1. Introduction
As part of the UK Climate Projections (UKCP) project, national climate scenarios have recently been provided at a resolution on par with weather forecasting (Kendon et al. 2019b). This is an international first, with the aim to provide an improved simulation of extreme precipitation and also other high-impact events at local scales for the coming decades. Until now, national climate scenarios have been based on climate models with grid spacings of order 10–100 km. These models rely on a parameterization scheme to represent the average effects of convection and this simplification is a known source of model error. In particular it leads to deficiencies in the diurnal cycle of convection, does not represent individual storms, and lacks memory from one time step to the next (Brockhaus et al. 2008; Hanel and Buishand 2010). Very high-resolution models (order 1 km grid spacing) can allow convection to be represented explicitly without the use of a parameterization scheme (Hohenegger et al. 2008; Kendon et al. 2012). Such convection-permitting models (CPMs) are now standard in short-range weather forecasting, where they have been shown to give a much more realistic representation of convection and are able to forecast localized extreme rainfall events not captured at coarser resolution (Done et al. 2004; Lean et al. 2008; Weisman et al. 2008; Weusthoff et al. 2010; Schwartz 2014; Clark et al. 2016). Due to the high computational cost, the use of CPMs in climate studies has been limited to seasonal-length simulations or single multiyear realizations, for typically small domains. These studies have shown that CPMs give a better representation of hourly rainfall characteristics (Kendon et al. 2012; Ban et al. 2014; Lind et al. 2016), including extremes (Chan et al. 2014), and the structure and evolution of storms (Prein et al. 2015; Stevens et al. 2020), and thus are able to provide credible projections of changes in hourly rainfall important for understanding future flood risk (Kendon et al. 2017; Dale et al. 2018). They also better represent the mesoscale dynamics and surface heterogeneities (Prein et al. 2015), and give more reliable projections of future climate change over mountains, coastlines, and cities. However, until now, due to the availability of only single realizations, it has not been possible to estimate uncertainty in future changes at these scales.
The UKCP Local projections were launched in September 2019 and consist of 12 projections, run at 2.2 km resolution over the United Kingdom (Kendon et al. 2019b). Each projection represents a plausible realization of the future climate up to 2080, assuming no curbs on greenhouse gas emissions (RCP8.5 scenario). The ensemble members differ due to natural climate variability and uncertainty in the driving model physics. In particular, the different driving-model simulations produce alternative mesoscale environments in which the CPM has freedom to develop alternative realizations of local weather, and thus the CPM ensemble gives an indication of uncertainties in future changes on local and hourly scales. In general the 2.2 km CPM projections show that the United Kingdom can expect warmer wetter winters and hotter drier summers in future, reinforcing the headline findings from coarser-resolution climate models. In terms of summer rainfall changes, the average changes are broadly consistent between the 2.2 km CPM and its driving 12 km regional climate model (RCM) ensemble, but the underlying changes in rainfall on a day-to-day and an hour-to-hour basis are quite different. In particular the CPM shows a greater shift to more intense rainfall in summer in future, and this tendency of higher-resolution models to show a greater intensification of summer rainfall is consistent with previous CPM studies (Kendon et al. 2014; Ban et al. 2015). However, the UKCP Local projections give a surprising result in winter, with the CPM showing greater increases than the RCM in winter mean precipitation. In this case, the ranges of outcomes from the CPM and RCM ensembles overlap, but with the CPM envelope of future changes showing a clear positive shift relative to that of the RCM, such that several CPM outcomes are above the maximum RCM response (Kendon et al. 2019b). This is contrary to previous CPM studies, which showed the CPM largely following its driving model in winter (Kendon et al. 2014).
In this paper we explore wintertime precipitation responses in the UKCP Local 2.2 km (CPM) ensemble, and why these differ from the driving 12 km model (RCM) projections. We assess to what extent the different representation of convection in the CPM is a factor, which includes the development of a new method to diagnose wintertime convective showers. This method is a simple one-step procedure that works by analyzing atmospheric stability conditions, utilizing the underlying physical basis of convection. Given that different types of precipitation are expected to respond differently to climate change (Berg et al. 2013), being able to partition total precipitation into convective and stratiform types is particularly valuable.
2. Methods
a. Models
The 2.2 km CPM is based on a recent configuration of the Met Office weather forecast model (which was made operational in November 2016), but with various changes to support its use in climate runs. The configuration is close to the Regional Atmosphere 1 midlatitude configuration (Bush et al. 2019) and is termed HadREM3-RA11M. The model includes a variable resolution rim, where the grid spacing transitions smoothly from 2.2 to 4 km, as this helps the initiation of showers before they enter the fixed 2.2 km resolution part of the domain (Tang et al. 2013). The variable-resolution rim region is excluded from all analysis presented here. The convection scheme is switched off entirely for both shallow and deep convection in the CPM, with the use of 3D Smagorinsky turbulent mixing (Smagorinsky 1963), a new mass conservation scheme (Zerroukat and Shipway 2017) that removes spurious moisture generated by the higher-order semi-Lagrangian advection scheme, and the new Met Office Urban Surface Exchange Scheme (MORUSES; Porson et al. 2010). Details of the 2.2 km HadREM3-RA11M model physics are provided in Kendon et al. (2019b). We note that at 2.2 km grid spacing smaller showers and convective plumes are not resolved, and as a result individual updrafts get represented on too large a scale with insufficient turbulent mixing. This leads to some inherent deficiencies in CPMs, including the tendency for heavy rainfall to be too intense (Kendon et al. 2012). Nevertheless, CPMs give a much more realistic representation of rainfall than coarser-resolution convection-parameterized models. A 2.2 km grid spacing was chosen for the UKCP Local projections as this was found to perform similarly to 1.5 km grid spacing in terms of the representation of hourly precipitation, but with the benefit of considerably lower computational cost (Fosser et al. 2019).
