Sensitivity of orographic precipitation enhancement to horizontal resolution in the operational Met Office Weather forecasts

Authors


Abstract

Rain gauge observations show that when averaged over a large number of cases of frontal systems passing over the UK, strong orographic rain enhancement occurs on the lee slopes of the first hills encountered by the southwesterly flow in the warm sector. The operational forecasts using 1.5 km grid spacing produced realistic looking mean rainfall patterns over the Lake District and Wales, with an area-averaged rain accumulation error of less than 2%. Model-level rain rates increase with decreasing altitude consistent with the seeder-feeder mechanism. Increasing the horizontal grid spacing in the operational weather forecast model decreases the amount of rain produced over the hills, thereby reducing forecast accuracy. The area-averaged rain accumulations are 11–24% smaller than observed at 12 km grid spacing and 33–48% smaller than observed at 40 km grid spacing.

In additional simulations of the 15 January 2011 case over the Lake District at 1.5 km grid spacing, replacing the orography with that used by the 12 and 40 km models reduced the area-averaged rain accumulations by 10 and 23% respectively. These changes were due to reduced cloud water and ice mixing ratios over the lower hills resulting in slower increases in rain rate with decreasing altitude. It is demonstrated that neglecting the horizontal advection of falling rain drops results in too much rain falling on the windward slope and not enough falling on the lee slopes. Copyright © 2012 British Crown Copyright, the Met Office. Published by John Wiley & Sons Ltd.

1 Introduction

It is well known that precipitation associated with frontal systems is enhanced in regions of significant topography. Douglas and Glasspoole (1947) found that the heaviest orographic rainfalls are associated with the strong southwesterly winds in the warm sector of a depression, just ahead of the cold front, which bring warm, moist air of subtropical origin to the UK. Hill et al. (1981) found that rain was heavy and continuous over the hills in the warm sector, but that the heaviest rain over the hills was usually associated with the passage of pre-existing mesoscale precipitation areas. Holgate (1973) found that it was this type of prolonged heavy rainfall rather than thundery activity that is the principle cause of flooding for the hills of North Wales and North-West England. The Cumbrian floods of 18–19 November 2009 (Eden and Burt, 2010; Sibley, 2010) and the Carlisle floods of 8 January 2005 (Roberts et al., 2009) are two prime examples of the effects of prolonged heavy precipitation over the hills of the Lake District. Both flooding events caused loss of life and large financial losses. It is generally believed that the seeder-feeder mechanism (Bergeron, 1965) is responsible for most orographic precipitation enhancement over the small to moderate hills of the UK, where low-level orographic clouds are unable to grow precipitation sized particles independently due to the limited time that an air parcel is located over the hill. Instead pre-existing (seeder) precipitation particles falling from aloft, for example from a frontal cloud or mesoscale precipitation area, collect water from the low-level orographic (feeder) cloud via riming (snow) or accretion (rain), thereby increasing the rainfall rate at low levels. This mechanism is complicated by the fact that the upper-level cloud can also be affected by the orography, and the seeder and feeder regions can just be different parts of the same cloud.

A number of authors have studied the sensitivity of simulated orographic precipitation to model horizontal grid spacing. The amount of orographic precipitation generally increases with decreasing grid spacing until the important orographic features are sufficiently resolved. Any further decreases in grid spacing will not necessarily improve model skill. The sensitivity to model grid spacing is highly dependent on the mountain range being studied. Over the narrow Wasatch mountain range in Utah model skill improved when decreasing the horizontal grid spacing to 1.33 km (Colle et al., 2005) while over the wide Sierra Nevada decreasing the horizontal grid spacing past 13.5 km gave no improvement in verification scores (Grubisic et al., 2005). Over the southern part of the European Alps model skill generally improves as the horizontal grid spacing decreases from several tens of kilometres down to a few kilometres (e.g. Buzzi et al., 2004; Pedemonte et al., 2005; Richard et al., 2007). Over the Reykjanes mountain ridge in Iceland, improvement was found when decreasing the horizontal grid spacing from 8 to 2 km (Rognvaldsson et al., 2007). Over the mountainous Pacific Northwest of the USA verification scores over several cool seasons were improved as horizontal grid spacing was decreased from 36 to 12 km (Colle et al., 2000, 2000). Improvements going from 12 to 4 km were restricted to heavy precipitation events. Large improvements with resolution were observed for a single 4 day flooding event (Colle and Mass, 2000) although the 12 and 4 km simulations had excessive shadowing in the lee. Further decreasing the grid spacing to 1.33 km did not improve skill in terms of verification scores over the whole domain but it produced more precipitation in the lee of the Cascades. Precipitation maxima were simulated immediately downwind of major peaks, as might be expected, but there were no observations to check that these actually existed.

