PUBLICATIONS. Journal of Geophysical Research: Atmospheres

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1 PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE Key Points: Diurnal variations of precipitation are evaluated with cumulus parameterization schemes KFtr scheme reproduces well the afternoon peak of precipitation over East Asia Modulation of trigger function can delay afternoon peak and reduce precipitation rate Correspondence to: I.-J. Choi, Citation: Choi, I.-J., E. K. Jin, J.-Y. Han, S.-Y. Kim, and Y. Kwon (2015), Sensitivity of diurnal variation in simulated precipitation during East Asian summer monsoon to cumulus parameterization schemes, J. Geophys. Res. Atmos., 120, 11,971 11,987, doi:. Received 16 JUN 2015 Accepted 3 NOV 2015 Accepted article online 5 NOV 2015 Published online 7 DEC 2015 Sensitivity of diurnal variation in simulated precipitation during East Asian summer monsoon to cumulus parameterization schemes In-Jin Choi 1, Emilia Kyung Jin 1, Ji-Young Han 1, So-Young Kim 1, and Young Kwon 1 1 Korea Institute of Atmospheric Prediction Systems, Seoul, South Korea Abstract The capability to simulate the diurnal variation of precipitation over East Asia region during the summertime of 2011 is investigated using five different cumulus parameterization schemes with the Weather Research and Forecasting model. A semidiurnal cycle with a 12 h interval over land and a diurnal cycle with a 24 h interval over ocean are commonly found in all simulations, consistent with the observed diurnal cycle. Two observed dominant peaks in the early morning and afternoon are reproduced in all simulations. With overestimated precipitation rate, however, the simulated afternoon peaks occur earlier than the observed peaks by 2 h for the Kain-Fritsch (KF) and Simplified Arakawa-Schubert schemes, and by 3 h for the Betts-Miller-Janjić and Tiedtke schemes. The overestimation of simulated precipitation frequency leads to amplitude and phase errors in the precipitation rate, and the early peak time of simulated precipitation intensity intensifies the phase error in the simulation over land. The KF scheme with alternative trigger function (KFtr) based on moisture advection provides slightly better results in terms of alleviating the overestimated precipitation rate and frequency and delaying the afternoon peaks. Additional sensitivity simulations based on the change of temperature perturbation in the trigger function of the KF and KFtr schemes demonstrate the afternoon peak tends to be delayed as temperature perturbation decreases, implying the significant role of convective initiation frequency in determining diurnal peaks of precipitation. Modulation of temperature perturbation alleviates the precipitation frequency bias, while it could not resolve the precipitation intensity bias. 1. Introduction The diurnal variation of precipitation is one of the fundamental cycles in the Earth s weather and climate systems, and it is largely controlled by the direct thermodynamic response to solar radiation. Over the East Asia region, including East China, the Korean peninsula, and Japan, previous in situ and satellite observational studies have reported the semidiurnal cycle of precipitation [Ramage, 1952; Lim and Kwon, 1998; Jung et al., 2001; Jung and Suh, 2005;Yu et al., 2007a, 2007b; Koo et al., 2009]. This phenomenon depends on the geographical location. Specifically, an early morning peak appears along the coastal region, while both a weak early morning peak and a strong late afternoon peak occur over the inland region. Various physical mechanisms have been suggested to explain the diurnal variation of precipitation [e.g., Brier and Simpson, 1969; Wallace, 1975; Dai and Deser, 1999; Dai and Wang, 1999;Sohn et al., 2013]. For instance, the semidiurnal cycle of precipitation over the U.S. Great Plains might be caused by the eastward propagating convections generated over the Rockies in the previous afternoon, as suggested in Chen et al. [2009]. While, an atmospheric circulation change induced by the semidiurnal land-sea differential heating [Huang and Chan, 2011] is one of the causes for semidiurnal cycle over East Asia American Geophysical Union. All Rights Reserved. The reproducibility of diurnal variation in precipitation has been addressed as one of the challenging issues in modeling weather and climate systems. A number of modeling studies have been performed on the diurnal variation of precipitation using global circulation models [e.g., Janowiak et al., 2007; Lee et al., 2007; Chao, 2013; Yuan, 2013], regional climate models [e.g., Dai et al., 1999; Koo and Hong, 2010; Jeong et al., 2013; Pohl et al., 2014], and even high-resolution cloud-resolving models [e.g., Sato et al., 2009; Lee et al., 2010]. Most model simulations have commonly pointed out the critical deficiencies of reproducing the diurnal cycle in precipitation (e.g., a phase shift problem occurring too early in the afternoon peak over land). Considering the diurnal variation of precipitation is a part of various temporal scales of East Asian Summer Monsoon (EASM) variability, the reproduction of diurnal variations of precipitation is crucial for the energy and hydrological CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,971

