to 0.3 hPa. Such differences are consistent with known temperature biases between the two satellite datasets discussed in Remsberg et al. (2008) and Schwartz et al. (2008). Above ∼1.0 hPa the difference in validation results and the known biases in each dataset versus correlative data, noted above, have magnitudes which are significantly smaller than those detailed in Figures 1 and 2. Hence we can confidently state that above ∼1.0 hPa temperature biases are primarily due to inaccuracies of the L50 analysis fields, not biases of the independent observational data.
Table 2. Summary of changes made to the UM from January 2005 to December 2010.
No. levels/model top
Resolution (lat. × long.)
USSP turned on
USSP turned off
USSP turned on
6.1. Lower mesospheric cold bias
From Figures 1 and 2 we find that for all seasons there is predominantly a cold bias across all latitudes in the uppermost levels of the L50 analyses. Figure 3(a,b,c) details the latitude time series of both L50 and L70 temperature biases versus EOS MLS data at 0.1 hPa, 0.15 hPa and 0.5 hPa, respectively. Also shown in Figure 3(d) is the time series of L50 monthly zonal mean temperature biases versus EOS MLS data meridionally averaged across isobaric surfaces as a function of altitude.
The persistence of the predominant cold bias in the lower mesosphere noted above is clearly seen in Figure 3(a,b). Here we find that the L50 temperature biases have a latitudinal independent cold bias signal of ∼2–10 K above ∼0.15 hPa for all months, except for polar latitudes at 0.1 hPa during summer months of both hemispheres where there are warm biases of ∼2–10 K. While such lower mesospheric cold biases are predominantly confined between ∼0.3 and 0.1 hPa, they do extend down to ∼0.8 hPa at tropical latitudes of months before March 2006, as clearly shown in Figures 1(a), 2(a) and Figure 3(c). The most likely cause of the cold biases from ∼0.8 to 0.3 hPa before March 2006 was the introduction of Atmospheric Infrared Sounder (AIRS) (Aumann et al., 2003) data to the operational system in February 2005. Here a bug in the AIRS assimilation code resulted in model radiance values for the uppermost levels where analysis increments are added (1.0 hPa) (Saunders et al., 2002), being calculated with surface temperatures. This resulted in negative analysis increments and cold biases at such levels of the L50 model, most prominent at tropical latitudes where the difference between upper pressure levels and surface temperatures is greatest. As the AIRS assimilation bug was fixed during the upgrade to 4D-Var assimilation, cold biases are not prominent below ∼0.3 hPa in months post March 2006.
Over a monthly time-scale it is a reasonable assumption that the mean state of the middle atmosphere is dynamically balanced, and the total mass of air above an isobaric surface is constant. It therefore follows that zonal-mean biases across an isobaric surface caused by misrepresenting the circulation should be zero when meridionally averaged over the globe. From Figure 3(d) we find that between ∼0.3 and 0.1 hPa the L50 analyses have a meridionally averaged bias (cold) of ∼2–10 K. Since the L50 model is free running in the lower mesosphere, analysis increments are not added and cannot directly impact model biases, and the latitudinal independent cold bias seen throughout the lower mesosphere is most likely associated with errors within the radiation scheme; however, the magnitude of such radiative biases may vary with latitude, as discussed in section 6.2.
In addition to the latitude-independent cold bias signal noted above, L50 analyses also have significantly larger cold biases in the polar regions approaching the model lid, as seen in Figures 1(a,b) and 2(a,b). Figure 3(a,b) also clearly shows that in the lower mesosphere polar cold biases have a strong seasonal cycle with maximum magnitudes of ∼30–45 K found for both winter hemispheres poleward of 50°. Such winter cold bias magnitudes are noticeably larger than the ∼10–20 K values typical of polar latitudes during equinox months as detailed in Figures 1(a,b), 2(a,b) and 3(a,b). Here we find that for winter and equinox seasons maximum cold biases are typically located at the model lid and decrease both with decreasing altitude and towards the Equator. For polar latitudes of both summer seasons, magnitudes of the warm biases at 0.1 hPa noted above decrease with altitude, reversing to cold biases of ∼2–10 K between ∼0.3 and 0.2 hPa.