The UKCP Local 2.2 km ensemble consists of 12 projections spanning the United Kingdom. It is driven by a 12-member ensemble of the 12 km RCM, which is produced by perturbing uncertain parameters in the model physics. Each 12 km RCM member spans Europe, and is in turn driven by the relevant member of the 60 km Hadley Centre global coupled model (HadGEM3-GC3.05) perturbed parameter ensemble (Murphy et al. 2018). The CPM and RCM are limited-area atmosphere-only models, with daily sea surface temperature and sea ice cover prescribed from the driving global simulation. Both the 12 km RCM (HadREM3-GA705) and 60 km global model use the GA7.05 atmospheric model, which is close to GA7 (Walters et al. 2019) but includes a number of updates. The 2.2 km CPM and 12 km RCM share the majority of their main physical components, but there are some notable differences. In particular the mass flux convection parameterization (Gregory and Rowntree 1990) is used in the RCM but switched off in the CPM; the RCM uses the prognostic cloud scheme (PC2; Wilson et al. 2008) while the CPM uses the Smith (1990) cloud scheme, because PC2 has not yet been implemented in the convection-permitting operational forecast model configuration (Kendon et al. 2019b); only the CPM includes prognostic graupel, which is a second category of ice with higher densities and fall speeds found in convective cloud; the RCM uses the new multilayer snow scheme (Best et al. 2011) while the CPM uses the simpler zero-layer snow scheme; and finally the RCM uses the simpler one-tile urban scheme rather than MORUSES (Kendon et al. 2019b).
We note that recently an error has been found in the graupel code in the UKCP CPM. The error was in the graupel autoconversion term, which controls the fraction of snow converted to graupel, and in general resulted in too much snow being converted to graupel. Tests to assess the impact of this graupel code error have been performed for one ensemble member (specifically the unperturbed standard member). These show that the impact on future changes in winter precipitation is small, with differences on fixing the graupel-code error within the CPM ensemble spread and considerably smaller than the difference between the CPM and RCM responses (see Figs. S1 and S2 in the online supplemental material). Thus, the key conclusions reported in this paper are unaffected.
Given the structural differences between the CPM and driving RCM, it was not possible to mirror the full set of RCM parameter perturbations in the CPM. Therefore, the same version of the HadREM3-RA11M model is used for each CPM ensemble member. As a result, the CPM ensemble samples uncertainty arising from natural climate variability and parametric uncertainties in the physics of the driving models, with the different driving-model simulations producing a range of synoptic and mesoscale environments within which local weather is constrained; however, it does not sample uncertainty in the CPM model physics itself. In addition, the CPM and RCM ensembles are driven exclusively by variants of the Met Office Hadley Centre model (HadGEM3-GC3.05), and lack information from other international climate models. As a consequence, we expect both the CPM and RCM ensembles to underestimate uncertainties in future changes. Nevertheless, the CPM ensemble analyzed here represents a major step forward, since all previous CPM information has been limited to single climate change realizations lacking any uncertainty context.
Data from two 20-yr periods are used here, corresponding to a baseline (1981–2000) and future (2061–80) period. The high emissions “business-as-usual” scenario RCP8.5 is used, which assumes unmitigated greenhouse gas emissions. In the future period, changes in greenhouse gas forcing follow member-specific CO2 concentration pathways, which vary due to uncertainty in carbon cycle feedbacks (Murphy et al. 2018). Aerosol forcing in the RCM and CPM is prescribed using the “Easy Aerosol” (Stevens et al. 2017) approach, whereby aerosol optical properties and cloud droplet number concentration are prescribed from the driving global simulation. Future changes in land use also follow the driving global model, allowing changes in the proportions of grasses, trees, and shrubs, while the urban land use fraction is held constant at present-day values. Further details of forcings and the experimental setup can be found in Kendon et al. (2019b).
b. Analysis methods
In the analysis here we primarily focus on two precipitation types, namely, convective showers and non-shower precipitation, which are defined as follows:
Convective showers. These are pure convective showers with as little coexistence as possible with stratiform precipitation. This category does not include convection embedded in frontal precipitation or large convective systems (which the United Kingdom does not get in winter anyway).
Non-shower precipitation. This includes anything that is not pure convective showers. It includes stratiform precipitation and may include convection that coexists with stratiform precipitation.
In the above definitions, stratiform precipitation is entirely associated with large-scale dynamics (including forced slantwise ascent) and is the dominant precipitation type in fronts (including cold, warm, or occluded fronts), while convective precipitation is associated with buoyancy-driven ascent. In addition to the above precipitation types, we also mention “large-scale” and “convective” precipitation as model-specific definitions according to the RCM parameterizations. Large-scale precipitation in the RCM is stratiform precipitation produced on the gridscale and is associated with large-scale condensation and autoconversion. Parameterized convective precipitation in the RCM is associated with local buoyancy and is produced by a mass-flux scheme that represents the effect of sub-grid-scale convection on the atmosphere in a grid box (Gregory and Rowntree 1990). In the CPM, all precipitation is produced on the grid scale and therefore a method is required for separating convective showers from non-shower precipitation.
The vertical gradient in wet-bulb potential temperature θw (or equivalent potential temperature θe) is a measure of the potential instability of the atmosphere. A decrease of θw (or θe) with height is a necessary (but not sufficient) condition for moist convection and the more θw decreases with height, the more the atmosphere is potentially unstable. Here we use this physical basis of convection to diagnose convective showers in the CPM. In particular convection is diagnosed at each 2.2 km grid point, excluding dry hours (<0.01 mm h−1), where there is a positive value of θw(925 hPa) − θw(700 hPa), instantaneously at the start of the hourly precipitation interval, somewhere within a 40 × 40 km2 neighborhood centered around each grid square. These levels are suitable because wintertime convection over the United Kingdom typically occurs within colder air masses in which showers are shallower than in summer and tend to be surface-based (ascent is from the boundary layer rather than an elevated layer). This allows us to exclude convection embedded within frontal zones. This method relies on the fact that the CPM only stabilizes the atmosphere at the local 2.2 km grid box and in the local vicinity of where showers are actually occurring, with the surrounding area remaining unstable (with θw decreasing with height). This method was found to perform well in detecting showers and in correctly identifying frontal rainfall as nonconvective. This is illustrated for selected days in December 1980 in supplemental Fig. S3. Since instantaneous values of θw were only output from the model every 6 h, only the hourly rainfall data from the corresponding hours is used when diagnosing convection.
