The impact of horizontal resolution on the ... - Wiley Online Library

Q. J. R. Meteorol. Soc. (2002), 128, pp. 2031–2044

The impact of horizontal resolution on the simulations of convective development over land By J. C. PETCH¤ , A. R. BROWN and M. E. B. GRAY Met Of ce, UK (Received 28 August 2001; revised 15 April 2002)

S UMMARY Cloud-resolving models (CRMs) can be used to provide subgrid information for use in improving the representation of the development of convection in large-scale models. However, for the CRM to be of value, it must itself give an accurate representation of the processes involved. In the work presented here we focus on the development of convection in simulations of both shallow and deep convection over land and consider sensitivity to the horizontal resolution in a CRM. In both shallow and deep cases it is found to be necessary to provide adequate resolution of the sub-cloud layer in order to obtain a satisfactory representation of the transport of moisture from the sub-cloud layer into the free troposphere. Typically this requires the horizontal grid spacings to be no coarser than around one quarter of the sub-cloud layer depth. Poorer resolution with the present model leads to signi cant delays in the development of convection. While a more sophisticated subgrid scheme could reduce the sensitivity to resolution, the work here has shown the resolution required to explicitly resolve the key processes. Using this improved resolution may be one technique for reducing the discrepancies between some model results and observations reported in earlier studies. K EYWORDS: ARM CRM Diurnal cycle

1.

I NTRODUCTION

The diurnal cycle of convection has a major impact on the energy balance of the Earth through the interaction of clouds with solar and infrared radiation. However, it is becoming apparent that most climate models tend to do a poor job of predicting the diurnal variability of convection over both oceans and land (e.g. Lin et al. 2000; Yang and Slingo 2001). One technique for improving the parametrizations in climate models is to use data from higher-resolution models such as cloud-resolving models (CRMs) to supplement observations. However, if CRMs are to be used in this way then it is important that they are validated as much as possible; in the case of the diurnal cycle, it is essential they reproduce the intensity and timing of convective events closely. The Atmospheric Radiation Measurement (ARM) program and the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) Working Group 4 are involved in a joint intercomparison project where results from various CRMs are being collated with the aim of using these data to improve parametrizations in largescale models. Observations taken at the ARM site based in the Southern Great Plains (SGP) of the US are used to force both CRMs and single-column versions of largescale models (SCMs) with the aim of using information from the CRMs to improve the parametrizations within the SCMs. The major ndings from the intercomparison of CRMs are described in Xu et al. (2002). Xu et al. (2002) found that although the majority of CRMs reproduced many aspects of the observations well, there were signi cant problems in capturing the timing of the initial development of convective events. In a number of events the development of convective precipitation in several CRMs was delayed by several hours relative to the observations. This is clearly a problem if results from CRMs are to be used to improve the timing of convection over land in large-scale models. A comparison ¤

Corresponding author: Met Of ce, London Road, Bracknell, Berkshire RG12 2SZ, UK. e-mail: jon.petch@metof ce.com c Crown copyright, 2002. °