Not many studies of the sensitivity of orographic precipitation to horizontal model resolution have been carried out over the UK, where most of the precipitation falls to the surface as rain. Roberts et al. (2009) produced Met Office Unified Model (MetUM®) simulations of a single orographic rain case over the Lake District, which produced the flooding event in Cumbria during January 2005. They found that decreasing the horizontal grid spacing from 12 to 4 km and then to 1 km increased the amount of orographic rain over the Lake District. An accurate analysis of the impact of horizontal grid spacing on model accuracy was hampered by the fact that the simulated frontal system produced too much rain. As a result the 1 km simulation produced too much rain everywhere, however it produced a more accurate rain distribution with respect to the orography than the lower resolution simulations. Lean (2002) demonstrated, also for a single case study, that at 12 km grid spacing the MetUM produces orographic enhancement which is consistent with the seeder-feeder mechanism, and that the amount of enhancement is sensitive to both the amount and distribution of both the lower-level and upper-level clouds. The upper-level cloud is affected by both large-scale effects and mountain waves propagating from the orography.

Deterministic weather forecasts are being produced at increasingly higher resolutions as computer power increases. The Met Office has recently started running its Unified Model operationally at variable horizontal resolution, with the horizontal grid spacing decreasing from 4 km at the boundaries to 1.5 km over the UK in the centre of the domain. High resolution forecasts are desirable as they are able to resolve small-scale features, while large-scale features are also better represented. However, coarse resolution forecasts still play an important role in that they are able to predict rainfall with greater lead times due to their lower demands on computer resources. Ensemble forecasts are typically produced at lower horizontal resolution, while regional climate forecasts typically have horizontal grid spacings of tens of kilometres.

The present study has two main aims. The first is to examine whether the MetUM is able to predict orographic rain enhancement via the seeder-feeder effect correctly when run at its current highest operational resolution. This is done by comparing against rain gauge observations. The second is to investigate how much of the observed orographic rain enhancement is reproduced by the MetUM at lower horizontal resolutions. If a significant amount is missed by the model then it may be beneficial to parameterize the effects of sub-grid scale orography on the rain fields. For this study we are not interested in how well the model is able to forecast frontal or warm sector rain in the absence of orography (the background rain field), only the amount by which it is enhanced by the hills of the UK. A number of cases of orographic rain enhancement are required in order to be able to average out errors in the background rain fields and also to average out rainfall variations which are not produced by orographic effects. Therefore, operational forecasts which were available from the archive were used, rather than running the model on a case study basis. In order to obtain general results, three different ranges of hills have been considered as shown by the solid boxes in Figure 1(a). These are the hills of South-West Scotland (highest peak at an altitude of 1.34 km), Wales (highest peak at an altitude of 1.06 km) and the Lake District in Cumbria, North-West England (highest peak at an altitude of 972 m). These regions were chosen to encompass the hills which typically produce significant orographic rain enhancement in situations of warm, moist southwesterly flow within warm sectors of depressions. When the model is run with a different horizontal grid spacing it is often necessary to make other changes to the model set-up, such as the time step used. These additional changes may also have an effect on the forecast rain fields. Therefore, simulations of a single case study over the Lake District (15 January 2011) were produced with a 1.5 km grid spacing but using orography from the models with larger grid spacings. This enabled us to quantify the extent to which the changes in the forecast rainfall amounts with changing resolution were due to changes in the underlying orography.

Figure 1.

Surface heights in metres from the MetUM using grid spacings of (a) 1.5 km and (b) 40 km. The coastlines are shown by thin solid lines. The solid boxes indicate the three regions of interest. The dotted boxes in (a) show the upstream areas over the sea used in Section 'Verification of orographic rain enhancements produced by operational forecasts'

The remainder of this paper is set out as follows. Section 'Methods' describes how orographic rain cases were selected, the set-up of the operational MetUM weather forecasts and how the forecasts were verified using rain gauge observations. The performance of the operational weather forecasts for the chosen cases of orographic rain enhancement is assessed in Section 'Verification of orographic rain enhancements produced by operational forecasts' Section '1.5 km simulations with different orography' details additional simulations at 1.5 km grid spacing where the orography is replaced by that used by the 4, 12 and 40 km models. Conclusions are given in Section 'Conclusions'.

2 Methods

2.1 Selection of cases

It was necessary to select cases from two separate periods in order to include weather forecasts over a range of horizontal resolutions. The first analysis period was the year 2009, when the global model used a horizontal grid spacing of 40 km. However, at that time the smallest grid spacing used by the Met Office operational weather forecasts was only 4 km. Therefore, the second analysis period begins in June 2010, when UK forecasts at 1.5 km grid spacing became available, and lasts until February 2011 when this analysis was initially carried out. By this time the global model grid spacing had been decreased from 40 to 25 km. Operational forecasts were produced at 12 and 4 km grid spacing during both of these periods.

