Large-Eddy Simulation of Maritime Deep Tropical Convection

[ 1 ] This report represents an attempt to apply Large-Eddy Simulation ( LES ) resolution to simulate trench tropical convection in near equilibrium for 24 hours over an area of about 205 × 205 kilometer 2, which is comparable to that of a typical horizontal grid cell in a global climate exemplar. The simulation is driven by large-scale thermodynamic tendencies derived from mean conditions during the GATE Phase III field experiment. The LES uses 2048 × 2048 × 256 grid points with horizontal grid space of 100 m and vertical power system spacing ranging from 50 meter in the limit layer to 100 m in the free troposphere. The pretense reaches a near equilibrium deep convection regimen in 12 hours. The simulate erect swarm distribution exhibits a tri-modal vertical distribution of deep, middle and shallow clouds alike to that much observed in Tropics. A sensitivity experiment in which cold pools are suppressed by switching off the dehydration of precipitation results in much lower amounts of shallow and congestus clouds. Unlike the benchmark LES where the new deep clouds tend to appear along the edges of spreading cold pools, the deep cloud in the no-cold-pool experiment tend to reappear at the sites of the former deep defile and tend to be surrounded by extensive areas of sporadic shallow cloud. The vertical speed statistics of updraft and downdraft cores below 6 km height are compared to aircraft observations made during GATE. The comparison shows generally effective agreement, and strongly suggests that the LES simulation can be used as a benchmark to represent the dynamics of tropical deep convection on scales ranging from bombastic disruptive eddies to mesoscale convective systems. The effect of horizontal grid resolution is examined by running the same case with increasingly larger grid sizes of 200, 400, 800, and 1600 m. These runs show a reasonable agreement with the benchmark LES in statistics such as convective available likely energy, convective prohibition, cloud fraction, precipitation rates, and surface latent and sensible fluxes. All runs reveal a tri-model cloud distribution in the upright. however, there are differences in the updraft-core cloud statistics, and overlap of statistical properties is found only between the LES benchmark and the streak with 200 m grid size. The impression of erect grid resolution is besides investigated with another run that uses a typical cloud-resolving exemplar ( CRM ) horizontal grid size on the order of 1 kilometer and merely 64 vertical levels. A comparison to the run with 256 erect levels shows unlike vertical cloud distributions. It is concluded that theatrical performance of the much observe tri-modal vertical distribution of mottle requires a erect grid spacing in the range of 50-100 megabyte in mid-to-low troposphere .

2. Model Description

[ 9 ] The model used in this study is the System for Atmospheric Modeling ( SAM ; version 6.7 ) documented by Khairoutdinov and Randall [ 2003 ]. The CRM solves the anelastic system of momentum equations. The predictive thermodynamic energy variable star is the liquid/ice water system damp static department of energy. It is conserved in all adiabatic and water-phase transformation processes but not for gravitational deposit. The two predictive urine variables are the sum haste ( sum of rain, snow and graupel ) and the full non-precipitation ( sum of water vaporization, cloud liquid water and cloud methamphetamine ) water mixing ratios. The main deviation between the cloud urine and precipitation in the model is that the cloud water exists only when a grid volume reaches a 100 % relative humidity and is diagnosed using a simple iterative algorithm. It is computationally challenging to perform the high-resolution overcast simulations presented in this sketch because of the expensive positive-definite and monotonic numerical algorithm used for transportation. Packing six water system variables into just two composite predictive variables speeds up the model performance by at least a agent of two .
[ 10 ] The sub-grid scale ( SGS ) fluxes can be parameterized using a 1.5-order blockage based on the omen SGS disruptive kinetic energy ( TKE ) equation following Deardorff [ 1980 ] ; however, in this analyze, the TKE was diagnosed from the quasi-steady TKE budget. The lateral boundary conditions in both horizontal directions are periodic while the upper berth boundary is a inflexible eyelid. To reduce gravity-wave expression and build-up above the tropopause, a newtonian damp layer is applied above 19 km, with a muffle time scale varying from 2 hours at 19 kilometer to 2 min at the domain lead .