Output from the convection parameterization scheme is used to determine convective precipitation in the RCM. However, this output includes any convection diagnosed in the column, whether surface-based showers or convection embedded in fronts. Therefore, to pick out grid cells that are dominated by convective showers and give a more like-for-like comparison with the CPM, parameterized convective precipitation is used in the RCM only for pixels where the nonconvective (traditionally called “large scale”) fraction of precipitation is less than 50%. Convective showers diagnosed using this method are shown in supplemental Fig. S4 (middle panels) for selected days in December 1980. It can be seen that this output is successfully detecting showers, and largely (although not completely) excluding convection that is embedded in fronts. For comparison only, also shown in supplemental Fig. S4 (bottom panels) is the convective component of precipitation diagnosed using the vertical gradient in θw, as done above for the CPM. In this case, the θw-diagnosis (which is carried out on the native grid scale of each model) is missing many convective showers in the RCM because the convection scheme represents the stabilization of the atmosphere due to sub-grid-scale convection within the 12 × 12 km2 grid box, rather than shower by shower (as is the case for the 2.2 km resolution CPM). Therefore, by not representing the subgrid spatial variability in convection it also lacks the subsequent spatial variation in convective instability present in reality.
To identify the contribution to the total change in mean precipitation from convective showers, we split the total change into two components:
where the first component is the contribution to the mean change from changes in convective showers PCS, termed here the “convective contribution,” and the second is the contribution from changes in non-shower precipitation PNS, which includes changes in total precipitation (stratiform + embedded convection) in frontal events and additionally in the RCM changes in large-scale precipitation collocated with showers (in the RCM, only the parameterized convective precipitation is used in the showers, while in the CPM, the convective diagnosis method assumes that all precipitation where the atmosphere is convectively potentially unstable is convective). The term P is mean present-day total precipitation, with the same sampling of hours used for all precipitation variables. A similar formula is used for the contribution to changes in precipitation occurrence, where mean precipitation is replaced by the frequency of precipitation.
3. Results
a. Future changes in winter precipitation
Future changes in winter precipitation across the United Kingdom in the 2.2 km CPM and driving 12 km RCM are shown in Fig. 1. In this case, we show the median of the future changes across each of the 12-member ensembles at each local grid box. Both the CPM and RCM show increases in mean precipitation in winter, but the increases over land are considerably larger in the CPM compared to the RCM (26% compared to 16% increase). It can be seen that this greater increase in the CPM comes from significant increases in hourly precipitation occurrence (defined as the frequency of wet hours, >0.1 mm h−1) in winter that are not seen in the RCM (17% increase in CPM compared to only 2% increase in RCM). Increases in hourly precipitation intensity (defined as the mean precipitation on wet hours) over land are actually larger in the RCM (9% increase in the CPM compared to 15% in the RCM), and so these do not explain the larger winter mean response in the CPM. This difference in future responses does not extend over the sea, with future increases in both hourly precipitation occurrence and intensity over the sea being comparable between the CPM and RCM. It should be noted that the frequency of precipitation in the present day is lower in the CPM than the RCM, with considerably more dry hours, which is in much better agreement with observations; despite larger increases in precipitation occurrence this remains the case in the future (Figs. S5 and S6). A detailed evaluation of the present-day performance of the CPM compared to the RCM is provided by Kendon et al. (2019b), who show that the RCM has too frequent but low-intensity precipitation, while the CPM has much lower biases in precipitation occurrence but tends to overestimate precipitation intensity especially in summer (see Figs. S7 and S8).
Future change in winter precipitation on hourly time scales. Median change in (left) mean precipitation, (center) precipitation occurrence, and (right) precipitation intensity in winter in the CPM and RCM ensembles. Changes (in %) correspond to the difference between the future (2061–80) and baseline (1981–2000) periods for RCP8.5. The average values over land and over sea points are shown separately. Wet hours are defined as >0.1 mm h−1 and results for the CPM are for precipitation regridded to 12 km scale.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
Looking at changes in the frequency of precipitation across different intensity bins (Fig. 2), it can be seen that in the CPM future increases over land are greatest in the light and moderate intensity bins (0.1–0.4 and 0.4–2.0 mm h−1), as dry events (<0.1 mm h−1) decrease. In contrast, in the RCM for lower intensities (0.1–0.4 mm h−1) the frequencies over land actually decrease (particularly in the east, creating some dry events of <0.1 mm h−1) while the frequencies of the higher (>0.4 mm h−1) intensity hourly events increase. Over the sea, both models show a decrease in dry events. It is notable that in the RCM there is a pronounced land–sea contrast in future changes in precipitation occurrence, with increases over the sea not extending over the land (Fig. 1). The intensity analysis shows that this is heavily influenced by the decrease in low intensity wet events (0.1–0.4 mm h−1) over land, which is not seen in the CPM.
Future change in the frequency of hourly precipitation events in different intensity bins in winter. Shown are maps of the future change in the frequency of events (given as the percentage of the total number of events for all events occurring in winter across all 12 ensemble members) in each of four intensity bins [(top to bottom) 0–0.1, 0.1–0.4, 0.4–2.0, and >2.0 mm h−1] for (left) CPM and (right) RCM. Future changes correspond to the difference between the future (2061–80) and present-day (1981–2000) periods. Results for the CPM are for precipitation regridded to 12 km scale to match that of the RCM.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
Looking at the individual member differences between the CPM and its parent RCM (Fig. 3), it can be seen that greater increases in mean precipitation (and precipitation occurrence) over land in the CPM compared to the RCM is a robust signal across the ensemble. To characterize differences across the ensemble we show the second lowest individual member differences, the median (or central estimate) of the individual differences and the second highest individual member differences, at each local grid point. In the case of precipitation occurrence, the land average of the low (high) estimate of member differences is 9% (23%), with the CPM response always considerably larger than that of its parent RCM. This robust difference over land points is not seen over the sea, where individual member response differences can either be positive or negative, with the median difference close to zero. For future changes in winter precipitation intensity, the CPM generally shows smaller increases than its parent RCM over land, but not in all cases, with individual member response differences close to zero for the high estimate.
