Meteorol Atmos Phys (2013) 122:145–158 DOI 10.1007/s00703-013-0280-6
ORIGINAL PAPER
Implementation of a new cumulus parameterization scheme based on an explicit time-dependent tilting cloud model in ARPS model Maryam Gharaylou • Peyman Zawar-Reza • Abbas-Ali A. Bidokhti • Majid-M. Farahani
Received: 30 January 2013 / Accepted: 3 September 2013 / Published online: 27 September 2013 Ó Springer-Verlag Wien 2013
Abstract A one-dimensional Explicit Time-dependent Tilting cloud Model (ETTM) that separates updraft and downdraft columns and takes into account the effect of cloud tilting on precipitation is introduced and incorporated into the Advanced Regional Prediction System (ARPS). Results of the stand-alone ETTM are compared with that of cloud resolving simulations using the ARPS mesoscale model. Inter-comparison is performed by qualitative examination of simulated parameters such as vertical distribution of fluxes of mass, heat, and moisture. Although there is a great degree of similarity between the vertical profiles, ETTM systematically underestimates magnitudes of all fluxes. Sensitivity tests carried with ETTM show that the effect of varying cloud radius and tilting angle is considerable on the simulated cloud behavior. Increasing the cloud radius, results in a corresponding increase in fluxes of mass, heat, and moisture, while increasing the cloud tilt angle has the opposite effect. Since ETTM showed promise as a suitable sub-grid cumulus parameterization scheme; it was incorporated into ARPS as an additional cumulus parameterization scheme (CPS) to be available for the wider community. Results of simulations using ETTM and other CPSs already available in ARPS were compared for 2, 4 and 10 km grid spacings to assess its utility. Simulation results of the 2 km grid showed that
Responsible editor: S. Hong. M. Gharaylou (&) A.-A. A. Bidokhti M.-M. Farahani Institute of Geophysics, University of Tehran, Post Box: 14155-6466, Tehran, Islamic Republic of Iran e-mail:
[email protected] P. Zawar-Reza Centre for Atmospheric Research, University of Canterbury, Christchurch, New Zealand
at this resolution, the simulated time series of updraft velocities using the new scheme (ETTM) compared well with the results of other schemes in the ARPS model. The simulations with horizontal resolution of 4 km that was compared with the convection resolving reference run (No-CPS-2KM) showed almost consistent results for all schemes except for one using KF scheme. The results of the simulation with the ETTM scheme and other schemes in the model with resolution of 10 km showed that at this resolution, there is not significant difference between the uses of these schemes.
1 Introduction Development of cumulus parameterization schemes (CPSs) has been the cornerstone of numerical weather prediction (NWP) for meteorological events where deep convection is significant. CPS is applied so that the effects of sub-grid scale convective clouds are taken into account when the model grid spacing is not of sufficiently high enough resolution to explicitly resolve the convective cells. In the NWP models, the sub-grid scale convection and microphysical processes by a CPS are usually represented through a one-dimensional (1D) cloud model. Onedimensional cloud models are appealing due to their relatively inexpensive computational demand. Although, availability of high-performance computing has meant that ultra-high resolution (100 m grid spacing) cloud resolving simulations are more common place (Bryan et al. 2003), 1D CPS still provides an attractive platform to carry out research on the dynamics of convective clouds. CPSs fall into three categories (Arakawa 2004; Lin 2007): (1) Kuo-type schemes (Kuo 1965, 1974), (2) adjustment schemes (e.g., Betts and Miller 1986; Manabe
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et al. 1965), (3) mass-flux schemes (e.g., Ooyama 1971). Because of the perceived shortcomings of the first two types, the mass-flux schemes have garnered more attention and have been developed further—see Arakawa and Schubert (1974), Fraedrich (1973, 1974), and Yano et al. (2004, 2005; Yano 2012). Many current global and regional atmospheric models now apply this method. A comprehensive review of this subject can be found in Plant (2010). The importance of CPS in proper simulation of severe weather events such as tropical storms, flash floods and convective storms has meant that many researchers have tackled developing better formulations (Kuo 1965, 1974; Krishnamurti and Moxim 1971; Ooyama 1971; Arakawa and Schubert 1974; Kreitzberg and Perkey 1976, 1977; Anthes 1977; Johnson 