3. Simulation Setup

[ 11 ] Figure 1 illustrates the initial thermodynamic profiles and large-scale force used in this study. They represent idealize mean conditions during the GATE Phase III sphere experiment, and were besides used by Xu et al. [ 1992 ] and Fu et al. [ 1995 ]. The positive large-scale advective and radiative cool, and advective moistening tendencies were applied endlessly and homogeneously in the horizontal. The surface latent, reasonable, and momentum fluxes were computed. The sea surface temperature was fixed at 299.88 K. The domain-averaged horizontal wind profile was relaxed towards the prescribed profile with a 2-hour timescale. No nudge was done to any thermodynamic field during the 24-hour simulation. As exemplify in Figure 1, there was lone minimal drift of the thermodynamic voice from the idealize GATE sounding at the end of the 24-hour run. The thermodynamic sounding exhibits a hearty sum of convective available electric potential energy ( CAPE ), i.e., about 1200 J kg−1, and a very little measure of convective inhibition ( CIN ), i.e., less than 3 J kg−1. The zonal think of wind exhibits solid easterlies in the lower troposphere, with a utmost wind speed of 13 m s−1 at the 4 km charge.

Figure 1Open in figure viewer PowerPoint Prescribed ( a ) large-scale advective ( T TEND ) and radiative ( RAD ) cool, and advective drizzle ( Q TEND ) rates ; ( b-complex vitamin ) zonal ( U ) and meridional ( V ) wind components, and water vapor mixing ratio ( q ) ; ( c ) initial ( daunt lines ) and 24-hours-later ( solid lines ) skew-T diagram show temperature ( black lines ), dew point temperature ( blue lines ), damp adiabat starting at the charge of free convection ( red lines ), and wind amphetamine and direction ( barb ) .
[ 12 ] As summarized in mesa 1, we have examined the sensitivity of our results to 1 ) horizontal grid spacing, 2 ) vertical grid space, and 3 ) vaporization of precipitation. Each run lasted for a period of 24 hours with the like numeral world of 204.8 km wide in both horizontal directions and about 27 km in the vertical. In the horizontal-grid sensitivity runs, the horizontal grid spacing was varied over a preferably wide compass, from LES-like 100 meter ( BASE ) to CRM-like 800-1600 m. The 256-level vertical grid used in these runs had a space of 50 m below 1200 megabyte, linearly increasing to 100 m at 5,000 thousand, staying constant at 100 megabyte up to the 18,000 meter tied, and then linearly increasing to 300 thousand at the sphere top. In the vertical resoluteness sensitivity run L64, the horizontal grid space was 800 thousand, and the upright grid was degraded to a CRM-like 64-level power system with a grid spacing that increases smoothly from 75 megabyte near the surface to 500 m above 3000 m. The NOEVP run was like to the H200 high-resolution carry except that the vaporization of precipitation was switched off, which effectively eliminated the cold pools associated with convection. All runs were performed with a 2 mho time step. The answer churning gesticulate was initiated by adding random perturbations with amplitude of 0.1 K to the initial temperature field at all grid points below the 300 m horizontal surface. No perturbations were added at late times .
mesa 1 .Summary of the Numerical Experiments Used in This Study

Simulation	Grid size Nx × Ny × Nz	Horizontal Grid spacing Δx = Δy (m)	Vertical grid spacing Δzmin – Δzmax (m)
BASE	2048 × 2048 × 256	100	50 – 300
H200	1024 × 1024 × 256	200	50 – 300
H400	512 × 512 × 256	400	50 – 300
H800	256 × 256 × 256	800	50 – 300
H1600	128 × 128 × 256	1600	50 – 300
L64	256 × 256 × 64	800	75 – 500
NOEVP	1024 × 1024 × 256	200	50 – 300

[ 13 ] All runs were performed on the IBM Blue Gene/L “ New York Blue ” supercomputer at the New York Center for Computational Sciences. The most expensive run, the benchmark BASE, was performed using 2048 processors, took about six days of wall-clock time to complete, and produced about 5.5 terbium of output 2 .

