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Evaluation of Trigger Functions for Convective Parameterization Schemes Using Observations E. SUHAS AND GUANG J. ZHANG Scripps Institution of Oceanography, La Jolla, California (Manuscript received 25 November 2013, in final form 7 March 2014) ABSTRACT Realistic simulation of different modes of atmospheric variability ranging from diurnal cycle to interannual variation in global climate models (GCMs) depends crucially on the convection trigger criteria. In this study, using the data from constrained variational analysis by the Atmospheric System Research program for singlecolumn models (SCM), the performance of the commonly used convective trigger functions in GCMs is evaluated based on the equitable threat score (ETS) value, a widely used forecast verification metric. From the ETS score, three consistently better-performing trigger functions were identified. They are based on the dilute and undilute convective available potential energy (CAPE) generation rate from large-scale forcing in the free troposphere (hereafter dCAPE) and parcel buoyancy at the lifting condensation level (Bechtold scheme). The key variables used to define these trigger functions are examined in detail. It is found that the dilute dCAPE trigger function performs the best consistently in both the tropical and midlatitude convective environment. Analysis of the composite fields of key variables of the trigger functions, based on the correct prediction, overprediction and underprediction of convection, and correct prediction of no-convection cases for convective onset, brings to light some critical factors responsible for the performance of the trigger functions. The lower-tropospheric advective forcing in dilute dCAPE trigger and vertical velocity in Bechtold trigger are identified to be the most importance ones. Suggestions are offered for further improvements.
1. Introduction Capturing convection at the right time and place is crucial for the realistic simulation of atmospheric variability ranging from weather to climate scales. Since most of the present-day global climate models (GCM) cannot explicitly resolve convection, the ensemble effect of convection is represented through parameterization. In a convective parameterization scheme (CPS), the possibility for convection is assessed based on a set of rules, collectively known as the ‘‘trigger function.’’ The trigger function activates the CPS if it detects a potential for deep convection. Hence, an accurate trigger function is important to the correct simulation of convection. To avoid any potential confusion on the terminology of trigger function among different communities, we should point out here that trigger function in this paper strictly means activation of convective parameterization, as commonly known in the convective parameterization
Corresponding author address: Guang J. Zhang, 9500 Gilman Dr., La Jolla, CA 92093-0221. E-mail:
[email protected] DOI: 10.1175/JCLI-D-13-00718.1 Ó 2014 American Meteorological Society
community. In the community of the physics of convection, triggering means the onset of convection, which will go through its life cycle afterward. This is different from the use of terminology in this study. Current convective parameterizations do not consider the history of convection and therefore cannot distinguish different stages of convection. As long as a set criterion is met, convection parameterization will be triggered or activated, regardless of at which stage of convection it may be in nature. Such shortcomings will be discussed at the end of the paper. The timing and location of the occurrence of convection influences the vertical distribution of temperature and moisture, gravity wave propagation and several other nonlinear feedbacks that have significant effects on the characteristics of the GCM simulation (Rogers and Fritsch 1996). In many CPSs, the physical basis of the trigger function is that convectively unstable air within the boundary layer under certain conditions can result in the onset of convection. The major difference among the different trigger functions basically lies in the identification of the source layer of convection and how it realizes the convective instability for cloud
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development. The commonly used parameters for releasing the convective instability of the boundary layer air are the grid-scale vertical velocity (Kain and Fritsch 1990; Donner 1993; Bechtold et al. 2001), boundary layer moisture convergence (Kuo 1974; Tiedtke 1989), and the amount of convective available potential energy (CAPE) (Arakawa and Schubert 1974; Zhang and McFarlane 1995, hereafter ZM95). However, the formulation of trigger functions in many of the CPSs is rather ad hoc and convection is often realized too easily. The overactivation of convection can lead to large errors in both the amplitude and variance of different modes of atmospheric variability (Dai 2006). The simulation of a large number of atmospheric phenomena is very sensitive to the activation criteria for convection. The case of the Madden–Julian oscillation (MJO) is a notable example. It is well known that the deficiency and wide range of skills in simulating the MJO by current generation GCMs are mainly due to the poor representation of convection and its interaction with the large-scale dynamics (Lin et al. 2006), and improvements in the simulation of MJO are often achieved by tweaking the convection triggering criteria. For example, a better performance of the CPS in simulating the MJO and convectively coupled equatorial waves was attained by adding a moisture trigger to the existing scheme and/or by modifying the closure (Wang and Schlesinger 1999; Zhang and Mu 2005; Lin et al. 2008). It was found that the incorporation of more stringent convective onset criteria could alleviate the deficiency of seasonal migration of the intertropical convergence zone (ITCZ) and ‘‘double ITCZ’’ biases of the aquaplanet GCMs (Wu et al. 2007; Chao and Chen 2004). A recent study by Liu et al. (2010) highlighted the role of trigger functions in the simulation of the ITCZ by the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) using Tiedtke (1989) and ZM95 CPSs. Another important area where the trigger function plays a crucial role is in the simulation of the diurnal cycle of convection and precipitation (Knievel et al. 2004; Xie et al. 2004b; Lee et al. 2007; Bechtold et al. 2004). The simulation of the diurnal cycle of precipitation has serious issues, and numerical experiments in a single-column model (SCM) framework reveal that the CPS is the main source of error. Sensitivity experiments show that certain CPSs work better for some specific geographic regions or cases and perform poorly over other regions, indicating the failure of CPSs to take into account the various dynamical and thermodynamic constraints (Liang et al. 2004). The common problem in the simulation of the diurnal cycle of precipitation is the peaking of precipitation too early, usually 2–4 h before
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the observed maxima. This issue is related to the weakness in the trigger function formulation (Betts and Jakob 2002; Xie et al. 2004b; Bechtold et al. 2004). A set of sensitivity experiments with four different trigger functions implemented in the relaxed Arakawa–Schubert CPS showed significant differences in the simulation of phase and amplitude of the diurnal cycle of precipitation over the U.S. Great Plains during the Northern Hemisphere summer (Lee et al. 2008). It is also found that the addition of large-scale dynamic constraints on the trigger function can significantly reduce the model bias and improve the diurnal cycle of the model precipitation (Xie et al. 2004b). In a recent development, several studies showed that the phase bias in the diurnal cycle of convection in the Laboratoire de Météorologie Dynamique–Zoom (LMDZ) model could be minimized by modifying the trigger and closure conditions by considering the cold pool in the deep convection scheme (Rio et al. 2009; Grandpeix and Lafore 2010; Rio et al. 2013). They introduced a new convection trigger variable called available lifting energy (ALE), which is based on the notion that the dynamical lifting of the boundary layer air by the cold pool gust front can trigger the onset of convection. It has also been reported that the nature and design of the trigger function can influence the simulation of extreme precipitation events (Truong et al. 2009) and the skill of short-range weather forecasts (Kain and Fritsch 1992; Bright and Mullen 2002). It is clear that the trigger function holds a pivotal position in a CPS and it can have significant impacts on the behavior and performance of the GCM. In spite of its importance to convective parameterization, and thus GCM simulation of climate, the trigger function in CPSs is ad hoc, and there is no systematic evaluation of its performance to date. Confidence can be gained by systematically assessing the performance of different trigger functions using observations from different climate regimes. In this study we evaluate and quantify the performance of commonly used trigger functions using data from intensive observation periods (IOP) of field campaigns and long-term forcing data prepared for SCMs by the Atmospheric System Research (ASR) program over different geographical locations. It is expected that the systematic evaluation and comparison of trigger functions will eventually lead to an improved design of convection trigger conditions and better GCM simulations of climate by reducing the biases of the existing schemes. The paper is organized as follows: Section 2 describes the trigger functions for convective parameterization schemes and the datasets used to evaluate them in the study. Section 3 gives a detailed description of the
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methodology adopted to evaluate the trigger functions. Section 4 presents the important results. Finally, section 5 provides a summary and discussion of the study.
2. Convection trigger functions and evaluation data a. Trigger functions We have identified eight trigger functions for convection initiation from widely used CPSs from both GCMs and regional climate models. They are briefly described below.