Daily weather forecasts produced by the 4 km model were extracted from the operational archive and cases of significant orographic rain were selected as those times when at least 100 (or 25 in the Lake District due to the smaller area) model grid-boxes with surface elevation above 300 m experienced a total precipitation rate of greater than 4 × 10−4 kg m−2 s−1 (equivalent to about 34 mm day−1 or 1.4 mm h−1). From these times an attempt was made to identify cases of warm sector flow by applying selection criteria based on the synoptic settings listed in Table 1 of Hill et al. (1981), who analysed observations during eight cases of orographic rain enhancement over South Wales. These criteria were that the low-level (850 hPa) flow: (1) was from the southwest quadrant, (2) had a wind-speed greater than 14 m s−1, and, (3) had a wet bulb potential temperature of greater than 282.5 K. These types of cases were sought as they are the principle cause of flooding in England (Holgate, 1973), for which it is therefore most important to be able to correctly predict the amount and location of orographic rain. As a final check that each case was associated with the passage of a well-defined frontal system, plots of the total precipitation rate from the 4 km forecasts were examined along with archived analysis charts.

Table 1. Start date and duration of each case identified by the selection procedure described in Section 'Selection of cases'
Lake DistrictWalesScotland
DateDuration (h)DateDuration (h)DateDuration (h)
  1. The bottom row gives the total number of cases and the total number of hours analysed for each region.

11 January 200997 March 2009210 January 200912
7 March 2009417 June 2009411 March 20092
11 March 2009311 July 200976 May 20094
18 November 20093017 November 2009118 September 20094
24 November 20091319 November 2009521 September 20094
5 December 2009624 November 200942 October 20095
  5 December 2009424 November 20096
6 July 201032 November 20107
26 October 2010123 November 20103
27 October 2010312 January 201112
1 November 2010214 January 201116
15 January 20111916 January 20113
2 February 20115
12 cases10912 cases787 cases37

The cases selected mainly occur between autumn and spring, from mid-September through to mid-March. As an example of the type of synoptic situation selected, Figure 2 shows the analysis chart at 1200 UTC on 15 January 2011. A fairly wide region of warm sector flow was lying over the UK at this time, resulting in orographic rain enhancement over the Lake District for 19 consecutive hours. Table 1 lists the cases identified in this way for both analysis periods. There were 12 cases each over the Lake District and Wales with 109 h over the Lake District and 78 h over Wales, a sufficient number of cases to give general results. Scotland was not included in the second analysis period due to the sparsity of the rain gauge network in the region of interest as described in Section 'Verification against rain gauge observations' and as a result only seven cases made up of 37 h were analysed.

Figure 2.

Analysis chart at 1200 UTC on 15 January 2011

2.2 Model set-up

The MetUM is a non-hydrostatic model which employs a semi-implicit semi-Lagrangian advection scheme (Davies et al., 2005). It uses a regular latitude-longitude horizontal grid with Arakawa ‘C’ staggering while a Charney-Phillips staggering is used in the vertical. The vertical co-ordinate is height based, with terrain following levels at the ground smoothly transitioning to ‘flat’ levels (concentric spheres) above a height of about 30 km. A comprehensive set of physical parameterizations are used to represent sub-grid scale processes. The mixed phase microphysics scheme is based on Wilson and Ballard (1999) and includes a prognostic rain variable in the 4 and 1.5 km models. This allows the raindrops to fall through multiple levels, allowing them to advect with the three-dimensional model wind field. Prognostic rain was not included in the 12 km simulations analysed in this study (although it has been added more recently). The boundary layer scheme described by Lock et al. (2000) represents the turbulent vertical transport of heat, moisture and horizontal momentum, with an improved entrainment parameterization described in Lock (2001). The model uses the Met Office Surface Exchange Scheme MOSES-II as described by Essery et al. (2001). Short and long wave radiative transfer are represented using the Edwards–Slingo radiation scheme, which is based on the two-stream equations (Edwards and Slingo, 1996). Convection is parameterized in the 40 and 12 km models by the Gregory and Rowntree (1990) mass flux scheme with CAPE closure. At 4 km grid spacing the model uses a modified version of the convection scheme in which the mass flux at cloud base is limited so as to only represent the effects of weaker convection that would not be resolved by the model grid (Roberts, 2003; Lean et al., 2008). At 1.5 km grid spacing no convection scheme is used.

The horizontal grid spacings of the operational weather forecasts produced during each analysis period are summarized in the second and third columns of Table 2. The 40 km global model used 70 vertical levels with the lowest level at an altitude of 20 m and the highest level at an altitude of 80 km. The 12 km mesoscale model also had its lowest level at 20 m. However, the number of levels increased from 38 during 2009 to 70 during 2010/2011, decreasing the mean vertical grid spacing in the troposphere by 42% as well as increasing the height of the model top from 40 to 80 km. Both the 4 km and the 1.5 km forecasts used 70 levels with the lowest level at an altitude of 5 m and the highest level at 40 km, with vertical grid spacings that were 70% of the 12 km model grid spacings during 2010/2011. The vertical grid spacing increases with height. In the 4 and 1.5 km models for example, the vertical grid spacing is 37 m at an altitude of 100 m, 116 m at 1 km, 163 m at 2 km, 203 m at 3 km, 257 m at 5 km and 304 m at 7 km.

