Evaluating convective parameterization closures using cloud ...

PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE 10.1002/2014JD022246 Special Section: Fast Physics in Climate Models: Parameterization, Evaluation and Observation

Evaluating convective parameterization closures using cloud-resolving model simulation of tropical deep convection E. Suhas1 and Guang J. Zhang1,2 1

Key Points: • Evaluate convective parameterization closures • Understand relationships between closure variables and convection • Use cloud-resolving model results for improving convective parameterization

Correspondence to: G. J. Zhang, [email protected]

Citation: Suhas, E., and G. J. Zhang (2015), Evaluating convective parameterization closures using cloud-resolving model simulation of tropical deep convection, J. Geophys. Res. Atmos., 120, 1260–1277, doi:10.1002/2014JD022246. Received 1 JUL 2014 Accepted 22 JAN 2015 Accepted article online 24 JAN 2015 Published online 19 FEB 2015

Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA, 2Center for Earth System Science, Tsinghua University, Beijing, China

Closure is an important component of a mass flux-based convective parameterization scheme, and it determines the amount of convection with the aid of a large-scale variable (closure variable) that is sensitive to convection. In this study, we have evaluated and quantified the relationship between commonly used closure variables and convection for a range of global climate model (GCM) horizontal resolutions, taking convective precipitation and mass flux at 600 hPa as measures for deep convection. We have used cloud-resolving model simulation data to create domain averages representing GCM horizontal resolutions of 128 km, 64 km, 32 km, 16 km, 8 km, and 4 km. Lead-lag correlation analysis shows that except moisture convergence and turbulent kinetic energy, none of the other closure variables evaluated in this study show any relationship with convection for the six subdomain sizes. It is found that the correlation between moisture convergence and convective precipitation is largest when moisture convergence leads convection. This correlation weakens as the subdomain size decreases to 8 km or smaller. Although convective precipitation and mass flux increase with moisture convergence at a given subdomain size, as the subdomain size increases, the rate at which they increase becomes smaller. This suggests that moisture convergence-based closure should scale down the predicted mass flux for a given moisture convergence as GCM resolution increases.

Abstract

1. Introduction In global climate models (GCMs), deep convection is a subgrid-scale phenomenon, and its collective effect is represented through convective parameterization schemes (CPSs). Most of the CPSs follow the mass flux framework in which the effect of convection is estimated using a one-dimensional bulk or spectral plume model. The mass flux-based CPSs are built on the assumption that the convective activity is regulated by the large-scale or grid-resolved fields and a statistical description of the ensemble of convective clouds can be made in terms of the large-scale variables, provided that a scale separation exists between the convective scale and the large-scale fields [Arakawa and Schubert, 1974; Arakawa, 2004; Yano et al., 2013]. Closure assumption is a crucial part of such CPSs, and it determines the intensity of the ensemble of convection in a GCM grid box with the aid of large-scale variables. An ideal closure variable should be based on a clearly identifiable hypothesis on parameterizability and should be physically associated with convection [Arakawa, 2004]. The overall performance of a CPS, to a large extent, depends on the how well the closure variable satisfies these conditions. Deterministic closure schemes are broadly classified into diagnostic and prognostic closures [Arakawa and Schubert, 1974; Pan and Randall, 1998]. Diagnostic closure is the most commonly used closure type. Different kinds of diagnostic closures are designed based on mechanisms that physically describe the interactions between convective and large-scale motions. Quasi-equilibrium (QE), moisture conservation, boundary layer QE, and free tropospheric QE constraints form the basis for many of the present-day closures [Arakawa and Schubert, 1974; Kuo, 1974; Raymond, 1995; Zhang, 2002, 2003; Bechtold et al., 2014]. According to the original QE hypothesis, instability created by the large-scale motion is immediately consumed by convective activity, whereby an equilibrium is maintained. Later, the instantaneous maintenance of QE was modified by allowing a finite time interval for relaxing toward equilibrium [Moorthi and Suarez, 1992; Zhang and McFarlane, 1995]. Convective available potential energy (CAPE) is often used as the closure variable in QE-based CPSs. The basic idea behind it is that CAPE is the energy available for convection. Moisture convergence is another closure variable in QE-based CPSs; it is based on the notion that the large-scale supply of moisture is balanced