1) KAIN–FRITSCH SCHEME The trigger function in the Kain–Fritsch (KF) scheme (Kain 2004) is determined by the thermodynamic state and large-scale ascent of air in the boundary layer. For a given sounding of the atmospheric state, the first step is to identify a potential source layer for convection. Beginning from the surface, a 60-hPa layer of air is mixed, and its lifting condensation level (LCL) pressure and temperature are calculated using Bolton (1980)’s formula. A temperature perturbation depending on the gridmean vertical velocity at the LCL is calculated using dT 5 k[wg 2 c(z)]1/3 ,
(1a)
where k is a constant (k 5 1 K s1/3 cm21/3), wg is the gridmean vertical velocity (cm s21), and c(z) is a threshold vertical velocity given by ( w0 (ZLCL /2000) , ZLCL # 2000 , (1b) c(z) 5 ZLCL . 2000 w0 , where w0 5 2 cm s21, and ZLCL is the height of the LCL above the surface in meters. The temperature perturbation dT is to account for the effect of grid-scale vertical velocity on convection initiation. If TLCL 1 dT . Tenv, the environmental temperature, the layer becomes a candidate for the source layer of convection. An air parcel from this layer is then lifted upward with a vertical velocity of
dT wp0 5 1 1 1:1 (ZLCL 2 Zsl ) Tenv
1/2 ,
(2)
where Zsl is the height at the base of source layer. With this initial vertical velocity, the air parcel is lifted upward with entrainment, which is specified, and water loading. If the vertical velocity of the parcel remains positive for a minimum depth of 3 km, convection is initiated. Otherwise, the procedure is repeated by moving up one model layer. The process continues until a convective source layer is found or the search has moved up above the lowest 300 hPa of
the atmosphere, where the search is terminated. The Kain–Fritsch scheme has been used as the default scheme (along with other schemes as options) in the NCAR Weather Research and Forecasting (WRF) model.
2) BECHTOLD SCHEME The trigger function in the Bechtold scheme (Bechtold et al. 2001) is modified from that of the Kain– Fritsch scheme, with changes as follows. The temperature perturbation is related to grid-scale upward motion in a different form: 1/2 1/3 wA , dT 5 sign(w)cw Dx
(3)
where cw 5 6 K m21/3 s1/3, Dx is the grid spacing in kilometers, w is the grid-scale vertical velocity, and A is the area of the domain and here A1/2Dx21 5 1. The cloud top is determined by the level of neutral buoyancy (LNB) as opposed to the zero vertical velocity level invoking the vertical velocity equation for a lifted parcel. In the Bechtold scheme convection is initiated when the parcel raised from the source layer satisfies the instability criteria at the LCL uparcel 1 dT . uenv and the estimated cloud height is at least 3 km.
3) TIEDTKE SCHEME The Tiedtke scheme (Tiedtke 1989) is a widely used convection scheme by the European modeling community. It assumes that convection will initiate if the atmospheric column has a net moisture convergence and the surface air is buoyant when lifted to the lifting condensation level, that is, ðp s ›q dp . 0, 2V $q 2 v ›p 0 and Tvp 1 DT . Tve at LCL , (4) where ps is the surface pressure, V is the horizontal wind velocity, v is the pressure velocity, q is the specific humidity, Tvp is the virtual temperature of the parcel, Tve is the virtual temperature of the environment, and DT is the perturbation temperature, which is set to 0.5 K. It also requires that the cloud thickness determined by the difference between the neutral buoyancy level and the LCL be greater than 3 km.
4) MODIFIED TIEDTKE SCHEME A modified version of the Tiedtke scheme has been used in the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) since 2004. There are two changes. First, a CAPE-based closure is used to replace the moisture
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convergence-based closure (Nordeng 1994). Second, the trigger conditions for convection initiation are changed (Jakob and Siebesma 2003; Bechtold et al. 2004). These include that 1) air in the lowest 350-hPa layer, not just surface air as in the original Tiedtke scheme, is searched for unstable parcels; 2) the air parcel’s vertical velocity instead of the neutral buoyancy level is used to determine cloud-top height; 3) the cloud thickness so determined must exceed 200 hPa (instead of 3 km as in the original Tiedtke scheme); and 4) both temperature and moisture perturbations are included in the calculation of initial updraft properties.
5) ZHANG–MCFARLANE SCHEME The Zhang–McFarlane scheme (ZM95), which uses CAPE as closure, has been used in the NCAR CAM since 1995. For convection trigger, it assumes that convection will initiate if an air parcel lifted adiabatically from the level of highest moist static energy below 600 hPa is convectively unstable with CAPE exceeding a threshold value (70 J kg21). Typically, this level is within the lowest couple of model layers. Recently, Neale et al. (2008) modified the Zhang–McFarlane scheme by including the effect of entrainment dilution in CAPE calculation. The entrainment rate decreases with height as z21 with a maximum entrainment rate equal to 1 3 1023 m21 at the LCL in CAPE calculation. Accordingly, the trigger function for convection is also revised, with the convection initiation level remaining the same, but the dilute CAPE exceeding the threshold value of 70 J kg21 for convection to initiate. This revised trigger (hereafter dilute CAPE) is currently used in the NCAR CAM, version 5 (CAM5). Another modification of the Zhang–McFarlane scheme was used to improve the simulation of MJO and ITCZ (Zhang 2002; Zhang and Mu 2005; Zhang and Wang 2006; Song and Zhang 2009; Zhang and Song 2010). In this version, the use of CAPE is replaced by the CAPE generation rate from large-scale forcing in the free troposphere (dCAPE). The term dCAPE is defined as the amount of CAPE generated by the largescale advective forcing during a time interval and is calculated by dCAPE 5 fCAPE[T 1 adv(T)dt, q 1 adv(q)dt] 2 CAPE(T, q)g/dt ,
(5)
where T and q are temperature and moisture, and adv(T)dt and adv(q)dt are the temperature and moisture increments by large-scale advection over a time period dt. This trigger function was first suggested by Xie and Zhang (2000) and used by Zhang (2002) for convection closure. For convection to initiate, the large-scale CAPE
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generation must be positive. In addition, the relative humidity of the air parcel at the initiation level must be greater than 80%. Based on a cloud-resolving model (CRM) simulation, Wu et al. (2007) replaced the relative humidity threshold with a requirement that the largescale CAPE generation exceed a threshold value of 65 J kg21 h21. In addition, we also consider dilute dCAPE by including the entrainment effect on CAPE generation by large-scale advection (Zhang 2009). The entrainment rate is the same as that used in Neale et al. (2008) for dilute CAPE calculation. The effect of entrainment on CAPE and dCAPE calculations was discussed in Zhang (2009). All four variants (CAPE, dilute CAPE, undilute dCAPE, and dilute dCAPE) of the trigger functions in the Zhang–McFarlane scheme will be evaluated.
6) DONNER SCHEME The Donner scheme (Donner 1993; Donner et al. 2001; Wilcox and Donner 2007) is used in a version of the Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model, version 3 (AM3) GCM. Its convection trigger utilizes cumulative information of vertical velocity at the convection initiation level and requires that the large-scale vertical velocity integrated over a time span be able to lift the parcel to the level of free convection (LFC): ðt 1 v(pinit ) dt # pLFC 2 pinit , (6) I5 t0
where t0 is the time when the pressure velocity v at the convection initiation level, chosen to be the first model level above the surface, starts to be negative (upward motion). It also requires that convective inhibition (CIN, the absolute value of the negative portion of CAPE) is small, CIN , 10 J kg21 [later, in Wilcox and Donner (2007), it was changed to CIN , 100 J kg21; however, our sensitivity tests (not shown) indicate that the results are not sensitive to CIN values for this range].
7) ARAKAWA–SCHUBERT SCHEME Various versions of the Arakawa and Schubert (1974) scheme are used in the National Aeronautics and Space Administration (NASA) Global Modeling Assimilation Office (GMAO) Goddard Earth Observing System, version 5 (GEOS-5) GCM (Moorthi and Suarez 1992), GFDL AM2 and the National Centers for Environmental Prediction (NCEP) operational Global Forecast System (GFS) model (Lee et al. 2007). In most versions of the Arakawa–Schubert scheme, a threshold cloud work function is used as the deep convection triggering criteria, which is similar to dilute CAPE in the NCAR CAM5. While the GFDL and NASA model use a fixed
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threshold value of cloud work function as the triggering condition, the triggering condition in the NCEP model is that a parcel lifted from the level of maximum moist static energy between the surface and 700 hPa must reach its LFC within 150 hPa of ascent (Lee et al. 2008; Han and Pan 2011). In the GFDL model, the lifting condensation level of the surface air is defined as the convection base. The NASA model uses the second lowest model level as cloud base, and the lifted air parcel has the average temperature and moisture of the lowest two model layers.