2 cycles associated with mean climate of EASM period [Neal and Slingo, 2003]. Therefore, the evaluation of the ability to correctly simulate the diurnal variation of precipitation has been regarded as an essential task for improving model performance for weather forecasts and climate simulations. The diurnal features of precipitation over land are strongly associated with the convection activity produced by surface radiative heating [Lee et al., 2007], so the simulation of diurnal variation in precipitation is highly sensitive to cumulus parameterization. Koo and Hong [2010] showed that the simulated phase of maximum precipitation over land is modulated by the cumulus parameterization scheme. The trigger function in the cumulus parameterization scheme might be the first issue examined for diurnal variations of precipitation due to its key role in convection initiation. Previous studies have reported the criterion to initiate moist convection tends to be too weak to capture the realistic diurnal variation of precipitation [Dai et al., 1999; Jeong et al., 2013]. Besides, the effect of convective entrainment and detrainment on the simulation of the tropical precipitation diurnal cycle was investigated by Wang et al. [2007], who suggested that enhanced fractional entrainment and detrainment rates slightly delayed the timing of maximum precipitation. A diagnostic convective closure linked to boundary layer forcing derived by Bechtold et al. [2014] significantly improved the diurnal cycle of convection. It is therefore meaningful and necessary to identify a cumulus parameterization scheme that appropriately simulates the diurnal variation of precipitation over East Asia, because none of the existing schemes perform equally well under all areas and conditions [Singh et al., 2006]. The present study aims to evaluate how well the diurnal variation of precipitation is simulated by a variety of cumulus parameterization schemes during the summer monsoon period. The simulated results from the cumulus parameterization schemes are assessed by mainly focusing on the timing and amount biases in the diurnal variation of precipitation. The comparisons of model performance for reproducing the diurnal variation of precipitation provide a potential pathway to improve cumulus parameterization schemes in numerical weather prediction models as well as global/regional climate models. The paper is organized as follows. Section 2 describes the model configuration, experimental setup, and data resources for the validation. The model performances are compared in terms of large-scale features and seasonal mean precipitation in section 3. The sensitivity of the diurnal variation in precipitation to the cumulus parameterization schemes is provided in section 4. Section 5 addresses the impact of trigger function on the simulated diurnal variation of precipitation with additional sensitivity simulations. Finally, summarized results and concluding remarks are included in section Model, Experimental Setup, and Data Resources The Weather Research and Forecasting (WRF) Advanced Research WRF (ARW) modeling system, version 3.6 (WRF hereafter) [Skamarock et al., 2008], is used in this study. All simulations are performed over the domain covering the EASM region centered at the Korean peninsula during June-July-August (JJA) According to the report by Korea Meteorological Administration, the second largest precipitation amount over the Korean peninsula was recorded in the summertime of the year 2011 since the observation has started in The horizontal resolution is set to 50 km with 107 (west-east) 78 (north-south) grid points and a 200 km buffer zone for prescribed lateral boundary conditions. The number of vertical layers is 30 up to 50 hpa. Checking the impact of vertical resolution, little change with increasing vertical layers (from 30 to 60) is confirmed in the diurnal variation of precipitation as well as spatial pattern of seasonal mean precipitation. Ensemble simulations are initialized at 0000 UTC on 21, 22, 23, 24, and 25 May 2011 and integrated continuously to 0000 UTC 2 September The first 7 11 days of ensemble simulations for a spin-up period are excluded. Initial conditions are obtained from the National Centers for Environmental Prediction/Department of Energy Atmospheric Model Intercomparison Project II Reanalysis data (RA2) with a grid and 18 vertical pressure levels [Kanamitsu et al., 2002]. Lateral boundary forcing is provided every 6 h by RA2 data, and observed sea surface temperature (SST) is prescribed every 24 h from the optimal interpolation SST weekly data set with a horizontal resolution of 1 1 [Reynolds and Smith, 1994]. The physics package for control (CTL) experiment includes the WRF single-moment 3-class microphysics scheme [Hong et al., 2004], the updated Kain-Fritsch (KF) cumulus scheme [Kain, 2004; Kain and Fritsch, 1990], the Yonsei University planetary boundary layer scheme [Hong et al., 2006],afive-layer thermal diffusion surface CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,972