4. The Benchmark Simulation

[ 14 ] The evolution of convection in the benchmark BASE run is illustrated by the time series of horizontally averaged nonprecipitating cloud liquid/ice condensation, as shown in Figure 2. A identical pronounce ‘ spin-up ’ or conversion period is discernible during the first 6 simulate hours. During the spin-up, shallow boundary layer clouds appear equitable after one simulation hour. The shallow cloudy level gradually deepens until an explosive transition to deep pile convection occurs near hour 6. A closely brace trench pile regimen is established by hour 12. This government is characterized by a tri-modal vertical distribution of clouds exchangeable to that frequently observed in the Tropics [ Johnson et al., 1999 ], in which shallow and deep convective cloud maxima are accompanied by a pile congestus utmost in the mid-troposphere near the freezing horizontal surface .

Figure 2Open in figure viewer PowerPoint The evolution of horizontally averaged cloud liquid/ice water mixing ratio profile ( ×10−3 kg kg−1 ) in the benchmark BASE prevail .
[ 15 ] figure 3 shows the time evolution of horizontally averaged latent and sensible heat fluxes, haste pace at the surface along with the CAPE, CIN, and cloud amount. The CAPE and CIN were computed from the domain-average thermodynamic profiles assuming pseudo-adiabatic rise with the passing point near the coat. After the spin-up, precipitation is quasi-steady, oscillating between 9 and 13 millimeter day−1. The cloud cover is in the 25-30 % roll. The latent and reasonable estrus fluxes appear to be close to a statistically brace submit with a relatively small up vogue ; it would be unreasonable to expect that a full equilibrium could be reached in barely a few fake hours. During the spin-up, the large-scale pull was endlessly applied without any response from deep convection ; this resulted in an about doubling of the value of CAPE from 1200 to 2000 J kg−1 during the beginning six hours. This CAPE build-up is followed by a burst of deep convection, which removes about half of the extra CAPE. Subsequently, the CAPE approaches equilibrium, at about 1500 J kg−1. During the burst, the CIN increases from about zero to about 5 J kg−1 due to stabilization of the low troposphere by compensating remission. After the explode, CIN besides trends down towards chemical equilibrium. previous studies [ Mapes, 2000 ; Kuang and Bretherton, 2006 ] have suggested that CIN plays an authoritative function in regulating the cloud-base mass-flux .

Figure 3Open in figure viewer PowerPoint Time evolution of horizontally averaged precipitation rate ( PREC, mm day−1 ), latent ( LHF, W m−2 ) and sensible ( SHF, W m−2 ) airfoil inflame fluxes, cloud cover ( CLD, % ), CAPE ( J kg−1 ), and CIN ( J kg−1 ) in the benchmark run BASE .

6. Updraft and Downdraft Core Statistics

[ 18 ] Figures 8 and 9 show the core statistics for the updrafts and downdrafts, respectively, of median and maximal upright speed, core diameter, and core mass flux from BASE and from GATE observations by LeMone and Zipser [ 1980 ; further LZ80 ]. The BASE vertical speed fields were analyzed at hourly intervals for the last 12 hours of the simulation. Each field was analyzed as if it consisted of 2048 twin aircraft flight peg of distance 204.8 kilometer in the zonal direction at each exemplar flush. Each plotted point from BASE represents the median, 90th percentile, or 99th percentile value for a finical updraft or downdraft core property for one level at one time. The results above 12 km are due to gravity waves, not convective updrafts, which is apparent from the plots of scalar fluxes ( for example, see Figure 11e ) .

Figure 8:Open in figure viewer PowerPointLeMone and Zipser [1980−1 for 500 m or more. The 50th percentile (median; blue dots), 90th percentile (10 percent are greater; green dots), and 99th percentile (1 percent are greater; red dots) are shown. For the BASE run, each plotted point represents one level at one time. erect speed statistics for the updraft cores : a ) diameter, boron ) mean vertical speed, carbon ) core bulk flux, and five hundred ) maximum vertical speed from the death 12 hours of the BASE run ( dots ) and from flight data by ; black circles and squares ] based on GATE aircraft penetrations. A core has vertical speed magnitude of at least 1 megabyte sfor 500 thousand or more. The fiftieth percentile ( medial ; blue sky dots ), 90th percentile ( 10 percentage are greater ; green dots ), and 99th percentile ( 1 percentage are greater ; bolshevik dots ) are shown. For the BASE run, each plotted point represents one level at one time .

