The Flexible Modelling Framework for the Met Office Unified Model (Flex-UM, using UM 12.0 release)

Abstract. The Met Office Unified Model (UM) is a world-leading atmospheric weather and climate model. In addition to comprehensive simulations of the atmosphere, the UM is capable of running idealised simulations, such as the dry physics Held–Suarez test case, radiative convective equilibrium and simulating planetary atmospheres other than Earth. However, there is a disconnect between the simplicity of the idealised UM model configurations and the full complexity of the UM. This gap inhibits the 5 broad use of climate model hierarchy approaches within the UM. To fill this gap, we have developed the Flexible modelling framework of the UM – Flex-UM – which broadens the climate model hierarchy capabilities within the UM. Flex-UM was designed to replicate the atmospheric physics of the Geophysical Fluid Dynamics Laboratory (GFDL) idealised moist physics aquaplanet model. New parameterisations have been implemented in Flex-UM, including simplified schemes for: convection, large-scale precipitation, radiation, boundary layer and sea surface temperature (SST) boundary conditions. These idealised 10 parameterisations have been implemented in a modular way, so that each scheme is available for use in any model configuration. This has the advantage that we can incrementally add or remove complexity within the model hierarchy. We compare Flex-UM to ERA5 and aquaplanet simulations using the Isca climate modelling framework (based on the GFDL moist physics aquaplanet model) and comprehensive simulations of the UM (using the GA7.0 configuration). We also use two SST boundary conditions to compare the models (fixed SST and a slab ocean). We find the Flex-UM climatologies are similar to both Isca 15 and GA7.0 (though Flex-UM is generally a little cooler, with higher relative humidity, and a less pronounced storm track). Flex-UM has a single InterTropical Convergence Zone (ITCZ) in the slab ocean simulation but a double-ITCZ in the fixed SST simulation. Further work is needed to ensure that the atmospheric energy budget closes to within 1-2Wm−2 , as the current configuration of Flex-UM gains 9-11 Wm−2 (the range covers the two SST boundary conditions). Flex-UM greatly extends the modelling hierarchy capabilities of the UM and offers a simplified framework for developing, testing and evaluating 20 parameterisations within the UM.

model". The aquaplanet formulation of the UM was developed by Neale (1999), building on the earlier work of Swinbank et al. (1988), and later published in Neale and Hoskins (2000a, b). This provided the foundation on which the AquaPlanet Experiment (APE) Williamson et al., 2013) was built. For many modelling centers around the world, the aquaplanet configuration is a benchmark model for testing model performance (Stevens and Bony, 2013;Voigt and Shaw, 2015) and for implementing new parameterisations. Indeed the aquaplanet UM has been illuminating for studying tropical 5 convection, for example the Madden-Julian Oscillation Inness et al., 2001), the double-ITCZ (Talib et al., 2018), atmospheric tides and the diurnal cycle (Woolnough et al., 2004), and the sensitivity of convectively coupled equatorial waves to entrainment (Peatman et al., 2018).
At the most idealised end of the UM model hierarchy is the "idealised UM". This model configuration broadly describes a number of idealisations including the Held-Suarez Newtonian relaxation (Held and Suarez, 1994;Mayne et al., 2014b), 10 radiative convective equilibrium (Holloway and Woolnough), and exo-planet configurations (Mayne et al., 2014a;Lines et al., 2018;Boutle et al., 2017;Sergeev et al., 2020). The global configuration of the idealised model has also been broadly used for testing and developing the current dynamical core of the UM (ENDGAME) (Wood et al., 2014).
When viewing all the possible UM configurations through the climate model hierarchy lens -the idea that simple models are connected to sophisticated models via incremental steps -a large gap emerges between the simplified parameterisations initialisation, the slab ocean is free to evolve. The implementation of the slab ocean is consistent with the slab ocean described in Section 2a) of Frierson et al. (2006). The slab ocean we developed for Flex-UM is already in use, for example for terrestrial exoplanets (Boutle et al., 2017).
In summary, the Flex-UM default configuration has been designed following the GFDL moist aquaplanet model. Each of the parameterisations have been implemented in a modular way so that each variant can be used in any suitable UM configuration. 5 The development of Flex-UM enables a broader use of climate model hierarchies for the UM, allowing us to not only better understand the behaviour of the UM, but also to better understand the climate system. The adaptations and newly implemented parameterisations of Flex-UM are in the process of being scientifically and technically reviewed. The code is available as a branch of the UM at version 12.0.
3 Model configurations and data 10