Table 2. Verification of the operational orographic rain forecasts against rain gauge observations as described in Section 'Verification against rain gauge observations'
Grid spacing (km)20092010–2011RMSE Lake DistrictRMSE WalesRMSE ScotlandCorr Lake DistrictCorr WalesCorr Scotland
  1. RMSE are in mm day−1. The availability of each model grid spacing is indicated for the two different analysis periods.

40YesNo25.39.816.20.34− 0.10.36
12YesYes15.68.010.00.530.590.61
4YesYes7.85.87.30.920.870.88
1.5NoYes5.75.5N/A0.900.88N/A

For all operational forecasts, the mean model orography is filtered in order to remove numerically undesirable grid-scale features. This is done using a Raymond filter (Raymond, 1988) tuned to reduce four grid-length-scale features by 50% while two grid-length-scale features are removed completely. Features on the scale of six grid-lengths are damped by less than 5%.

2.3 Verification against rain gauge observations

As operational weather forecasts are produced at progressively higher horizontal resolution they are able to resolve smaller scale features so that model fields are more realistic. However, it has proved difficult to show this improvement using traditional verification statistics due to the highly variable nature of fields such as precipitation. For convective precipitation in particular, traditional point-by-point verification can give large errors even for a good high resolution precipitation forecast due to its stochastic nature, e.g. Done et al. (2004). A shower in slightly the wrong location gives large errors which provide a double penalty in a root mean square calculation. Fuzzy verification techniques improve the verification of precipitation at high resolutions by comparing an observation at a point with a number of surrounding grid-boxes rather than just the closest. However, great care would have to be taken in regions of significant orography to select appropriate grid-boxes. While verification scores may be degraded at high resolution over flat terrain for the reasons described above, model skill tends to improve using smaller grid spacings over mountains during events with large amounts of precipitation as shown by Zangl (2007) for the Northern Alps. This is because small-scale horizontal variations in a precipitation field produced by the underlying topography are more predictable than non-orographic variations. Mass et al. (2002) discussed at length the problems inherent in verifying high resolution simulations. Errors in timing and position are unfairly amplified as grid spacing decreases due to features being better represented. As stated previously, this study is not concerned with assessing how well the model predicts the passage of the frontal systems producing the background rain, and therefore the observed and simulated rainfall accumulations were averaged over all selected times before calculating the verification statistics.

Mean daily rainfall accumulations from Environment Agency and Scottish Environment Protection Agency rain gauges have been used to verify the orographic rain forecasts. Mean daily rainfall accumulations were extracted from the MetUM forecasts at each gauge position by interpolating from the four surrounding grid-points. From these values an area-averaged rain accumulation was calculated within the regions shown by the solid boxes in Figure 1. This method enables a direct comparison with the observed rainfall area-averages. The root mean square error (RMSE) and correlation co-efficients (corr) were calculated using Equations ((1)) and ((2)), where Fi and Oi are the forecast and observed rain accumulations at rain gauge i averaged over all times. N is the number of rain gauges used. Rain gauge locations in the Lake District are shown by the symbols in Figures 3 and 5.

display math(1)
display math(2)

Successful verification relies on the accuracy of the observations, and rain gauges are not without their problems. For these cases all of the precipitation fell to the surface as rain thereby avoiding the large difficulties in measuring snowfall amounts. However, they are all characterized by large low-level wind-speeds, often in excess of 30 m s−1, due to the presence of the low-level jet in the warm sector. Exposed rain gauges are known to underestimate rainfall by 5–15% because of wind effects and evaporation (Groisman and Legates, 1994).

Figure 3.

The first two panels show temporally averaged rain accumulations (colour bar in mm day−1) over the Lake District for all warm sector cases identified during 2009, as forecast by the (a) 12 km and (b) 4 km models. Contour lines show the underlying model orography (metres) while the asterisks show the positions of the rain gauges. Panels (c) and (d) show the temporally averaged rain accumulations (mm day−1) observed by the rain gauges using the same colour scale as panels (a) and (b). The grey shading shows (c) surface heights from a 100 m resolution digital terrain data set and (d) the 4 km model orography (metres)

Another problem which is particularly troublesome when investigating orographic rain enhancement is that rain gauges are widely spaced, being primarily located on the surrounding low-lying regions. Those gauges which are located within a range of hills tend to be located within valleys. Sparse observations increasingly undermine model verification as resolution increases: many of the small-scale structures are not observed adequately or even at all (Mass et al., 2002). The cases analysed here are characterized by windy warm sector conditions with enhancement produced by relatively small-scale hills. In such conditions the region of maximum rain enhancement is displaced onto the lee slopes of the hill due to the significant horizontal advection of raindrops as they fall to the surface. Therefore, the lack of observations on the summits of the hills may not be a problem.