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by consumption by convective processes. There are also arguments that boundary layer processes control convection [Raymond, 1995; Rio et al., 2009, 2012; Hohenegger and Bretherton, 2011; Gentine et al., 2013]. An example is the activation control of convection based on the hypothesis that deep convection intensity is controlled by the low-level processes that govern its initiation [Mapes, 1997]. This hypothesis has garnered much attention in recent years among researchers developing a unified shallow and deep convection scheme. It relates the mass flux at the cloud base to the relative strength of convective inhibition (CIN) at the top of the subcloud layer and the amount of boundary layer turbulence. A formulation involving a combination of turbulent kinetic energy (TKE) and CIN is used as the closure variable [Hohenegger and Bretherton, 2011; Fletcher and Bretherton, 2010]. A recent study that followed the activation control framework introduced a new closure variable called available lifting energy [Rio et al., 2009, 2012]. It is based on the idea that boundary layer thermals and cold pools provide energy and power to lift and sustain convection. Most GCMs that use deterministic CPSs often fail to reproduce the observed spatial distribution, variance, and probability distribution of precipitation [Dai 2006]. The poor performance of the GCMs in simulating the dominant modes of different spatial and temporal variabilities is mainly attributed to the CPS and its closure assumption. For example, simulation of Madden-Julian Oscillation, equatorial waves, El Niño–Southern Oscillation, Asian monsoon, and diurnal cycle of precipitation are sensitive to the CPSs, and the closure is one of the main sources of error [Zhang and Mu, 2005; Lin et al., 2006, Wu et al. 2007, Neale et al., 2008; Rio et al., 2012]. The nature and type of closure assumption determine the behavior of a CPS and influence the realistic simulation of these phenomena. Several studies show that the performance of the GCMs in simulating some of these phenomena can be improved by introducing new closure assumptions/variables. For example, the early peaking of diurnal precipitation can be minimized by using either free tropospheric QE assumption or coupling the convection scheme with a cold pool scheme [Zhang, 2003; Bechtold et al., 2014; Rio et al., 2009]. Closure is also important to realistic short- and medium-range weather forecasts in the tropics and midlatitudes [Yano et al., 2013]. Hence, the choice of a closure variable in the CPS has a crucial effect on the performance of a GCM. The selection of a closure variable is usually based on the assumed relationship between the closure variable and convection. Hence, an understanding of the behavior of a closure variable in relation to convection is very important. Many studies have examined the relationship between commonly used closure variables and convection using field experiment data [e.g., Zhang, 2002, 2003; Donner and Phillips, 2003; Davies et al., 2013]. Since the field experiment data sets are constrained by precipitation from convection, e.g., in the variational analysis technique of Zhang and Lin [1997], the diagnosed convective activity and the large-scale fields may not provide completely independent information. Another shortcoming of using field experiment data is that these experiments are designed for representing a typical GCM horizontal resolution of 200 km or so. As GCM resolutions increase to 50 km or higher [Bacmeister et al., 2014], currently available field data cannot be used to assess the validity of closure assumptions for high-resolution GCMs. The advancement of cloud-resolving models (CRMs) and their realistic simulation of convective systems over the past decade make them excellent data sources for convective parameterization development and evaluation. In particular, the CRM domain can be divided into subdomains of varying sizes to mimic the GCM grid spacing at different resolutions. Therefore, the data can be used to examine if the current convection parameterization schemes are scale aware as the GCM resolution increases. Of course, CRM simulations are not completely free from drawbacks [Bryan et al., 2003; Varble et al., 2011, 2014; Fridlind et al., 2012]. Bryan et al. [2003] showed that the explicit simulation of the detailed structure of a convective system is sensitive to the grid size of the model. A recent CRM intercomparison study by Varble et al. [2014] found that the CRMs tend to overestimate maximum vertical velocities in deep convective updrafts, thus producing stronger updraft mass flux. Nevertheless, as long as the fine structure of the spatiotemporal convective variability is not of primary importance, CRM simulations of the ensemble of convective clouds can be used for guiding the evaluation and development of convection parameterization in GCMs. The objective of this study is twofold. First, it investigates the possible relationship between commonly used closure variables and convective activities for the horizontal resolution typical of current GCMs using CRM simulation output. It is expected that the analysis would bring out the pros and cons of various closure assumptions. Second, we investigate the scale awareness of these closures as the averaging size, mimicking the GCM grid spacing, becomes smaller. It intends to provide some information on the suitability of existing

