The benefits of the Met Office variable resolution NWP model for forecasting convection

Authors


ABSTRACT

High-resolution NWP models which can explicitly allow convection (albeit poorly resolved) are usually run in limited-area domains, and are nested inside coarser resolution models with parametrized convection. The mismatch of the grids and model physics at the boundaries of the limited-area fine resolution model can be a major source of model error. Two major issues are the change in the representation of convection (parameterized to explicit) as air enters the fine resolution model and the limited boundary updating frequency. In this paper, a variable-grid, fine-resolution, limited-area version of the Met Office's Unified Model (UM), developed with the aim of addressing this and related problems with nested models is described. In this variable resolution model, the grid size varies smoothly from coarser (but still convection permitting) resolution at the outer boundaries to a uniform fine resolution in the interior of the domain. In this paper we present results from a comparison of this variable grid model with the analogous results from an equivalent nested model set with uniform high-resolution model nested inside a lower resolution one. The comparison is carried out for a number of convective cases. It is found that the variable resolution model gives very similar results to the nested model system in the inner fixed resolution part of the domain away from the boundaries, both in individual case studies and when statistics are aggregated over cases. This gives confidence in the validity of the variable resolution approach. It is shown that the variable resolution model also gives the hoped for benefits of reducing artefacts at the boundaries.

1. Introduction

Until recently only models with gridlength more than 10 km and parametrized convection have been used in conventional operational numerical weather prediction (NWP), but the quantitative forecasting of precipitation from severe convection has had very limited success using this approach. The development of high resolution NWP models has led to improved forecasting capability for severe events and NWP models with gridlength less than 5 km are now common. However, with gridlength more than about 4 km, large scale convection must still rely on a parameterization scheme. An alternative approach is to run higher resolution models which allow convection (albeit poorly resolved) to occur explicitly. This approach is showing considerable promise (Lean et al., 2008), especially where details of surface forcing (land/sea contrast, orography and land use) play a dominant role in controlling where convection is triggered. However, such high resolution models inevitably have to be run over relatively small areas, nested inside coarser resolution models which do not explicitly represent convection.

Most nested models, including the Met Office's Unified Model (UM), adopt a non-interactive approach in which a coarse resolution model is run to provide time-dependent lateral boundary conditions (LBCs) for a high resolution model with open boundaries nested within the coarse resolution domain: see, for instance, the reviews and critiques by Staniforth (1997), Warner et al. (1997), Laprise et al. (2008) and Davies (pers. comm., 2011). The various problems associated with LBCs in nested models are well documented in these reviews and by Davies (1983), Errico et al. (1993), Alpert et al. (1996) and Paegle et al. (1997). For instance, these boundary conditions (LBCs) are often over-specified and hence introduce numerical errors near the boundaries, especially near the out-flow boundaries (Robert and Yakimiw, 1986). Sometimes, this can even lead to numerical instability (Baumhefner and Perkey, 1982). Also, the mismatch of the grids and the model physics at the boundaries of the limited-area fine resolution model can be a major source of model error, see Nutter et al. (2004) for a detailed analysis of this issue in a modified barotropic channel model. To reduce the impact of these computational errors introduced by the LBCs, blending (or relaxation) is commonly used, see Davies (pers. comm., 2011) for a description of this in the UM code, and Marbaix et al. (2003) for a sensitivity study. However, this in turn can destabilize the dynamical balance of an incoming flow (Staniforth, 1997). Horizontal diffusion can smooth out some of this undesirable noise, but this can also smooth out useful information provided by the already poorly resolved coarse resolution model. In the particular case of precipitation forecasts, problems are often seen with explicit convection taking quite a distance to spin up as an unstable flow enters the domain (Lean et al., 2008). In addition practical models usually update the boundary conditions significantly less often than every time step and this can lead to artefacts, particularly in frontal rainband features.