3 Table 1. Main Features of Five Different Cumulus Parameterization Schemes Used in This Study Scheme Type Trigger Entrainment Formulation Closure KF Mass-flux Perturbation based on low-level vertical motion Variability of cloud radius and cloud-depth CAPE closure threshold allowed SAS Mass-flux Parcel buoyancy Height and RH dependent Quasi-equilibrium closure BMJ Adjustment CAPE, cloud depth threshold value, and moist sounding needed Convection profiles and relaxation time depends on cloud efficiency TDK Mass-flux Moisture convergence RH dependent CAPE closure KFtr Mass-flux Perturbation based on local average moisture advection Same as KF Same as KF scheme [Dudhia, 1996], the unified Noah land surface model [Chen and Dudhia, 2001], a simple cloud-interactive shortwave radiation scheme [Dudhia, 1989], and a rapid radiative transfer model for longwave radiation [Mlawer et al., 1997]. Sensitivity experiments for the cumulus parameterization schemes are additionally carried out with the updated version of the Simplified Arakawa-Schubert (SAS) scheme [Pan and Wu, 1995; Han and Pan, 2011; Lim et al., 2014], the Betts-Miller-Janjić (BMJ) scheme [Betts and Miller, 1993; Janjić, 1994, 2000], the Tiedtke scheme (TDK) [Tiedtke, 1989; Zhang et al., 2011], andthekain-fritsch schemewith an alternative trigger function weighted by moisture advection (KFtr) [Ma and Tan, 2009]. The same experimental setup except the cumulus parameterization scheme is applied to the sensitivity simulations. All schemes used in this study are a mass-flux parameterization for cumulus convection except for the BMJ scheme. The KF and KFtr schemes use the different trigger function, which is based on the perturbation calculated by vertical motion and weighted by moisture advection, respectively. They use a simple cloud model with moist updrafts and downdrafts, allowing for the variability of cloud radius and cloud-depth threshold, with the convective available potential energy (CAPE) closure assumption. The effect of the convection-induced forcing on cumulus momentum transport is only included in the SAS and TDK schemes. The SAS scheme uses a parcel buoyancy method for the trigger function, and permits entrainment into the updraft and detrainment from the downdraft between the updraft-air originating level and the level of free convection. Also, the SAS scheme employs a quasi-equilibrium closure instead of the CAPE closure used in other schemes. The TDK scheme uses the trigger function based on moisture convergence and considers organized entrainment-detrainment and turbulence entrainment-detrainment with CAPE closure. The BMJ scheme is a convective adjustment scheme, which is totally different with other mass-flux type schemes, and its reference profiles are based on a sounding structure obtained from tropical convection. The main features of each cumulus parameterization scheme are compared in Table 1. To ensure the predictability of simulated precipitation and its diurnal cycle, Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) with horizontal resolution and 50 S to 50 N coverage [Huffman et al., 2007] is used. TMPA data have been widely used to investigate the diurnal variation of precipitation over land and ocean [Su et al., 2008], and the reliability of precipitation data during the EASM period for evaluating the significance of the diurnal variation of precipitation has already been confirmed [Zhou et al., 2008; Koo et al., 2009]. The TMPA product used in this study is the 3B42 version 7, and each 3B42 data set represents a nominal ±90 min span around the nominal UTC hour. For temporal consistency between WRF simulation and TMPA observation, WRF output is recorded every 90 min and regenerated to a 3 h accumulated precipitation over the time range of ±90 min as in TMPA. For the comparison, the TMPA data are horizontally interpolated onto the model grid scale of 50 km, and the analysis is performed in a region with a latitude lower than 50 N where the TMPA data are available. 3. Evaluation of Model Performance Over East Asia 3.1. Large-Scale Features The synoptic features of the RA2 reanalysis data and CTL simulation are compared in Figure 1. In both the RA2 and CTL simulation, the spatial distribution of sea level pressure (SLP) shows high pressure in the Northwestern Pacific and low pressure over China (i.e., the east-west pressure gradient), which is well known as a typical SLP pattern during the EASM period. The simulated high-pressure system over the Northwestern CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,973

4 Journal of Geophysical Research: Atmospheres Figure 1. Large-scale features from (left) RA2 data set and simulated by (right) CTL with KF cumulus parameterization scheme for (a and b) sea level pressure (hpa), (c and d) 850 hpa wind (arrow) and relative humidity (%, shading), (e and f) 500 hpa geopotential height (gpm; solid line) and temperature (K; shading), and (g and f) 200 hpa geopotential height (gpm; solid line) and wind (arrow) averaged over East Asia during JJA Pacific tends to be extended to the west compared to that of RA2. A strong low-level jet (LLJ) in the lower troposphere (shown in Figures 1c and 1d) is the main mechanism for advecting moist and unstable air northward into the midlatitude region, where it ultimately becomes precipitation. The LLJ is well simulated in WRF compared to that of RA2, transporting the air along the western edge of a Northwestern Pacific high. The horizontal distribution of relative humidity at 850 hpa shows wet biases over land and dry biases over ocean. CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,974