1977; Fritsch and Chappell 1980a, b; Yamazaki and Ninomiya 1981; Molinari 1982; Tiedtke 1989; Kain and Fritsch 1990, 1993; Grell 1993; Haines and sun 1994; Hu 1997; Gallus 1999; Kain 2004). Important processes that should be featured in a modeled convective cloud’s lifecycle include: (1) an updraft initiated by low level instabilities leading to saturation and subsequent activation of microphysical and dynamical processes, and (2) convective downdrafts that cause cooling and moistening of the lower troposphere (i.e., below cloud environment), consuming cloud water content through evaporation. In the past 4 decades, cloud models employing different assumptions have been developed, usually neglecting one or more of the important processes by necessity. For example, Asai and Kasahara (1967) and Kasahara and Asai (1967) originally introduced a cumulus ensemble model that included both downdraft and updraft characteristics to study the physical properties of cumulus clouds. Subsequently, Arakawa and Schubert (1974) incorporated the transport of sub-cloud layer air by the updraft into the cloud column, but neglected the downdraft mass transport, leading to simulated sub-cloud layer that was too warm and dry. Johnson (1976) addressed this issue by inserting the downdraft effect as an inverted plume, where the downdraft was assumed to exist as a consequence of drag force due to precipitation and also considered its evaporative cooling effects. He also approximated the convective-scale downdrafts as synoptic scale cumulus fluxes, yet the interaction between updraft and downdraft cells as a means for transferring cool and moist air to the lower troposphere was neglected. Yano et al. (2010) and Yano and Beizig (2012), but with different geometry, have developed and used a new approach [segmentally constant approximation (SCA)] to parameterize convection based on Asai and Kasahara (1967) and Kasahara and Asai (1967) in a non-hydrostatic model. In SCA, each model box is partitioned into three parts; two concentric cylinders (representing up- and downdraft columns) and the third is
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the quiescent surrounding environment. From 1980s onwards, a concerted effort has been made to improve the inclusion of convective downdrafts in the CPS (Molinari and Corsetti 1985; Frank and Cohen 1987; Cheng and Arakawa 1997; Chen and Sun 2004). The research presented here is based on the cloud model developed by Chen and Sun (2004; hereafter CS2004). This Explicit Time-dependent Tilting cloud model (ETTM) features detailed equations for an updraft and a downdraft, where similar dynamic and thermodynamic processes govern both. The updraft is initiated with a thermal bubble, while evaporative cooling and the drag force of precipitation maintain the downdraft. Both the updraft and the downdraft employ non-hydrostatic pressure, entrainment, cloud microphysics, and lateral and vertical eddy mixing. A tilting angle for the cloud is specified to separate a portion of the downdraft from the updraft cell to account for vertical wind shear since convective cells can develop considerable depth. The fallout of precipitation from the tilted updraft column should improve the approximation of CPS to real cases. To verify their model, CS2004 used the 3D nonhydrostatic cloud resolving set-up of the Weather Research and Forecasting model (WRF, Chen and Saio 2010). Haines and Sun (1994) compared the amount and vertical variation of different fluxes obtained from a quasi 1D cloud model and a 3D cloud model with and without vertical wind shear. Here, to investigate their assumption, considering the vertical wind shear, we try to reproduce heating and drying profiles, and heat and moisture fluxes throughout the life cycle of a cloud cell in ETTM against the 3D model. It is of interest to evaluate the 1D ETTM using the same metrics as 3D model, and compare its performance against the simulated features of the 3D cloud produced by Advance Regional Prediction System (ARPS). To achieve this, we first present the results for a standalone version of the ETTM, and subsequently we examine its performance as a CPS within the ARPS model by comparing its capabilities with other CPS already available in ARPS. In the next section, a brief description of the ETTM formulations is provided, followed by the experimental setup used for the 3D ARPS simulation. Subsequently, the results of simulations and qualitative inter-comparison exercises are summarized. The discussion revolves around the sensitivity experiments, which shed light on the differences between the two models.