Model set-up
The newly implemented and adapted parameterisations within Flex-UM were designed based on the benchmark Frierson (2007) version of the slab ocean GFDL moist aquaplanet. The Isca modelling framework (Vallis et al., 2018) is an outgrowth of the GFDL aquaplanet, sharing the spectral core and many of its parameterisations. In Section 4.1 we compare the slab-ocean configurations of Flex-UM and Isca. In order to directly compare these two models, Flex-UM was configured to be as similar 15 as possible to the Isca default configurations: an albedo of 0.31, no diurnal or seasonal cycle, constant incoming solar ration of 1360 W m −2 and a 2.5 m slab ocean depth. One difference is that Isca has solar absorption in the grey radiation scheme (consistent with Frierson (2007) while Flex-UM does not (consistent with Frierson et al. (2006)). This is discussed in more detail in Section 4.1. 1(e), with the exception of the polar side of the mid-latitudes.

Data
The Flex-UM model climatologies are compared to monthly ERA5 reanalysis climatologies (Hersbach et al., 2020;Copernicus Climate Change Service, 2017), the fifth generation of atmospheric reanalysis from ECMWF. The climatologies are computed 5 over the January 1979 to December 2020 time period. The horizontal resolution of the data is 0.25 • × 0.25 • and all available vertical levels are used between 1000-100 hPa (27 vertical levels). The ERA5 surface pressure was used to create a mask for discarding data that has been extrapolated to the 1000 hPa pressure level if the surface pressure is less than 1000 hPa.
Extrapolation is prone to errors in the data and this is especially important in computing the mass stream function.
Two Flex-UM simulations are evaluated in this paper, the fixed-SST and slab-ocean aquaplanet configurations. The Flex-  GA7.0 output is post-processed from 85 hybrid levels onto 17 pressure levels between 1000 hPa and 10 hPa.
The horizontal and vertical resolutions are different between the reanalysis and models, and between the UM simulations as well (see Table 1). This was by design, as we ran the GA7.0 and Isca simulations at their standard resolutions. Flex-UM was 5 run at a similar resolution to Isca so that the two simulations are as similar as possible. This resolution choice was because the primary goal of Flex-UM is to implement the intermediate complexity parameterisations from Isca into the UM, and then compare the two models. We note that when comparing Flex-UM and GA7.0, the key differences in the climatologies are highly unlikely to be the result of resolution differences, as the Flex-UM model physics is very different to the GA7.0 case.
All climatologies are plotted on their native resolution and data used to make difference plots have been linearly interpolated 10 in the vertical to 12 common levels sets between 1000 hPa and 100 hPa, and horizontally regridded to a common resolution of 2.8 • × 2.8 • (the native resolution of Flex-UM).
The initial conditions for the Flex-UM and Isca simulations are an isothermal atmosphere with near-zero moisture. As such, their simulations require a suitable spin-up. A 10-year spin-up was discarded from the simulations, which is standard for these types of models, and the models were run for a further 10 years. The GA7.0 simulations do not need a long spin up as the 15 simulations start from initial conditions using a climate simulation that was spun-up for 30 years (as standard for GA7.0).
However, for consistency with the other simulations, a 20 year run was performed and the first 10 years discarded as spin up.
We note that the ERA5 dataset used in this study is 42 years long and the model runs are 20 years. In general it is good practice to use a common time period between datasets, however, as the purpose of this paper is to validate an idealised model, the simplifications in the model physics will dominate over any differences in the reanalysis time period. For this reason, we felt 20 there was no need to restrict the ERA5 data to the common 20 year period. The reanalysis and model simulations will be compared in Section 4. For each dataset, the climatological precipitation and zonal-means of temperature (T), relative humidity (RH), zonal wind (u), and the mass stream function (Ψ) will be shown. The RH is computed with respect to water above 0 • C for all datasets, ice below -23 • C for ERA5, ice below -20 • C for Isca and ice below 0 • C for the UM, and interpolated for temperatures in between for ERA5 and Isca. In this study, we also show the 25 atmospheric energy budget, which is a simple global balance between the radiation lost to space, heat absorbed by the surface, and the heat released at the surface, given by: is precipitation (P = P rain + P snow ). However, it is more accurate to use LH = L c P rain + L s P snow or LH = L c P precip + L f P snow where L s and L f are the latent heat of sublimation and fusion, respectively. More discussion on this can be found in have all been modified and we speculate these modifications have impacted the moisture conservation. Further investigation will be required to identify if this is indeed the problem.