CPM minus parent RCM member differences in winter precipitation changes on hourly time scales. (left) Second lowest, (center) central, and (right) second highest member differences for future changes in (top) mean precipitation (middle) precipitation occurrence, and (bottom) precipitation intensity, in winter. The average values of the local member response differences over land and over sea points are shown separately. Wet hours are defined as >0.1 mm h−1 and results are for precipitation regridded to 12 km scale.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
b. Contribution from convective showers
We now examine to what extent the different future changes in wintertime precipitation occurrence over land in the CPM compared to the RCM are related to the type of precipitation (stratiform/frontal or convective). Convection, although less prominent than in summer, still occurs in winter in the form of convective showers, especially over the sea, and in association with cold fronts and organized bands. In the CPM, the convection parameterization scheme is switched off and therefore there is no specific “convective” precipitation output that we can directly diagnose, with all precipitation coming from condensation associated with vertical motion represented on the model grid. Therefore, in order to separate out the behavior of convective from stratiform precipitation, a method for partitioning between the two types is needed (Lang et al. 2003). A method has been developed here, using the vertical gradient in wet-bulb potential temperature (θw) between 925 and 700 hPa (see section 2). This method is particularly appropriate for identifying convective showers that are surface based (i.e., that originate from the boundary layer), such as showers that are triggered over the sea in winter. For the RCM, we use output from the convection parameterization scheme using a method that aims to detect only surface-driven convective showers, which is approximately equivalent to what the θw-diagnosis method applied to the CPM is identifying (see section 2). In particular, we exclude cases where there are significant amounts of both parameterized “convective” and “large-scale” precipitation occurring simultaneously in the RCM, as this typically indicates a front with embedded convection, with the precipitation often coming from a combination of slantwise ascent and convection above. Here we wish to isolate “pure” convective showers, and identify whether future changes in these are explaining the different wintertime precipitation responses between the CPM and RCM.
The fraction of winter mean precipitation coming from convective showers in the CPM and RCM ensembles, for both the present-day and future climate is shown in Fig. 4. The convective fraction is consistently higher in the CPM than RCM, over both land and sea. In particular, on average about 20% of precipitation in winter over land in the present day is convective in the CPM compared to less than 10% in the RCM; while over the sea about 40% of precipitation is diagnosed as convective in the CPM compared to 30% in the RCM. If we use all output from the convection parameterization scheme (i.e., not only selecting surface-driven convective showers, but also cases of convection associated with cold fronts) then the convective fraction of precipitation in the RCM only increases slightly (to just over 10% and 30% over land and sea respectively), with values still considerably lower than those in the CPM. We note that if we apply the θw diagnosis method to the RCM the convective fraction over land is still lower at 9% (but note in this case the calculation is done at the 12 km grid scale and so not directly comparable to the CPM, and also we expect the θw method to miss convective showers in the RCM; see section 2). Thus, the higher convective fraction of precipitation found in the CPM is unlikely to be due simply to the different diagnosis methods to detect convective showers. We note that in addition to the use of explicit as opposed to parameterized convection, differences between the CPM and RCM may be due to more local variability in the 2.2 km resolution CPM (e.g., that can allow convection locally to overcome a stable layer) that is not seen in the 12 km resolution RCM, and also feedback from existing convection that can trigger further convection in the CPM (see section 4).
Fraction of winter mean precipitation coming from convective showers (CF) in the (top) present-day (1981–2000) and (bottom) future (2061–80) periods for the (left) CPM and (right) RCM. Convective showers in the CPM are diagnosed using vertical gradients in wet-bulb potential temperature (θw) and in the RCM using the convection parameterization output, when there is more “convective” precipitation diagnosed than “large-scale dynamic” precipitation. Shown is the central estimate locally across the CPM and RCM ensembles, respectively. The average values of the local CF values over land and over sea points are shown separately. For the CPM, results are for hourly precipitation on the native 2.2 km grid with 6-hourly sampling and for the RCM for hourly precipitation at 12 km RCM grid scale.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
The fraction of precipitation occurrences coming from convective showers (see Fig. S9) shows similar results over land with about 20% of occurrences in the CPM and less than 10% in the RCM; however, over the sea both models show a similar fraction (about 40%) of occurrences coming from convective showers. This confirms that differences in convective fraction over the land are due to model differences in the frequency rather than intensity of convective showers, while over the sea convective showers occur with a similar relative frequency but higher intensity in the CPM compared to the RCM. While the fraction of precipitation from convective showers shows a clear land–sea contrast at large scales in both models, only the CPM shows a gradual, and physically realistic, gradient in convective fraction across coastal regions (Fig. 4). In the RCM, a pronounced land–sea contrast is seen in both the present day and future.
On quantifying the convective contribution to future changes (see section 2), we find that changes in the mean precipitation from convective showers contribute about 40% of the overall mean precipitation change in winter over land in the CPM (central estimate of convective component is 11.3% out of total 26.8% increase, Fig. 5; we note that the overall changes quoted in Fig. 5 differ slightly from those in Fig. 1 for the CPM as 6-hourly sampling of hourly precipitation is used, corresponding to the times of θw output, whereas in Fig. 1 hourly precipitation data from all hours are used). Over the sea, changes in convective showers can contribute 50% or more of the overall mean precipitation change (central estimate of 11.0% increase out of 21.4% increase), although this can be as low as 20% in some members (Table 1). For future changes in precipitation occurrence (Fig. 5), changes in convective showers contribute about 60% of the overall change over land, and about 70% of the overall change over the sea, with this relative contribution being robust across CPM members. Thus, a large part of the future increase in precipitation occurrence over land (and sea) in the CPM in winter is coming from an increase in the frequency of convective showers. These showers are most likely to be triggered over the sea, where the warmer ocean and higher levels of atmospheric moisture favor more triggering of convection, and are then advected inland, persisting for longer, with potentially further development over land. This is supported by an analysis of the atmospheric moisture budget which shows that the average increase in precipitation (of 1.0 mm day−1) considerably dominates over the increase in evaporation (of 0.2 mm day−1) over U.K. land (Kendon et al. 2019b), and instead is coming from an increase in moisture flux convergence over land (including moisture advected from the sea that is converted into precipitation and the advection of showers themselves). We note that in summer the processes are different, with more triggering of convection over the warm land surface, and thus the advection of convective showers triggered over the sea is much less important (see section 4).