Based on the theory discussed in section 4, the strong seasonal cycle in cold biases at winter polar latitudes of the L50 analyses would suggest that dynamical forcing in the extratropical winter lower mesosphere is too weak; analysis temperatures are too close to their radiatively determined values. Since such biases are present in the lower mesosphere, such insufficient forcing is dominated by the misrepresentation of small-scale gravity waves within the UM. As noted above, analysis increments from the assimilation scheme are only added below 1.0 hPa, and thus have no direct impact on such large biases in the lower mesosphere. Such polar biases in the winter mesosphere are typical of middle atmospheric GCMs (Garcia and Boville, 1994; Beagley etal., 1997; Pawson et al., 2000). As detailed in Shepherd and Shaw (2004), Shaw and Shepherd (2007) and Shaw et al. (2009), employing a ‘sponge layer’ (increased horizontal diffusion approaching the model lid which is active on the mean flow) within middle atmospheric models can drive the mean meridional circulation, resulting in temperature biases. As the USSP scheme uses a transparent lid and the UM does not include such a sponge layer, horizontal diffusion is constant approaching the model lid; the mean meridional circulation of the L50 analyses (also L70) are not effected by such errors.
As noted in section 4, the mean meridional circulation of the lower mesosphere under equinox conditions results in descending motion at polar regions of both hemispheres. Therefore the observed cold biases at polar regions of such months are consistent with the above conclusion that extratropical wave forcing in the lower mesosphere of the L50 model is insufficient. Since the vertical propagation of planetary waves is known to be primarily restricted to the winter seasons (Charney and Drazin, 1961), the existence of such cold biases in polar regions of equinox months places additional confidence that biases associated with an underestimated meridional circulation in the lower mesosphere of the L50 model are dominated by insufficient gravity wave forcing.
Subtracting the meridionally averaged zonal mean bias across an isobaric surface for a particular month from the zonal mean bias distribution itself, to a certain degree, represents the separation between biases caused by diabatic and adiabatic effects. While resulting biases from such an approach are more consistent with gravity wave effects in the lower mesosphere, they also contain errors from radiative effects that vary with latitude. Figure 4 details the biases obtained from the above method using the monthly zonal mean biases of Figure 1. The bias distributions in the lower mesosphere of Figure 4(a,b), cold winter polar and warm summer polar biases for each hemisphere, along with smaller-magnitude cold polar biases of both hemispheres during equinox months, highlight the importance of underestimating gravity wave forcing in the L50 model. Here cold biases in the winter polar regions have magnitudes between ∼20 and 35 K, while summer polar warm biases range between ∼15 and 20 K.
Unfortunately fields of gravity wave forcing are not archived for the stratospheric assimilated dataset. However, it possible to obtain ‘off-line’ estimates of such forcing by applying the USSP scheme to analysed fields of temperature, wind and geopotential height (Long et al., 2012, pers. comm., hereafter DL12). The results of DL12 show that gravity wave forcing in the L50 model is largest in the lower mesosphere during solstice seasons, with maximum magnitudes in each hemisphere typically smaller than ∼20 m s−1 per day. Such off-line distributions of forcing are consistent with those presented in Scaife et al. (2002), and as noted in DL12 are noticeably smaller (or at the lower limit) than estimates from previous studies conducted by Hamilton et al. (1999), Jiang et al. (2006), Marks (1989), Pulido and Thuburn (2008), Smith and Lyjak (1985) and Watanabe et al. (2008). Hence such off-line studies are consistent with the above L50 temperature bias distributions, again placing additional confidence in the inference that gravity wave forcing in the lower mesosphere is too weak.