8) PETERS AND NEELIN CRITICAL COLUMN WATER VAPOR TRIGGER
Using observational data, Peters and Neelin (2006) and Neelin et al. (2009) found that convective precipitation is highly correlated to column-integrated water vapor, following a power-law relationship above a critical value of column water vapor wc: w 2 wc b P5a wc
for
w . wc ,
(7)
where a 5 0.15 and b 5 0.23 are fitting constants for their data. The critical value of column water vapor wc for convection initiation was found to increase approximately linearly with tropospheric mean temperature; it varies from 56 to 70 mm for the tropospheric mean temperature range of 268–274 K. Similar correlation between precipitation and column saturation was noted by Bretherton et al. (2004). For convection parameterization, when the column water vapor exceeds this critical value, convection will be triggered. For our evaluation, we will use wc as a function of the tropospheric mean temperature as determined from Neelin et al. (2009). Although it has not been incorporated into any convection scheme, a recent theoretical study by Stechmann and Neelin (2011) using this trigger function together with a stochastic model shows that it can reproduce many important features of transition from nonprecipitating to strong convection.
b. Evaluation data Intercomparison and ranking of the trigger functions are carried out using IOP field data and long-term SCM forcing data. We will mainly use the atmospheric temperature, water vapor mixing ratio, large-scale vertical velocity, dry static energy advection, moisture advection, and surface pressure and temperature fields. The three IOP datasets used in this study are from the Atmospheric Radiation Measurement (ARM) program, produced using the constrained variational analysis of Zhang and Lin (1997) at the Southern Great Plains (SGP) site for the 1997 summer IOP (ARM-SGP), Tropical Warm Pool–International Cloud Experiment
FIG. 1. Convection depth estimated from trigger functions in Kain–Fritsch scheme (red) and Tiedtke scheme (blue). Observed precipitation is shown (black) to indicate the actual timing of convection during the SGP 1997 IOP.
(TWP-ICE) IOP, and the Midlatitude Continental Convective Clouds Experiment (MC3E) IOP, all at a 3-hourly interval. The ARM-SGP data are available for the period from 19 June to 18 July 1997 with 50-hPa vertical resolution from 965 to 115 hPa (Zhang et al. 2001). The TWP-ICE data for the period of 22 January–12 February 2006 have a vertical resolution of 25 hPa and covers the pressure levels from 1015 to 40 hPa (May et al. 2008). The MC3E data have a 25-hPa vertical resolution from 965 to 40 hPa and cover the period from 22 April to 1 June 2011. We also use two long-term SCM forcing datasets available for the SGP site and Darwin, Australia. The SCM data over the SGP site (hereafter SCM-SGP) consist of 11 Northern Hemisphere summer season (1999– 2009) hourly data with 25-hPa vertical resolution from 1000 to 100 hPa. It was produced using the National Oceanic and Atmospheric Administration (NOAA) mesoscale model Rapid Update Cycle analysis product constrained by the ARM surface and top-of-theatmosphere flux observations (Xie et al. 2004a). The Darwin, Australia, SCM data (hereafter SCM-Darwin) are from the ASR principal investigators (PI) product by Christen Jakob. The SCM-Darwin 6-hourly data are available for three wet seasons of 2004/05, 2005/06, and 2006/07. The vertical resolution of the data is 25 hPa from 1015 to 40 hPa. Because of space limitations, we mainly show the results for the SCM-SGP and SCM-Darwin datasets. However, the analysis of the other datasets is included in the discussion.
3. Methodology The performance of a trigger function can be assessed by the estimated cloud height from the trigger function as an indicator for convection. Figure 1, which shows the
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cloud depth obtained from the trigger functions, gives an example for the Kain–Fritsch scheme and the Tiedtke scheme using the ARM-SGP 1997 IOP data. Observed precipitation is used to indicate the time of convection. Clearly, both schemes underpredict the convection occurrence, more so with the Tiedtke scheme than the Kain–Fritsch scheme. For instance, both miss the prediction of convection for day 15, and the Tiedtke scheme completely misses the prediction of convection for days 10–11 and near the end of the observation period (days 26–29). A more objective analysis of the performance of the trigger functions using different datasets can be made with the help of a suitable quantitative metric. The performance of a trigger function in capturing the occurrence of convection at the right time is quantified using common skill score metrics developed for evaluating yes or no categorical forecast verification (Woodcock 1976; Schaefer 1990; Hogan et al. 2009). The skill score calculation starts with the creation of a predicted versus observed events contingency table. The 2 3 2 contingency table is formed based on the observed and predicted events. For observed events, precipitation is used as a proxy for convection, and a precipitation rate greater than or equal to 0.5 mm h21 is used as the threshold value for deep convection. This may introduce some uncertainties, as it is well known that convective systems contain both convective and stratiform precipitation. However, without radar data it is not possible to distinguish the two. Nevertheless, a reasonably large precipitation rate should be a good indication of convection. We tested other threshold values and the results do not seem to be sensitive to the choice of threshold value as long as it is reasonable. For predicted events, the criteria in each trigger function for deep convection are used. Based on the predicted and observed convection at each time, we tabulate the data into four categories: (i) correct prediction, (ii) overprediction and (iii) underprediction of convection, and (iv) correct no-convection prediction. For each of the datasets, contingency tables are created by counting the number of times that fall in each of the four categories for each trigger function. Table 1 gives an example of selected trigger functions for the SCM-SGP and SCM-Darwin datasets. A trigger function may do better in one category but relatively worse in another category compared to a different trigger function. For instance, for the SCM-SGP dataset, the trigger function of the Bechtold scheme has significantly more correct prediction and fewer underprediction cases of convection than the dilute dCAPE trigger function. However, it has many more overprediction cases of convection and fewer correct prediction cases of no-convection than the dilute dCAPE trigger. Thus, a skill score metric taking into account all of these categories is desirable.
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TABLE 1. Contingency table for the four trigger functions using the SCM-SGP and SCM-Darwin datasets. Symbols a, b, c, and d represent the number of data points that fall into the correct prediction, overprediction and underprediction of convection, and correct no-convection prediction categories, respectively. Trigger function SCM-SGP Dilute dCAPE Undilute dCAPE Bechtold Dilute CAPE SCM-Darwin Dilute dCAPE Undilute dCAPE Bechtold Dilute CAPE
a
b
c
d
1373 1776 1995 1286
644 4292 4833 4310
1337 934 715 1424
26 886 23 238 22 697 23 220
162 209 165 133
9 171 279 315
89 41 86 118
1480 1319 1210 1174
The skill of a trigger function lies in its ability to correctly capture convective episodes with least biases in terms of over- and underprediction. Predicting the noconvection cases should be considered trivial, even though the number of such cases may be large, as evident in Table 1. Hence, an ideal skill score formula should suitably weight each of the four categories. The Heidke skill score (HSS), symmetric extreme dependency score (SEDS), and equitable threat score (ETS) methods satisfy this condition to various degrees and are suitable for the quantitative assessment of the performance of trigger functions (Schaefer 1990; Hogan et al. 2009). Formulas used for calculating each of these skill scores are given by HSS 5 SEDS 5 ETS 5
2(ad 2 bc) , (a 1 c)(c 1 d) 1 (a 1 b)(b 1 d) log[(a 1 b)/n] 1 log[(a 1 c)/n] 2 1, log(a/n) a 2 (a 1 b)(c 1 d)/n , a 1 b 1 c 2 (a 1 b)(c 1 d)/n
(8)
and
(9)
(10)
where a, b, c, and d stand for the number of occurrences of correct prediction, overprediction and underprediction of convection, and correct prediction of noconvection cases, and n is the total number of data points (n 5 a 1 b 1 c 1 d). A skill score value close to 1 indicates excellent performance by the trigger function and close to 0 implies poor performance. The above three skill score estimates for the dilute dCAPE trigger function using the TWPICE data are shown in Table 2. HSS and SEDS show relatively higher scores than ETS. A closer examination reveals that the HSS gives equal weight to correct
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TABLE 2. Skill scores of dilute dCAPE by different metrics for TWP-ICE data. Trigger function
HSS
SEDS
ETS
Dilute dCAPE
0.72
0.73
0.56
prediction of convection and no-convection and hence show a tendency to give a higher score to a trigger function that produces more correct prediction of noconvection cases. The higher SEDS skill score arises from giving more weight to the correct prediction of the convection case compared to the overprediction and underprediction cases. While it is important to have more cases of correct prediction of convection, it is equally important to have fewer cases of over- and underprediction of convection. The ETS is similar to HSS, but is more efficient in treating the bias toward correct no-convection cases. Thus, although all three skill score metrics give qualitatively similar information on the performance of a trigger function, the relatively lower bias associated with the ETS formulation makes it our choice metric for further analysis.