Evaluating the Flex-UM Climatology
In this section we compare Flex-UM climatologies with ERA5 reanalysis, the simplified climate modelling framework Isca, and two comprehensive UM simulations using the GA7.0 configuration. Two SST aquaplanet boundary conditions are used in 25 this study: a slab ocean aquaplanet for comparing Flex-UM to Isca in Section 4.1 and GA7.0 in Section 4.3, and a fixed-SST aquaplanet for comparing to GA7.0 in Section 4.2. The fixed-SST aquaplanet is constant throughout the simulation and does not interact with the atmosphere. The slab-ocean aquaplanet is free to evolve and exchanges fluxes with the surface in the vertical (there is no horizontal transport).
Before considering the model data, we first present the ERA5 reanalysis climatologies in Fig. 2. We do not expect that Flex-

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UM will replicate all of the structure seen in ERA5, however, ERA5 climatologies provide a reference point so that we can assess the realism of the idealised models in this paper. The general structure of the zonal-mean climatologies for temperature, Pacific convergence zone (SPCZ) in the equatorial SH Pacific Ocean region.
Perhaps less well known is the atmospheric energy budget shown in Fig. 2(e), the area weighted global means are shown in the legend. The radiation lost to space (LWC in blue) peaks in the SH and the radiation gains from solar absorption (SWA in orange) peak in the NH near the equator. Both the LWC and SWA reduce to zero at the poles. The latent heat generated from precipitation (LH in red) shows two peaks for the ITCZ and SPCZ. The sensible heat released from the surface (SH in green) 10 is small at all latitudes. The residual atmospheric energy budget (i.e. the net in Equ. 1) is small but non-zero (-3.6 W m 2 ) and the shape of the residual zonal-mean mirrors the LH from precipitation.
In the following sections we directly compare Flex-UM with both Isca and GA7.0, and will make more general comparisons to ERA5. All of the model simulations in this study are aquaplanets, that do not attempt to model the full complexity of the atmosphere, and so direct differences with ERA5 will not be presented. Rather we will make general comparisons to ERA5 to 15 highlight the realism of the model simulations.