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of two-dimensional (2D) and three-dimensional (3D) simulations from some models showed that the use of a third dimension had little impact on the timing of precipitation. However, suggestions for the delay included the coarse resolution of the CRMs (most used a horizontal grid spacing of 2 km), the lack of any mesoscale circulations in the initialization of the models, and the use of horizontally uniform large-scale forcing and surface uxes. It is likely that all of these suggestions for the delay will be important during some parts of the simulation. The work presented in this paper will investigate just one of these, the impact of resolution. There have been previous studies into the impacts of changes in horizontal grid length in CRM simulations of deep convection but all have considered convection over the ocean. Petch and Gray (2001), noting that most CRM studies typically used a 1 or 2 km horizontal grid length, considered the impact of reducing the grid length. Using data from the Tropical Ocean–Global Atmosphere-Coupled Ocean–Atmosphere Response Experiment (TOGA-COARE) to force the model, they showed that horizontal resolution had some impact on time-mean properties of convection and was very important for the timing of convective events. A 2 km grid length was shown to delay both the clearing and increase of cloud by between 3 and 6 hours when compared with both a 1 km and a 500 m horizontal grid length. Grabowski et al. (1998) compared horizontal grid lengths of 2 km and 200 m in a CRM forced using data from the Global Atmosphere Research Program (GARP) Atlantic Tropical Experiment (GATE) and also found that this had an impact on the timing of convective events but that in general it was not systematic. Although the mechanisms for the initiation and development of deep convection over the ocean are different to those over land (hence the difference in the strength and timing of the diurnal cycle), these previous studies do suggest that horizontal resolution may be important when modelling convection. Furthermore, obtaining realistic simulations of the initiation of deep convection over land, which is strongly forced from the surface, may be more critically dependent on having a reasonable representation of boundary-layer processes and the development of shallow-cumulus convection. Studies aimed speci cally at examining boundary-layer turbulence (e.g. Mason and Brown 1999) and shallow cumulus (e.g. Siebesma and Cuijpers 1995; Brown 1999) typically use grid spacings of 100 m or ner. Hence, even the nest resolutions used in the deep-convection simulations described above are at best marginal in terms of their ability to allow explicit resolution of these processes, and therefore rely heavily on their parametrization of subgrid transport. In the work presented here we will consider the impacts of the horizontal grid length in simulations of three cases of convection over the ARM SGP site. The CRM used is one which was seen to have a larger delay in the initiation of convection than several other CRMs for some of the rain events. First we consider a simulation of nonprecipitating shallow convection which is mostly driven by observed values of surface heat ux in the daytime. This case is of interest in its own right, and also conveniently illustrates many of the issues which are of relevance for cases of deeper convection. Second we will consider semi-idealized simulations of precipitating convection which is forced using observed surface heat uxes and interactive radiation from a 4-day period. Finally, we run one of the observational-based cases from Xu et al. (2002) to see if the increased resolution improves the CRM simulation when compared with observations. In each case we will focus on the initiation and development of the deep convection. Section 2 describes the shallow-cumulus case, section 3 describes the semi-idealized simulations of precipitating convection and section 4 describes the observational-based simulations of deep convection. A summary and conclusions are given in section 5.

IMPACTS OF RESOLUTION ON CONVECTIVE DEVELOPMENT

2.

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S IMULATION OF SHALLOW CUMULUS

The basic model is described by Shutts and Gray (1994) and only a short summary of the aspects relevant to the shallow-cumulus simulations is given here. The model provides a numerical simulation of the ltered Navier–Stokes equations subject to the anelastic approximation. Prognostic equations are carried for each of the three momentum components, and also for the conserved scalar variables, r T , the total water mixing ratio and TL , the liquid-water static energy. The latter is de ned through: TL D T C

.gz ¡ Lv rL / cp

(1)

where T is the temperature, g is the acceleration due to gravity, z is the height above the surface, L v is the latent heat of vaporization, r L is the liquid-water mixing ratio and cp is the speci c-heat capacity of air at constant pressure. The two scalar prognostic variables are advected using Leonard et al.’s (1993) ULTIMATE QUICKEST scheme, whereas momentum is advected using the Piacsek and Williams (1970) centred difference scheme. Of particular relevance for the present study is the fact that the model uses an all-or-nothing saturation scheme, with r L set diagnostically to be equal to max.0; rT ¡ rsat /, where rsat is the saturation mixing ratio. Heat and moisture uxes are imposed at the no-slip surface (which has a roughness length of 0.035 m). The horizontal boundary conditions are periodic. The top boundary is formed by a stress-free rigid lid, with a damping layer below it (but above the region of interest) to prevent re ection of gravity waves. The subgrid turbulence scheme is based on the Smagorinsky–Lilly model. This is essentially a three-dimensional version of a rst-order mixing-length closure. The subgrid stress tensor, ¿ ij , and the subgrid scalar ux, Y j , of a scalar X are parametrized through ³ ´ @ui @uj 2 ¿ij D ¡½l S Fm C @xj @xi ³ ´ @X 2 Yj D ¡½l S Fh @xj where 1 S D 2 2

³

@uj @ui C @xj @xi

´2 :