4. Results a. Performance of trigger functions The performance of the trigger functions is evaluated and ranked according to their ETS values. Figure 2 shows the ETS values of all trigger functions evaluated for each of the five datasets. Only the four best performers are labeled in each dataset. For the long-term SCM forcing data at SGP, the ETS value for dilute dCAPE is the highest, almost double that of the second best performer, the trigger function used in the Bechtold scheme. The skill score for undilute dCAPE trigger is slightly lower than that for the Bechtold scheme. The Tiedtke scheme is the next best performer (the dilute CAPE, which is in dark blue color and not labeled in the figure, is a close fifth). For the 3-yr SCM-Darwin forcing data, dilute dCAPE again stands out as the best performer, with a skill score close to 0.6. The next highest skill score is for undiluted dCAPE, with a value of more than 0.4, followed by Bechtold scheme, with a skill score of 0.2. The dilute CAPE trigger also shows some skill (the Tiedtke scheme, not labeled in the figure, is a close fifth in this case). For the relatively short IOP datasets, the TWP-ICE case shows that undilute dCAPE trigger performs slightly better than the dilute dCAPE. The next best performers (dilute CAPE and Bechtold scheme) have significantly lower skill scores. For the two midlatitude convection IOPs (ARM-SGP and MC3E), dilute dCAPE again performs the best. For ARM-SGP,
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the undilute dCAPE comes second, followed by the Kain–Fritsch scheme and Bechtold scheme. For the MC3E dataset, the second best performer (Bechtold scheme) has a significantly lower ETS score, followed by the undilute dCAPE and dilute CAPE trigger, which have even lower ETS scores. The trigger function based on dilute dCAPE stands out clearly as the best performer for four out of five datasets. Both dilute and undilute versions of the dCAPE trigger function have comparable skills over the tropical region, whereas over the midlatitude region dilution seems to be a crucial factor, as indicated by the lower skill score for undilute dCAPE trigger function. This is consistent with the results of Zhang (2009), which shows that the dilution effect of entrainment on CAPE and dCAPE strongly depends on the environmental moisture. In a moist environment, as in the case of TWP-ICE IOP and multiyear SCM-Darwin forcing data, entrainment of environmental air is less effective in diluting CAPE and CAPE change, whereas in a dry environment such as the SGP site, entrainment has a much more significant effect on CAPE and CAPE change. Apart from the two versions of the dCAPE trigger functions, the Bechtold trigger function also shows consistently better ETS scores. The skill of the Bechtold trigger function does not show much variation from one climate regime to the other. It is well known that convective activity has significant diurnal variations, and convective parameterization schemes have difficulties in capturing this variation (Betts and Jakob 2002; Bechtold et al. 2004). Does the skill of a trigger function show any diurnal variation? We use the SCM-SGP data for this analysis since the SCM-SGP hourly data are available for 11 summer seasons and the diurnal cycle of convection is more pronounced over midlatitude land region. Figure 3 shows the ETS values of dilute dCAPE, Bechtold and undilute dCAPE trigger functions with respect to the local solar time of the day (LST). For reference, precipitation amount is also shown. The precipitation rate reaches a maximum at 0500 LST and a minimum at 1400 LST. In general, for all three trigger functions, the ETS values show a pattern of diurnal variation similar to that of precipitation. The diurnal variation of the ETS values from the dilute dCAPE trigger function shows a maximum ETS skill score of close to 0.5 at 0100 LST and a minimum slightly more than 0.2 at 1200 LST. The ETS values from the Bechtold trigger function show a similar diurnal variation except with larger relative amplitude of diurnal variation, with a maximum of 0.3 at 0200 LST and a minimum of 0.1 at 1400 LST. The undilute dCAPE trigger has the least amount of diurnal variation among the three, although it also has relatively low ETS values in early afternoon and
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FIG. 2. ETS estimate of different trigger functions for SCM-SGP, SCM-Darwin, TWP-ICE, MC3E, and ARM-SGP datasets presented in descending order of their skill scores. The first four better-performing trigger functions are labeled, and only trigger functions with positive ETS values are plotted.
high ETS values around midnight. Among the three trigger functions, the dilute dCAPE trigger function has the highest value at every hour, by 50% in early morning hours and by more than 100% in early afternoon compared to Bechtold or undilute dCAPE triggers. The diurnal variation of the ETS skill scores suggests that the trigger functions perform better when convection intensity is high and not as good when convection intensity is moderate or weak.
b. Composite analysis The performance of each trigger function is related to the underlying physics involved in the design of the trigger function. For instance, the good performance of the dilute dCAPE trigger function can be mainly attributed to the inclusion of destabilization effects of large-scale dynamics on convection. To understand why a trigger function works well in some cases and not as well in other cases, in the following we examine the underlying physics of the three better-performing trigger functions through the composite analysis of key variables. In addition, we also include the dilute CAPE
trigger in the NCAR CAM5, a model widely used by the climate modeling community. To start with, we composite the convection-sensitive variables that are used in the trigger functions, such as temperature, water vapor mixing ratio, vertical velocity, and large-scale advection of moisture and dry static energy for the observed convection and no-convection periods using the SCM-SGP data (Fig. 4). We also examined other variables such as CAPE, CIN, and columnintegrated water vapor. However, they do not show much separation between convection and no-convection cases and therefore are not plotted. Since temperature and moisture vary significantly with height, only deviations from the mean profiles are shown. There is a clear separation between convective and nonconvective largescale conditions in all fields. The convective composite is characterized by warm anomalies in the upper troposphere and cold anomalies in the lower troposphere along with a very moist lower troposphere. There is significant ascending motion in the entire troposphere, with a maximum at 350 mb (1 mb 5 1 hPa). Correspondingly, there is positive large-scale advection in moisture and
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FIG. 3. Diurnal variation in the ETS skill score for the (top) dilute dCAPE, (middle) Bechtold, and (bottom) undilute dCAPE trigger functions (bars) along with the mean diurnal cycle of precipitation (mm h21; blue line).
negative advection in dry static energy. For the nonconvective environment, the atmosphere is warm and dry throughout the troposphere. Associated with it is the weak descending motion, dry and warm advection. Although the separation between convective and nonconvective composite fields is very distinct, the spread within each category (shaded areas) is significant. The overlapping regions of the fields between the convective and nonconvective categories are likely to be the cases the trigger functions will fail. Next, we composite these fields based on the four categories, namely, correct prediction, overprediction and underprediction of convection, and correct no-convection
prediction. We examine the case of dilute dCAPE trigger function first. Figure 5 shows the stratified composite fields of moisture, temperature, dry static energy advection, and moisture advection for SCM-SGP and SCM-Darwin datasets. The four categories are distinctly separated in the stratified composite fields. Since the separation among different categories of the composite profiles at the Darwin site is qualitatively similar to those at the SGP site, we will focus on the latter only. The composite fields for correct prediction and correct no-convection prediction cases are quite similar to the convection and no-convection profiles in Fig. 4. The moisture difference near the surface is up to 2 g kg21
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FIG. 4. Composite (a) temperature anomaly, (b) water vapor mixing ratio anomaly, (c) vertical velocity, (d) more moist advection, and (e) dry static energy advection fields for convection (red line) and no-convection (blue line) categories calculated using the SCM-SGP data. The standard deviation of each category is shown in shading.
between categories of correct prediction of convection and no-convection, and the temperature differences are up to 3 K between underprediction and overprediction categories. The atmosphere is the moistest for correct convection prediction and driest for correct no-convection prediction throughout the troposphere. The air for the overprediction of convection is moist in the lower troposphere below 850 hPa and dry above. The opposite is true for the underprediction composite. The cold anomalies for underprediction are much larger and over a deeper layer (up to 500 hPa) than for correct prediction. Combining the temperature and moisture field composites, it appears that lower-tropospheric moisture is an important factor in triggering convection, whereas negative anomalies in lower-tropospheric moisture and temperature are both important in suppressing convection in the dilute dCAPE trigger function. This can
be understood from the basic criterion for convection, that is, there must be convective instability in the atmosphere for convection to be triggered. Both moisture and temperature anomalies in the lower troposphere contribute to CAPE (1 g kg21 of water vapor anomaly is equivalent to 2.5 K in equivalent potential temperature anomaly in CAPE calculation). It is interesting to note that despite the cold and dry anomalies in the underprediction case, convection is actually observed. This mostly corresponds to the situation when convection already exists, and the lower-tropospheric thermodynamic fields are affected by the cooling and drying from convective downdrafts (to be discussed later). An examination of the composites of dry static energy advection and moisture advection reveals some interesting characteristics of the dilute dCAPE trigger function as well. For the case of correct prediction of
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FIG. 5. Composite (a) water vapor mixing ratio anomaly, (b) temperature anomaly, (c) moisture advection, and (d) dry static energy advection fields for correct prediction (red line), overprediction (blue line) and underprediction (black line) of convection, and correct noconvection prediction (green line) categories using the dilute dCAPE trigger function, calculated using the (top) SCM-SGP and (bottom) SCM-Darwin datasets.