A possible solution to overcome these difficulties is a variable resolution model. Courtier et al. (1991) and Cullen (1993) described the strategies initiated by Meteo-France and the UK Met Office respectively, and the possible benefits to be gained. Côté et al. (1998a, 1998b) review the design implications in detail, and outline the implementation into the GEM model used by the Canadian Meteorological Centre. Fox-Rabinovitz et al. (1997) and Fox-Rabinovitz (2000) performed numerical experiments with a stretched grid version of the dynamical core of the Goddard Earth Observing System a general circulation model. Particular consideration is given to Côté et al. (1998b) and Fox-Rabinovitz et al. (2000) who describe a detailed comparison between their respective global variable-resolution models and high uniform resolution models with respective emphases on mesoscale phenomena and the effect of orography. In all these studies, the potential benefits were identified, as noted recently by Davies (pers. comm., 2011), who also drew attention to possible limitations due to greater costs and issues concerned with parameterizations at different grid scales. At the UK Met Office a variable-grid, fine-resolution, limited-area numerical weather forecast (NWP) model, based on the UM code has been developed. Note that, unlike the cases described above, it is a limited-area model, rather than a global model. The grid size varies smoothly from coarse resolution at the outer boundaries to a uniform fine resolution in the interior of the domain. The variable resolution region allows replacement of one nest with an effectively two way nested system which is updated at every time step. Having a variable resolution model also enables movement of the lateral boundaries with the driving model far away from the region of interest (forecasting region) at much lower cost than simply extending the high resolution domain.

This paper will describe the variable resolution grid design and test results using this variable grid. A comparison between the variable resolution model with an equivalent set of conventionally nested models will be presented. This study will focus on the representation of precipitation in the model, looking particularly at the convection spin up and initiation issues.

2. Numerical model setup

2.1. Model description

The current UM solves the non-hydrostatic, deep atmosphere dynamic equations using a semi-implicit,semi-Lagrangian numerical scheme (Davies et al., 2005). The model runs on a rotated latitude/longitude horizontal grid with Arakawa C staggering. It has a hybrid height-based vertical coordinate system, which is terrain-following near the surface and horizontal (in height) at the model top. The model level spacing is variable but defined to vary smoothly, with the grid stretched quadratically throughout most of the model. A Charney-Philips staggered grid is used in the vertical. The UM includes a comprehensive set of parameterizations, including two-stream radiation (Edwards and Slingo, 1996), a nine-tile surface exchange scheme (MOSES II, Essery et al., 2001), boundary layer dynamics (Lock et al., 2000) and mixed phase cloud microphysics (Wilson and Ballard, 1999). It also optionally includes a mass flux convection parameterization (Gregory and Rowntree, 1990), the use of which is discussed more fully in the next section.

2.2. Convection and diffusion

The Met Office has a 4 km UK model which is being replaced by a 1.5 km (variable resolution) one. The traditional low resolution (gridlength greater than 10 km) models suffer from a number of well known problems stemming from the use of the convection parameterization. In general the convection does not correctly organize and often does not have sufficient intensity. These problems are greatly improved in the 4 km UK model. It is hoped that higher resolution models would be able to help this situation by resolving the convection explicitly. However there is a lot of evidence that at order 1 km gridlength, convection is still severely under-resolved and this leads to problems. At 4 km resolution it is found that neither running with its conventional convection parameterization as used in lower resolution models or running with no convection parameterization produces satisfactory results. As discussed by Lean et al. (2008) and Roberts (2003) it has been found that the best option is to use the convection parameterization but with the mass flux limited to encourage strong convection to take place explicitly. In practice the mass flux is limited in such a way as to encourage all convective rain to be produced explicitly. However, it is clear that solutions of this type do not produce a satisfactory representation of convection in all situations: erring towards the explicit convection side tends to miss shallow convection (particularly in winter). When convection is produced explicitly it tends to have delayed initiation and then be too strong with the convective cells too large. These are artefacts of the large gridlength relative to the scales of the convection.