The rain gauge network is fairly dense over the Lake District as shown in Figure 3(c). Within the 52 km × 72 km averaging area there are 73 rain gauges, which approximates to 1 gauge per 51 km2. Some of these rain gauges are ideally situated on the lee slopes of the highest peaks, enabling them to observe some of the largest amounts of orographic rain produced (red symbols in Figure 3(c)). This region is therefore ideal for investigating how well the MetUM is able to simulate orographic rain at high resolution. In Wales the 111 km × 200 km averaging area contains 153 rain gauges. Accounting for the fact that about a quarter of this area is over the sea, this equates to a coverage of roughly 1 gauge per 108 km2 on land, with quite a few in the region of maximum rain enhancement predicted by the model. However, their locations are perhaps not as ideal as in the Lake District. The rain gauge network over Scotland, on the other hand, has an uneven density, with numerous gauges located towards the east coast but less within the southwestern region of orographic rainfall enhancement (60 gauges within the 125 km × 189 km averaging area equates to 1 gauge per 400 km2). It would therefore be difficult to verify the highest resolution forecasts over Scotland properly. In the following sections, therefore, comparisons of rainfall distributions with respect to orography are only shown for the Lake District in North-West England. However verification scores are shown for all three regions.

3 Results

3.1 Verification of orographic rain enhancements produced by operational forecasts

In order to assess how well the MetUM is able to reproduce orographic rain enhancement at various horizontal grid spacings, the observed and simulated rainfall fields have been averaged over all days of interest during each period before comparing. Figure 3 shows the mean surface rainfall distributions for the Lake District (averaged over all 2009 cases) from the (a) 12 km and (b) 4 km operational forecasts and (c,d) as observed by the rain gauges. It can be seen from the observed rain accumulations plotted in Figure 3(c) that the temporally averaged rainfall patterns are dominated by orographic effects. Large amounts of rain tend to fall over the first hills encountered by the southwesterly flow, with maximum rainfall amounts occurring on their lee slopes. This dries out the air so that subsequent hills are not able to produce as much rain.

Due to the small-scale nature of the topography in North-West England and Wales, the 40 km model orography is totally unrealistic, as seen in Figure 1(b). The hills of the Lake District, Pennines and the Southern Uplands are represented as a single elongated hill of limited height and the Welsh mountains as a single round hill. As a result the hills of the Lake District are unable to enhance the surface rainfall in the 40 km forecasts. The general shape of the orography is improved in the 12 km model. The Lake District can now be discerned as a separate hill, although there is no fine-scale detail. The model produces some orographic rain over the Lake District as shown in Figure 3(a), although most rain falls on the windward slope of the model orography instead of the lee slope. It will be shown in Section '1.5 km simulations with different orography' that this is because the 12 km operational forecasts neglected the horizontal advection of falling raindrops at the time. The 4 km model resolves some of the smaller scale orographic features and Figure 3(b) shows that significant orographic rainfall enhancements are forecast in roughly the correct locations. The largest amounts of rain fall on the lee slopes of the highest model peak. However, the maximum rainfall amount is 34% smaller than observed.

The performance of the operational orographic rain forecasts at 40, 12 and 4 km horizontal grid spacing during 2009 is compared in Figure 4 for (a) the Lake District, (b) Wales and (c) Scotland. Figure 4 shows a direct point by point comparison of the forecast and observed rain amounts at each rain gauge location. The solid diagonal line indicates where the points would lie for a perfect forecast. Points lying below this line are locations where the model on average does not produce as much rain as observed. Table 2 lists the mean rainfall verification statistics within each region (solid boxes in Figure 1) while Table 3 gives the mean model bias in the area-averaged rainfall accumulation at each grid spacing as a percentage of the observed accumulations. The results from the two analysis periods were combined in these two tables by (1) calculating the statistics for each period separately, and then (2) averaging the results over both periods.

Figure 4.

Simulated versus observed values of mean rainfall accumulations (mm day−1) for the hills of (a) the Lake District, (b) Wales and (c) Scotland. Squares, triangles and asterisks show results from the 40, 12 and 4 km operational forecasts respectively. The diagonal line indicates perfect agreement

Table 3. Mean bias at each model grid spacing as a percentage of the observed mean rainfall accumulations
Grid spacing (km)Lake District (%)Wales (%)Scotland (%)
40− 48− 33− 41
12− 24− 13− 11
4+ 11+ 18+ 15
1.5− 20N/A

Figure 4 demonstrates that the mean observed rain accumulation varies horizontally from less than 10 mm day−1 up to 42, 57 and 98 mm day−1 over the hills of the Wales, Scotland and the Lake District respectively. As demonstrated in Figure 3(c), these horizontal variations are dominated by orographic effects, with the largest rain accumulations in the lee of the highest hills. There are two possible reasons for the much larger maximum rain amounts observed over the Lake District. Firstly, two of the rain gauges are located on the lee slope of one of the highest peaks in the Lake District, which produces very localized increases in surface rain. The second is that for the 2009 cases included in Figure 4, the mean event duration over the Lake District is almost 11 h, compared to just over 5 h in the other two regions.