convection, there is large positive moisture advection and cold dry static energy advection throughout the troposphere. For underprediction, there is also positive moisture advection, but at a much smaller magnitude. The dry static energy advection is smaller too than in the correct prediction case. The main difference seems to be in the lower troposphere below 800 hPa. A majority of the underprediction events occurred due to the lack of enough temperature and moisture advection in the lower troposphere. For the overprediction case, there is large positive moisture advection, but cold dry static energy advection is only modest. The similarity in the large-scale advective fields for the correct prediction and overprediction cases is confined to the lower troposphere only (below 800 hPa). For the no-convection case, there is small dry and warm advection. For the SCM-Darwin dataset, again the similarities in moisture and dry static energy advections between correct prediction and overprediction, and between no-convection and underprediction, are confined to below 800 hPa. The
differences of advective fields among the categories and the importance of lower-tropospheric advection can be understood from the design of the dCAPE trigger function. It determines the onset of convection by considering the large-scale dynamic destabilization of the atmosphere in addition to the existence of conditional instability. For dilute dCAPE the entrainment of environmental air is included. Since entrainment is most effective in the lower troposphere, advection there is weighted more than in the layers above in dCAPE calculation. The vertical profile of the stratified composite fields of the Bechtold trigger function is similar to that of the dilute dCAPE, and it also exhibits distinct separation among the four categories. Figure 6 shows the stratified composites of moisture, temperature, and vertical velocity fields for SCM-SGP and SCM-Darwin datasets. Composite analysis of vertical velocity is performed in place of large-scale advection, since vertical velocity is the key parameter in the Bechtold trigger function. The
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FIG. 6. Composite (a) water vapor mixing ratio anomaly, (b) temperature anomaly, and (c) vertical velocity fields for correct prediction (red line), overprediction (blue line) and underprediction (black line) of convection, and correct no-convection prediction (green line) categories using the Bechtold trigger function, calculated using the (top) SCM-SGP and (bottom) SCM-Darwin datasets.
composite temperature and moisture fields have similar vertical distributions to the stratified composite fields for the dilute dCAPE trigger function. This is because CAPE is also a prerequisite for convection in the Bechtold scheme. Since large-scale vertical velocity is used in determining the occurrence of convection, the composite of vertical velocity is positive for correct prediction of convection and negative for correct no-convection prediction. The overprediction and underprediction cases have more complex features. The underprediction case has large upward motion comparable to the correct prediction case in the middle and upper troposphere. However, in the lower troposphere
below 800 hPa, it has negligible upward (SCM-SGP) or downward (SCM-Darwin) motion. Conversely, for the overprediction case, despite weak large-scale downward motion in the middle and upper troposphere, there is significant upward motion in the lower troposphere below 800 hPa. Since the trigger criteria for the Bechtold scheme involves the perturbation temperature at the LCL, which in turn is a function of the lower-tropospheric vertical velocity, the latter is a key parameter leading to erroneous (over or under) predictions. A weak or negative lower-tropospheric vertical velocity leads to underprediction of convection in spite of strong upward motion in the upper troposphere. Likewise, despite downward
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motion in most of the troposphere, significant upward motion in the lower levels can falsely predict an occurrence of convection. Thus, while the higher skill of the Bechtold scheme may be attributed to its ability to mimic the moist physics in the boundary layer, consideration of the lower-tropospheric vertical velocity alone in the trigger function may not be optimal. The stratified composite fields of moisture, temperature anomaly, dry static energy advection, and moisture advection for the SCM-SGP dataset for the undilute dCAPE trigger function are similar to those for dilute dCAPE, except that undilute dCAPE underprediction and correct prediction of convection share similar moisture profiles and overprediction and correct noconvection prediction share similar moisture profiles. For the dilute CAPE trigger function, the over (under) prediction is associated with warmer (cooler) temperature anomaly and moist (dry) boundary layer. Since CAPE is largely determined by the boundary layer moisture and temperature fields (Zhang 2002, 2003), warm and moist boundary layer would favor large CAPE and overactivation of convection. The opposite is true for the underprediction case. The probability distribution of precipitation for the overprediction and underprediction cases of the four trigger functions are examined to test whether the trigger function show any systematic bias related to the intensity of convection. Figure 7 shows the percentage of missed and overly predicted convection events by the four trigger functions. The percentage of missed precipitation events by the dilute dCAPE and Bechtold trigger functions drastically decrease with the increase of precipitation intensity, indicating that both schemes were successful in capturing the strong convection events. The dilute dCAPE trigger function misses about 40%–60% of the 0.5–1 mm h21 precipitation events, while the Bechtold scheme misses only 20%–40% of the 0.5–1 mm h21 precipitation events. On the other hand, the percentage of overpredicting convection is the smallest for the dilute dCAPE trigger function. It shows only a 2% chance to activate the CPS when there was precipitation less than 0.5 mm h21, while the other three trigger functions show about 12%–18% probability to overpredict such events.
c. Scope for improving the trigger function and sensitivity tests The composite analysis of the key variables of the trigger functions gives important insights into the working of the trigger functions for correct prediction, overprediction and underprediction of convection, and correct no-convection prediction cases. This information can be used for improving the performance of the
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existing schemes. For example, in the case of dilute dCAPE trigger function, its performance can be improved by optimizing either the dCAPE threshold value or entrainment rate. Figure 8 shows the ETS value of dilute dCAPE trigger function for different dCAPE threshold values and entrainment rates. The default values used in the results presented so far are 65 J kg21 h21 for the dCAPE threshold value and 1 3 1023 m21 for the fractional entrainment rate. The ETS calculation for different dCAPE threshold values is carried out by fixing the entrainment rate to the default value. A recent study by Wang and Zhang (2013) shows that the undilute dCAPE trigger function with a 100 J kg21 h21 threshold value significantly reduces the biases in temperature and moisture fields of the CAM model. Our analysis for the dilute dCAPE trigger function (Fig. 8) shows that the dCAPE threshold value in the range of 40–60 J kg21 h21 is optimal for an entrainment rate of 1 3 1023 m21. Similarly, with a default threshold value of 65 J kg21 h21, the optimal entrainment rate is in the range of 0.5–0.75 3 1023 m21. Although the dCAPE trigger functions can capture significant portion of convective events, some convective events may be related to processes other than large-scale advection. For instance, localized convection primarily driven by boundary layer forcing will not be captured by the dCAPE trigger function. The inclusion of boundary layer forcing may further improve the skill of the trigger function (Bechtold et al. 2014). In the Bechtold trigger function, the decision making is largely influenced by the boundary layer conditions. The similarity of the lower troposphere composite fields of the correct prediction and overprediction cases of the Bechtold scheme underscores this notion. The overdependency of the Bechtold scheme on the boundary layer parameters often results in its failure to capture the decay phase of convective events. The decay phase was identified from the convective events that persisted for more than 4 h in the SCM-SGP data and was defined as the latter half of the event. A quick look finds that of the 506 underprediction times, 63% (319 times) were associated with the decay phase of convection. It is likely that convective downdrafts from the water loading and evaporative cooling of precipitation during the decay stage of convection can reduce large-scale upward motion, leading to a weak upward velocity or subsidence in the lower troposphere. In addition, they can produce dry and cold boundary layer air as seen in Figs. 4 and 5. A weak, upward velocity can reduce the perturbation temperature, and the Bechtold trigger function thus fails to activate. This bias in the Bechtold trigger function can be reduced by incorporating an upper-tropospheric parameter such as large-scale vertical velocity that is
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FIG. 7. Percentage distribution of the underpredicted events as a function of precipitation intensity (0.5 mm h21 and above) for (a) dilute dCAPE, (b) Bechtold, (c) undilute dCAPE, and (d) dilute CAPE trigger functions, respectively. A bin size of 0.5 mm h21 is used for classifying the precipitation events. (e) Percentage distribution of the overpredicted events for precipitation intensity less than 0.5 mm h21 for the four trigger functions.