By contrast, the 1.5 km resolution model does much better at resolving the dynamics of convection even though it is still under-resolved. It is found that the best practical solution is to run it without a convective parameterization scheme although artefacts due to the grid resolution are still present. There is still an issue with very shallow showers and, in future, it may be necessary to develop a shallow convection parameterization. The 1.5 km model also has an advantage in that it contains a better representation of orography and other land surface parameters. In common with many NWP models, the UK4 uses horizontal diffusion to control the convective scales and prevent them from collapsing to the gridscale. In the 1.5 km models a Smagorinsky type turbulence scheme based on the sub-grid model used in the Met Office Large-eddy simulation (LES) (Brown et al., 1994) is used which seeks to parameterize sub-grid turbulence.

2.3. Variable resolution UM

The Met Office horizontal variable resolution UM shares the dynamical core with the regular resolution UM. However, the horizontal grid spacing is no longer uniform. Instead a variable resolution grid has been designed which varies smoothly from a high resolution area in the interior domain to a coarse resolution outer domain. The whole model domain is divided into three regions. The inner high resolution uniform resolution region, the outer coarse resolution region, and in between is the transition zone (see Figures 1 and 2). In this variable resolution transition zone, the grid varies smoothly from fine resolution in the middle to coarse resolution toward the outer boundaries in each direction. As described by Davies (1983), Vichnevetsky (1986) and Fox-Rabinovitz et al. (1997), a smoothly-varying grid can help to reduce the numerical errors introduced by the variable grid structure, such as local flow distortion and degradation caused by the resolution increase, or wave reflection caused by the spurious group velocity change due to the resolution change.

Figure 1.

A schematic picture of a variable resolution grid domain

Figure 2.

UKV orography (L) and model domain (R). The area of the right hand figure defines the outer boundary of the UKV domain. The inner rectangle is the region of the domain with a 1.5 km grid, the area between the inner and second rectangle is the transition zone between 1.5 and 4 km and the area outside the second rectangle is the 4 km area. This figure is available in colour online at wileyonlinelibrary.com/journal/met

The Met Office horizontal variable resolution model defines the grids in the same way as the uniform resolution model counterpart. That is, each grid cell is rectangular, the horizontal grid staggering arrangement is the same as for an Arakawa C grid, with wind components u and v arranged on the same rotated latitude/longitude as the pressure term. The essential change from the uniform resolution is that the grid spacing is now non-uniform, which shall be described in detail.

In each of the horizontal dimensions (see Figure 1), a uniform fine resolution area is defined in the middle, with a grid length Δs. The grid length is then stretched at a constant stretching (or inflation) factor r, that is Δsi+1 = rΔsi until the grid size Δs reaches its desirable coarse resolution length. The domain is then extended to a further uniform coarse resolution region in the outer domain, as described in Côté et al. (1998a). This is a very effective way to stretch the grid, for each successive doubling of resolution, only ln2/lnr number of points is needed. For example, if an inflation ratio of 10% is chosen, that is r = 1.1, then ln2/lnr ≈ 7 and only 7 grid points are needed to increase from the interior fine resolution Δs to 2Δs and a further 7 points to 4Δs. So, for a 1 km fine resolution domain in the middle, with 14 point variable resolution zone, the resolution is stretched to 4 km.

In the UK 1.5 km variable resolution model (UKV), the inflation ratios are set to 3.8 and 4.1% along latitude and longitude direction respectively. Figure 2 shows the UKV orography and model domain. There are three sub-domains, the inner 1.5 km resolution domain with 622 × 810 grid points in longitude and latitude direction, respectively. The narrow zone between the inner domain and the second domain is the transition zone, in which the grid spacing (resolution) varies from 1.5 to 4 km. A further 4 km coarse resolution zone is than added to form the outer area of the UKV domain. Note that, as a result of stretching, in this outer area the grid boxes are either 4 × 4 km (in the corner areas) or 4 × 1.5 km (to the east or west of the red line) or 1.5 × 4 km. In total, there are 744 × 928 grid points in the UKV.