While the warm biases seen in the summer polar latitudes of the lower mesosphere of Figure 4(a,b) are consistent with an underestimated mean meridional circulation, the observed biases in Figure 1(a,b) and 2(a,b) are not; as noted above, summer polar biases in the lower mesosphere are predominantly cold (where one would expect underestimated dynamical forcing to be associated with insufficient adiabatic cooling and warm biases). Thus biases in the L50 analyses from ∼0.3 to 0.1 hPa are caused by a combination of misrepresenting the lower mesospheric circulation and additional sources of error. As both EOS MLS and SABER data have cold biases of ∼1–5 K between ∼0.3 and 0.1 hPa, it is possible that L50 analysis cold biases at this altitude could be slightly larger than those present in Figures 1(a,b) and 2(a,b). Hence it is not possible that biases in the observational data could alone account for the analysis cold biases seen at summer polar latitudes in the lower mesosphere. As discussed below, cold biases at summer polar latitudes of the L50 analyses are associated with both unrealistic representations of the circulation and diabatic heating from ozone in the lower mesosphere.
From the evidence presented above it is apparent that biases in the extratropical lower mesosphere of the L50 analyses are generally dominated by insufficient gravity wave forcing. The distribution and seasonal evolution of temperature bias, driven by a combination of deficiencies in both the gravity wave and radiation schemes (which may vary with latitude), are consistent with this inference except for polar latitudes during the summer season of both hemispheres. Here small-magnitude cold biases are inconsistent with an underestimated mean meridional circulation for the summer season, where it is apparent that biases from weak gravity wave forcing do not dominant over those associated with the radiation scheme.
Under solstice conditions in the summer lower mesosphere there is net radiative heating, while in the opposing polar winter hemisphere there is net radiative cooling (Callis et al., 1987; Rosenfield et al., 1987; Shine, 1989). In the L50 analyses the Edwards and Slingo (1996) radiation scheme calculates short-wave heating due to ozone using the monthly prescribed climatology of Li and Shine (1995). Previously Mathison et al. (2007) noted that ozone mixing ratios of the Li and Shine climatology in the lower mesosphere were significantly smaller than those from more recent field estimates such as the Stratospheric Processes And their Role in Climate (SPARC) climatology (Randel and Wu, 1999), European Centre For Medium-Range Weather Forecasts (ECMWF) operational ozone analyses (Simmons et al., 2005), and experimental Met Office ozone analyses based on observations from both the EOS MLS and Solar Backscatter Ultraviolet radiometer (SBUV) instruments (Jackson, 2007). In the lower mesosphere, mixing ratios of these newer estimates are ∼2.2–2.8 times greater than those of the Li and Shine climatology for January 2006; see Figure 6 of Mathison et al. (2007). While the consistency of such differences highlights the deficiency of the Li and Shine climatology, as noted in Mathison etal. (2007) the above estimates of ozone mixing ratios still contain considerable uncertainty.
Evidence from model experiments given in Mathison et al. (2007) shows that upgrading the Li and Shine climatology, using the more recent fields noted above, has a significant impact on temperatures in the lower mesosphere. The resulting change in average 24 h forecast temperatures between the control and experiment fields over the first 15 days of February 2006 can be seen in Figure 8 of Mathison et al. (2007). Largest temperature differences are seen between ∼0.3 and 0.1 hPa, where all experimental ozone fields show an increase of forecast temperatures, with maximum magnitudes of ∼20–25 K seen between the Southern Hemisphere (SH) pole and mid latitudes of the NH. It is therefore possible that deficiencies in the Li and Shine ozone climatology contribute significantly to the cold biases of the L50 analyses in the summer lower mesosphere. This argument is supported by Figure 13 of Mathison et al. (2007), who, using a version (before March 2006) of the L50 UM, detail the impact on analysis temperature biases (w.r.t. EOS MLS data) over the first 15 days of February 2006 when replacing the Li and Shine climatology with direct observations of ozone mixing ratios from the EOS MLS and SBUV instruments. Here the introduction of the updated ozone fields results in cold biases of the NH winter polar regions being reduced by ∼5 K, and cold biases in the SH summer polar regions being reversed to warm biases of ∼4–20 K. While replacing the Li and Shine climatology with more recent and realistic representations of ozone mixing ratios would therefore most likely result in warm biases at summer polar latitudes in the lower mesosphere of the L50 analyses, such biases are theoretically consistent with the conclusion that cold biases in the opposing polar winter hemisphere are primarily due to an insufficient mean meridional circulation.