The 40 km operational forecasts do not produce enough rain over the hills. There is virtually no orographic rain enhancement over the Lake District and Wales, resulting in very little variation in rain amounts across those regions as seen in Figure 4(a) and (b). At locations where more rain was observed the negative model bias becomes larger. Table 2 shows that the RMSE varies from 9.8 mm day−1 over Wales to 25.3 mm day−1 over the Lake District. The correlation co-efficient is never larger than 0.36 and is in fact negative over Wales due to the occurrence of a maximum in the mean 40 km forecasts, which is in a different place to the one observed. Table 3 shows that the area-averaged rain accumulations are 33–48% lower than observed, with the largest model bias over the Lake District. The 12 km operational forecasts were more accurate than the 40 km forecasts, with smaller RMSEs and larger correlation co-efficients as shown in Table 2. This is because they produced more rain over the hills in better agreement with observations as shown in Figure 4. However, the 12 km model was still missing 11–24% of the observed area-averaged rain accumulations, with the largest model bias again over the Lake District.

Looking at Table 2 it would initially appear that the 4 km forecasts of orographic rain are reasonably accurate, with smaller RMSEs and higher correlation co-efficients than the 12 km forecasts. However Table 3 tells a different story. It seems that the 4 km operational forecasts produced up to 18% more area-averaged rain over the hills of the UK than observed by the rain gauges. Too much rain is produced at most rain gauge locations as shown in Figure 4. In order to investigate the possible differences in frontal rain amounts, two regions were selected over the sea as shown by the boxes drawn with dotted lines in Figure 1. These lie immediately upstream of the hills in North Wales and the Lake District. It was found that for the same times as sampled over orography, the 4 km forecasts produced just over 10% more area-averaged rain over the sea than the 1.5 km forecasts. This suggests that the prediction of too much rain over the hills is actually a result of the simulated frontal systems producing too much rain. The fact that it is nothing to do with the representation of orography will be further demonstrated in the next section.

The operational 1.5 km forecasts during 2010/2011 produced average rainfall distributions over the Lake District and Wales which look very similar to those observed by the rain gauge network. This is demonstrated for the Lake District in Figure 5. The area-averaged rainfall amounts are exactly the same as observed in Wales and only 2% less than observed in the Lake District (Table 3). The RMSE is 5.6 mm day−1 and the correlation co-efficient is 0.89 when averaged for Wales and the Lake District (Table 2). The 1.5 km operational forecasts therefore do an excellent job in reproducing the observed rainfall distributions in Wales and the Lake District. However, the maximum value is 30% less than observed over the Lake District and 19% less than observed in Wales.

Figure 5.

(a) Temporally averaged rain accumulations (colour bar in mm day−1) over the Lake District for all warm sector cases identified during 2010/2011 as forecast by the 1.5 km model. Contour lines show the underlying model orography (metres) while the asterisks show the positions of the rain gauges. The straight black line marks the position of the vertical transect shown in Figure 8. (b) Temporally averaged rain accumulations (mm day−1) observed by the rain gauges using the same colour scale as panel (a), while the grey shading and contour lines show the 1.5 km model orography (metres)

To summarize the results in this section for cases of warm sector flow, the amount of orographic rain enhancement produced by the Met Office operational forecasts increases as the horizontal grid spacing is reduced, providing better agreement with observations and improving mean forecast accuracy. The 1.5 km forecasts produce the correct amount of area-averaged rain, with errors of less than 2%. Maximum rain enhancements are produced in the correct location, although their magnitudes are smaller than observed. Forecasts using grid spacings larger than 10 km would benefit from a scheme to parameterize the effects of sub-grid scale orography on the rain field, as not enough rain is produced over the hills of the UK.