In the light of the discussion in Section '2.2. Convection and diffusion' it is clear that there is a question about what to do about the treatment of convection in the variable resolution model given that the UK4 runs with a mass flux limited convection scheme but the 1.5 km model is run with no convection scheme. Currently the UKV model does not use a convection scheme over the whole domain. Although this simplifies things in that it is not necessary to write gridlength dependent parameterizations it could potentially lead to problems. It is known from previous research (Roberts, 2003) that running the 4 km model with no convection scheme produces too intense showers. However, in the UKV, the 4 × 4 km grid squares are only at the corners of the domain where this effect on the area of interest in the central 1.5 km part of the domain is likely to be limited. In the other regions around the edge (which are more likely to affect the centre of the domain) the grid squares are 1.5 × 4 km which means that running with no convection scheme is likely to be more justified because of the reduced area. This is borne out by the fact that the model produces acceptable results when run in this way as shown in the present paper.

In the present paper the performance of UKV with that of the 4 km UK model (UK4) is compared, and also with UKR, a nested system of 1.5 and 4 km one-way nested models. UKR is set up as an equivalent UK fixed resolution model with a 1.5 km resolution model (UK1p5) exactly the same size as the UKV's inner domain, one way nested with a boundary updating frequency of 30 min within a 4 km resolution model (UK4) which covers the same domain as the UKV.

Both UKV and UKR (UK4 + UK1p5) models are run with 70 vertical levels on a terrain-following hybrid-height vertical co-ordinate with Charney-Philips staggering. The soil moisture fields are generated from observations using the UM surface exchange scheme (Smith et al., 2006). A modified mass flux convection scheme as described by Roberts (2003) is used in the UKR's 4 km coarse resolution forcing model UK4, while no convection schemes are used in the UKR's 1.5 km model UK1p5 and the UKV model.

The Met Office's current 12 km resolution North Atlantic European model was run to provide the initial condition and boundary values for the 4 km resolution UKR and UKV models. For the purposes of the comparison between the UKV model and the nested system described in the present paper there was no additional data assimilation in the high resolution models with any high resolution structure spinning up from the 12 km starting data. This is in contrast to the operational UKV model which uses 3d-var data assimilation on a 3 h cycle with additional nudging of radar rain rates. Currently this is implemented with data assimilation being carried out on a 3 km grid with data being interpolated to and from the UKV grid.

3. Computational efficiency of the variable resolution model

In practice, an important consideration is the computational efficiency of the variable resolution model. If the variable resolution code were to add a great deal to the cost of the model this would negate the other benefits (for example the boundary effects described later could be made less important by simply increasing the size of the domain).

A large effort was put into developing an efficient departure point search routine in the interpolation code, since this has been identified as a bottleneck for the variable resolution UM code. The look-up table method, in which the horizontal variable grid is meshed onto a regular grid, with the finest (smallest) variable resolution grid spacing, to create a look-up table, is used for the UKV model. Several test cases have been set up to test the code efficiency, especially two idealized experiments, a flow over a hill and a cold pool case. Both were run with a uniform grid structure, using the usual regular resolution UM code compared with the variable resolution code. These tests showed a less than 10% difference in CPU time.

Next, the CPU rate is introduced, defined as the CPU time used for each grid-box, each time-step, in order to compare the computational efficiency of the variable resolution model against an equivalent nested system of regular resolution models in a real forecasting environment. A nested forecasting model will have to run at least two models, a high resolution model covering the area of interest, and a coarse resolution model to supply the boundary conditions for the high resolution model. The comparisons were done on the same computing platform, namely the SX6 of the NEC supercomputer, and hence with the same parallelization overhead. The scalability of the UM is that going from 3 to 6 SX8 nodes gave a speed up of 1.75 (2.0 being perfect scalability). The nested forecasting system implies certain overheads in terms of CPU time. That is to produce boundary files at a regular interval, the parallelization process is run for both models, and further requires two models to be run for a single forecast.