6.3. Stratopause warm bias
Figures 1(a,b) and 2(a,b) both show that for L50 analyses the cold bias regions from ∼0.3 to 0.1 hPa discussed above are predominantly accompanied by a warm bias region directly below. Such warm bias regions are generally found from ∼2.0 to 0.3 hPa over various latitudes.
After March 2006, with respect to EOS MLS data the L50 analyses predominantly have latitude-independent warm biases from ∼1.0 to 0.3 hPa with magnitudes consistently ∼6–14 K, as clearly shown in Figure 3(c). The exception to this is at polar latitudes of the winter months for both hemispheres, where warm bias values are noticeably reduced. From Figure 3(d) we find that between ∼0.8 and 0.3 hPa L50 analyses after March 2006 have a meridionally averaged bias (warm) of ∼6–10 K with respect to EOS MLS data. Biases at this altitude in the L50 analyses are primarily associated with deficiencies of the radiation scheme, evident from their significant reduction over all seasons shown in Figure 4(a,b). SABER validation results also show a latitude-independent signal; however, warm biases extend further downwards to ∼2.0 hPa and have magnitudes ∼2–6 K smaller than EOS MLS results. Such bias differences are consistent with the temperature differences between the EOS MLS and SABER instruments noted above.
For months before March 2006 warm biases at tropical latitudes have a smaller vertical extent compared to months after March 2006, evident by the cold biases presented in Figure 3(c), and primarily occur between ∼1.5 and 0.9 hPa. This difference is most likely due to the correction of the AIRS data assimilation code detailed above. From known biases in the SABER data it is possible that the warm biases in this region could be smaller than that suggested in Figures 1(a,b) and 2(a,b).
As noted above, warm biases between ∼2.0 and 0.3 hPa of the L50 analyses (most prominent after March 2006) are primarily associated with inaccuracies of the radiation scheme at these levels. One of the major features of the Edwards–Slingo scheme is the fact that the resolution of the incorporated spectral bands is not fixed. This flexibility is achieved by the use of dependent pre-processed spectral files which can be used in subsequent versions of the UM. Both the spectral files and the Edwards–Slingo radiation scheme were initially developed to accurately represent tropospheric radiative heating, and were not optimized for stratospheric and mesospheric conditions.
With the introduction of the semi-Lagrangian dynamical core in October 2003, the spectral files used by the Edwards–Slingo scheme were upgraded to those from the Hadley Centre Global Environment Model (HadGEM) (Davies et al., 2005). Here the HadGEM spectral files use the Kurucz and Bell (1995) solar spectrum. In the upper stratosphere ozone dominates the radiative transfer in the short wave, with a peak at ∼0.25 μm (Hartley Band). Previously Zhong et al. (2008) showed that the use of the Kurucz solar spectrum with the Edwards and Slingo (1996) radiation scheme produced ozone heating rates between ∼2.0 and 0.4 hPa, which were ∼0.5–1.0 K per day larger than those from a line-by line-model.
Previously Thelen (2006) noted that radiative heating rates in the long-wave region due to CO2 and O3 produced by HadGEM spectral files were qualitatively similar to those from the GFDL line-by-line model; however they underestimated the cooling due to H2O by ∼0.8 K per day at ∼1.0 hPa. Such results are consistent with those presented in Jackson et al. (2001), who, using a 49-level configuration of the UM, found that long-wave heating rates from the Edwards–Slingo scheme using HadCM3 spectral files were only consistent with those from a line-by-line model up to ∼2 hPa. Around and above the stratopause region long-wave cooling was found to be too small, with largest differences of the order 1–1.5 K per day found between ∼2.0 and 0.3 hPa.