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closures for high-resolution GCMs. The paper is organized as follows. Section 2 describes the different closure variables and the CRM model used in the study. Section 3 presents the important results and their discussions. Section 4 provides a summary and conclusion of the study. Figure 1. Domain averaged 3-hourly GCE CRM precipitation data (black line) and 3-hourly TWP-ICE precipitation data (red dashed line) for the period from 5 to 10 February 2006.

2. Data and Methodology

In this study we use the simulation output from a three-dimensional CRM, the Goddard Cumulus Ensemble (GCE) model [Tao and Simpson, 1993] prescribed with large-scale forcing derived from Tropical Warm Pool International Cloud Experiment (TWP-ICE) to evaluate the relationship between commonly used closure variables and convection. The TWP-ICE experiment was carried out during the northern Australian summer monsoon season of 2006 (January and February) [May et al., 2008]. The period from 21:00 UTC on 4 February 2006 to 21:00 UTC on 10 February 2006 is chosen, which was a typical monsoon break period characterized by intense afternoon thunderstorms and squall lines. The GCE model is nonhydrostatic and anelastic. The model domain covers an area of 256 × 256 km2 over the Atmospheric Radiation Measurement Program intensive observation period Darwin site. The model has 41 vertical levels with model top height at approximately 21 km. It has a 1 km horizontal resolution and a vertical resolution ranging from 42.5 m at the bottom to 1 km at the top, and it uses a time step of 6 s for integration (see Zeng et al. [2008, 2011] for further details of the model). The simulation used in this study is the same as the T06H experiment in Zeng et al. [2011]. One caveat should be noted here. While 1 km horizontal resolution has been used in most CRM simulations as a trade-off between model resolution and domain coverage, sensitivity analysis of CRM studies showed that such grid spacing is too coarse to adequately resolve the updrafts and downdrafts of individual clouds [Bryan et al., 2003; Fridlind et al., 2012]. Also, the domain size of 256 × 256 km2 may be somewhat too small for large convective systems. However, since we are mainly concerned with the collective properties of convective clouds within a GCM-sized region, this should not affect our main results in quantifying the relationship between convection and large-scale (or GCM grid scale) variables as represented by averages over various subdomain sizes. The GCE model is capable of explicit simulation of tropical convection. Figure 1 shows the simulated precipitation rate averaged over the CRM model domain and the observed precipitation. For comparison with observations, which is available every 3 h, CRM-simulated precipitation is averaged to a 3 h time interval. There is, in general, a good agreement between the observed and simulated precipitation events except on 7 February when there is a time shift between them. Since the CRM uses prescribed large-scale forcing, the good agreement between the observed and simulated precipitation averaged over the CRM domain is to a large extent expected. However, as the subdomain size decreases, the model-generated large-scale circulation becomes dominant and starts to dictate the location and intensity of convective activity, whereas the influence of prescribed forcing in a subdomain diminishes quickly. Thus, our analysis will focus on subdomain sizes of 128 km and smaller. We use 6 min interval vertical profiles of temperature; mixing ratios of water vapor, liquid, and ice; wind velocity; and precipitation rate for further analysis. To assess the validity of the closure assumptions for different horizontal resolutions corresponding to contemporary GCMs, the CRM data over the 256 × 256 km2 domain are averaged over different horizontal subdomains of grid sizes 128 km, 64 km, 32 km, 16 km, 8 km, and 4 km, respectively. When a model’s grid spacing falls below about 10 km, it reaches the grey zone where a clear-scale separation between grid scale and subgrid scale no longer exists, and the parameterizability of convection becomes questionable [Arakawa, 2004; Arakawa et al., 2011; Arakawa and Wu, 2013]. Therefore, examining the possible relationships between convection and area-averaged variables for subdomain sizes of 8 km and 4 km will provide useful information on the parameterizability of convection when GCMs or numerical weather prediction models reach such high resolutions. When the 1 km horizontal resolution CRM data over the 256 × 256 km2 domain are divided into four quadrants, each having size of 128 × 128 km2, the data are averaged over each quadrant, and the resultant data are treated equivalent to the output of a