sensitive to convection. The skill of the Bechtold trigger function may also be improved by modifying the perturbation temperature formula by incorporating a stochastic effect. The perturbation temperature is expected to capture the subgrid-scale forcing, and it is crudely parameterized in the Bechtold trigger function through the grid-scale vertical velocity. The effectiveness of stochastic trigger formulation has been demonstrated in recent studies (Rochetin et al. 2014a,b) to simulate the transition from shallow to deep convection. In addition to rectifying the issues in instability criteria, it is also possible to tune the cloud height threshold in the Bechtold as well as the other trigger functions. Inspection of cloud-top heights estimated from the Bechtold trigger function (not shown) indicates that a significant portion of the underprediction cases satisfy the instability criteria at the cloud base, but fail to
meet the minimum cloud height requirement. About 40% of such cases show a cloud height estimate in the range of 2–3 km. Poor skills exhibited by the other trigger functions may be due to an inappropriate choice of the trigger threshold. To check on this, we performed a series of sensitivity tests by varying the values of the trigger thresholds. Improvements of optimized trigger skill over the default trigger condition are shown in Fig. 9. The default and optimized trigger formulations for these trigger functions are listed in Table 3. The skills of the dilute CAPE, Zhang–MacFarlane, Arakawa–Schubert, and Donner trigger functions can be significantly improved by changing their threshold value and incorporating a relative humidity (RH) threshold. The performance of the Tiedtke trigger function can be optimized by setting the minimum moisture convergence
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FIG. 8. The ETS estimates corresponding to different (left) dCAPE threshold values and (right) entrainment rates of the dilute dCAPE trigger function for (top) SCM-SGP, (middle) TWP-ICE, and (bottom) SCM-Darwin datasets.
threshold to 3 3 1026 kg m22 s21. The poor skill associated with the KF trigger function was related to the cloud height estimation. The KF scheme was primarily designed for mesoscale models. When it is adapted to the larger horizontal grid spacing of GCMs, the entrainment rate, which is proportional to the grid size, is too large, producing weak vertical velocity and eventually leading to a cloud height estimate lower than the minimum required threshold. This bias can be reduced by adopting a buoyancy-based cloud height estimation. In our analysis of the trigger functions, it was noted that often deep convection was not initiated even when there were sufficient instability or dynamical processes to lift the parcel to the LFC. Both instability and moisture are found to be crucial for triggering convection. While a moisture-based trigger formulation (e.g., RH at the parcel origin greater than 80% or column-integrated water greater than a critical value) shows a better skill compared to an instability or dynamical lifting-based trigger formulation, a combination of both shows a significantly higher skill.
In our analysis, precipitation is used as a proxy for convection. Thus, the use of a precipitation threshold value for convection is subjective. A detailed analysis of the sensitivity of the skill score to the precipitation
FIG. 9. ETS estimates corresponding to default (red) and optimized (blue) trigger formulation of Tiedtke, dilute CAPE, Kain–Fritsch (KF), Donner, Arakawa–Schubert (AS), and Zhang– MacFarlane (ZM) trigger functions for SCM-SGP data.
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TABLE 3. Default and optimized trigger formulation for dilute CAPE, Zhang–MacFarlane, Kain–Fritsch, Arakawa–Schubert, Donner, and Tiedtke trigger functions. Trigger function
Default trigger formulation
Optimized trigger formulation
Dilute CAPE
Dilute CAPE . 70 J kg21
Zhang–McFarlane
CAPE . 70 J kg21
Kain–Fritsch
Positive buoyancy at the LCL and estimated cloud height .3 km
Arakawa–Schubert
Lifting pressure ,150 hPa
Donner
Integrated vertical velocity is sufficient enough to lift the parcel to its LFC and CIN , 100 J kg21 Existence of vertically integrated moisture convergence, positive buoyancy at the LCL, and cloud height .3 km
Tiedtke
threshold value is performed to gain further confidence in the results. If the skill score is sensitive to the choice of precipitation threshold value, it would also affect the ranking and evaluation of the trigger function. We have repeated the HSS, SEDS, and ETS skill score calculation of dilute dCAPE, Bechtold, undilute dCAPE, and dilute CAPE trigger functions with different precipitation thresholds (Fig. 10). The analysis shows that the skill scores do not vary significantly with the choice of the threshold value. Also, the ranking of the trigger function is not sensitive to either precipitation threshold value or skill score type. The dilute dCAPE scheme shows a tendency to improve its skill score with the increase of the precipitation threshold. This seems reasonable, as weak precipitation rate may be more associated with stratiform rain, and the trigger function thus will perform relatively poorly. The skill of the other three trigger functions does not show any systematic dependence on precipitation threshold value. A stratified composite analysis of moisture, temperature, apparent heat source, and moisture sink for different precipitation threshold values also agree with the finding that a 0.5 mm h21 precipitation threshold value is the apt choice for deep convection.
5. Summary and discussion We have evaluated and ranked the performance of the commonly used trigger functions against field observations and long-term SCM datasets using the ETS value, a widely used forecast verification metric. The evaluation and ranking of the trigger functions are not
Dilute CAPE . 20 J kg21 and RH at the parcel origin .70% CAPE . 100 J kg21 and RH at the parcel origin .80% Positive buoyancy at the LCL and estimated cloud height .3 km (estimate cloud height using buoyancy instead of vertical velocity equation) Lifting pressure difference ,200 hPa and RH at the parcel origin .70% Integrated vertical velocity is sufficient enough to lift the parcel to its LFC and RH . 70% Vertically integrated moisture convergence .3 3 1026 kg m22 s21, positive buoyancy at the LCL, and cloud height .3 km
significantly sensitive to the choice of the evaluation metric or the threshold value used for deep convection. Based on the ETS value, we have identified three consistently better-performing trigger functions. A detailed analysis of the key variables of these trigger functions, together with those of the dilute CAPE trigger function, are carried out to understand their biases. The stratified composite analysis and the probability distribution of the key variables of the four trigger functions for the correct prediction, overprediction and underprediction of convection, and correct no-convection prediction cases bring out their shortcomings and also present some scope for further improving these schemes. The dilute dCAPE trigger function is ranked as the best-performing scheme. It is further noted that the dilute dCAPE trigger function performs well over the tropics as well as the midlatitudes. The dilute dCAPE scheme is designed on the notion that the large-scale advection of temperature and moisture can lead to the destabilization of the atmosphere and initiate deep convection. The dilute dCAPE allows the interaction between the parcel and the environment and inhibits overactivation of convection. Sensitivity analysis for the choice of threshold value reveals that the same threshold value would work equally well over the tropics and midlatitudes. It was also found that the skill of the dilute dCAPE trigger function does not heavily depend on a particular threshold value. The inclusion of the destabilization effect of large-scale dynamics in the dCAPE design helps improve its performance to a large extent. The dilute and undilute versions of the dCAPE trigger functions have the same basic design except for
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FIG. 10. (top) HSS, (middle) SEDS, and (bottom) ETS estimates of the dilute dCAPE, Bechtold, undilute dCAPE, and dilute CAPE trigger functions, for different precipitation thresholds, for the (left) SCM-SGP and (right) SCM-Darwin datasets.