The spectral files used in the operational L50 model are essentially identical to those in the HadGEM models, with minor changes to the representation of atmospheric aerosols. It is therefore reasonable to expect that the use of HadGEM spectral files in the L50 analyses would lead to similar heating rate biases to those discussed above. Here the combined inaccuracies of both the short- and long-wavelength regions could likely lead to possible excessive net heating rates of ∼1.0–2.0 K per day from ∼2.0 to 0.4 hPa in the L50 analyses. With the radiative time-scale of the atmosphere in this region ∼5–7 days (Gille and Lyjak, 1986; Haynes, 2005), it is plausible that the estimated heating rate errors described above could result in warm temperature biases of the order ∼5–14 K from ∼2.0 to 0.3 hPa. Such estimated warm biases have similar magnitudes to the observed warm biases detailed in Figures 1(a,b) and 2(a,b), but with ∼4–6 K larger values for pressure levels closer to 0.3 hPa. However, as described above, deficient ozone mixing ratios in the currently operational Li and Shine ozone climatology produce temperature values between ∼0.6 and 0.3 hPa which are too cold when compared to temperatures produced by more recent and accurate representations of ozone concentrations. Accounting for these cold temperatures could adjust the above hypothetical warm biases to values which are qualitatively similar to those observed. The underestimated ozone concentration of the Li and Shine climatology in the lower mesosphere would also allow a larger number of photons from incident radiation to reach the stratopause, thus contributing to the warm bias seen in this region. Therefore deficiencies in both the Li and Shine ozone climatology and the spectral files used in the Edwards–Slingo radiation scheme contribute to biases seen between ∼2.0 and 0.3 hPa in the L50 analyses.
7. L70 analyses temperature bias
Figures 1(c) and 2(c) detail the monthly zonal mean temperature biases of the L70 analyses versus EOS MLS and SABER data, respectively. In the upper mesosphere the magnitude of known biases in both the EOS MLS and SABER data, discussed above, are noticeably smaller than the biases presented in Figures 1(c) and 2(c). Thus, as for the L50 analyses, we can confidently state that temperature biases are primarily due to inaccuracies of the L70 analyses fields.
7.1. Upper mesosphere warm bias
In the upper mesosphere the L70 analyses are dominated by strong warm biases which have a clear seasonal signal. Largest biases are confined to summer polar latitudes of each hemisphere, with maximum magnitudes occurring at the model lid and decreasing in value as they extend downward to typically ∼0.07 hPa. Here maximum warm bias magnitudes of ∼40–60 K are found during December 2010 and June 2010. For equinox months the L70 analyses predominantly have a warm bias of ∼6–14 K across all latitudes when approaching the model lid. Based on the theory of section 4 and arguments presented in section 6.1, such bias distributions are consistent with the inference that gravity wave forcing within the UM is too weak; there is insufficient adiabatic cooling in summer polar upper mesosphere from an underestimated mean meridional circulation. The results of Figure 4(c) show that misrepresentation of the circulation is the dominant source of error for temperature biases in the summer polar upper mesosphere of the L70 analyses; however, as noted above, circulation biases diagnosed as in Figure 4(c) may also contain errors form deficiencies in the radiation scheme which vary in latitude.
As for the L50 analyses, the off-line estimates of gravity wave forcing in the L70 analyses detailed in DL12 are noticeably smaller (or on the lower limit) than those from previous studies, with maximum magnitudes of ∼50–60 m s−1 per day seen approaching the model lid during solstice seasons. Again, such off-line estimates suggest that gravity wave forcing in the upper mesosphere of the L70 analyses is too weak, consistent with the distribution of temperature biases noted above.
From Figure 3(d) we find that L70 analyses have a meridionally averaged warm bias of ∼6–14 K approaching the model lid. As noted above, such biases are associated with deficiencies within the radiation scheme, which may vary with latitude. From Figure 4(c) we find that for equinox months, where there exists a weak (compared to solstice conditions) upper mesospheric circulation, biases associated with the misrepresentation of gravity wave forcing have magnitudes primarily below ∼6 K approaching the L70 model lid. Such biases are weaker than those presented for similar regions in Figures 1(c) and 2(c). Therefore, under equinox conditions biases associated with the radiation scheme are dominant approaching the L70 model lid and, unlike those associated with diabatic heating from ozone (discussed in Section 6.2), are predominantly latitude independent. Reasons for this latitude-independent warm bias approaching the L70 model lid are discussed below.
It was noted above that the L70 analyses contain a latitude-independent warm bias when approaching the model lid. Possible reasons for such a bias in this region include misrepresenting the breakdown of local thermodynamic equilibrium (LTE), deficiencies of the spectral files used in the radiation scheme and the exclusion of additional physically processes parametrized by the gravity wave scheme.