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GCM of 128 km horizontal resolution. The data for 64 km, 32 km, 16 km, 8 km, and 4 km GCM resolutions (hereafter referred to as subdomains) are obtained similarly. We assume that the CRM convective precipitation averaged for a subdomain represents the effect of an ensemble of convective clouds of the corresponding spatial domain. The average convective precipitation in a subdomain is derived from the total precipitation over all convective grid points divided by the subdomain area. A convective grid point is defined as the grid point where vertical velocity is greater than 1 m/s or less than 1 m/s and the sum of the mixing ratios of water vapor, cloud liquid, and ice water is greater than 1 × 105 kg/kg. We quantify the relationship between closure variables and convection by correlating closure variables and convective precipitation. Another measure of convective activity is convective mass flux. Mass flux (M) at a given pressure level is defined as M ¼ σρw

(1)

where σ is the fractional area coverage, ρ is the air density, and w is the vertical velocity averaged over all the convective grid points at a given pressure level. The convective parameterization closure variables tested in this study are listed below. 1. Moisture convergence: The vertical integral of moisture convergence was used as a closure variable for convective parameterization by Kuo [1974], Bougeault [1985], and Tiedtke [1989]. It is defined as Mc ¼

p p 1 s 1 s ∂q ∂q ∂q dp ∇ðVqÞdp ¼ u þv þω g0 g0 ∂x ∂y ∂p

∫

∫

(2)

where V = (u, v) and ω are the zonal, meridional, and vertical components of wind, q is the specific humidity, g is the acceleration due to gravity, and Ps is the lowest model pressure level. The mass continuity equation is used to express moisture convergence in advection form in equation (2). 2. CAPE: It is used as a closure variable in many CPSs that follow the QE framework [e.g., Fritsch and Chapell, 1980; Betts and Miller, 1986; Kain and Fritsch, 1990; Zhang and McFarlane, 1995; Bechtold et al., 2001]. CAPE is defined as the vertical integral of buoyancy of an air parcel lifted from the source level to the neutral buoyancy level. pb

CAPE ¼

∫ Rd

T vp T ve dlnp

(3)

Pt

where Tvp and Tve are the virtual temperature corresponding to the parcel and environment, respectively, Pb and Pt represent the pressure at the source level and neutral buoyancy level, respectively, and Rd is the gas constant for dry air. 3. Dilute CAPE: It is the same as CAPE in equation (3), except that the calculation of Tvp includes the dilution effect from entrainment of environmental air. Compared to CAPE closure, dilute CAPE closure shows improvements in the simulation of dominant modes of variability. It has been used in the latest version of the National Center for Atmospheric Research Community Atmosphere Model version 5 model [Neale et al., 2008; Wang and Zhang, 2013] and an updated version of Kain-Fritsch scheme in Weather Research and Forecasting [Kain, 2004]. In the dilute CAPE calculation, we have used the same entrainment formulation as given in Zhang [2009]. The fractional entrainment rate decreases with height as 1/z with a cloud base value of 1 × 103 m1. pffiffiffiffiffiffiffiffi 4. TKE expðCIN=TKEÞ: This is a closure variable proposed by activation control hypothesis and is mainly used in idealized models and convection schemes that extend the shallow convection scheme to deep convection schemes [Mapes, 1997; Fletcher and Bretherton, 2010; Hohenegger and Bretherton, 2011]. CIN is defined as the vertical integral of buoyancy between parcel source level and the level of free convection (LFC). plf c