A convective event on 25 August 2005 was used as the timing study case. The synoptic situation consisted of a westerly flow following the passage of a cold front associated with a surprisingly deep low for this season. To save on overall computing costs, a small domain covering only the Southeast of England was used for this study. All models are run for 12 h forecasting time (11 h model run time), with a 50 s time-step and 38 vertical levels. The total number of grid-boxes is the total number of horizontal grids times 38 levels, and the total number of time-steps is 792 for each model. The CPU rates are then the total number of grid-boxes divided by the total number of time steps (792) for each model. The results of this comparison are shown in Table 1. As shown in this table, for this example, the CPU rate used is lower in the variable resolution model compared to the total nested system, mostly because of the overhead of running two models rather than one in the nested system. In terms of overall CPU used the variable resolution model comes out as expensive compared to either of the two models in the nested system because it has more grid points. However, the details of this comparison are dependent on the relative sizes of the domains involved. The CPU rates vary mostly due to the number of iterations required in the solver which depends on the grid-length and time step used. However it can be concluded from these results that the variable resolution model is not, intrinsically, much more expensive than the fixed resolution one.

Table 1. CPU time comparison of the real case study
Model4 km (m1)1.5 km (m2)Nested (m1 + m2)VarRes
Resolution (km)41.54/1.51.5–4
Number of horizontal grid288 × 360 = 103 680300 × 300 = 90 000m1 + m2 = 193 680484 × 556 = 269 104
Total elapsed CPU Times(s)22250.022161.044411.061301.0
CPU rate × 10−6 (cpu/tstep/grid-box)7.138.187.627.57

4. Case studies

To examine the performance of UKV, results of UKV and UKR covering the domain of UK1p5 were compared. Special attention is paid to the representation of convection and in particular spin up of explicit convection at the boundaries as highlighted by Lean et al. (2008). Two types of convective events are included:

  1. organized convection advected in from outside the domain, and,

  2. initiation of convective storms and showers within the domain.

A variety of cases (see Table 2), including some very strong sharp frontal systems (e.g. 8 January 2008 and 17 June 2009), and some weak scattered shower events (e.g. 14 April 2008), were run. All runs were for 18 h, with a total of 16 such runs as listed in Table 1. As expected, in all the cases the UKV and UK1p5 produced very similar results over the UK1p5 domain. Both models shared the same dynamic core and both have a better representation of the orography and land-sea contrasts than UK4.

Table 2. A list of the cases studied. There are 16 runs and 18 h forecasting time for each run
DateRun start hour (UTC)Case description
08 January 20080600,1200Frontal rain from west, and large cyclonic flow formed over Scotland and North of England.
14 April 20080000Scattered showers in the SE of England.
5 August 20081200,1800Scattered showers in the SE of England.
29 August 20080600Scattered showers in the SE of England.
30 August 20080600,1200Scattered showers in the SE of England.
29/30 October 20080600,1200Ottery St Mary storm.
10 June 20090000Scattered showers in the SE of England.
15 June 20090000Slow moving showers and storms in slack westerly flow over many parts of UK.
17 June 20090600Frontal rain, heavy in the north and west.
18 June 20090600Showers in strong westerly flow.
23 June 20090000Convective initiation over Pennines and N York Moors
23 July 20090600Line of heavy showers from SW peninsula and (to lesser degree) from Anglesey in SW flow.