Here .u1 ; u2 ; u3 / is the velocity and ½ is the density. l is the neutral subgrid lengthscale. This has a constant value of l 0 , except very close to the surface where it becomes proportional to distance from the surface as described in Brown et al. (1994). Stability dependence is introduced through F m and F h which are functions of the local Richardson number, which is calculated taking account of the effects of moist processes as described in MacVean and Mason (1990). The effects of F m and F h are to give a sharp fall off of subgrid mixing ef ciency in stable conditions, with no mixing at all when the Richardson number exceeds a critical value of 0:25. The case considered in the present study is based on an idealization of observations from the ARM SGP site, and formed the basis of the sixth GCSS Working Group 1 intercomparison study (Brown et al. 2002), and so only brief details are given here. The initial pro les of potential temperature and water-vapour mixing ratio, valid at 0530 h local time (1130 UTC), are shown in Fig. 1(a). Random temperature perturbations,

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J. C. PETCH et al. Potential temperature (K)

290 3

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Figure 1. Initial conditions and forcing data for the shallow-cumulus simulation. (a) Initial pro les of temperature and water-vapour mixing ratio; (b) time series of imposed surface sensible- and latent-heat ux.

of maximum amplitude 0.1 K, were applied in the lowest 200 m in order to initiate turbulence. An initial wind of .10; 0/ m s ¡1 was speci ed at all levels, and a large-scale pressure gradient was imposed such that, with the Coriolis parameter appropriate for 36± N, this wind was in geostrophic balance. Time-varying surface uxes were imposed as shown in Fig. 1(b). Additional forcing terms (not detailed here) were also applied to represent the effects of radiation and large-scale advection, but separate tests con rmed that their in uence was small. The domain used was 6:4 km £ 6:4 km in the horizontal, with a depth of 4.4 km (and a damping layer above 3.5 km). The standard intercomparison run used a horizontal grid spacing of 67 m, which is typical of that commonly used for shallow-convection studies. Here additional runs were performed both with improved resolution (in order to look for numerical convergence) and also with resolution degraded in order to deliberately obtain an under-resolved turbulent boundary layer (as will often be the situation in deep-convection studies). This led to a series of runs with horizontal mesh spacings (1x) of 20 m, 40 m, 67 m, 100 m, 200 m, 400 m and 800 m. In all cases the basic length-scale of the subgrid model (l 0 ) was set to 0.23 times this spacing. A uniform vertical grid was used. Its spacing was 40 m, except in the highest-resolution run in which it was 20 m. In all bar the coarsest-resolution simulations the behaviour was qualitatively similar. In each case the very stable layer in the lowest 50 m (Fig. 1(a)) was rapidly eroded by the increasing surface sensible-heat ux, and a cloud-free convective boundary layer then grew through the initially slightly stable layer extending up to around 800 m. The rst clouds appeared at the top of this level, and the convective cloud top then rose steadily through the initially approximately conditionally neutral layer up to 2.5 km. The surface forcing was decreasing by the time the clouds reached the more stable layer above 2.5 km, and the convection gradually weakened with no clouds remaining in any of the simulations by 2000 h local time. Although, as noted above, the behaviour of most of the simulations was qualitatively similar, there were differences in the details, in particular with respect to the timing of the onset of cumulus convection. Even though uncertainties in the speci cation of the initial pro les and large-scale forcing mean that the observations cannot here be

IMPACTS OF RESOLUTION ON CONVECTIVE DEVELOPMENT 25

2 (b)

(a)

400 m 200 m 100 m 67 m 40 m 20 m

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Figure 2. Time series of (a) maximum cloud cover and (b) the maximum resolved vertical-velocity variance, hw 0 w 0 imax , from the shallow-cumulus simulations. Results are plotted for horizontal resolutions of 400 m, 200 m, 100 m, 67 m, 40 m and 20 m and these variances were calculated directly on the grids. The stars in (b) show 0:47w¤2 (where w¤ is the convective velocity scale). This is the maximum value of the best t to the free-convective observations of Lenschow et al. (1980).