Future change in winter precipitation and the convective contribution to this change from convective showers. Central estimate across the 12-member ensemble of (top) the future change and (bottom) the convective contribution to this change for (left) mean precipitation in the CPM, (left center) precipitation occurrence in the CPM, (right center) mean precipitation in the RCM, and (right) precipitation occurrence in the RCM in winter. In the CPM, convective showers are diagnosed using vertical gradients in wet-bulb potential temperature, and in the RCM using output from the convection parameterization scheme when the convective fraction of hourly precipitation is >0.5. The convective contribution to the overall change is given by the change in precipitation from convective showers divided by present-day total precipitation (see section 2). Changes correspond to the difference between the future (2061–80) and present-day (1981–2000) periods, for RCP8.5. The average local values over land and over sea points are shown separately. For the CPM, results are for hourly precipitation on the native 2.2 km grid with 6-hourly sampling and for the RCM for hourly precipitation at 12 km RCM grid scale.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
Future change in winter precipitation and the convective contribution to this change from convective showers averaged separately over land points and sea points. Ranges correspond to the average of the low to high estimates, corresponding to the second lowest and second highest projection locally across the 12-member ensemble, with the central estimate given in bold. The averages of local values over land points and in parentheses over sea points are given. Results are provided for (left) the future change (2060–80 minus 1980–2000) and (right) the component of this change coming from convective showers for mean precipitation and precipitation occurrence in the CPM and RCM in winter.
In the RCM, we find that changes in the mean precipitation from convective showers only contribute about 10% of the overall mean precipitation change over land in winter (central estimate of convective component is 1.6% out of total 16.4% increase; Fig. 5), but more similarly to the CPM contribute about 40% of the mean precipitation change over the sea (central estimate of 8.7% increase out of 21.0% increase). For future changes in precipitation occurrence over land, the contributions from increasing numbers of convective showers and from increasing non-shower precipitation occurrence (where “non-shower” refers to all other precipitation, including stratiform precipitation and convection embedded in fronts; see section 2) are both smaller in the RCM than CPM in absolute terms. In particular, increases are 10.3% from convective plus 7.7% from non-shower precipitation in the CPM compared to 1.4% plus 0.8% in the RCM (central estimate). In the RCM the relative contribution (compared to the total occurrence change) from the increasing frequency of convective showers is high, but with a much smaller overall change in total precipitation occurrence. Over the sea, the increase in the frequency of convective showers is a large contributor to the overall change in precipitation occurrence in both the CPM and RCM (~70% of the total in the CPM and ~90% in the RCM). Thus, differences in future changes in winter precipitation occurrence between the CPM and RCM are due to both greater increases in the frequency of convective showers and greater increases in non-shower precipitation occurrence over land in the CPM. We note that the latter category includes light large-scale precipitation collocated with convective showers in the RCM, as well as large-scale (stratiform) rain and embedded convection within fronts. Analysis looking at the changes in the frequency of convective showers, and separately non-shower events, across different intensity bins in the RCM (Fig. 6) shows small increases in convective showers over land overall (consistent with Table 1) and larger increases (in light and moderate events) over the sea. For non-showers, there are decreases almost everywhere in the light category and increases (especially in the west and over high orography) in the moderate and heavy events. These competing changes lead to a small overall increase in non-shower events over land (with increases in the west and decreases in the east of the United Kingdom). Figure S10 shows similar results but for all-convective and separately all-large-scale precipitation (output from the parameterizations) in the RCM; in other words, in this case the “convective” precipitation includes that in both shower and non-shower events. The difference between the plot for all-convective precipitation and that for convective showers (in particular the greater future increase in all convective events in supplemental Fig. S10 compared to that for convective-showers only in Fig. 6, apparent for the 0.1–0.4 and 0.4–2.0 mm h−1 categories) indicates that there is an increase in convection in non-shower events (i.e., more embedded convection in future over land) in the RCM.
Future change in the frequency of convective shower events and non-shower events in different intensity bins in winter in the RCM. Shown are maps of the future change in the frequency of events (given as the percentage of the total number of events for all events occurring in winter across all 12 RCM ensemble members) in each of four intensity bins {(top to bottom) 0–0.1, 0.1–0.4, 0.4–2.0, and >2.0 mm h−1] for (left) convective showers and (right) all other precipitation events (including large-scale precipitation collocated with showers and the total precipitation in non-shower events). Future changes correspond to the difference between the future (2061–80) minus present-day (1981–2000) periods.
Citation: Journal of Climate 33, 17; 10.1175/JCLI-D-20-0089.1
Given that we expect the CPM and its driving RCM to see the same frequency of fronts, the result above that there are greater increases in non-shower precipitation occurrence over land in the CPM than RCM may relate to greater increases in embedded convection within frontal systems in the CPM in the future (although we do see some increase in embedded convection in the RCM), potentially greater increases in orographic rainfall, and/or greater increases in light stratiform precipitation in the CPM. For the latter, once convection has become organized it tends to develop a stratiform component, and this could lead to greater increases in the non-shower precipitation category in the CPM compared to the RCM (with the RCM showing a future decrease in light non-shower/large-scale precipitation occurrence; Fig. 6 and Fig. S10). We note that “embedded convection” here relates to the convective component of precipitation in a variety of situations with mixed dynamic and convective precipitation, including showers developing along a line of forcing, and is likely to be associated with features that can persist longer than pure convective showers. On repeating the above analysis but excluding regions of high orography (with surface elevation above 200 m) we find a very similar result, namely, that future changes in precipitation occurrence over low-lying regions are much larger in the CPM compared to the RCM (17.7% compared to 2.4%), with the contributions to this from increasing convective showers and increasing non-shower precipitation occurrence both larger in the CPM (10.0% and 7.7%, respectively, in CPM and 1.6% and 0.6%, respectively, in the RCM). This indicates that different orographic precipitation responses are not the main driver of the different land responses between the CPM and RCM. Instead it is likely that the different representation of convection, both in the form of showers triggered over the sea and embedded within frontal systems, is a major driver. It may also be that the RCM acts to stabilize the atmosphere much more over the sea than the CPM, affecting both convective and dynamic precipitation over the land. In addition, the increased horizontal resolution of the CPM will have implications for the representation of precipitation and this may also be an important factor (independent of the explicit convection). Although we have only discussed convection in this paper to keep the problem more tractable and focused, it may be the case that frontal systems can remain more active over land in a CPM because mesoscale structures associated with slantwise instability are better represented. This is speculative and would be an interesting area for further investigation.
4. Discussion
In this section we further discuss the differences in winter precipitation changes between the CPM and RCM, reported above, in terms of our understanding of how the convection parameterization scheme in the RCM operates and the local processes captured in the CPM. We contrast these to the differences in summer. We provide possible explanations of why these results differ from earlier CPM studies, which showed the CPM following the driving model for changes in winter. We also discuss the wider implications of this study, including the extent to which we may expect these differences over the United Kingdom to extend to other regions. We conclude that national climate scenarios based on traditional coarser-resolution climate models may underestimate future increases in winter precipitation, especially where wintertime convective showers are a key contributor, since the processes important for the advection and further triggering of showers are only well captured in CPMs.