In the upper mesosphere the breakdown of LTE impacts long-wave radiative cooling, which is primarily due to carbon dioxide. Recent studies (L. Coy, 2010, personal communication) using a high-altitude version of the GEOS-5 model (Reinecker et al., 2007) show that accounting for LTE breakdown in the long-wave radiation calculations had a significant impact on model temperatures at 0.01 hPa. This study compared the monthly zonal mean temperatures for January 2007 with radiative fluxes calculated from: (a) the NASA climate radiation scheme (CLIRAD) based on LTE assumptions in the short-wave (Chou and Suarez, 1999) and long-wave (Chou et al., 2001) regions; (b) independently calculated long-wave fluxes including the effects of LTE breakdown using the Fomichev et al. (2004) scheme blended with the CLIRAD long-wave values below 75 km. Using the long-wave heating rates of (b) the temperatures at 0.01 hPa were ∼15–25 K cooler across all latitudes, with maximum differences seen in the Tropics and minimum differences seen in the SH summer polar regions. This evidence would suggest that the breakdown of LTE in the long-wave region has a non-trivial effect approaching 0.01 hPa; therefore the exclusion of such effects in the Edwards–Slingo radiation scheme would contribute to the warm bias seen approaching the L70 model lid.
Another possible cause of biases due to the radiation scheme is the inherent inaccuracy of the spectral files in the upper mesospheric region (J. Manners, personal communication 2010). This inaccuracy occurs due to the fact that the spectral files were originally optimized for tropospheric conditions; hence they are particularly poor in the upper mesosphere. Any inaccuracy in these spectral files will also be compounded by relatively poor vertical resolution of the upper mesosphere. While it is known to the Met Office that the spectral files in the upper mesosphere are highly questionable, to date no definitive study has been made on their impact (J. Manners, personal communication 2010). Therefore it is impossible to comment confidently on the magnitude and sign of the temperature biases that they produce. However, based on the above evidence, it is most likely that they contribute to a warm bias in the upper mesosphere.
In addition to forcing the momentum budget, it is well known that gravity wave breaking can produce direct local heating and heat transport, associated with the turbulence generated from gravity wave breaking (Alexander and Dunkerton, 1999; Fritts and Werne, 2000; Holton, 1982; Lindzen, 1981). While direct heating due to turbulent frictional dissipation is known to be positive definite, and significant to the overall heating budget of the upper mesosphere (Lübken, 1997), previous studies suggest that vertical eddy heat diffusion due to gravity wave-generated turbulence acts to cool the atmosphere (Fomichev et al., 2002; Becker, 2004) and dominates in the upper mesosphere. Therefore, not including direct heating and heat transport within the USSP scheme could contribute to the warm biases seen in the upper mesosphere of the L70 analyses. The inclusion of such direct thermal processes has also been shown to have a significant impact on the mean meridional circulation in the upper mesosphere, with direct cooling typically (dependent on the Prandtl number) acting to strengthen the circulation (Huang and Smith, 1991). It is therefore likely that temperature biases in the upper mesosphere of the L70 analyses are caused by a combination of not including direct thermal effects of gravity wave breaking and the associated impact on the circulation, insufficient momentum forcing supplied by the USSP scheme and the radiative effects discussed above.
7.3. Lower mesosphere cold bias
In the lower mesosphere of the L70 analyses temperature biases in the SH winter polar regions show a distinct improvement when compared to those for the L50 analyses, as clearly shown in Figures 1(c), 2(c) and 3(a,b). Here SH polar cold biases from ∼0.3 to 0.1 hPa have magnitudes of ∼2–10 K –noticeably smaller than the ∼30–45 K values typical of the L50 analyses. This improved representation in the L70 analyses is both expected and explained by the downward control arguments of Haynes et al. (1991). Since both model configurations employ the transparent lid condition and have identical launch values of momentum flux, the increased vertical domain of the L70 analyses, approximately three scale heights above the model lid of the L50 model, would better represent the eddy forcing above the lower mesosphere and hence produce a more accurate representation of the circulation and hence winter polar temperature structure.