the inclusion of entrainment. The skill of the undilute dCAPE is as good as the dilute version for the tropics, while the inclusion of entrainment is crucial for the midlatitudes, and the undiluted dCAPE skill is much lower than the dilute dCAPE skill. The simplest representation of boundary layer moist physics is the main highlight of the Bechtold trigger function. The decision making of the Bechtold trigger function, to a large extent, is influenced by the vertical velocity in the lower troposphere. The sole dependency on the vertical velocity often makes the Bechtold trigger function miss the decay phase of convection. It is also found that the Bechtold trigger function overly activates
the CPS if it observes large vertical velocity in the boundary layer. The dilute CAPE trigger function is not as good as the other three better-performing schemes; however, it gains inclusion into the class of betterperforming trigger functions mainly due to its relatively better performance in the tropics. The analysis carried out in this study reveals that many of the trigger functions exhibit poor skill in activating convection at the right time and location. In most of such schemes, the activation of CPS is constrained by the requirement that the parcel ascending from the first model level itself should meet the instability criteria. Such a design would prevent the scheme in detecting
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potentially unstable layers at higher levels, and this may often lead to underprediction of convection, mainly nighttime convection. In a recent study (Lee et al. 2008), a set of sensitivity experiments using different trigger functions in the relaxed Arakawa–Schubert CPS framework also showed that the trigger functions that relaxes the first model level parcel origin constraint performs better than the others. Hence, the identification of the source layer for convection is a crucial factor. Based on our analysis, more realistic and better-performing trigger functions can be formulated by selecting the most unstable layer as a parcel origin and incorporating a condition that accounts for convection initiation from downdraft-induced cold pools. Scale awareness or scale adaptable design is another important area where the majority of the existing trigger functions need immediate attention. Only the Bechtold scheme includes the grid size–sensitive parameters in their convection trigger formulation. The dCAPE trigger function implicitly includes the effect of the domain size through the largescale advection terms, as large-scale advective tendencies depend on the grid resolution. Convection has a life cycle, with different stages from its onset (or triggering) to its dissipation stage. Present convection schemes are unable to reproduce this cycle and its organization at mesoscale explaining the duration and propagation of convection. Most present convection schemes have no memory, and the trigger function is computed at each GCMs time step to decide on the activation of the convection scheme. This oversimplification of present convection schemes means that the same trigger function has to treat very different stages (initiation, mature, and dissipation) and different degrees of organization that depend on different environment characteristics (vertical profiles of temperature, humidity, shear, vertical velocity, forcing, etc.). It means that the ‘‘trigger function’’ issue in GCMs is not physically well posed at the present time. Prognostic convection schemes that consider the history of convection will avoid some of these shortcomings. All of the IOP and long-term SCM forcing data used in this study are from the ARM-SGP and TWP-ICE sites. Since convective parameterization schemes are used in global models, it would be necessary to consider other regions as well, for example, over semiarid continental regions such as the Sahel in Africa. Because of dryness, shear, and strong CAPE, but a strong CIN barrier, convection triggering is not easy. It would be important in the future to use observations in such regions [e.g., data from the African Monsoon Multidisciplinary Analyses (AMMA) IOPs]. Other factors such as soil moisture can be important in triggering convection as well. Taylor et al. (2012) showed that current
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convection schemes in large-scale models tend to be oversensitive to surface evaporation, erroneously favoring daytime rain over wet soils, in contrast to cloudresolving models and observation. Therefore, the surface–atmosphere coupling should be considered in the future to treat the onset of convection on the continent. The ARM data used in this study are intended for typical GCM resolutions of 28–38 longitude–latitude. As GCMs’ resolutions increase, how well will the trigger functions perform? High-resolution observation-based data are not available to answer this question. However, the output from cloud-resolving models can serve this purpose. The ultimate test of a convection trigger function is using it in single-column model and GCM simulations. These will be the subjects of our future studies. Acknowledgments. This research was supported by the Office of Science (BER), U.S. Department of Energy under Grant DE-SC0008880, the PNNL Contract DOE/PNNL 190110, the National Oceanic and Atmospheric Administration Grant NA11OAR4321098, and the National Science Foundation Grant AGS1015964. We thank the three anonymous reviewers for constructive comments that have helped improve the manuscript significantly.
REFERENCES Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31, 674–701, doi:10.1175/1520-0469(1974)031,0674: IOACCE.2.0.CO;2. Bechtold, P., E. Bazile, F. Guichard, P. Mascart, and E. Richard, 2001: A mass flux convection scheme for regional and global models. Quart. J. Roy. Meteor. Soc., 127, 869–886, doi:10.1002/ qj.49712757309. ——, J.-P. Chaboureau, A. Beljaars, A. K. Betts, M. Kohler, M. Miller, and J.-L. Redelsperger, 2004: The simulation of the diurnal cycle of convective precipitation over land in a global model. Quart. J. Roy. Meteor. Soc., 130, 3119–3137, doi:10.1256/qj.03.103. ——, N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, and N. Bormann, 2014: Representing equilibrium and nonequilibrium convection in large-scale models. J. Atmos. Sci., 71, 734–753, doi:10.1175/JAS-D-13-0163.1. Betts, A. K., and C. Jakob, 2002: Study of the diurnal cycle of convective precipitation over Amazonia using a single column model. J. Geophys. Res., 107, 4732, doi:10.1029/2002JD002264. Bolton, D., 1980: The computation of equivalent potential temperature. Mon. Wea. Rev., 108, 1046–1053, doi:10.1175/ 1520-0493(1980)108,1046:TCOEPT.2.0.CO;2. Bretherton, C. S., M. E. Peters, and L. E. Back, 2004: Relationships between water vapor path and precipitation over the tropical oceans. J. Climate, 17, 1517–1528, doi:10.1175/ 1520-0442(2004)017,1517:RBWVPA.2.0.CO;2. Bright, D. R., and S. L. Mullen, 2002: Short-range ensemble forecasts of precipitation during southwest monsoon. Wea.
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Forecasting, 17, 1080–1100, doi:10.1175/1520-0434(2002)017,1080: SREFOP.2.0.CO;2. Chao, W. C., and B. Chen, 2004: Single and double ITCZ in an aqua-planet model with constant SST and solar angle. Climate Dyn., 22, 447–459, doi:10.1007/s00382-003-0387-4. Dai, A., 2006: Precipitation characteristics in eighteen coupled climate models. J. Climate, 19, 4605–4630, doi:10.1175/JCLI3884.1. Donner, L. J., 1993: A cumulus parameterization including mass fluxes, vertical momentum dynamics, and mesoscale effects. J. Atmos. Sci., 50, 889–906, doi:10.1175/1520-0469(1993)050,0889: ACPIMF.2.0.CO;2. ——, C. J. Seman, R. S. Hemler, and S. Fan, 2001: A cumulus parameterization including mass fluxes, convective vertical velocities, and mesoscale effects: Thermodynamic and hydrological aspects in a general circulation model. J. Climate, 14, 3444–3463, doi:10.1175/1520-0442(2001)014,3444: ACPIMF.2.0.CO;2. Grandpeix, J.-Y., and J. P. Lafore, 2010: A density current parameterization coupled to Emanuel’s convection scheme. Part I: The models. J. Atmos. Sci., 67, 881–897, doi:10.1175/ 2009JAS3044.1. Han, J., and H. L. Pan, 2011: Revision of convection and vertical diffusion schemes in the NCEP global forecast system. Wea. Forecasting, 26, 520–533, doi:10.1175/WAF-D-10-05038.1. Hogan, R. J., E. J. O’Connor, and A. J. Illingworth, 2009: Verification of cloud fraction forecasts. Quart. J. Roy. Meteor. Soc., 135, 1494–1511, doi:10.1002/qj.481. Jakob, C., and A. P. Siebesma, 2003: A new subcloud model for mass-flux convection schemes: Influence on triggering, updraft properties, and model climate. Mon. Wea. Rev., 131, 2765–2778, doi:10.1175/1520-0493(2003)131,2765: ANSMFM.2.0.CO;2. Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170–181, doi:10.1175/ 1520-0450(2004)043,0170:TKCPAU.2.0.CO;2. ——, and J. M. Fritsch, 1990: A one-dimensional entraining/ detraining plume model and its application in convective parameterization. J. Atmos. Sci., 47, 2784–2802, doi:10.1175/ 1520-0469(1990)047,2784:AODEPM.2.0.CO;2. ——, and ——, 1992: The role of convective ‘‘trigger function’’ in numerical forecasts of mesoscale convective systems. Meteor. Atmos. Phys., 49, 93–106, doi:10.1007/BF01025402. Knievel, J. C., D. A. Ahijevych, and K. W. Manning, 2004: Using temporal modes of rainfall to evaluate the performance of a numerical weather prediction model. Mon. Wea. Rev., 132, 2995–3009, doi:10.1175/MWR2828.1. Kuo, H. L., 1974: Further studies of the parameterization of the influence of cumulus convection on the large-scale flow. J. Atmos. Sci., 31, 1232–1240, doi:10.1175/1520-0469(1974)031,1232: FSOTPO.2.0.CO;2. Lee, M.-I., and Coauthors, 2007: An analysis of the warm-season diurnal cycle over the continental United States and northern Mexico in general circulation models. J. Hydrometeor., 8, 344– 366, doi:10.1175/JHM581.1. ——, S. D. Schubert, M. J. Suarez, J.-K. E. Schemm, H.-L. Pan, J. Han, and S.-H. Yoo, 2008: Role of convection triggers in the simulation of the diurnal cycle of precipitation over the United States Great Plains in a general circulation model. J. Geophys. Res., 113, D02111, doi:10.1029/2007JD008984. Liang, X.-Z., L. Li, A. Dai, and K. E. Kunkel, 2004: Regional climate model simulation of summer precipitation diurnal cycle over the United States. Geophys. Res. Lett., 31, L24208, doi:10.1029/2004GL021054.