used to provide a ‘truth’, we can still seek to nd evidence of numerical convergence with improving resolution—simulation results which appear to be converged may be reliable, whereas those that lie a signi cant distance from any converged result must certainly be regarded as unreliable. Figure 2(a) shows time series of the maximum cloud cover (at any one level) from the various simulations. This statistic provides a convenient way of illustrating the sensitivity of the simulated convection to resolution, and it should be emphasized that other statistics (e.g. total cloud cover, liquid-water path) show a consistent variation. The best-resolved simulations (horizontal resolutions of 20 m, 40 m, 67 m and 100 m) show reasonably converged behaviour, particularly after around 1200 h local time. This suggests that all of these resolutions are probably adequate to at least broadly capture the main cumulus circulations. Even here though, the timing of the onset of convection does show some sensitivity to resolution; the increase in maximum cloud cover from zero to values of around 15% occurs at similar rates but systematically later as the resolution becomes coarser. With 200 m resolution the delay is more serious (cloud cover increasing approximately one hour after that in the simulation with 20 m resolution) and the simulation never quite recovers to match the better-resolved ones. The 400 m resolution simulation rst produces clouds approximately another hour later, and in this case the clouds are clearly unrealistic, showing a very noisy pattern with no spatial coherence. The 800 m simulation results are not shown as that simulation completely failed to produce any clouds before producing mean saturation at around 1730 h local. The instability of the mean pro les to moist ascent then led to model failure in this case. The changes in behaviour as a function of resolution can be understood in terms of the representation of the turbulence in the convective boundary layer (CBL) before cloud formation, and in the sub-cloud layer (SCL) after cloud formation. Figure 2(b) shows time series of the maximum value of resolved vertical-velocity variance in the CBL/SCL from the various simulations. As buoyancy production of turbulence dominates over shear production in this case, the variance is expected to scale convectively. Therefore, the gure also shows the variation of 0:47w ¤2 , which is the maximum variance predicted

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by the best t to the free-convective observations of Lenschow et al. (1980). Here, w ¤ , the convective velocity scale, has been calculated using the height of the minimum in the buoyancy ux pro le as the length-scale. The minimum occurs at the top of the CBL before cloud formation and at the top of the SCL after cloud formation, and its height does not vary signi cantly with model resolution. Encouragingly, the best-resolved simulations are in good agreement with this observational result. However, with poorer resolution, the simulations are less able to explicitly represent the turbulent eddies, and the resolved vertical-velocity variance only increases at later times and also does not reach such large values. The relative lack of variability in the sub-cloud layer (illustrated here through the vertical-velocity variance) inhibits the ability of these simulations to form cumulus clouds. Accordingly, cloud formation is delayed, as shown in Fig. 2(a). The variation of the resolved variance (and hence of the timing of cloud formation) with resolution appears to be intuitively reasonable in terms of the number of grid points required in order to resolve the dominant eddies in the CBL/SCL. At 1000 h local time, all of the simulations have a CBL/SCL depth (z i ) of around 800 m. The means that the 20 m resolution simulation has 1x D z i =40 and the dominant eddies (with horizontal scale of around z i ) are well resolved. 40 m, 67 m and 100 m continue to provide broadly adequate resolution of these eddies (1x D z i =8 for 100 m spacing), but with 200 m grid spacing (1x D zi =4/ the errors introduced are much more serious. Unsurprisingly, 400 m spacing is worse again (only two points per z i ), and 800 m spacing completely fails to resolve any CBL turbulence at all.

3.