The finding that there is little future increase in convective showers over land in winter in the RCM is consistent with the fact that the convection parameterization scheme triggers on the basis of local instability. In winter over land, even in a warmer climate, the land surface and atmospheric boundary layer will be relatively cold in terms of θw compared to the airmass above, because there is very little solar heating of the land surface when days are short and the sun angle is low. By comparison over the sea, the convection scheme is expected to trigger whenever a cooler airmass advects over a warmer ocean surface. Given that the convection scheme acts locally without direct memory, it has no ability to advect the diagnosed convection over the land or to initiate further showers from outflows. The parameterized model can advect the environmental conditions associated with convection, which could then lead to convection being diagnosed over land. However, in practice this tends not to happen, or to only produce weak convection, because of the colder, less unstable surface conditions. Hence, it is expected that there would be a contrast between the occurrence (and potentially changes in the occurrence) of convection over land and sea in the RCM. We note that this inability of convection parameterized models to advect showers inland is well known from numerical weather prediction (NWP) and in fact was one of the motivations for developing a kilometer-scale model for U.K. weather forecasts. An example from NWP is shown in supplemental Fig. S11, for a case of wintertime showers being advected inland, which clearly shows that showers present over western regions of Ireland and Scotland in the radar and 1.5 km forecast model are missing from the convection-parameterized global model.
In summer, we do not see such a pronounced land–sea contrast in the future changes, with large decreases in precipitation occurrence of about 30% over both land and sea, in the CPM and RCM (Fig. S12). In summer, the greatest differences between the CPM and RCM instead are in changes in precipitation intensity, with considerably larger increases in the CPM (7% compared to 1% increase in the RCM) over land. These differences compared to winter can be explained by the dominance of land-driven convection in summer. In future, higher levels of atmospheric moisture with warming favor increases in rainfall intensity, with these increases in the CPM likely amplified by local dynamical feedbacks within convective storms. Such processes are also expected to operate in winter, but in this season we find greater increases in mean intensity over land in the RCM than CPM. This seems to be due, at least in part, to a decrease in the occurrence of weak events in the RCM, which then do not go into the average. It may be the case that the convection scheme in the RCM acts to stabilize the atmosphere much more over the sea. These environmental conditions would then be advected inland following the flow, impacting both the occurrence and intensity of showers over land. In the CPM by contrast, winter convective showers (which are mostly triggered over the sea and advected inland, but with potential further development over land) are both more frequent and on average more intense when they occur.
The time and space scales over which showers stabilize the atmosphere are dependent on the meteorological situation. Typically, there is a large degree of inhomogeneity in the environment, which forms envelopes for preferred showery activity. For example, larger showers can produce cold pools that temporarily stabilize the atmosphere over a wider area but can also trigger further showers due to uplift at their leading edge. These complex dynamic and thermodynamic controls and feedbacks are captured with better physical realism in the CPM (due to the higher resolution and explicit representation of convection), but it is still important to recognize that even the 2.2 km grid is too coarse to fully capture convective processes, many of which operate on much smaller scales in reality. The convection scheme in the RCM is representing convection as an entirely sub-grid-scale process, preventing instability growing on its coarser grid, but particularly because of the underlying assumptions being used in its formulation it is likely to be less effective than the CPM at stabilizing the atmosphere in a realistic way—although this is something we cannot quantify.
Here we have shown that, using this information on how convective showers act, it is possible to develop a metric to diagnose convection in a CPM in winter, which at least visually appears to be acting correctly. Other methods that use spatial gradients in the rainfall field to diagnose convective versus stratiform rain (Poujol et al. 2019; Lang et al. 2003) can be used successfully in summer when convective rainfall is generally more intense, but these are less successful at detecting less intense wintertime showers. We note that a number of different convective–stratiform separation techniques have been used in previous studies based on spatial gradients in surface rainfall fields, vertical velocities, and/or radar reflectivities or using precipitation fall speeds (Lang et al. 2003), but in all cases these rely on specific thresholds within the algorithm to diagnose convection. Recently, Poujol et al. (2019) developed a physically based algorithm for separating precipitation types over complex topography, which works by detecting convective overturning cells and the production of local potential vorticity in a multistep process. By comparison, the method reported here uses information on the atmospheric stability conditions that are the underlying physical basis for convection, and has the benefit of being a simple single-step procedure that is not dependent on subjective thresholds.
We note that the difference in wintertime mean precipitation responses between the CPM and RCM found here is in contrast with earlier CPM studies (Kendon et al. 2014, 2017), which showed the CPM following the driving model for changes in winter. One reason for this may be the small domain size of the earlier CPM simulations, such that events advected in at the boundary were not fully spun up over the United Kingdom. The longer sea fetch (beyond any spinup zone) in the current CPM compared to previous simulations may also make a difference if the CPM acts to stabilize the atmosphere less over the sea than the RCM. In addition, there have been many changes to the model physics between the earlier simulations (Kendon et al. 2014) and the recent UKCP Local projections that may explain the difference. For example, changes to the mixing settings and boundary layer perturbations in the CPM (Fosser et al. 2019) will tend to favor more convective showers. However, further work is needed to confirm the relative importance of these and identify other potential factors.
We may expect to see similar differences between convection-permitting and convection-parameterized models in other parts of Europe under the influence of westerly flow, where maritime showers are advected inland in winter. For example, Vanden Broucke et al. (2019) noted the importance of wintertime convective storms advected from the North Sea for precipitation over Flanders. Looking at this in a single pan-European 2.2 km climate change simulation carried out at the Met Office (Berthou et al. 2018), we see greater future increases in wintertime precipitation occurrence in the 2.2 km compared to its 25 km driving model over parts of mainland Europe (as well as over the United Kingdom), especially along coastal regions of northern France, Belgium, Netherlands, Germany, and Denmark (see Fig. S13). In these regions, only the 2.2 km model shows an increase in precipitation occurrence. We note that these showers may be intense locally, but appear light when averaged over a large (25 km) grid square.