CIN ¼

∫ Rd

T vp T ve dlnp

(4)

pb

Note that CIN so defined is positive, representing the inhibition energy the parcel needs to overcome before reaching the LFC. In GCMs, TKE is from planetary boundary layer parameterization. Here since CRM provides

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high-resolution data, TKE is directly calculated from the CRM wind fields and is averaged vertically below the cloud base and horizontally over the GCM-sized subdomain in concern. " p # 1 1 s 1 2 2 2 u’ þ v’ þ w’ dp dA TKE ¼ (5) A Δp p 2

∫

∫

b

where u′, v′, and w′ are the zonal, meridional, and vertical wind anomalies that are obtained by removing the respective mean fields; Δp is the thickness of the subcloud layer; ps is the surface pressure, and A is the subdomain area to represent the GCM grid size. Since TKE is the most weighted factor in the formula and since it shows significant relationship with convection [Fletcher and Bretherton, 2010],phere ffiffiffiffiffiffiffiffi we also separately examine the relationship between TKE and convection in addition to the expression TKEexpðCIN=TKEÞ. The TKE estimated using the 1 km resolution CRM data may underestimate the magnitude of true TKE associated with convection. Nevertheless, as we are only interested in the statistical relationship between convection and TKE, it should not affect the results qualitatively. 5. Saturation fraction: It is the column-integrated water vapor divided by that of saturation water vapor with respect to the same temperature profile. ,p p f¼

s

s

pt

pt

∫ qdp ∫ qs dp

(6)

This is used as a closure variable in simple theoretical models [Raymond and Fuchs, 2007]. There are other closures, in particular, the free tropospheric quasi-equilibrium closure proposed by Zhang [2002] and recently modified by Bechtold et al. [2014]. Since this category of closures involves the calculation of large-scale forcing and the associated generation of CAPE, it requires much more work to process the data. Thus, we defer a systematic analysis to a future study.

3. Results 3.1. General Description In this section, we first examine the relationship between different closure variables and convection for the 128 km subdomain, similar to the horizontal resolution of the present-day GCMs. Figure 2 shows the scatterplots of convective precipitation as a function of different closure variables. The range of each closure variable is divided into a number of bins, and the mean precipitation corresponding to the values of the closure variable falling into each bin is calculated and plotted as red dots. Among the closure variables, only moisture convergence, TKE, and saturation fraction show some kind of relationship with convection. Moisture convergence shows an approximately linear relationship with convective precipitation when moisture convergence is greater than zero, and the relationship breaks down when moisture convergence is negative (Figure 2a). For negative moisture convergence, there is also precipitation, although the number of data points is small. Further examination indicates that these are often associated with the dissipating periods of convection when there are downdrafts in the lower troposphere (Figure 10). Undilute and dilute CAPEs do not show any relationship, similar to what was found in observations [Zhang, 2003, 2009; Davies et al., 2013; Peters et al., 2013]. TKE shows a strong linear relationship with convective precipitation. However, pffiffiffiffiffiffiffiffi no relationship is observed between TKE expðCIN=TKEÞ and convective precipitation (Figure 2e). It is due to the insensitivity of CIN to the state of convection. For saturation fraction (Figure 2f), there is little precipitation when the saturation fraction is below 0.8. Above it, precipitation increases dramatically. However, there are many instances of no or little precipitation even when saturation fraction is above 0.8, such that the bin average precipitation only increases with saturation fraction modestly. While convective precipitation is a useful measure of convective activity, in convective parameterization schemes, the closure variable is related to convective mass flux, often at the cloud base. However, in CRM simulations, identifying cloud base is a nontrivial issue. First, the cloud base defined in convective parameterization schemes does not necessarily mean the visual cloud base, which can be identified in CRMs through proper use of threshold values of cloud water. Second, the identification of convective cloud base in CRM can be sensitive to the vertical velocity threshold. Although mass flux at cloud base is used in convective parameterization closures, the mass flux framework propounds that the strength of convection can be SUHAS AND ZHANG