5 Figure 2. Horizontal distributions of monthly averaged precipitation (mm month 1 ) observed by (a) TMPA and simulated by the (b) KF, (c) SAS, (d) BMJ, (e) TDK, and (f) KFtr cumulus parameterization schemes and (g k) the difference between simulated precipitation and TMPA observation over East Asia during JJA A subtropical high and a midlatitude trough over the west of the Korean peninsula are clearly seen in the 500 hpa geopotential height (GPH) field, providing the appropriate conditions for a heavy rainfall event. The spatial patterns of 500 hpa GPH and temperature as well as 200 hpa GPH and horizontal wind are quite well simulated, although they appear slightly zonal in the CTL simulation. Overall, the simulated large-scale patterns are quite similar to those of the RA2 data set, regardless of the difference in cumulus parameterization schemes CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,975

6 (not shown), suggesting that the model bias is attributable to the incomplete cumulus parameterization schemes because they all suffer from similar fundamental weaknesses both in numeric and/or physics [Kang and Hong, 2008] Seasonal Mean Precipitation Before validating the diurnal variations of precipitation, seasonal mean precipitation during the EASM period is verified in order to check the reliability of the simulations. Impact of cumulus parameterization schemes on the summer monsoon precipitation over East Asia has been widely investigated in previous studies [e.g., Kang and Hong, 2008; Chen et al., 2010; Yang et al., 2015]. Figure 2 shows the horizontal distribution of monthly averaged precipitation during JJA 2011, obtained from the TMPA data and simulated by five different cumulus parameterization schemes, and the differences between the simulations and TMPA observation. The simulated precipitation from all the simulations reproduces the overall pattern of observed precipitation from TMPA well, while the small details of precipitation patterns are different in each cumulus parameterization scheme. It is obvious that the KF and KFtr schemes can capture strong precipitation over the central area of the Korean peninsula, but they fail to simulate two other local maxima at eastern China and the Kyushu region in Japan (Figures 2b and 2f). The SAS scheme does not simulate all three local maxima of observed precipitation (Figure 2c). The BMJ and TDK schemes show similar spatial patterns of precipitation, with smoothed local maxima compared to those of the TMPA observation, as shown in Figures 2d and 2e. The differences between simulated precipitation and TMPA observation indicate both the underestimation of heavy precipitation over three local maxima and the overestimation of light precipitation over land and ocean in the KF scheme (Figure 2g). This confirms the results of Kim et al. [2010], suggesting that the KF scheme tends to produce more precipitation to reduce instability under relatively unstable atmospheric conditions with excessive low-level moisture. The SAS scheme largely underestimates the precipitation over the region where a major monsoon band is located (Figure 2h), which is consistent with Lim et al. [2014] pointing out a much weaker monsoon circulation compared to the observation. The BMJ and TDK schemes underestimate the precipitation over southern China as well as local maxima (Figures 2i and 2j). Because the precipitation in the BMJ scheme is estimated directly from the amount of latent heat, the less latent heat released from less simulated moisture amount in the BMJ scheme than that in the KF and SAS schemes could be responsible for the underestimated precipitation. Also, the underestimated precipitation in the TDK scheme was also reported by Ali et al. [2015]. They pointed out that the slow convective process in the TDK scheme decreases the ascending motion of the air before the condensation level and creates a more stable structure with less precipitation. The overestimation of light precipitation is found to a remarkable degree over the oceanic area of the Northwest Pacific below 30 N in the KF and KFtr schemes possibly due to the exaggerated oceanic convection or weak entrainment. The KFtr scheme tends to alleviate the overestimated precipitation produced by the KF and SAS schemes mainly due to a larger contribution nonconvective precipitation to the total precipitation [Ma and Tan, 2009; Pohl et al., 2014], but does not influence the overestimated precipitation over ocean (Figure 2k). The model allows the total precipitation to separate convective precipitation through a cumulus parameterization scheme and nonconvective precipitation through a cloud microphysics scheme. Figure 3 shows the spatial pattern of convective rain ratio (CRR) averaged during JJA 2011 from TRMM 3A12 product version 7 monthly data and the model simulations. Note that the observed CRR is obtained by retrieval algorithm to partition precipitation into convective and nonconvective categories [Kummerow et al., 2001]. Since the classification of convective and nonconvective precipitation between model simulation and TRMM observation is fundamentally different, the CRR should be compared only by a qualitative manner. It is evident that the observed CRR is high in the tropical region, but low is the midlatitude region, which is also identified in all simulations except the SAS scheme. The highest and the lowest CRR are found in the SAS (86.4%, domainaveraged value) and KFtr (58.7%) schemes over land and in the SAS (72.9%) and BMJ (50.6%) schemes over ocean, respectively. The large CRR value over the continent and subtropical oceanic region in the SAS scheme is partly attributable to the convection being more easily triggered with larger cloud base convective mass flux due to the choice of threshold value for vertical velocity. A modification in trigger function from the KF scheme to the KFtr scheme exhibits a decrease of CRR over most of the analysis domain, especially over the midlatitude continent. The BMJ and TDK schemes show comparable CRR distributions over both the continent and the ocean, with a relatively lower CRR than those of the KF and SAS schemes and higher than that of the KFtr scheme. CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,976