4.1. Comparison of aggregated rainfall statistics

In this section statistics aggregated over all the cases run are examined in order to obtain an overall idea of the performance of the models. First, the overall amount of rain being produced by the three models. In Figure 3(a) the area-average rainfall rate over the UK1p5 domain is plotted as a function of the forecasting time averaged over all 16 model runs. For consistency, the UK1p5 and UKV model data are first aggregated onto the 4 km model grid. The general agreement between the three models is very good. As discussed by Lean et al. (2008), all models are expected to start with very small rainfall rates at T + 1 and then overshoot towards T + 6 as the instability builds up while the convection which was spinning up is released. These data confirm that the 4 km model spins up convection more slowly and then overshoots more. The key point for this study, however, is that the UK1p5 nested model produces very similar overall rain rate to the UKV, showing that having a variable resolution model does not, in itself, change the results too much compared to the equivalent nested system. The UKV tends to produce slightly more rain and this could be related to the boundary convection spin up issues discussed later.

Figure 3.

(a) Domain-averaged rainfall rate over the UK1p5 domain from all 16 runs. (b) Cell numbers as a function of rainfall rate threshold (mm/hr) over the UK1p5 domain averaged over all cases. The UK1p5 and UKV model data are aggregated onto the 4 km grid. The solid lines are from the UK1p5 model, the long-dashed lines are from the UKV model and the short-dashed lines are from the UK4 model

Figure 3(b) shows the number of cells as a function of rainfall rate threshold (mm h−1) over the UK1p5 domain averaged over all cases. As before, the UK1p5 and UKV model data are aggregated onto the 4 km model grid. There are significant differences between the models, especially at the lower end of the rainfall rate threshold. The difference can be as much as 50%, that is the number of cells in UK4 is only half those in UK1p5 and UKV. Again, the UKV and UK1p5 models produce very similar results. At the lower rain rate thresholds the UKV produces more cells which could be related to many small cells when the convection is spinning up at the boundaries.

Both these diagnostics imply that the UKV model produces encouragingly similar results to the equivalent nested system, UKR. In order to obtain more information on this the neighbourhood Fraction Skill Score (FSS) method described by Roberts and Lean (2008) has also been used. In this case it has been used to compare UKV against UK1p5 over the 1.5 km high resolution domain (as opposed to comparing the models against radar as is more normally done). This method uses probabilities of exceeding a threshold: the threshold may be either a fixed accumulation of rain or a percentage threshold (e.g. the top 80% of grid points in the domain) which removes any overall bias in the rainfall. The probabilities are calculated from the number of grid points which exceed the threshold over a square neighbourhood around each grid point. The size of the neighbourhood defines a scale over which the particular comparison is made. It is expected in convection resolving models that, due to the short predictability time of small scales, verification will be poor at the gridscale but will improve as the verification scale is increased. When the scale is increased to the size of the model domain the FSS simply relates to how the amount of rain over the whole domain compares.

In this case the FSS is calculated for the UKV compared to the UK1p5 as a function of horizontal scale for the rainfall accumulation from T + 6 to T + 9 aggregated over all the cases. Accumulation thresholds of 2 and 8 mm over the accumulation period and percentile thresholds of 95 and 80% are used.

Figure 4 shows the results of this calculation. The curves have the expected form, with low FSS scores at the gridscale increasing as the scale length increases. According to Roberts and Lean (2008) a measure of an acceptable forecast quality is an FSS value of 0.5 + fo where fo is the fractional coverage at the threshold concerned. For the 80% threshold this equates to 0.6 and for 95% 0.525. At the gridscale (extreme left of the curves) the FSS curves already have values around this and the curves increase rapidly, showing good agreement between the forecasts. At the right hand side of the curve the FSS in the case with accumulation thresholds tends to 1 which shows that the number of points above the threshold over the whole domain agrees. This is consistent with the domain average results shown previously. Hence the FSS analysis shows, generally, good agreement between the models with most differences being at the gridscale as would be expected from predictability considerations.

Figure 4.