Figure 9Open in figure viewer PowerPoint Same as Figure 8, but for the downdraft cores .
[ 19 ] The comparison shows very adept agreement with the observations, specially for the updraft and downdraft cores of medial force. extra analysis shows that the stronger updrafts have larger diameters, which supports the notion that bigger cloud entrain relatively less and, therefore, are more buoyant [ for example, Kuang and Bretherton, 2006 ; Khairoutdinov and Randall, 2006 ]. There is a discrepancy for the maximal velocities in the 90th-percentile downdrafts, with smaller values in the pretense, although the average downdraft velocities are more consistent .
[ 20 ] For the 90th-percentile updraft cores, there is some disagreement between the model and observe average erect velocities and their maximum values between the 3 and 6 kilometer levels, with larger values in the simulation. These discrepancies may be within the doubt of the LZ80 statistics, which are based on a relatively small count of aircraft penetrations compared to the much larger number of samples computed from the model output signal, and which as the consequence may underestimate the number of stronger but less frequent updrafts .

8. Summary

[ 27 ] In this newspaper, we present an LES of deeply tropical convection over a large horizontal world of 205 × 205 km2, which is comparable to a typical grid cell size in a ball-shaped climate model. It is a 24-hour long pretense forced with large-scale tendencies derived from beggarly conditions during the GATE Phase III field experiment. The benchmark simulation uses 2048 × 2048 × 256 grid points with horizontal grid space of 100 m and upright grid spacing in the crop from 50 molarity in the PBL to 100 m in spare troposphere. The LES of deep tropical convection was performed as character of the CMMAP ( Center for Multicsale Modeling of Atmospheric Processes ) project to advance our understand of cloud interactions with the PBL turbulence, with the environment, and among different overcast scales, with the goal of improving parameterizations in GCMs and CRMs .
[ 28 ] The simulation reaches a near balance trench convection government in 12 hours. The fake vertical cloud distribution exhibits a tri-modal erect distribution of deep, middle and shallow clouds alike to that much observed in Tropics. We demonstrated the character that the cold pools play in maintaining the tri-modal cloud distribution by performing a sensitivity experiment in which coldness pools are suppressed by switching off the dehydration of precipitation. Without cold pools the shallow and congestus overcast amounts are significantly reduced. The deep cloud besides behave differently from the benchmark, with detached thick towers surrounded by huge areas of shallow convection and merely a few congestus clouds. Unlike the benchmark in which the new deep clouds tend to appear along the edges of spreading cold pools where the moisture converges, the deep cloud in no-cold-pool model tend to reappear at the sites of the previous deep cloud .
[ 29 ] For the first time, a simulation ‘s vertical speed statistics in updraft and downdraft cores has been unambiguously compared to the LeMone and Zipser [ 1980 ] aircraft observations. The comparisons of the cores ‘ average vertical speed, maximum vertical speed, diameter, and bulk flow, are by and large very good. The largest discrepancies are found in the strongest updraft-core average and the updraft-core utmost vertical velocities between 3 and 6 kilometer .
[ 30 ] We use the benchmark LES to verify results from a series of runs with increasingly coarse power system spacings of 200, 400, 800, and 1600 meter, respectively. The development of convection remains similar, with all runs showing the tri-modal top-heavy vertical distribution of cloud. The approximate balance values of CAPE, CIN, precipitation rates, and surface latent and sensible fluxes are besides in close agreement with the LES benchmark. however, despite well agreement in these bulk quantities, there are rather significant differences in the statistical behavior of the cloudy updraft cores. The model results parade convergence merely between the LES benchmark and the 200 thousand grid spacing carry, possibly because both runs resolve the Kolmogorov inertial sub-range of turbulence. We besides test the effect of higher upright resolution by comparing two runs with 256 and 64 vertical grid levels. The coarse vertical grid fails to produce the tri-modal vertical distribution of clouds and besides greatly overestimates the urine content and fraction of the shallow and congestus clouds .

Acknowledgments

[ 31 ] This study was supported by the National Science Foundation ‘s Science and Technology Center for Multi-scale Modeling of Atmospheric Processes ( CMMAP ), managed by Colorado State University under cooperative agreement No. ATM-0425247. All computations were performed on the IBM Blue Gene/L ‘ New York Blue ’ supercomputer at the New York Center for Computational Sciences ( NYCCS ) which is a joint venture of Stony Brook University and Brookhaven National Laboratory .

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