This study shows that the improved representation of convection in CPMs, along with the increased horizontal resolution, can significantly impact future projections in seasonal-mean precipitation for a relatively large area (e.g., the United Kingdom as a whole), and also for a season (in this case winter) which is not the primary convective season. So the impact goes well beyond projections of local precipitation extremes in convectively dominated seasons and regimes, which has been the main focus of convection-permitting climate studies to date (Kendon et al. 2014; Ban et al. 2015; Kendon et al. 2019a). These results for the United Kingdom may be more widely applicable to other regions where wintertime convective showers are a key contributor, with the processes important for the advection and further development of showers only well captured in CPMs. Thus, the results reveal, for the first time, an important limitation of national climate scenarios based on traditional coarser-resolution climate models. In particular, such scenarios may underestimate future increases in winter mean precipitation, with implications for river flows, flood risk, and water resource management.
These results come from an ensemble of convection-permitting simulations over the United Kingdom using exclusively the Met Office model, sampling uncertainty in the local response due to natural climate variability and parametric uncertainties in the physics of the driving models. An important avenue for future research is to assess whether the results here are also found in other CPMs run over Europe as part of the CORDEX Flagship Pilot Study (Coppola et al. 2018) and European Climate Prediction System (EUCP) (Hewitt and Lowe 2018) projects. This will identify whether the potential for CPMs to give larger future increases in winter precipitation is a robust consequence of the increased horizontal resolution and improved representation of convection.
Acknowledgments
We gratefully acknowledge funding from the Joint U.K. BEIS/Defra Met Office Hadley Centre Climate Programme (GA01101).
Data availability statement
Hourly precipitation data from the UKCP Local 2.2 km projections and daily precipitation data from the UKCP Regional 12 km projections are publicly available from the Centre for Environmental Data Analysis (CEDA) archive (https://catalogue.ceda.ac.uk). Other UKCP data used here are available upon request from the corresponding author.
REFERENCES
Ban, N., J. Schmidli, and C. Schär, 2014: Evaluation of the convection-resolving regional climate modeling approach in decade-long simulations. J. Geophys. Res. Atmos., 119, 7889–7907, https://doi.org/10.1002/2014JD021478.
Ban, N., J. Schmidli, and C. Schär, 2015: Heavy precipitation in a changing climate: Does short-term summer precipitation increase faster? Geophys. Res. Lett., 42, 1165–1172, https://doi.org/10.1002/2014GL062588.
Berg, P., C. Moseley, and J. O. Haerter, 2013: Strong increase in convective precipitation in response to higher temperatures. Nat. Geosci., 6, 181–185, https://doi.org/10.1038/ngeo1731.
Berthou, S., E. J. Kendon, S. C. Chan, N. Ban, D. Leutwyler, C. Schär, and G. Fosser, 2018: Pan-European climate at convection-permitting scale: A model intercomparison study. Climate Dyn., 55, 35–59, https://doi.org/10.1007/S00382-018-4114-6.
Best, M. J., and Coauthors, 2011: The Joint UK Land Environment Simulator (JULES), model description—Part I: Energy and water fluxes. Geosci. Model Dev., 4, 677–699, https://doi.org/10.5194/gmd-4-677-2011.
Brockhaus, P., D. Lüthi, and C. Schär, 2008: Aspects of the diurnal cycle in a regional climate model. Meteor. Z., 17, 433–443, https://doi.org/10.1127/0941-2948/2008/0316.
Bush, M., and Coauthors, 2019: The first Met Office Unified Model/JULES regional atmosphere and land configuration, RAL1. Geosci. Model Dev., https://doi.org/10.5194/GMD-2019-130
Chan, S. C., E. J. Kendon, H. J. Fowler, S. Blenkinsop, N. M. Roberts, and C. A. T. Ferro, 2014: The value of high-resolution Met Office regional climate models in the simulation of multi-hourly precipitation extremes. J. Climate, 27, 6155–6174, https://doi.org/10.1175/JCLI-D-13-00723.1.
Clark, P., N. Roberts, H. Lean, S. P. Ballard, and C. Charlton-Perez, 2016: Convection-permitting models: A step-change in rainfall forecasting. Meteor. Appl., 23, 165–181, https://doi.org/10.1002/met.1538.
Coppola, E., and Coauthors, 2018: A first-of-its-kind multi-model convection permitting ensemble for investigating convective phenomena over Europe and the Mediterranean. Climate Dyn., 55, 3–34, https://doi.org/10.1007/S00382-018-4521-8.
Dale, M., A. Hosking, E. Gill, E. J. Kendon, H. J. Fowler, S. Blenkinsop, and S. C. Chan, 2018: Understanding how changing rainfall may impact on urban drainage systems; lessons from projects in the UK and USA. Water Pract. Technol., 13, 654–661, https://doi.org/10.2166/wpt.2018.069.
Done, J., C. A. Davis, and M. L. Weisman, 2004: The next generation of NWP: Explicit forecasts of convection using the Weather Research and Forecasting (WRF) model. Atmos. Sci. Lett., 5, 110–117, https://doi.org/10.1002/asl.72.
Fosser, G., E. J. Kendon, S. C. Chan, A. Lock, and N. Roberts, 2019: Optimal configuration and resolution for the first convection permitting ensemble of climate projections over the United Kingdom. Int. J. Climatol., 40, 3585–3606, https://doi.org/10.1002/joc.6415.
Gregory, D., and P. R. Rowntree, 1990: A mass-flux convection scheme with representation of cloud ensemble characteristics and stability dependent closure. Mon. Wea. Rev., 118, 1483–1506, https://doi.org/10.1175/1520-0493(1990)118<1483:AMFCSW>2.0.CO;2.
Hanel, M., and T. A. Buishand, 2010: On the value of hourly precipitation extremes in regional climate model simulations. J. Hydrol., 393, 265–273, https://doi.org/10.1016/j.jhydrol.2010.08.024.
Hewitt, C. D., and J. A. Lowe, 2018: Toward a European climate prediction system. Bull. Amer. Meteor. Soc., 99, 1997–2001, https://doi.org/10.1175/BAMS-D-18-0022.1.
Hohenegger, C., P. Brockhaus, and C. Schär, 2008: Towards climate simulations at cloud-resolving scales. Meteor. Z., 17, 383–394, https://doi.org/10.1127/0941-2948/2008/0303.
Kendon, E. J., N. M. Roberts, C. A. Senior, and M. J. Roberts, 2012: Realism of rainfall in a very high-resolution regional climate model. J. Climate, 25, 5791–5806, https://doi.org/10.1175/JCLI-D-11-00562.1.