Additionally to the above downward control argument, one would expect further inaccuracies of the L50 lower mesospheric circulation to be compounded by dynamical and physical boundary conditions at the model lid. In order to conserve mass throughout the model domain the prognostic vertical velocity w is set to zero at the model lid, implying no dynamical heating/cooling at the top potential temperature level of the L50 model. This non-physical feature due to the limited vertical domain is not apparent at ∼0.1 hPa in the L70 analyses; hence one would expect a more realistic representation of the circulation and temperature at this altitude.
While winter polar cold biases in the lower mesosphere of the L70 analyses show a distinct improvement (compared to L50 analyses) in the SH, those in the NH do not. For December 2009 there is a spuriously cold polar vortex in the NH from ∼4 to 0.5 hPa with maximum magnitudes of ∼35–45 K. As detailed in Long (2011), such biases are related to the assimilation process which from November 2009 applies analyses increments to the mesosphere. Here unrealistic vertical correlations in the background covariance matrix resulted in analysis increments of the stratosphere, producing spurious (negative) temperature increments throughout the mesosphere. This problem was subsequently addressed by the Met Office, resulting in analyses increments no longer being added in the mesosphere for months after December 2009. Such cold polar biases during December 2009 are therefore uncharacteristic of the L70 analyses, where during January 2010 winter polar cold biases of ∼14→18 K (not shown) are smaller than typical L50 analyses values of ∼22→30 K for the same region.
Consistent with the L50 analyses, there is a meridionally averaged cold bias signal of ∼6–14 K from ∼0.3 to 0.1 hPa for the L70 analyses. As noted above, such biases are associated with deficiencies of the radiation scheme. Since this feature is prominent in both L70 and L50 analyses at similar altitudes, additional confidence can be placed in the assumption that the cause of such cold biases is due to errors caused by the Li and Shine ozone climatology, which remains in operational use for the L70 model.
However, there are minor discrepancies between the magnitudes of the latitudinal independent cold bias signals seen in the L50 and L70 analyses. Here the latitude-independent cold bias magnitudes of the L70 analyses are smaller than those seen in the L50 model by ∼4 K, most noticeable at mid latitudes of each hemisphere. One possible explanation is that the L70 analyses contain additional information about radiative processes in the atmosphere above, such as radiative heating due to molecular oxygen, which is treated in the Edwards–Slingo scheme, and is known to be non-trivial above ∼0.1 hPa (Andrews et al., 1987). It is possible that such additional heating information is effectively propagated downwards by radiative transfer in the L70 analyses, while in the L50 analyses the total downward long-wavelength radiative flux and downward short-wavelength diffuse radiative flux in the Edwards–Slingo scheme are set to zero at ∼0.1 hPa. It is therefore possible that this additional diffuse heating in the L70 analyses could reduce the magnitude of the latitude-independent cold bias when compared to L50 values.
7.4. Stratopause warm bias
Again consistent with the L50 analyses, warm bias regions occur in the L70 analyses below the cold biases of the lower mesosphere discussed above. However, the latitude-independent nature of this warm bias in the L70 analyses from ∼0.8 to 0.3 hPa is not as prominent as that displayed in the L50 analyses, as shown by Figure 3(c). The spectral files used in the L70 analyses are identical to those used in the L50 model except for the vertical resolution of the monochromatic layers used, which are based on the vertical grid employed in each model. The L70 analyses have coarser vertical resolution and model levels which occur at different altitudes from the L50 model in the upper stratosphere and lower mesosphere. It is plausible that these differences result in the warm biases caused by deficiencies in the analyses spectral files to occur at different altitudes in the L70 analyses compared to the L50 model. Since the latitude-independent warm biases of both models have similar magnitudes, additional confidence can be placed in the assumption that the cause of this bias is due to inaccuracies of the spectral files used in the two different model configurations.
We have detailed the monthly zonal mean temperature biases of Met Office global analyses using independent observation data from the EOS MLS and SABER experiments. Analyses created using the L50 and L70 versions of the UM have the largest temperature errors in the mesosphere. The magnitude of such mesospheric biases is significantly larger than known biases of the EOS MLS and SABER data for this altitude range, placing confidence in the fact that the biases are due to deficiencies of the UM.