S EMI - IDEALIZED SIMULATIONS OF PRECIPITATING CONVECTION

The version of the model used for these simulations is con gured to run in 2-D but otherwise solves the same dynamical equations as the model used to simulate the shallow convection. The vertical domain size is 20 km using 120 levels with a stretched grid. The grid spacing stretches from 75 m in the boundary layer to 165 m in the free troposphere and then up to 250 m at the domain top. Surface uxes and surface skin temperature (for the thermal infrared radiation scheme) are prescribed from observations. Simulations are carried out using a xed horizontal domain of 250 km with horizontal grid lengths of 2 km, 1 km, 500 m, 250 m and 125 m. The ratio of the basic length-scale (l 0 ) to the horizontal grid length is kept xed at 0.14. This value is rather smaller than that used for the shallow-cumulus simulations, although separate tests suggested that the results were not sensitive to this choice. Additional parametrizations for the deep case include the more detailed vecategory bulk microphysical scheme of Swann (1998), with the adjustments described in Brown and Heyms eld (2001). With this parametrization, the model includes prognostic variables for total water substance (vapour and liquid), rain, snow, graupel and cloud-ice mixing ratio, and cloud-ice number concentration. As with the shallow simulation there is no subgrid condensation scheme so saturation in the grid box is required to produce liquid water. Also included is a fully interactive solar and thermal infrared radiation scheme which is described in Edwards and Slingo (1996), and is con gured in the same way as it has been used for climate research (Pope et al. 2000). This is a broad-band scheme with six bands in the solar and nine bands in the thermal infrared with all hydrometeor types (including graupel) explicitly treated using the methods described in Petch (1998). Although the radiation is called on every grid point in the model, it is only called at 5 minute intervals due to the computational expense of such a detailed scheme.

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Figure 3. Time series of insolation, surface sensible-heat ux and surface latent-heat ux used to force the model in the semi-idealized simulations. Shown is (a) the 4-day time series and (b) a diurnal composite of the 4 days, created and plotted to give maximum insolation at local noon.

The model is initialized and forced using data derived from the ARM SGP site; this is case A from Xu et al. (2002). Observed pro les of temperature, moisture and horizontal winds taken at 2330 UTC 26 June 1997 are used with the temperature in the lowest 200 m modi ed to include a random perturbation with a maximum amplitude of 0.25 K. Pro les of large-scale tendencies of heat and moisture which are applied in Xu et al. (2002) are ignored in this semi-idealized case, although the winds are relaxed back to observed as was done in that paper. The lack of any large-scale forcing simpli es the problem as the convection is mainly driven by diurnally varying forcing, i.e. surface uxes of latent and sensible heat and radiation; these are shown in Fig. 3 with a diurnal composite of the 4 days also shown. The diurnal composite (which is also used in the results from this run) is created using a time series of 1-hour means and then averaging the same time from all 4 days together. The data is plotted with local noon (i.e. the minimum solar zenith angle) at approximately 12 hours on the x-axis. The use of the full 4 days allows us to consider the complexities of multi-day simulations often used in CRM studies. The surface precipitation from the simulations using the range of resolutions is shown in Fig. 4(a) and a diurnal composite of the 4-day period (created in the same way as Fig. 3(b)) is shown in Fig 4(b). It can be clearly seen that the horizontal grid length has a large impact on the timing and strength of the precipitation. Typically, at lower resolutions the precipitation begins later and is stronger and more abrupt when it does nally begin; this is consistent with the errors seen with several models in Xu et al. (2002) when they compared precipitation with observations. On average over the 4 days, the 2 km grid-length simulation rains 6 hours later than the one using the 125 m grid length and, when it does begin to rain, it peaks at twice the rainfall rate of the higherresolution run. The rain rate in the higher-resolution simulations (500 m and above) typically builds up more steadily than that in the lower-resolution runs. Two other features from the multi-day plot of precipitation (Fig. 4(a)) are noteworthy. Firstly the general tendency for the lower-resolution runs to begin later and more abruptly can be seen on all days, showing that this effect is not an artefact of the initialization of the model. Secondly, it can be seen that in this type of complex precipitation simulation other secondary effects, distinct from the diurnal cycle of the surface and boundary layers, can also impact on the development of convection. This can be seen on the third day’s precipitation event where the simulation using the 125 m grid

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J. C. PETCH et al. 1

1

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Precipitation rate (mm hr )

2 km 1 km 500 m 250 m 125 m

1


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Figure 4. Time series of surface precipitation rate from the 4-day semi-idealized simulations of precipitating convection. Results are plotted for horizontal resolutions of 2 km, 1 km, 500 m, 250 m and 125 m. Shown is (a) the 4-day time series and (b) a diurnal composite of the 4 days, created and plotted to give maximum insolation at local noon. TABLE 1. T OTAL PRECI PI TABLE WATER (kg m¡2 ) AFTER 2.5 DAYS OF THE SEMI - IDEALIZED CASE Resolution