Slab ocean aquaplanet: Flex-UM vs Isca
The motivation for developing Flex-UM was to replicate the idealised parameterisations within the GFDL moist aquaplanet model. As such, we directly compare Flex-UM with the Isca climate model, which is based off the GFDL moist aquaplanet.
The temperature and RH from the slab ocean aquaplanet simulations for Flex-UM and Isca are shown in Fig. 3. Both Flex-UM 20 and Isca have similar temperature structures to ERA5 and to each other. Flex-UM is generally cooler than Isca, especially in the upper troposphere and lower stratosphere. The general structure of the RH distribution is broadly similar in Flex-UM and Isca with a few notable differences. Compared to Isca, Flex-UM has a higher RH in the middle and upper troposphere from the subtropics poleward, and higher RH in the tropical upper tropopause. Compared to ERA5, both Flex-UM and Isca have higher RH at all latitudes. While the difference in RH between Flex-UM and Isca is large in the polar regions, the specific 25 humidity difference is very small in these regions, where their zonal-mean difference is less than 0.5 gkg −1 (not shown), owing to the cooler polar temperatures where the specific humidity is small. So while the Flex-UM polar regions might be closer to saturation than the Isca polar regions, the moisture content is too small to make a meaningful difference in the two simulations.
The zonal-mean zonal wind and mass stream function from the slab ocean aquaplanet simulations for Flex-UM and Isca are shown in Fig. 4. Flex-UM and Isca both capture the general structure of the zonal wind seen in ERA5 (the subtropical and show the spatial distribution seen in ERA5. Rather, it is more common for the precipitation to peak on the equator (a single ITCZ), or for two peaks to occur on either side of the equator (double ITCZ). Isca has a single ITCZ and a second peak in precipitation in the storm tracks near 40 • in each hemisphere (seen in Fig. 5(b) and in the LH of Fig. 5(e)). The peak equatorial precipitation for Isca is 18 mmday −1 and in the storm tracks 5 mmday −1 . Compared to Isca, Flex-UM has a broader ITCZ with less equatorial precipitation which peaks at 14 mmday −1 on the equator. The storm tracks are less pronounced in Flex-UM, where the subtropical precipitation reduces to 5 mmday −1 but does not have a local subtropical minimum or a local 5 storm track maximum.
Compared to ERA5, the precipitation is higher in both Flex-UM and Isca, hence the larger LH component of the atmospheric energy budget Fig. 5(d-e). The shape of the zonal-mean LWC is similar in ERA5, Flex-UM and Isca. The Isca LWC is much larger than ERA5 and Flex-UM, which is due to more outgoing LW radiation (OLR) and a smaller net surface flux (not shown).
The LWC in Flex-UM is similar to ERA5 but a little lower, and each LW radiative flux of Flex-UM is smaller than ERA5 and Including downward solar absorption in Flex-UM will be considered for later configurations of Flex-UM. We expect that including downward solar absorption will warm the atmosphere, which will bring the climatological temperature closer to the Isca model. We would then expect that other elements of the general circulation in Flex-UM would be closer to Isca. troposphere, especially the tropics between 600-200 hPa, and warmer above 200 hPa. Flex-UM has a higher RH throughout most of the troposphere (800-300 hPa), especially poleward of 50 • and within the off-equatorial tropics, and drier near the surface and above 300 hPa. The upper tropospheric tropical peak RH in Flex-UM occurs at a lower altitude compared to GA7.0 and peaks on either side of the equator, which is consistent with a double ITCZ structure (seen more clearly in the precipitation plots in Fig. 8). Flex-UM subtropical jet is more distinct from the eddy-driven jet compared to GA7.0. We also note that Flex-UM and GA7.0 are weakly superrotating aloft, where the equatorial wind is westerly instead of easterly. Superrotation in idealised models is not uncommon, and has previously been found in aquaplanets, shallow-water and Held-Suarez models (Mori et al., 2013;Blackburn et al., 2013;Showman and Polvani, 2010;Lutsko, 2018).
The Hadley circulation in Flex-UM is narrower, shallower, weaker and pushed off the equator in both hemispheres, while 10 GA7.0 is more like ERA5. As seen in the Flex-UM and Isca slab ocean mass stream function plots in Fig. 4d-e), the Flex-UM fixed-SST simulation has an unrealistic upper Hadley cell shape and the mass stream function in the NH polar region does not represent the polar cell. In GA7.0, the Hadley cell shape is more realistic, which we attribute to higher horizontal and vertical resolution, however the NH near surface Ψ remains unrealistic.
The precipitation and atmospheric energy budget from the fixed-SST aquaplanet simulations for Flex-UM and GA7.0 are 15 shown in Fig. 8. The double ITCZ in Flex-UM is evident in the precipitation map Fig. 8a) and in the zonal-mean LH Fig. 8d). There is also a small double peak of precipitation in GA7.0, though not separated enough to be considered a double ITCZ.
The Flex-UM tropical precipitation peaks are shallower and broader than GA7.0, the storm tracks precipitation is higher, and the subtropical precipitation is higher than expected compared to the storm tracks. Compared to GA7.0, the LH in Flex-UM is considerably larger in the global mean, due to more rainfall (despite the shallower precipitation peaks at the equator). The SWA in Flex-UM is zero, discussed in more detail in Section 4.1, and in GA7.0 the SWA is similar to ERA5 although a little The double ITCZ seen in the fixed-SST simulations for Flex-UM (and also very weakly in GA7.0) is a common structure seen in aquaplanets Rios-Berrios et al., 2020). The double ITCZ problem is also a well know model 10 bias in comprehensive GCM where precipitation over the Pacific Ocean is too zonal, see for example Tian (2015); Zhang et al.
(2015). The double ITCZ in aquaplanets is known to be sensitive to a number of model choices and is sensitive to feedbacks between the convection, cloud radiative effects and the large-scale circulation. Whether a single or double ITCZ occurs in an aquaplanet model has been shown to depend on the choice of convection scheme and the convection scheme parameters such as entrainment (Möbis and Stevens, 2012). However, the double ITCZ also occurs in comprehensive GCM simulations without 15 convection schemes where only resolved precipitation occurs (Maher et al., 2018). The appearance of a single or double ITCZ also depends on cloud radiative effects (Harrop and Hartmann, 2016;Popp and Silvers, 2017), and the energy balance near the equator (Kang et al., 2008;Bischoff and Schneider, 2016). It has also been shown that the single and double ITCZ can result from no changes in the parameterisaitons but from changes in the model resolution and dynamics core (Landu et al., 2014).
Understanding the mechanisms that control the ITCZ and the occurrence of the double ITCZ are long standing problems and 20 areas of active research.