Kendon, E. J., N. M. Roberts, H. J. Fowler, M. J. Roberts, S. C. Chan, and C. A. Senior, 2014: Heavier summer downpours with climate change revealed by weather forecast resolution model. Nat. Climate Change, 4, 570–576, https://doi.org/10.1038/nclimate2258.
Kendon, E. J., and Coauthors, 2017: Do convection-permitting regional climate models improve projections of future precipitation change? Bull. Amer. Meteor. Soc., 98, 79–93, https://doi.org/10.1175/BAMS-D-15-0004.1.
Kendon, E. J., R. A. Stratton, S. Tucker, J. H. Marsham, S. Berthou, D. P. Rowell, and C. A. Senior, 2019a: Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale. Nat. Commun., 10, 1794, https://doi.org/10.1038/s41467-019-09776-9.
Kendon, E. J., and Coauthors, 2019b: UKCP convection-permitting model projections: Science report. Met Office Tech. Rep., 153 pp., https://www.metoffice.gov.uk/pub/data/weather/uk/ukcp18/science-reports/UKCP-Convection-permitting-model-projections-report.pdf.
Lang, S., W. Tao, J. Simpson, and B. Ferrier, 2003: Modeling of convective-stratiform precipitation processes: Sensitivity to partitioning methods. J. Appl. Meteor., 42, 505–527, https://doi.org/10.1175/1520-0450(2003)042<0505:MOCSPP>2.0.CO;2.
Lean, H. W., P. A. Clark, M. Dixon, N. M. Roberts, A. Fitch, R. Forbes, and C. Halliwell, 2008: Characteristics of high-resolution versions of the Met Office Unified Model for forecasting convection over the United Kingdom. Mon. Wea. Rev., 136, 3408–3424, https://doi.org/10.1175/2008MWR2332.1.
Lind, P., D. Lindstedt, E. Kjellstrom, and C. Jones, 2016: Spatial and temporal characteristics of summer precipitation over central Europe in a suite of high-resolution climate models. J. Climate, 29, 3501–3518, https://doi.org/10.1175/JCLI-D-15-0463.1.
Murphy, J. M., and Coauthors, 2018: UKCP18 land projections: Science report. Met Office Tech. Rep., 191 pp., https://www.metoffice.gov.uk/pub/data/weather/uk/ukcp18/science-reports/UKCP18-Land-report.pdf.
Porson, A., P. A. Clark, I. N. Harman, M. J. Best, and S. E. Belcher, 2010: Implementation of a new urban energy budget scheme in the MetUM. Part I: Description and idealized simulations. Quart. J. Roy. Meteor. Soc., 136, 1514–1529, https://doi.org/10.1002/qj.668.
Poujol, B., S. P. Sobolowski, P. A. Mooney, and S. Berthou, 2019: A physically based precipitation separation algorithm for convection-permitting models over complex topography. Quart. J. Roy. Meteor. Soc., 146, 748–761, https://doi.org/10.1002/QJ.3706.
Prein, A. F., and Coauthors, 2015: A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. Rev. Geophys., 53, 323–361, https://doi.org/10.1002/2014RG000475.
Schwartz, C. S., 2014: Reproducing the September 2013 record-breaking rainfall over the Colorado Front Range with high-resolution WRF forecasts. Wea. Forecasting, 29, 393–402, https://doi.org/10.1175/WAF-D-13-00136.1.
Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Part I: The basic experiments. Mon. Wea. Rev., 91, 99–164, https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.
Smith, R. N. B., 1990: A scheme for predicting layer clouds and their water content in a general circulation model. Quart. J. Roy. Meteor. Soc., 116, 435–460, https://doi.org/10.1002/qj.49711649210.
Stevens, B., S. Fiedler, S. Kinne, K. Peters, S. Rast, J. Musse, S. J. Smith, and T. Mauritsen, 2017: MACv2-SP: A parameterization of anthropogenic aerosol optical properties and an associated Twomey effect for use in CMIP6. Geosci. Model Dev., 10, 433–452, https://doi.org/10.5194/gmd-10-433-2017.
Stevens, B., and Coauthors, 2020: The added value of large-eddy and storm-resolving models for simulating clouds and precipitation. J. Meteor. Soc. Japan, 98, 395–435, https://doi.org/10.2151/jmsj.2020-021.
Tang, Y., H. Lean, and J. Bornemann, 2013: The benefits of the Met Office variable resolution NWP model for forecasting convection. Meteor. Appl., 20, 417–426, https://doi.org/10.1002/met.1300.
Vanden Broucke, S., H. Wouters, M. Demuzere, and N. P. M. van Lipzig, 2019: The influence of convection-permitting regional climate modeling on future projections of extreme precipitation: Dependency on topography and timescale. Climate Dyn., 52, 5303–5324, https://doi.org/10.1007/s00382-018-4454-2.
Walters, D., and Coauthors, 2019: The Met Office Unified Model Global Atmosphere 7.0/7.1 and JULES Global Land 7.0 configurations. Geosci. Model Dev., 12, 1909–1963, https://doi.org/10.5194/gmd-12-1909-2019.
Weisman, M. L., C. Davis, W. Wang, K. W. Manning, and J. B. Klemp, 2008: Experiences with 0–36-h explicit convective forecasts with the WRF-ARW model. Wea. Forecasting, 23, 407–437, https://doi.org/10.1175/2007WAF2007005.1.
Weusthoff, T., F. Ament, M. Arpagaus, and M. W. Rotach, 2010: Assessing the benefits of convection-permitting models by neighborhood vertification: Examples from MAP D-PHASE. Mon. Wea. Rev., 138, 3418–3433, https://doi.org/10.1175/2010MWR3380.1.
Wilson, D. R., A. C. Bushell, A. M. Kerr-Munslow, J. D. Price, and C. J. Morcrette, 2008: PC2: A prognostic cloud fraction and condensation scheme. I: Scheme description. Quart. J. Roy. Meteor. Soc., 134, 2093–2107, https://doi.org/10.1002/qj.333.
Zerroukat, M., and B. Shipway, 2017: ZLF (zero lateral flux): A simple mass conservation method for semi-Lagrangian-based limited-area models. Quart. J. Roy. Meteor. Soc., 143, 2578–2584, https://doi.org/10.1002/qj.3108.