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Figure 2. Scatterplots of convective precipitation (mm/h, y axis) against different closure variable (x axis) over theffi 128 km pffiffiffiffiffiffiffi 2 2 subdomain for (a) moisture convergence (mm/h), (b) CAPE (J/kg), (c) dilute CAPE (J/kg), (d) TKE (m /s ), (e) TKE exp ðCIN=TKEÞ (m/s), and (f) saturation fraction. The red dot represents the mean convective precipitation corresponding to each closure variable bin.

related to mass flux at any pressure level at or above the cloud base [Fletcher and Bretherton, 2010; Yano et al., 2013]. Therefore, in order to identify the pressure level at which mass flux is the best measure of convection, we examine the relationship between convective precipitation and mass flux at all pressure levels. Figure 3 shows the lead-lag correlation between mass flux at various pressure levels and convective precipitation. The strong correlation between convective precipitation and mass flux at all pressure levels indicates the physical connection between the two. At all pressure levels, significant correlation is observed when mass flux leads convective precipitation. Maximum correlation is observed between convective precipitation and mass flux around 600 hPa. The amplitude of correlation is higher (~0.94) when mass flux at 600 hPa leads convective precipitation by about 18 min. The lead time of maximum correlation is longer in the lower levels

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than in the upper levels. For example, at 900 hPa, the lead time is 24 min, and at 400 hPa, it is close to 6 min. This reflects the vertical development of convection, with shallow convection developing first, followed by deeper convection. We quantify the relationship between different closure variables and measures of convection using canonical correlation analysis. Since the common approach of simultaneous correlation analysis does not provide any causality information, we adopt a lead-lag correlation analysis strategy. The lead-lag correlation coefficients are estimated in each subdomain, and the average value is computed over all subdomains. Figure 4a shows the lead-lag correlation between closure variables and convective precipitation. Negative (positive) lags mean that closure variable lags (leads) convective precipitation. Since the linear relationship between moisture convergence and convective precipitation was found to Figure 3. Lead-lag correlation between convective be restricted to positive values of moisture convergence, precipitation and mass flux at different pressure levels data points with negative moisture convergence are for the 128 km subdomain. The positive (negative) excluded from the analysis. On the grounds that values on x axis represent the mass flux leading (lagging) correlation analysis assumes linear relationship, the convective precipitation by a given amount of time. logarithmic values of saturation fraction are correlated with convective precipitation. It is found that except moisture convergence and TKE, none of the closure variables show strong correlation (Figure 4a). Higher correlation is found when moisture convergence leads convective precipitation. Highest value of correlation coefficient (~0.7) between moisture convergence and convective precipitation is observed at 18–24 min lead, and the high correlation persists for a lead time of about 60 min. For negative lag, the correlation drops quickly. The fact that the correlation is high (low) when moisture convergence leads (lags) convective precipitation suggests that moisture convergence acts as a forcing of convective precipitation. Although dilute and undilute CAPEs do not show any relationship with convective precipitation at lag 0, they exhibit a moderate correlation when they lead convective precipitation (by 2.5 h for dilute CAPE and 3 h or more for undiluted CAPE. The latter has a maximum correlation coefficient of about 0.4 at a lead time of about 3 h, and it persists for several h). As evident from Figure 2d, TKE and convective precipitation show strong correlation (Figure 4a). In contrast to moisture convergence, TKE shows higher Figure 4. (a) Lead-lag correlation between convective precipitation correlation when it lags convective and different closure variables for the 128 km subdomain. The positive precipitation by 6–12 min. The correlation pffiffiffiffiffiffiffiffi (negative) values on the x axis represent the closure variable leading between TKE expðCIN=TKEÞ and (lagging) convective precipitation by a given amount of time. (b) Same as convective precipitation is very low Figure 4a but for mass flux at 600 hPa. SUHAS AND ZHANG


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(