The largest biases seen in the L50 analyses occur at the uppermost levels above ∼0.3 hPa. Here there is a large cold bias of ∼30–45 K seen in the winter polar regions of both hemispheres. Such large cold biases are not apparent at polar latitudes of the equinox seasons, where cold biases have magnitudes of ∼15 K. From the seasonal evolution of biases presented above it is evident that the mean meridional circulation of the mesosphere is underestimated, and that dynamical forcing supplied by the USSP gravity wave scheme is insufficient in the L50 model. We have shown that misrepresentation of the lower mesospheric mean meridional circulation is the dominant cause of temperature bias in the winter polar regions of the L50 analyses.
Strong warm biases are present in the upper mesosphere of the L70 analyses approaching the model lid. Here warm bias magnitudes of ∼40–60 K are seen at summer polar latitudes. The seasonal evolution of such biases is consistent with the above inference that gravity wave forcing within the UM is insufficient, where biases associated with this deficiency dominate for solstice seasons. For equinox months latitudinal-independent warm biases of ∼6–14 K are seen approaching the L70 model lid –evidence that biases associated with the radiation scheme dominate for this season.
We have shown that the major difference between L70 and L50 analyses occurs in the lower mesosphere polar winter, where there is a large decrease in the cold bias of this region. Such a reduction is expected by the increased vertical domain of the L70 model better representing the mean meridional circulation of the lower mesosphere, through increased knowledge of the wave forcing above, thus highlighting the positive impact of increasing the model lid in November 2009.
Both L50 and L70 analyses have warm biases between ∼2.0 and 0.3 hPa with similar magnitudes, ranging from ∼6 to 14 K. The presence of such biases in both model configurations and their latitudinal independent nature would suggest they are associated with deficiencies within the Edwards–Slingo radiation scheme.
The results of this work have been discussed within the context of previous studies based on the middle atmospheric configuration of the UM, with the following conclusions.
Unlike the winter polar lower mesosphere, the opposing summer polar temperature biases of the L50 analyses are not dominated by misrepresenting the mean meridional circulation; here additional sources of errors occur from inaccurate diabatic heating calculations playing a significant role. Based on the previous studies of Jackson et al. (2008) and Mathison et al. (2007), such heating rate errors have been attributed to the currently operational ozone climatology of Li and Shine (1995). Here the ozone climatology has been shown to produce insufficient radiative heating in the lower mesosphere, consistent with the latitude-independent cold bias signal seen above ∼0.3 hPa for all months of the L50 analyses.
Previously both Jackson et al. (2001) and Thelen (2006) noted that the spectral file used with the Edwards–Slingo radiation scheme underestimate long-wave cooling; with Zhong et al. (2008) also noting that the Kurucz and Bell (1995) solar spectrum produces excessive ozone heating. Such inaccuracies lead to excessive heating rates of ∼1–2 K per day between ∼2 and 0.3 hPa, which is consistent with the observed warm biases of ∼6–14 K seen in both L50 and L70 model configurations noted above.
In addition to large biases associated with insufficient gravity wave forcing, the L70 analyses also have a latitude-independent war bias of ∼6–14 K approaching the model lid. Likely reasons for this warm bias are the inaccuracy of spectral files for this altitude, which were originally optimized for tropospheric conditions and the fact that the operational radiation scheme does not account for the breakdown of LTE, which as shown by previous modelling studies can lead to a warm bias of ∼15–25 K across all latitudes. It is also likely that not including the direct thermal effects associated with gravity wave-induced turbulence could contribute to upper mesospheric biases in the L70 analyses, both through the absence of cooling due to eddy vertical diffusion and the subsequent impact this may have on the strength of the mean meridional circulation. Diagnosing the contribution and magnitude of the above possible sources of error for the L70 analyses is an area for further research.
This work was funded by the Great Western Research project through grant GWR/270. We would like to thank Andrew Bushell and Peter Leggett for their detailed and helpful advice.