Precipitable water

Difference from 125 m

125 m 250 m 500 m 1 km 2 km

38.5 39.5 40.1 39.3 39.1

– 1.0 1.6 0.8 0.6

length begins to precipitate later than the lower-resolution runs. This is not consistent with previous days. However, it can be seen that there is a secondary peak in the rain rate in this high-resolution run in the afternoon on the previous day. This leads to a greater drying of the atmosphere in this run compared with others and, thus, the third day has different initial conditions at sunrise. This can be seen in Table 1 which shows the precipitable water after 2.5 days (0530 h local time) of the simulation; clearly the 125 m run is drier than any of the other simulations and this could explain the reason for this run precipitating later. All the main impacts of resolution seen in the precipitation rate can be seen in many other diagnostics related to convection including cloud fraction, cloud-top height and mass ux. For brevity these will not be shown here, but a further example is given in Figs. 5(a) and (b) which, respectively, show the time series and diurnal composite of total column hydrometeor content (this includes all hydrometeor types). As with the precipitation rate we can see the earlier and more steady build up of cloud in the higherresolution runs. We can also see the impact of the secondary peak in the late afternoon of the second day of the high-resolution run on the development of convection during the third day. This secondary peak of rainfall and hydrometeor content in the 125 m run also appears on the afternoon of the third day and may be another feature of using a higher resolution. However, this will not be discussed further here as it is beyond the scope of this paper which focuses on the initiation and development of the convection, but will be considered in a later study.

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IMPACTS OF RESOLUTION ON CONVECTIVE DEVELOPMENT 800 2 km 1 km 500 m 250 m 125 m

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Figure 5. Time series of total column hydrometeor content from the 4-day semi-idealized simulations of precipitating convection. Results are plotted for horizontal resolutions of 2 km, 1 km, 500 m, 250 m and 125 m. Shown is (a) the 4-day time series and (b) a diurnal composite of the 4 days, created and plotted to give maximum insolation at local noon.

Figure 6. Time–height contour plots showing diurnal composite of total (resolved and subgrid) water ux for (a) 2 km grid length and (b) 125 m grid length. The contour interval is 50 W m¡2 and the water term includes vapour and liquid cloud water.

It should be noted that the complex nature of these multi-day runs, due to the potentially strong feedback of previous days’ events on the subsequent development of convection, means care should be taken in interpreting the results. To look for some convergence of results as we go to higher resolution we should focus on the development of convection on the rst day only. This is consistent with the shallow case which also only considers 1 day. From Figs. 4(a) and 5(a) it can be seen that there is general agreement between all the runs using a grid length of 500 m or less. This convergence is less apparent in the composite plots (Figs. 4(b) and 5(b)) which contain later days where various different feedbacks may have occurred at different resolutions. Figure 6 shows time–height contour plots of the total (resolved and subgrid) vertical water-vapour ux in the model for grid lengths of (a) 2 km and (b) 125 m. The main difference between these is that the simulation using a 2 km grid length transports moisture only within the boundary layer during the early parts of the day, whereas the 125 m run transports moisture into the free troposphere more readily. This can be seen clearly by focusing on the lowest contour which shows that the 2 km simulation does not transport more than 50 W m ¡2 out of the CBL/SCL (which is about 1.5 km deep) until 1100 h local time, whereas the 125 m run transports this amount by 0600 h local time, i.e. there is at least a 5-hour delay in the low-resolution simulation. The runs of

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Figure 7. Time–height contour plots showing diurnal composite of resolved water ux for (a) 2 km grid length and (b) 125 m grid length. The contour interval is 50 W m¡2 and the water term includes vapour and liquid cloud water.