3.2 1.5 km simulations with different orography

When the horizontal model grid spacing is reduced the underlying hills are better represented, as demonstrated by Figure 1. However, even in the absence of orography the finer horizontal grid spacing will be able to resolve smaller scale features in the atmosphere, while large-scale features are also better represented. When the model is run with a different horizontal grid spacing it is often necessary to make other changes to the model set-up, such as the time step used. These additional changes may also have an effect on the forecast rain fields. A simulation of the prolonged warm sector orographic rain event which occurred over the Lake District on 15 January 2011 was produced with a horizontal grid spacing of 1.5 km. This simulation is referred to as simulation P because a prognostic rain variable was used. The simulation was initialized using the operational analysis at 0300 UTC and driven using boundary conditions from the operational 12 km forecast. The synoptic situation at 1200 UTC on this day is shown in Figure 2. Simulation P produced an area-averaged rainfall over the hills of almost 60 mm day−1, with a maximum value of 154 mm day−1 immediately to the lee of the highest model peak. Three additional simulations were produced, which were identical to simulation P except that the orography was replaced with that used by the 40, 12 and 4 km models. These simulations will be referred to as simulations P40, P12 and P4, respectively. For P40 and P12 the orography data sets were bi-linearly interpolated onto the 1.5 km resolution model grid. As the 1.5 km model domain is larger than the 4 km model domain this could not be done for P4. Instead the 1.5 km orography was smoothed to produce surface heights which are similar to those used by the 4 km model.

Table 4 gives the percentage reduction in rain accumulations produced by simulations P40, P12 and P4 compared to simulation P. Comparison against the simulation with high resolution orography instead of against observations enables use of the entire model rain field instead of using only those values at rain gauge locations. This approach is justified by the fact that the 1.5 km forecasts are very accurate in terms of the area-averaged rain accumulations produced over the hills and the horizontal distribution of the rain, as shown in the previous section.

Table 4. Percentage changes in rain accumulations produced by the simulations with 1.5 km grid spacing when the 1.5 km orography is replaced with that used in the 4, 12 and 40 km models
Model orographySimulation referenceChange in area average (%)Change in maximum value (%)
  1. Results are for the 15 January 2011 orographic rain case over the Lake District.

4 kmP4− 5− 4
12 kmP12− 10− 24
40 kmP40− 23− 53

Table 4 shows that simulation P4 reduced the area-averaged rain by 5% compared to simulation P. The fact that the operational 4 km forecasts produce too much area-averaged rain can therefore not be explained by the representation of the orography. Using increasingly lower resolution orography while keeping everything else the same has the effect of reducing the amount of rain produced over the hills. The difference in rain accumulations between simulations P40 and P is shown in Figure 6. Much less rain is produced over the hills by simulation P40, with the maximum value reduced by 53% compared to simulation P (Table 4). The model surface in the surrounding low-lying areas is higher in simulation P40 than in simulation P, with the result that the rainfall over the surrounding low-lying areas is slightly increased in simulation P40 compared to simulation P. This is particularly true over the valley separating the Lake District from the Pennines where the air remains too moist because the Lake District upstream did not remove enough water from the atmosphere. The differences between simulations P12 and P are similar to the differences between P40 and P, but the magnitudes of the differences are smaller. The maximum rainfall over the hills produced by simulation P12 is 24% less than that produced by simulation P. Simulations P40 and P12 produce 23 and 10% less area-averaged rain than simulation P respectively (Table 4). Changes to the underlying orography therefore produce significant changes in the predicted area-averaged rain accumulations. It is likely, however, that some of the differences in the operational forecasts are due to other changes in model set-up, e.g. the vertical or horizontal grid spacing or the time step used.

Figure 6.

Differences in rain accumulations (contour lines in mm day−1) between simulations P and P40. Solid/dashed lines show regions where the 40 km model orography produces less/more rain than the 1.5 km model orography and the thick line shows the zero contour. Grey shading shows the original 1.5 km model orography used in simulation P (metres)

The operational 12 km forecasts did not use a prognostic rain variable and as a result they neglected the horizontal advection of falling raindrops. Simulation P12 did use a prognostic rain variable as the set-up was the same as for the UKV. Therefore, an additional simulation was performed in which the advection of falling raindrops was neglected, referred to as NP12. The difference between simulations NP12 and P12 are shown in Figure 7. It can be seen that neglecting the advection of falling raindrops for cases like this one with fast low-level winds will result in too much rain falling on the windward slope and too little falling on the lee slopes. Similar results were obtained using 1.5 km model orography when the prognostic rain variable was not used. Lean and Browning (2012) also demonstrated the importance of wind drift when using 1.5 km model orography for the 18 November 2009 case of orographic rain over the Lake District.

Figure 7.