2 The ETTM model The source code for the ETTM as described in CS2004 is not in the public domain (i.e., it is not available for research
Implementation of a new cumulus parameterization scheme based on an explicit
or modification by the wider scientific community). Therefore, based on their formulations, a slightly different algorithm was independently developed by us. A detailed introduction to the ETTM is not provided here; but the complete list of equations and assumptions of the model is available in CS2004. The ETTM coordinate system is axis-symmetric cylindrical with a constant radius (R) mapped on (r, u, Z); where r is radius, u is tangential angle, and Z is height in tilting coordinates. The model’s dynamics are based on 1D framework developed by Asai and Kasahara (1967). According to horizontal integration procedure suggested by Asai and Kasahara (1967), for any variable A, A denotes the horizontal area-average in-cloud value, A0 is the deviation from the horizontal area-average incloud value, A~ is the lateral boundary average in-cloud value, and A00 is the deviation value from the lateral boundary average in-cloud value. Each is calculated according to: 1 A ¼ p R2
Z2p ZR A r dr dw; 0
1 A~ ¼ 2p
A0 ¼ A A
0
Z2p A dw;
ð1Þ ~ A00 ¼ A A:
0
Prognosed variables (which are all available as model outputs) are: vertical velocity W (m s-1), ice equivalent potential temperature hei (K), mixing ratios qx (g kg-1), where x indicates water classes including cloud water (c), water vapor (v), and ice water (i) and mixing ratios qy (g kg-1), where y indicates water classes including rain water (r), snow (s) and graupel (g). For convenience, we have summarized the important and relevant information below. The governing equations for the in-cloud dependent variables are: W þ W 0W 0Þ oW 2 ~~ 1 o qðW 00 00 g ¼ ðU W þ U W Þ oZ ot R q hv hv0 2b2 J1 ðaÞ o p ðZÞ T þ bg bgQ oZ hv0 qa R 2J1 ðaÞ p ðZÞ þ bg 1 ð2Þ Cp a p0 h i hei þ h0ei W 0 Þ o qðW ohei 2 ~ 1 00 h00 Þ ¼ ðU hei þ Ug ei oZ R ot q 1 d h þ microðhei Þ þ ðLv qv Lf qi Þ ð3Þ Cp dt T qx þ q0x W 0 Þ o qx 2 ~ 1 o qðW 00 00 g þ Px ¼ ðU q~x þ U qx Þ oZ R q ot ð4Þ
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h i qy þ q0y W 0 Þ o qðW o qy 2 ~ 1 00 q00 Þ ¼ ðU q~y þ Ug y oZ R q ot b oðqVty qy Þ þ Py þ Rin q oZ
ð5Þ
Here Lv, Lf, q, and, T are the latent heat of vaporization and fusion, density and temperature within the cloud, respectively. Also, a = tan a0, b = sec a0 and a0 is the angle from the vertical axis z to the tilting axis Z. Cp is the specific heat of air at constant pressure level. Vty is the terminal velocity of rain, snow and graupel. Px, Py and the last two terms in (3) act as microphysical sources and sinks of qx, qy and hei respectively. U is radial velocity in the tilting coordinates. Ice equivalent potential temperature hei (K) is calculated from: Lv qv Lf qi hei ¼ h 1 þ ð6Þ Cp T Cp T Non-hydrostatic pressure pnh should be expressed as pnh (r, z) = p* (z) 9 J0(r), where J0(r) is the zeroth order of Bessel function of the first kind (Holton 1973). The radius of cloud satisfies the first root of J0(r) = 0 with x = arR-1 and a = 2.4048. Pressure perturbation formulation is described in detail by CS2004. gQT is the drag force due to the weight of precipitation. In a tilted updraft at an angle a0, the produced precipitation (rain, snow, or graupel) separates from the tilted updraft due to gravity and triggers a downdraft, which is governed by the same dynamic and thermodynamic equations. After formation of the downdraft, the interaction between updraft and downdraft is included in the dynamics of the cloud (CS2004). The radius of downdraft is assumed to be 40 % of that of the updraft (Lemone and Zipser 1980) and the effect of downdraft on updraft is ignored. The fraction of precipitation that remains with the updraft, Rin, is calculated as following: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a0 4R2 cos1 H tan H tan a0 4R2 H 2 tan2 a0 2R Rin ¼ 2pR2 ð7Þ where, H (= Vty 9 Dt) indicates the downward distance the original precipitation column has shifted in one time step (Dt) due to the terminal velocity (Vty). The radius of the updraft is R, thereby the ratio of precipitation falling into the downdraft is 1 - Rin. The bulk microphysics parameterization incorporated in the ETTM is described in Lin et al. (1983) and Rutledge and Hobbs (1984); where the interaction between the six water substances mentioned above includes evaporation/sublimation, deposition/condensation, freezing, melting, evaporation, aggregation, accretion, and Bergeron processes.