250 m, 500 m and 1 km (not shown) do not transport more than 50 W m ¡2 out of the boundary layer until 0600 h, 0800 h and 1000 h local time, respectively; this suggests some convergence between the 125 and 250 m runs. To understand why vertical transport is weaker in the lower-resolution runs it is worth looking at the resolved component of the total water ux for the same simulations; this is shown for the 2 km and 125 m runs in Fig. 7. It is clear from this that the transport in the 125 m run is largely resolved. In contrast, the 2 km run is resolving very little of the total moisture transport, especially earlier in the day when it should be penetrating the stable region at the top of the CBL/SCL. By comparing Fig. 6 and Fig. 7 it is clear that the subgrid scheme in the lower-resolution simulation is unable to generate a structure of relative humidity which can produce condensation, whereas the highresolution simulations do have condensation which can provide further energy to the resolved eddies. The impact of changing the resolution is consistent with that obtained in the shallow-cumulus simulations—here the 125 m simulation has 1x D z i =12 and the 250 m simulation has 1x D z i =6, both of which can at least crudely resolve the dominant eddies. The 500 m simulation has 1x D z i =3 which is borderline and the 2 and 1 km simulations have 1x > z i and, therefore, fail to resolve turbulence. 4.

O BSERVATIONAL - FORCED SIMULATIONS OF DEEP CONVECTION

To investigate whether increased horizontal resolution can improve comparisons with observations, the 4-day semi-idealized case is repeated using the observed largescale tendencies of temperature and moisture as was done in Xu et al. (2002). Pro les of the large-scale forcing are linearly interpolated in time from 3-hourly data and the horizontal winds are relaxed back to the observed values on a 2-hour time-scale. Initialization, surface forcing and other aspects of the simulation are identical to the semi-idealized case. The version of the model used for these simulations is also the same as that used for the semi-idealized study although a larger domain size is used. The horizontal domain size is now 500 km and runs have again been made with horizontal grid lengths of 2 km, 1 km, 500 m, 250 m and 125 m. This case will be harder to interpret than the idealized cases because much of the precipitation is dominated by large-scale events (Xu et al. 2002) which are forced from above the sub-cloud layer. However, if we focus on the rst day (27 June 1997), then there is evidence in the observations of a weak diurnal cycle forced mainly by the surface uxes. Figure 8 shows (a) the large-scale forcing and (b) the corresponding precipitation rates from the rst day (27 June with the x-axis showing local time). It can be seen that

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Figure 8. Forcing and results from the observational-based simulation on 27 June 1997 with the x-axis showing local time. Shown is (a) the combined temperature and moisture large-scale forcing, and (b) the observed and modelled surface precipitation rate. For (a) the moisture forcing is normalized by Lv /cp (Lv is the latent heat of vaporization and Cp is the speci c-heat capacity of air at constant pressure) to be combined with the temperature forcing, and the contour interval is 2.5 K day¡1 .

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Figure 9. Forcing and results from the observational-based simulation on 29 June 1997 with the x-axis showing local time. Shown is (a) the combined temperature and moisture large-scale forcing and (b) the surface precipitation rate including observations. The contour interval for (a) is 5 K day¡1 .

the forcing is tending to stabilize the pro le through the afternoon and evening and thus suppress convection. This is evident in the precipitation which is rather less than in the rst day of the idealized case. However, the sensitivity to model resolution remains. Furthermore, it is clear that the higher-resolution runs (grid lengths of 500 m or less) show a much better agreement with observations than either the 1 km simulation which is delayed by over 4 hours and the 2 km simulation which completely misses this rain event. The third day (29 June) of this simulation is also of interest for two main reasons. Firstly, the period is forced much more strongly by the large scale and produces much heavier precipitation. Thus it allows us to see the impact of model resolution on the timing of this type of rain event. Secondly, it again raises some additional issues related to the impact of the previous days on the diurnal cycle. Figure 9 shows the same

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J. C. PETCH et al. TABLE 2.

T OTAL PRECI PI TABLE WATER (kg m¡2 ) AT 0800 H LOCAL TIME , 29 J UNE 1997

Resolution

Precipitable water

Difference from 125 m

125 m 250 m 500 m 1 km 2 km

37.9 37.5 38.1 39.4 38.2

– ¡0.4 0.2 1.5 0.3

quantities as Fig. 8 but this time for 29 June (with the x-axis again showing local time on this day). The stronger forcing is clearly seen (note the contour interval is now 5 K day¡1 ) and it now acts to destabilize the atmosphere. This has the impact of producing precipitation rates about 10 times heavier than seen on 27 June 1997. However, the high-resolution models (especially the 125 m run) still tend to give a closer match to observations, although none of them capture the weak rainfall during the morning. Satellite pictures (not shown) suggest that this early rainfall could be due to the advection of clouds into the domain. Currently, a large-scale forcing term for hydrometeors is not available for the ARM site. Another feature to note from this day is that the 1 km simulation seems to precipitate earlier than expected, given previous results. As with the semi-idealized simulations, one possible explanation for this is the state of the model before this rain event. The 1 km run is much more moist before the rain event due to less rainfall over the previous days. This can be seen in Table 2 which shows that there is signi cantly more precipitable water in the 1 km run than any of the other runs. It may also explain why there is a more notable difference between the 125 and 250 m runs than was seen on the rst day (27 June 1997). 5.