Differences in rain accumulations (contour lines in mm day−1) between simulations P12 and NP12. Solid/dashed lines show regions where neglecting the horizontal advection of falling raindrops increases/decreases the surface rainfall and the thick line shows the zero difference contour. Grey shading shows the underlying 12 km model orography used in both simulations (metres)

A vertical transect has been selected through the model domain so as to pass directly over the highest peaks of the Lake District, oriented along the mean 850 hPa wind direction. Its position is shown by the line in Figure 5(a). The total cloud water and ice mixing ratio QT (kg kg−1) along this transect is shown in Figure 8, averaged from 0800 UTC on 15 January 2011 until 0100 UTC the following morning. This was calculated as QT = Qliquid + Qice, where Qliquid is the liquid water mixing ratio and Qice is the ice mixing ratio. The melting level was at an altitude of approximately 2.2 km on this day. In simulation P, ascent over the hills increases QT by up to a factor of 3 compared to the upstream value as shown in Figure 8(c). Rain rates increase towards lower levels all the way to the surface over the hills because there is no dry sub-cloud layer to evaporate the raindrops. This increase in rainfall rates with decreasing altitude is consistent with the seeder-feeder effect, whereby pre-existing raindrops falling from aloft grow rapidly by accretion of orographic cloud water. The maximum rainfall rates near the surface are downstream of the QT maxima aloft due to the horizontal advection of raindrops by the strong winds during the time it takes for them to fall to the surface. Comparing Figure 8(c) with Figure 8(a) and (b) demonstrates that the lower hills in simulations P40 and P12 produce smaller increases in QT. Rain rates still increase with decreasing altitude towards the surface but the rate of increase is slower.

Figure 8.

Cross sections of the total cloud water mixing ratio QT (grey scale, kg kg−1) along the transect shown in Figure 5(a) from simulations (a) P40, (b) P12 and (c) P. QT was calculated as Qliquid + Qice, where Qliquid and Qice are the liquid water and ice mixing ratios respectively. Fields are averaged from 0800 UTC on 15 January 2011 until 0100 UTC the following morning. Solid and dashed contour lines show model level rain and snow rates every 0.0002 kg m−2 s−1. Black silhouettes show the underlying model orography. The south-west (upstream) end is on the left hand side

4 Conclusions

The strongest enhancement of rain by flow over orography is known to occur within warm sectors of depressions, which are characterized by strong, warm and moist low-level flows from the southwest. The performance of the Met Office operational weather forecasts were assessed against rain gauge observations for a large number of such cases: 12 over the Lake District in Cumbria (North-West England), 12 over the hills of Wales and 7 over the mountains of South-West Scotland. Patterns of mean orographic rainfall, produced by averaging the daily rainfall accumulations observed by the rain gauges over all selected cases, show orographic rain enhancement over the first hills encountered by the southwesterly flow. The largest amounts of rain fall over the lee side slopes due to the horizontal advection of falling raindrops. Subsequent hills are unable to produce as much enhancement due to the air being much drier. Averaging the rainfall accumulations over a large number of cases acts to remove horizontal variations produced by non-orographic effects while also averaging out errors in the frontal rain intensities and locations.

The operational forecasts using 1.5 km grid spacing produced realistic looking rainfall patterns on average with a correlation co-efficient of 0.89 and an area-averaged rain accumulation error of less than 2%. Rain rates increase with decreasing altitude in the model, consistent with the seeder-feeder effect. The maximum rainfall accumulations are still on average 20–30% less than observed. Increasing the horizontal grid spacing in the operational weather forecast model reduces the amount of rain produced over the hills, thereby reducing forecast accuracy. The mean area-averaged rain accumulations produced by the 12 km forecasts are up to 24% smaller than observed. The mean area-averaged rain accumulations produced by the 40 km forecasts are up to 48% smaller than observed. Forecasts using grid spacings larger than 10 km would therefore benefit from a scheme to parameterize the effects of sub-grid scale orography on the rain field, as not enough rain is produced over the hills of the UK.

In additional simulations of the 15 January 2011 case over the Lake District at 1.5 km grid spacing, replacing the orography with that used by the 12 and 40 km models reduced the area-averaged rain accumulations by 10 and 23% respectively. These changes were due to reduced cloud water and ice mixing ratios over the lower hills resulting in slower increases in rain rate with decreasing altitude. Changes to the underlying orography, therefore, produce significant changes in the predicted area-averaged rain accumulations. It is likely, however, that some of the differences in the operational forecasts are due to other changes in model set-up, e.g. the vertical or horizontal grid spacing or the time step used.

It was demonstrated that neglecting the horizontal advection of falling rain drops results in too much rain falling on the windward slope and not enough falling on the lee slope. It is therefore very important to account for this effect in order to predict the location of the surface rainfall correctly.

The operational rain forecasts using a 4 km grid spacing produced too much rain over the hills compared to both the rain gauge observations and the 1.5 km operational forecasts. They also produced more rain than the 1.5 km forecasts over the sea immediately upstream of the hills. It was demonstrated that the prediction of too much rain by the 4 km operational forecasts could not be explained by their representation of the orography.

Acknowledgements

This analysis is based upon rainfall data kindly supplied by the Environment Agency (Environment Agency ©) and SEPA (SEPA ©). We acknowledge Jorge Bornemann for providing the orography ancillary files for the 1.5 km simulations shown in Section '1.5 km simulations with different orography' and Rob Warren (personal communication) for carrying out preliminary research on this subject using case study simulations.

Ancillary