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Forward finite differencing solves the time derivates in the governing equations, while the advective vertical derivates are solved by an upstream scheme. First-order advective differencing is achieved by 1-2-1 central averaging for advective velocity to decrease the influence of strong damping inherent in this method. An explicit scheme is used for the vertical eddy diffusion and the tri-diagonal matrix method is used for solving the pressure perturbation equation. Vertical fluxes of rain, snow, and graupel are obtained by the central-in-space method. Time stepping is done in 1 s increments and the total integration time is 70 min. The vertical resolution is set to 500 m for each of the 34 vertical levels, placing the top of the domain at 17 km. The initial ice, cloud water, rain water, snow and graupel mixing ratio is set to zero at all levels and water vapor mixing ratio is set to the environmental value. The upper- and lower-boundary use the non-slip condition. ETTM also requires that radius and tilting angle of the up- and downdraft cells be specified, these are determined based on the information obtained from the 3D simulations with ARPS, as described below. The radius of the updraft and downdraft are set to 4,000 and 1,600 m, respectively (radius of downdraft being 40 % of the updraft as described above). According to the simulations with ARPS, the tilting angle is set to 11.2°. Practically, obtaining the radius of the cloud could be done by considering the value of the relative humidity of 3D domain of the model exceeding 100 %. Also the cloud angle to the vertical direction could be calculated by using vertical wind shear and the value of the relative humidity. Convection in ETTM is initiated using an initial potential temperature perturbation according to the following relationship (CS2004): pz h0 ¼ 0:367 sin z 1; 500 m ð8Þ 1; 500 Figure 1 illustrates the environmental sounding including temperature, relative humidity, and pressure used to initialize all simulations. This sounding was obtained on 20 May 1977 over Del City, Oklahoma, when a super-cell storm spawned 16 tornados, and is a standard inclusion in the ARPS model package. This sounding is used frequently for research, making it a reference case for many studies (see for example Ray et al. 1980). The convective available potential energy of this sounding is calculated at 3,900 J/ kg. For this work, the vertical variability of wind direction is ignored to make the comparison between the 1D CPS and the 3D ARPS more meaningful.
3 ARPS set-up ARPS was developed at the Center for Analysis and Prediction of Storms of the University of Oklahoma and solves the 3D, compressible, filtered Navier–Stokes equations
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Fig. 1 Initial vertical sounding depicting initial temperature (°C) and dew points (°C) profiles
(Xue et al. 2000, 2001). ARPS provides the user with a vast variety of parameterizations and numerical schemes. Here we only express the relevant settings for this study. The domain of simulation includes 67 grid points in east–west and north–south directions, and the spacing between each grid point is set at 1 km. The vertical resolution is 500 m with 34 levels, similar to the ETTM. The lateral boundary condition is open while the rigid condition is applied for both the upper and the bottom boundaries. For consistency with ETTM, the second-order time and space finite difference method is used for time integration of the horizontal and vertical advections of variables. For the microphysics option, the single-moment cloud microphysics scheme developed by Lin et al. (1983) was chosen, and for the sub-grid scale eddy diffusion coefficients, the turbulence scheme of Smagorinsky (1963) with constant turbulent Prantel number of 0.33 is used. Convection is initiated by an ellipsoidal thermal bubble, which is one of the default options, and is defined by the following equation (Klemp and Wilhelmson 1978): p Dh ¼ Dh0 cos2 b 2
b\1
ð9Þ
where, Dh0 is the amplitude at the center of the disturbance and b is a non-dimensional radius given by " #12 x xc 2 y yc 2 z zc 2 b¼ þ þ ð10Þ xr yr zr The subscript c refers to the location of the center of the perturbation, while r denotes its radial dimension in each
Implementation of a new cumulus parameterization scheme based on an explicit
direction (xc = 48 km, yc = 16 km, xr = yr = 10 km, zr = 1.5 km). Initial potential temperature perturbation amplitude set to 3 K (Dh0 = 3 K). Gharaylou et al. (2009) conducted sensitivity tests with ARPS to study the effect of the thermal bubble (its depth and amplitude) on the evolution of the convective cell. They showed that with larger amplitude, maximum vertical velocity occurs earlier, but it is less intense, and that increasing the depth of the bubble enhances the maturity time of the formed cloud cell. Therefore, we used the trigger function as a rough ‘tuning parameter’ to make sure that the time evolution of maximum velocity for both models was coincidental. The amplitude of initial potential temperature perturbation for ARPS is set at 3 K, while for ETTM it is set at 0.37 K. This inconsistency in amplitude of the initial potential temperature perturbation has negligible effect on the evolution of fluxes of mass, heat, and moisture and is used to make the qualitative inter-comparison tractable. Similar to ETTM, ARPS was also run for 70 min with the time step of 1 s. The initialization sounding is the same as the one used for ETTM.