The UKV against UK1p5 Fraction Skill Score (FSS) for rainfall accumulation over T + 6 to T + 9 using accumulation thresholds of 2.0 mm (solid line) and 8.0 mm (dashed line) (a) and using percentile thresholds of 95% (solid) and 80% (dashed) (b)

4.2. Examination of specific convective cases

The next sections are devoted to a more detailed examination of some specific cases. It has already been shown that when aggregated the results from all the cases look very similar when comparing the UKV to the equivalent nested system, UKR. However, it is instructive to understand when there are differences in specific cases. First, the 15 June 2009 case is analysed here. This was a case where convective showers initiated over the Pennines. Figure 5 shows a snapshot of the rainfall rate for the case of 15 June 2009, from the model outputs and radar observations at T + 8 h or 1100 UTC, the time the convective storm was initiated. It is clear that all models performed well and managed to initiate the convective storm at the right time and roughly at the right location. To examine this further, Figure 6 shows the averaged rain rate around the convective cell over a 0.4° by 0.4° area. Consistently with the previous figure, all models initiate the convective storm roughly at the same time. It also shows that the UK4 model produced a slightly more intense cell than others. Similar results were found for the case of 23 June 2009 (not shown here).

Figure 5.

Comparison of model and radar rainfall rate for 15 June 2009

Figure 6.

Area averaged rainfall rate for 15 June 2009 over a 0.4° by 0.4° small area around the convective storm initiation. The solid line is from the UK1p5 model, the long-dashed line is from the UKV model and the short-dashed line is from the UK4 model

Another important issue which was also highlighted by Lean et al. (2008) is the spin up of convection as air enters the domain. If the driving model uses a convection parameterization then explicit convection will take a finite length of time to initiate as the air enters the high resolution model. This can lead to regions free of showers near the inflow boundary which are pure artefacts of the location of the domain. It is hoped that one of the benefits of the variable resolution model is that the low and variable resolution parts of the domain should allow showers to spin up before reaching the high resolution area. Effectively, the low resolution part of the domain is used to push the boundary spin up effects further away from the area of interest with lower cost than simply extending the high resolution domain. In order to investigate this the 17 June 2009 case with scattered showers in a westerly flow has been examined. Figure 7 shows accumulated rain amounts from the three models. An equivalent plot of meridional averages is shown in Figure 8. In the UK4 model the showers are quite slow to spin up, reflecting the slow initiation of showers with this gridlength. In the UK1p5 model which gets its boundary conditions from the UK4 there is also a noticeable although faster spin up effect. The convection spins up faster in a 1.5 km model than at 4 km due to the shorter gridlength. In comparison, the UKV model spins up the convection much faster, although some spin up is still clearly evident in the domain shown. The UKV model is therefore more successful than the nested system at moving the spin up region away from the inner domain. This is due to the fact that the convection spins up faster if the grid cells are smaller and the grid cells upwind of the inner domain are smaller partly due to the fact that there is the variable region and partly due to the 1.5:4 aspect ratio of the gridlength in the most part of the low resolution region.

Figure 7.

Total rain accumulation over the 18 h forecasting period for 17 June 2009 case in the western portion of the UK1p5 domain. From UK1p5 (a), UKV (b) and UK4 (c). A much improved “spin up” of convection in the UKV can be seen

Figure 8.

Meridional average total rain accumulation of the 19 h forecasting period for 17 June 2009 case. The solid line is from UK1p5 model, the short-dashed line is from the UKV model and the long-dashed line is from the UK4

4.3. Examination of specific frontal cases

Next follows analysis of the models' performance when strong frontal systems are present. On 8 January 2008 there was a cold front crossing from west to east in the evening with strong and sharp line convection. All models show very similar representations of the front and, when compared with radar observations, the representation of the line convection is remarkably good.

Figure 9 shows the forecast rainfall rate at T + 6 h. It is clear that all models give broadly very similar results for the intensity and the position of the line convection, and the cyclonic rain structure associated with the wind behind the frontal line. As would be expected, the front is sharper in the high resolution models but, again, the key point is the similarity in the representation between the UKV and UKR models.