7665
Lin, J.-L., and Coauthors, 2006: Tropical intraseasonal variability in 14 IPCC AR4 climate models. Part I: Convective signals. J. Climate, 19, 2665–2690, doi:10.1175/JCLI3735.1. ——, M.-I. Lee, D. Kim, I.-S. Kang, and D. M. W. Frierson, 2008: Impact of convective parameterization and moisture triggering on GCM-simulated convectively coupled equatorial waves. J. Climate, 21, 883–909, doi:10.1175/2007JCLI1790.1. Liu, Y., L. Guo, G. Wu, and Z. Wang, 2010: Sensitivity of ITCZ configuration to cumulus convective parameterization on an aqua planet. Climate Dyn., 34, 223–240, doi:10.1007/ s00382-009-0652-2. May, P. T., J. H. Mather, G. Vaughan, K. N. Bower, C. Jakob, G. M. McFarquhar, and G. G. Mace, 2008: The Tropical Warm Pool International Cloud Experiment. Bull. Amer. Meteor. Soc., 89, 629–645, doi:10.1175/BAMS-89-5-629. Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa–Schubert: A parameterization of moist convection for general circulation models. Mon. Wea. Rev., 120, 978–1002, doi:10.1175/ 1520-0493(1992)120,0978:RASAPO.2.0.CO;2. Neale, R. B., J. H. Richter, and M. Jochum, 2008: The impact of convection on ENSO: From a delayed oscillator to a series of events. J. Climate, 21, 5904–5924, doi:10.1175/2008JCLI2244.1. Neelin, J. D., O. Peters, and K. Hales, 2009: The transition to strong convection. J. Atmos. Sci., 66, 2367–2384, doi:10.1175/ 2009JAS2962.1. Nordeng, T. E., 1994: Extended versions of the convective parameterization scheme at ECMWF and their impact on the mean and transient activity of the model in the tropics. ECMWF Tech. Memo. 206, 41 pp. Peters, O., and D. Neelin, 2006: Critical phenomena in atmospheric precipitation. Nat. Phys., 2, 393–396, doi:10.1038/nphys314. Rio, C., F. Hourdin, J.-Y. Grandpeix, and J.-P. Lafore, 2009: Shifting the diurnal cycle of parameterized deep convection over land. Geophys. Res. Lett., 36, L07809, doi:10.1029/2008GL036779. ——, and Coauthors, 2013: Control of deep convection by subcloud lifting processes: The ALP closure in the LMDZ5B general circulation model. Climate Dyn., 40, 2271–2292, doi:10.1007/s00382-012-1506-x. Rochetin, N., F. Couvreux, J.-Y. Grandpeix, and C. Rio, 2014a: Deep convection triggering by boundary layer thermals. Part I: LES analysis and stochastic triggering formulation. J. Atmos. Sci., 71, 496–514, doi:10.1175/JAS-D-12-0336.1. ——, J.-Y. Grandpeix, C. Rio, and F. Couvreux, 2014b: Deep convection triggering by boundary layer thermals. Part II: Stochastic triggering parameterization for the LMDZ GCM. J. Atmos. Sci., 71, 515–538, doi:10.1175/JAS-D-12-0337.1. Rogers, R. F., and J. M. Fritsch, 1996: A general framework for convective trigger functions. Mon. Wea. Rev., 124, 2438–2452, doi:10.1175/1520-0493(1996)124,2438:AGFFCT.2.0.CO;2. Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570–575, doi:10.1175/ 1520-0434(1990)005,0570:TCSIAA.2.0.CO;2. Song, X., and G. J. Zhang, 2009: Convection parameterization, tropical Pacific double ITCZ, and upper-ocean biases in the NCAR CCSM3. Part I: Climatology and atmospheric feedback. J. Climate, 22, 4299–4315, doi:10.1175/ 2009JCLI2642.1. Stechmann, S. N., and J. D. Neelin, 2011: A stochastic model for the transition to strong convection. J. Atmos. Sci., 68, 2955–2970, doi:10.1175/JAS-D-11-028.1. Taylor, C. M., R. A. M. de Jeu, F. Guichard, P. P. Harris, and W. A. Dorigo, 2012: Afternoon rain more likely over drier soils. Nature, 489, 423–426, doi:10.1038/nature11377.
7666
JOURNAL OF CLIMATE
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, doi:10.1175/1520-0493(1989)117,1779: ACMFSF.2.0.CO;2. Truong, N. M., T. T. Tien, R. A. Pielke Sr., C. L. Castro, and G. Leoncini, 2009: A modified Kain–Fritsch scheme and its application for simulation of an extreme precipitation event in Vietnam. Mon. Wea. Rev., 137, 766–789, doi:10.1175/ 2008MWR2434.1. Wang, W., and M. E. Schlesinger, 1999: The dependence on convection parameterization on the tropical intraseasonal oscillation simulated by the UIUC 11-layer atmospheric GCM. J. Climate, 12, 1423–1457, doi:10.1175/1520-0442(1999)012,1423: TDOCPO.2.0.CO;2. Wang, X., and M. Zhang, 2013: An analysis of parameterization interactions and sensitivity of single-column model simulations to convection scheme in CAM4 and CAM5. J. Geophys. Res., 118, 8869–8880, doi:10.1002/jgrd.50690. Wilcox, E. M., and L. J. Donner, 2007: The frequency of extreme rain events in satellite rain-rate estimates and an atmospheric general circulation model. J. Climate, 20, 53–69, doi:10.1175/ JCLI3987.1. Woodcock, F., 1976: The evaluation of yes/no forecasts for scientific and administrative purposes. Mon. Wea. Rev., 104, 1209–1214, doi:10.1175/1520-0493(1976)104,1209:TEOYFF.2.0.CO;2. Wu, X., L. Deng, X. Song, G. Vettoretti, W. R. Peltier, and G. J. Zhang, 2007: Impact of a modified convective scheme on the Madden-Julian oscillation and El Niño–Southern Oscillation in a coupled climate model. Geophys. Res. Lett., 34, L16823, doi:10.1029/2007GL030637. Xie, S., and M. H. Zhang, 2000: Impact of the convection triggering function on single-column model simulations. J. Geophys. Res., 105, 14 983–14 996, doi:10.1029/2000JD900170. ——, R. T. Cederwall, and M. H. Zhang, 2004a: Developing longterm single-column model/cloud system–resolving model forcing using numerical weather prediction products constrained by surface and top of the atmosphere observations. J. Geophys. Res., 109, D01104, doi:10.1029/2003JD004045.
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——, M. Zhang, J. S. Boyle, R. T. Cederwall, G. L. Potter, and W. Lin, 2004b: Impact of a revised convective triggering mechanism on community atmosphere model, version 2, simulations: Results from short-range weather forecasts. J. Geophys. Res., 109, D14102, doi:10.1029/2004JD004692. Zhang, G. J., 2002: Convective quasi-equilibrium in midlatitude continental environment and its effect on convective parameterization. J. Geophys. Res., 107, doi:10.1029/2001JD001005. ——, 2003: Convective quasi-equilibrium in the tropical western Pacific: Comparison with midlatitude continental environment. J. Geophys. Res., 108, 4592, doi:10.1029/2003JD003520. ——, 2009: Effects of entrainment on convective available potential energy and closure assumptions in convection parameterization. J. Geophys. Res., 114, D07109, doi:10.1029/2008JD010976. ——, and N. A. McFarlane, 1995: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmos.–Ocean, 33, 407–446, doi:10.1080/07055900.1995.9649539. ——, and M. Mu, 2005: Simulation of the Madden–Julian oscillation in the NCAR CCM3 using a revised Zhang–McFarlane convection parameterization scheme. J. Climate, 18, 4046– 4064, doi:10.1175/JCLI3508.1. ——, and H. Wang, 2006: Toward mitigating the double ITCZ problem in NCAR CCSM3. Geophys. Res. Lett., 33, L06709, doi:10.1029/2005GL025229. ——, and X. Song, 2010: Convection parameterization, tropical Pacific double ITCZ, and upper-ocean biases in the NCAR CCSM3. Part II: Coupled feedback and the role of ocean heat transport. J. Climate, 23, 800–812, doi:10.1175/2009JCLI3109.1. Zhang, M. H., and J. L. Lin, 1997: Constrained variational analysis of sounding data based on column-integrated budgets of mass, heat, moisture, and momentum: Approach and application to ARM measurements. J. Atmos. Sci., 54, 1503–1524, doi:10.1175/ 1520-0469(1997)054,1503:CVAOSD.2.0.CO;2. ——, ——, R. T. Cederwall, J. J. Yio, and S. C. Xie, 2001: Objective analysis of ARM IOP data: Method and sensitivity. Mon. Wea. Rev., 129, 295–311, doi:10.1175/1520-0493(2001)129,0295: OAOAID.2.0.CO;2.