4 ARPS outputs In this paper, we have adopted a similar methodology as detailed in Haines and Sun (1994) for inter-comparison of modeled convective clouds. Because of 3D nature of the ARPS cloud and its non-stationarity in space, the storm track utility of ARPS is used to locate and extract appropriate data from the center of the convective storm. Therefore, the vertical profiles belong to the grid point that has the maximum vertical velocity in the modeled domain. East–west oriented vertical cross sections of storm structure are provided in Fig. 2; the time slices are at the 34, 55, and 69 min marks. During the cumulus stage, both the updraft and downdraft cells increase in intensity; the updraft column is typically enveloped by downdraft motion. After this stage, the maximum updraft (downdraft) intensity significantly increases from 18.22 m s-1 (-7.46 m s-1) to 44.12 m s-1 (-18.09 m s-1; Fig. 2b–e), showing the growth rate in the upward motion is larger than downward motion as the initial thermal bubble grows rapidly and evolves into a convective cell. It is also clear that, the maximum temperature anomaly in the updraft reaches 17.74 K at about 8 km height, underneath the maximum vertical velocity. A region of cold anomaly forms on the top of cloud due to overshoot cooling (Fig. 2f).
5 Comparison results of ETTM with ARPS Fundamentally, the suitability of the ETTM in realistically producing salient features of a convective storm should be
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determined by detailed comparison with in situ datasets, but as far as we are aware, such a dataset is not yet available. Figure 3 illustrates an inter-comparison of the profiles of maximum in vertical velocity, potential temperature anomaly, and water vapor mixing ratio anomaly from both simulations. Comparison of the simulated convective cells when they are at their most vigorous stage forms the basis for our qualitative assessment. Although there is close similarity in form between the profiles, in general the ETTM tends to underestimate the strength of all variables. The height of the peak in vertical velocity is also lower in the ETTM, and it occurs at about 10 km, 2 km lower than the ARPS prediction. Yet the potential temperature anomaly maxima occur at the same height for both. The trends in vertical profiles for water vapor anomaly are very similar (except at the very bottom), with ETTM predicting a relatively drier column. The source of these differences can probably be attributed to the one-way interaction between 1D ETTM cloud and its environment (which is constant throughout the simulation), whereas in the ARPS simulation there is a feedback between the cloud and its environment. By one-way interaction, we mean that the ETTM gets affected by its environment but does not change it in return (i.e., no feedback). For further analysis, vertical profiles of fluxes of total mass, heat, and moisture produced by ETTM and ARPS model are examined, these are calculated as follows: Fm ¼ qu Wu Bu þ qd Wd Bd Fh ¼ Cp qu Wu Bu ðhu h0 Þ þ Cp qd Wd Bd ðhd h0 Þ
ð11Þ
Fq ¼ qu Wu Bu ðqvu qv0 Þ þ qd Wd Bd ðqvd qv0 Þ The subscripts u and d distinguish the updraft and downdraft components, respectively. Bu and Bd are the horizontal coverage area of the updraft and the downdraft cells. The radius of updraft and the downdraft cells are set to 4,000 and 1,600 m in the ETTM, respectively, which are determined from the mature stage in ARPS cloud scheme (see next section). Similar calculations are carried out for ARPS using the vertical velocity profile at the maturing stage through a radius of 4,000 m. This radius is assigned to the cloud cell based on 3D simulation with ARPS with this value for bubble size. To show that the underestimation by ETTM is not from sources such as the perturbation bubble radius, or the imposed tilting angle, several sensitivity tests were performed. The relationship between total fluxes of mass, heat, and moisture by varying cloud radii in ETTM is presented in Fig. 4. As the radius of the cloud increases from 2,000 to 6,000 m, all total fluxes increase accordingly. This happens because increasing the cloud radius minimizes the role of lateral eddy diffusion and entrainment/detrainment terms. Kuo and Raymond (1980) show a similar relationship