Figure 9.

Surface rain rate at T + 6 forecast time for the 8 January 2008 case from UK1p5 (a), UKV (b) and UK4 (c) models

However, looking in more detail at the region near the southern boundary, the boundary updating in the nested model has a profound effect on the spin-up of the frontal line structure. In order to investigate this in more detail, this case was rerun with the UKR nested models with only hourly updating of the boundary between the UK4 and the UK1p5 models. Figure 10 shows the broken frontal structure in the UK1p5 model caused by the boundary updating at 1 h and 30 min periods, compared with the frontal structure from the UKV model. The advantage of using the variable resolution model is clearly seen here. Even an updating frequency of 30 min used in this study in the UK1p5 model is clearly too long, especially for a fast moving front. In practice, updating of the boundaries of a nested system more frequently than every 30 min is often not practical due to the large sizes of the files involved. The variable resolution model can be regarded in this context as analogous to a two-way interactive nested model, with boundary updating at every time step, while the smooth transition between the inner high resolution area and the outer region in effect enlarges the effective region of validity.

Figure 10.

Surface rain rate at T + 6 forecast time for the 8 January 2008 case for the southwest portion of the UK1p5 domain. Parts (a) and (b) are from the nested 1.5 km UK1p5 model, (a) with hourly boundary updating and (b) with 30 min boundary updating. Part (c) is from the UKV model

5. Summary and discussion

In this paper, a variable-grid, fine-resolution, limited-area numerical model has been described. It is expected that, among other benefits, this model should give an improvement in the forecasting of convective precipitation. The grid size varies smoothly from coarse resolution, 4 km, at the outer boundaries to a uniform fine 1.5 km grid length in the interior of the domain. This model is intended to replace the existing 4 km resolution NWP model and become the Met Office new UK forecasting model. Having a lower resolution outer domain reduces the nesting ratio with the driving model or, alternatively, removes the need for an intermediate grid length model for which there might not be any other need. In this case it allows non-running of a 4 km model, which is a difficult grid length for representing convection. Some test results using this variable grid model have been presented and compared with those using an equivalent nested conventional set of 4 and 1.5 km models.

In all the cases studied the variable resolution model produces very similar results, within the inner high resolution part of the domain, as the 1.5 km model nested inside the 4 km model. This has been shown by aggregating results over a large number of cases. This is very encouraging in that it implies that, as would be hoped, variable resolution does not in itself change the results significantly. As would be expected, when significant differences do occur it is mainly in the area of the boundaries.

One obvious benefit of the variable resolution model is that in the nested system the boundaries are not updated as frequently as they should be due to the large amount of storage required and computational cost, and this can lead to artefacts. Particularly noticeable is the breaking up of fronts which is often observed. This often looks realistic but, on investigation, turns out to be due to the boundary updating in the model. It has been shown that the variable resolution model does not tend to introduce these artefacts.

A second important benefit is the mitigation of the effect of showers spinning up as they enter the domain of a high resolution model. In conventional models this can lead to an unrealistic zone with no showers inside the inflow boundary. The variable resolution model overcomes this problem partly by making the transition more gradual but also by adding more grid points at a lower cost than would have been the case with a fixed resolution model. In effect, the boundaries are pushed further away from the area of interest at lower cost due to the extra flexibility in design of the domain introduced by variable resolution.

In conclusion, the variable resolution model provides a way to realize the benefits of a high resolution model at a lower cost than would otherwise be possible by reducing the cost of moving the boundaries further away and by removing the need for an intermediate model.

Acknowledgements

We would like to thank Junichi Ishida, Terry Davies and Peter Clark for their contributions to the coding of the variable resolution UM and setting up the model. We would also like to thank Nigel Roberts for discussion of the cases and verification scores.

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