S UMMARY

The timing of the development of convection during the diurnal cycle is an important issue for the global energy balance. In a recent intercomparison of several CRMs it was shown that the models had problems predicting the development of a number of convective events (Xu et al. 2002). In some cases, the onset of rainfall in the models was delayed by several hours when compared with observations. Several possible reasons were suggested for the delay, one of which was the coarse resolution of the CRMs (most used 2 km). This work has used one of the CRMs from the intercomparison and tested this hypothesis by examining the sensitivity of the development of both deep and shallow convection to the horizontal grid length used in the model. In the simulation of shallow convection the model was initialized using pro les and forced with surface uxes for a 14-hour period derived from observations over the ARM SGP site. In both the semi-idealized and the observational-based simulation of deep convection, the CRM was forced for a 4-day period also using ARM SGP data. The semi-idealized case used only observed surface uxes and, therefore, although the convection could not be compared with observations, it did have a similar diurnal cycle on all 4 days. This allowed us to use plots of 4-day composites to show some statistical representation of the diurnal cycle and consider issues related to the impact of resolution on multi-day simulations. The observational-based case used both the surface forcing and large-scale tendencies of temperature and moisture due to observed vertical and horizontal advection. While this was forced from both the surface and aloft thus making the interpretation of the results harder, it did allow us to make direct comparisons with observations.


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The results from the different cases were consistent in demonstrating the importance of providing adequate representation of the eddies in the sub-cloud layer. Failure to do so resulted in a delayed spin-up of convection relative to that obtained in the betterresolved simulations, and also relative to the observations in the last deep-convection case. In general, the worst problems were avoided as long as the horizontal resolution was no coarser than one quarter of the sub-cloud layer depth and evidence of convergence was seen in the simulation of shallow cumulus with a horizontal grid length of approximately one eighth of the sub-cloud layer depth or less. Evidence of convergence in the multi-day simulations of deep convection was harder to detect due to the more complex nature of these runs. It was shown that differences in convection on earlier days (not related to the development) can impact on development in later days. However, the general impact of resolution on the development of convective precipitation could be seen on all days of the simulation. The poor results obtained at the coarser resolutions were associated with an inability of the subgrid scheme in the model to compensate for the lack of resolved transport out of the sub-cloud layer. Hence, improvements to the subgrid scheme might lead to improved results and a decreased sensitivity to resolution. Indeed it can be seen from Xu et al. (2002) that some models do not always show delays in the development of convection as large as the model used in this study, and this may well be due to the use of a different subgrid scheme. It has also been found that the sensitivity to resolution of the timing of the onset of cumulus convection in the shallow case (David Lewellen, personal communication) and the observational-based deep case (Francoise Guichard, personal communication) can be lessened through the introduction of a subgrid condensation scheme. However, for research aimed at improving parametrization of the formation and development of shallow and deep convection in large-scale models, it is bene cial if CRMs can resolve the important processes, and so not be strongly dependent on uncertain subgrid parametrizations. Here we have suggested that this can be done if the horizontal grid spacings is no coarser than around one quarter of the sub-cloud layer depth. For cases where a resolution of the order of a kilometre needs to be used then the importance of the subgrid transport scheme should be well understood.

A CKNOWLEDGEMENTS

J. Petch conducted much of this work under the EUROpean Cloud Systems (EUROCS) contract and would also like to acknowledge the input and support of other participants of EUROCS particularly Francoise Guichard. A. R. Brown would like to thank Malcolm MacVean and GCSS WG1 participants. We would also like to thank two anonymous reviewers for their input.

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