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Fig. 2 The x–z cross section of storm structure through the maximum vertical velocity for the case study with a the x and z direction wind vector (m s-1), b vertical velocities (m s-1), and c the perturbation
potential temperature (K). The solid and dashed lines denote positive and negative values, respectively. Time (min) of the simulation is noted along the left side
where entrainment/detrainment acts as a sink in the momentum equation, and increasing the cloud’s radius results in decreasing entrainment/detrainment. Radii greater than 6,000 m are not included since CS2004 showed that above this value, there is significant change in simulated convective behavior. Total fluxes for the ARPS cloud (radius 4,000 m) are also included in Fig. 4. Only the peak total flux of mass reaches the same magnitude as that of ARPS when the
radius for ETTM is set at 6,000 m, occurring 4 km above that of ARPS prediction (Fig. 4a). But similarity in form is more apparent between the models for total heat and moisture fluxes (Fig. 4b, c). The maxima for these variables always occur at the same level for different radii of ETTM and ARPS clouds. Another sensitivity test for the radius of the initial perturbation bubble was also conducted for ARPS (Fig. 5). In comparison with Fig. 4 each total flux exhibited the same behavior as that in ETTM, where
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Fig. 3 Comparison of a maximum vertical velocity (m s-1), b maximum potential temperature anomaly (K), and c maximum water vapor mixing ratio anomaly (g kg-1) for ETTM and ARPS model for the storm simulation case
Fig. 4 Comparison of vertical total a mass flux (9108 kg), b heat flux (91012 J), and c moisture flux (9106 kg) for ETTM and ARPS model for the storm simulation case varying radius of the cloud in ETTM with 5 radii: 2, 3, 4, 5, 6 km
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Fig. 5 Comparison of vertical total a mass flux (9108 kg), b heat flux (91012 J), and c moisture flux (9106 kg) for ARPS model for the storm simulation case varying radius of the bubble in ARPS with 9 radii: 2, 3, 4, 5, 6, 7, 8, 9, 10 km
increasing the radius led to increases in total flux. The altitude of the maxima remains almost at the same height, except there is a marked variation for the moisture flux for the largest radius. The effect of titling angle on ETTM is examined in Fig. 6. This was only applied to the case where the radius is 4,000 m in ETTM. As the tilting angle increases, total fluxes decrease in magnitude. Yet there is less sensitivity to tilting angle above 20°. This result is consistent with findings by CS2004, where the higher angles are thought to increase the contribution of downdraft causing a net reduction in total fluxes. The strength of dependency of the depth of vertical distribution of fluxes, is a function of radius of cloud for example it is not as large as CS2004 for cloud with radius of 4,000 m but its vertical distribution of fluxes are varying with angle of tilting significantly for cloud with radius of 3,000 m (Fig. 7). The dependency of updraft and downdraft strength to the tilting angle has an influence on the vertical distribution of fluxes.
time of convection, the rate of convection activity and closure assumptions—determine modification of largescale environment due to the rate of convection activity (Haines and Sun 1994; Chen and Sun 2004). Many cloud researchers have implemented and tested a simple 1D cloud model into a CPS such as Kreitzberg and Perkey (1976), Anthes (1977), Fritsch and Chappell (1980a, b), Frank and Cohen (1987), Tiedtke (1989), Grell (1993), Hu (1997), and with a slightly sophisticated approach, Kain and Fritsch (1990, 1993). Here, all three mentioned components are considered for implementation of ETTM as a new CPS into ARPS model. We briefly highlight the technical steps that are needed to implement a new scheme in convective parameterization (ETTM) in ARPS below:
6 Steps for implementation of the new CPS including ETTM
2.
Three aspects should be considered in a CPS: the trigger function, which determines the location and occurrence
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1.