Comparison of slab: Flex-UM and GA7
Finally, we compare the slab ocean aquaplanet simulations of Flex-UM and GA7.0 and compare the fixed-STT and slab ocean simulations for both models. The temperature and relative humidity for the slab ocean simulations are shown in Fig. 9. The precipitation and atmospheric energy budget from the slab ocean aquaplanet simulations for Flex-UM and GA7.0 are shown in Fig. 11. Unlike the fixed-SST case, the Flex-UM slab ocean has a single ITCZ and the small double peak seen in GA7.0 fixed-SST simulation is absent in the slab ocean simulations. In the slab ocean Flex-UM case, the LH and LWC is larger 10 compared to the fixed-SST case. The LWC in the Flex-UM slab ocean case has a small dip at the equator, which is not expected, and originates in the LW surface fluxes (not shown). We suspect this LWC dip is the result of the increased equatorial relative humidity in the slab ocean simulation which would increase the optical depth. The SWA in Flex-UM is zero, as discussed in

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A climate model hierarchy is a sequence of models connecting idealised to comprehensive models, via a series of intermediate complexity models. Climate model hierarchies are grounded in truth through comparisons to observations. We use comprehensive climate models to simulate the Earth system and idealised models to understand fundamental processes within the Earth system. Climate model hierarchies connect our robust physical laws to our complex reality (Maher et al., 2019). 5 The Met Office UM is a world-leading atmospheric weather and climate model capable of modelling the full complexity of the Earth system and more idealised configurations such as the Newtonian relaxation in the Held-Suarez test case or radiative convective equilibrium. However, there are very few idealised parameteristion options within the UM, limiting the broad use of hierarchical modelling for the UM. In this study we introduce the Flexible modelling framework of the UM -Flex-UM-which greatly enhances the climate model hierarchy capabilities for the UM by including multiple new and adapted idealised param-10 eterisations. These include newly implemented idealised parameterisations of convection, large-scale precipitation, radiation, boundary layer, and SST boundary conditions (using both a fixed-SST and slab ocean configurations). These parameterisations and surface conditions were developed by replicating the GFDL moist physics aquaplanet (Frierson et al., 2006;Frierson, 2007). We have implemented Flex-UM in a modular way, so that one or more schemes can be altered at a time. Hence Flex-UM is a framework rather than a specified model configuration.
The goal for developing Flex-UM was to broaden the climate model hierarchy capabilities within the UM. Having achieved this goal, the next natural question is to consider what can Flex-UM be used for? The slab ocean configuration has already been used for simulating terrestrial exoplanets (Boutle et al., 2017) and the simplified Betts-Miller convection scheme has recently been used for a convection scheme intercomparison by Hwong et al. (2021). The parameterisations of Flex-UM will play a role in developing and evaluating the next generation of dynamical core for the UM (named LFRic after Lewis Fry Richardson) 5 and in evaluating the next generation of convection scheme within the UM (named CoMorph). In addition to supporting model development and evaluation, Flex-UM can also be used to address bold science questions within an easier to understand setting.
Answering bold science questions is a fundamental motivation for using climate model hierarchies and Flex-UM enhances this capability within the UM.
Code and data availability. The UM code and its configuration files are subject to Crown Copyright. A licence for the UM can be requested from https://www.metoffice.gov.uk/research/approach/collaboration/unified-model/partnership. The source code for Flex-UM will be available as branch of the UM at version 12.0 and will be available at https://code.metoffice.gov.uk/trac/um/browser (to access this link you first need to apply via the link above). The Flex-UM simulations in this study were completed using modifications to the UM version 11.7 and the GA7.0 simulations were completed using version 11.6. The simplified Betts-Miller scheme and slab-ocean code used in this study are already on the UM code trunk at version 11.7 as part of the Trac code management system (see link above). The grey radiation scheme, boundary also publicly available at https://github.com/penmaher/streamfunction. The Isca climate model is publicly available at https://github.com/ ExeClim/Isca. The simulations in this study were generated using Isca commit ID 66a50d9 (commit date 21 May 2021