Generate a new module for the new convective parameterization that consists of the ETTM model. This module’s outputs determine the rate of convection and redistribution of thermodynamic and dynamic variables based on ETTM model. Generate another module to get pressure, potential temperature and specific humidity as inputs from the ARPS model and feed them to the module in step 1. The outputs of this module are potential temperature and moisture tendencies and the precipitation rate. In
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Fig. 6 Comparison of vertical total a mass flux (9108 kg), b heat flux (91012 J), and c moisture flux (9106 kg) for ETTM for the storm simulation case varying tilting angle of the cloud in ETTM with 5
tilting angle: 10°, 20°, 30°, 40°, 50°. The radius of cloud was considered 4,000 m
each time step ARPS refers to ETTM model. The fixed new configuration of the variables is set to the predicted values of these variables and so two-way interaction is implemented. Introduce a new package in the Makefile file of the ARPS model. Make change in some parameters of the input Name list of ARPS model. Modifying some programs in the ARPS model such as cumulus3d, tinteg3d, adas, difobs. For instance, in cumulus3d program the source/sink terms calculated in temperature and moisture equations and in tinteg3d program, the time integration of the dynamics of the basic governing equations orchestrate for a single time step.
reference modeled data has enough resolution to be considered a cloud resolving model (CRM), hereafter referred to as No-CPS-1KM (i.e., no CPS at 1 km resolution). The maximum and minimum amounts of each resolution are obtained much smaller than those ones in the next selected resolution. Therefore, in 4 km resolution, simulations of ARPS model with its different CPSs and the new scheme were compared with simulation with 2 km resolution without any scheme. In this way, at least it is possible to compare the performance of existing schemes. Finally, in 10 km resolution this comparison was done just with simulation of ARPS without any scheme. Note that for the inter-comparison of CPSs in a controlled environment, setup and initial sounding (20 May 1977) of ARPS is the same as described in Sect. 3 except that the time step is 5 s. These initial conditions are used for all simulations using available CPSs in ARPS [Kuo, Kuo along with warm rain microphysics of Kessler, Kain-Fritsch (KF) and Betts-Miller (BMJ) schemes] and also in the new CPS—namely ETTM. To study the life cycle of convective cells, we set the coordinates of initialization center of thermal bubble at (16, 48 km) for 1 km, at (32, 96 km) for 2 km, at (64, 192 km) for 4 km and at (320, 960 km) for 10 km horizontal resolution. First, we run ARPS without a CPS with a 2 km
3. 4. 5.
7 ARPS runs with the ETTM as a CPS This section presents the results of incorporation of ETTM into ARPS as a CPS, in addition, comparison with already existing CPS is also provided. To begin with, since suitable observational data is not available, we generated a reference high-resolution (1 km resolution) dataset with ARPS. The
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Fig. 7 Same as Fig. 6 but for cloud with radius of 3,000 m
horizontal grid spacing (No-CPS-2KM) to determine whether this model can detect any convection in this resolution explicitly (Gilliland 2007). The other performances using the above four schemes and new scheme including ETTM with this resolution (2 km) could be done to determine whether these schemes are capable of improving the explicit simulation or that we do not need to use them in this resolution. The results of these simulations were performed separately with 4 and 10 km resolutions. Figure 8 shows the results of 2 km resolution simulation using ETTM as a CPS in ARPS model. Similar to Fig. 2, the east–west oriented vertical cross sections of storm structure are provided; as it can be seen the general structures of two simulations are quite similar but quantitatively different. The simulation using ETTM as its CPS underestimates the results of simulation without CPS. Since the transfer of moist warm air into the convective cell is an important feature in study of convective clouds, simulated upward and downward velocities are evaluated for all simulations using different CPSs. Figure 9a shows time series of upward velocities for all simulations with 2 km resolution. As can be seen, the simulated upward velocities with the new scheme (ETTM) and the No-CPS1KM (running ARPS as a CRM) have identical trends but with a difference of about 11 m s-1 between them.
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Simulation with No-CPS-2KM and KF scheme also results in similar upward velocities. The simulated vertical velocity with No-CPS-2KM, KF and BMJ schemes not only differ from the simulated upward velocities from NoCPS-1KM, but also do not have the same tendency. Time series of the predicted downward velocities of 2 km resolution runs for all simulations are shown in Fig. 9b and show that the increase and decrease of simulated downward velocities is the same as No-CPS-1KM but there is a time delay between them. Simulated upward and downward velocities for all simulations with 4 km resolution (Fig. 9c, d) have been compared with result of the No-CPS-2KM scheme. Almost all simulations except simulation of KF scheme were consistent. The results of the simulation with new scheme and other schemes in the ARPS with resolution of 10 km (Fig. 9e) showed that in this resolution, there is not any superiority between the uses of these schemes, as they are not probably resolved in this resolution.
8 Discussion A one-dimensional ETTM cloud model which takes into account the separation of precipitation from an updraft cell
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Fig. 8 The x–z cross section of storm structure through the maximum vertical velocity for the case study with a the x and z direction wind vector (m s-1), b vertical velocities (m s-1), and c the perturbation potential temperature (K). The solid and dashed lines denote positive
and negative values, respectively. Time (min) of the simulation is noted along the left side. The simulation with 2 km resolution using ETTM as CPS in ARPS model
into a downdraft column is compared with a 3D simulation with ARPS. The ETTM is based on formulations presented in CS2004, although the results presented here are from an algorithm that was developed independently. The ETTM is developed so that it could be implemented as a CPS in ARPS.
Results of comparison with predictions of ARPS show that, the ETTM maximum heat and moisture fluxes are almost at the same heights, but ETTM underestimates their magnitudes. ETTM could not simulate the total mass flux consistent with that of the ARPS. The
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156 BMJ_2km Kuo_Kessler_2km
(a) Vertical velocity (m/s)
Fig. 9 Maximum vertical velocity (m s-1) for simulations performed with different cumulus parameterization schemes. a and b shows upward and downward velocities for 2 km horizontal resolution, respectively, c and d are the same as a and b but for 4 km resolution and finally e shows upward velocities for 10 km resolution
M. Gharaylou et al. ETTM_2km KF_2km
No CPS_2km No CPS_1km
30 25 20 15 10 5 0
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(b) 0 -1 0 -2 -3 -4 -5 -6 -7 -8
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(c)
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8 7 6 5 4 3 2 1 0 0
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0 0
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-0.5 -1 -1.5 -2 -2.5
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(e) Vertical velocity (m/s)
ETTM_4km KF_4km
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0.25 0.2 0.15 0.1 0.05 0 0
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maximum mass flux occurs at lower altitude than that of ARPS, and its magnitude is also less. This could be explained by the fact that the vertical velocity profile that is used for mass flux computation is extracted from
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the mature stage that updraft is dominant while the downdraft is not as strong as to affect the vertical motion. Because of the critical effect of vertical heat and moisture fluxes on cloud development (Haines and Sun
Implementation of a new cumulus parameterization scheme based on an explicit
1994), the ETTM scheme has the required ability to be used as a CPS. Sensitivity analysis by changing the radius and tilting angle in the ETTM shows that, for the larger radius of cloud there are higher flux magnitudes. Also, the greater the tilting angle, the smaller the mass flux magnitude due to downdraft effect. The radius of updraft and downdraft columns and the tilting angle for the ETTM simulation are obtained from the mature stage of cloud in ARPS simulation. Therefore, some of the differences in the profiles of the cloud variables could be explained by the effect of arbitrary fixing of the radii and the titling angle. The environmental profile in the ETTM is time-independent, whereas in ARPS there is a two-way interaction between cloud and the surrounding. ETTM was also incorporated into ARPS as a new CPS and the results of simulation using ETTM and other CPSs were compared at 2, 4 and 10 km grid spacing. Simulation results with 2 km resolution showed that in this resolution, the simulated time series of updraft velocities using the new scheme (ETTM) compared well with the results of other schemes in the ARPS model. The simulated vertical velocity values simulated with KF and No-CPS-2KM schemes not only were much different from No-CPS-1KM scheme simulation, but also did not have the same tendency. This result also was true about simulation results with BMJ scheme. The simulations with horizontal resolution of 4 km that was compared with No-CPS-2KM scheme showed almost consistent results for all schemes except for that of KF scheme. The results of the simulation with new scheme and other schemes in the model with resolution of 10 km showed that in this resolution, there is not any superiority between the uses of these schemes.
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