7 Figure 3. Spatial distribution of convective rain ratio (CRR, %) from (a) TRMM observation, and defined as the ratio of convective precipitation to total precipitation averaged during JJA 2011 from the (b) KF, (c) SAS, (d) BMJ, (e) TDK, and (f) KFtr schemes. 4. Diurnal Features of Precipitation 4.1. Spectral Analysis of 3 h Accumulated Precipitation In order to examine the periodicity of diurnal variation in precipitation rate, a spectral analysis is performed using a forward complex discrete Fourier transform with 3-hourly precipitation data. The power spectral density (PSD) of the precipitation rate with respect to the period averaged over the whole domain, land, and ocean is shown in Figure 4. Note that the PSD is averaged across the spectral bins of period (i.e., x axis) with an interval of 1 h. It is commonly found in all simulations that the simulated period in precipitation is well matched with that observed from the TMPA. Differences are found in the characteristics between the period of precipitation over land and ocean. Over land, the observed precipitation rate has a dominant period of 24 h (i.e., diurnal cycle) with a secondary peak at a period of 12 h (i.e., semidiurnal cycle). This is consistent with the previous observational studies performed using rain gauge data over the Korean peninsula, which showed that the precipitation in Korea exhibits a semidiurnal cycle [e.g., Jung et al., 2001; Yu et al., 2007a, 2007b]. Those variations in diurnal and semidiurnal cycles are reproduced well in the simulation, but the amplitude of simulated PSD is larger than that of observed PSD. The separation of total precipitation into convective and nonconvective precipitation demonstrates that the semidiurnal cycle is attributable to the variation of convective precipitation (Figures 4d and 4f). Over ocean, the dominant period is 24 h in both the simulations and observation, in which both convective and nonconvective precipitations play a role in determining the periodicity of precipitation (Figures 4c, 4e, and 4g) Diurnal Variations of Precipitation To investigate the diurnal variation of precipitation, both observed and simulated precipitation rates for the three months are composited to the UTC daily time frame every 3 h. The 3-hourly observed and simulated precipitation data on a UTC frame are interpolated to the 1-hourly precipitation on a UTC frame using a cubic spline method. The 1-hourly precipitation data are then converted from the UTC frame to the local standard time (LST) frame based on the longitudinal dependency. The diurnal variations of composited precipitation are compared in terms of total, convective, and nonconvective precipitation rates averaged over the whole analysis domain, land, and ocean (Figure 5). Over the whole analysis domain, the diurnal variation of total precipitation rate observed from the TMPA has two peaks in the early morning at 0500 LST and late afternoon at 1600 LST. Additionally, the amplitude of the late afternoon peak is larger than that of the morning peak. While most cumulus parameterization schemes reproduce the afternoon peak, the relatively weak morning peaks are not clearly simulated, especially in the TDK and BMJ schemes. The simulated afternoon peaks also CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,977

8 Figure 4. Power spectral density (PSD, mm 2 h 2 /s 1 ) of (a and b) total precipitation rate, (c and d) convective precipitation rate, and (e and f) nonconvective precipitation with respect to period. The results over land are seen in the left plot, and those over ocean are shown in the right plot. CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,978

9 Figure 5. Diurnal variations of (a) total precipitation rate (mm h 1 ), (b) convective precipitation rate (mm h 1 ), and (c) nonconvective precipitation rate (mm h 1 ) over (left) the whole analysis domain, (middle) the land, and (right) the ocean. Simulated and observed diurnal variations are represented by solid and dotted lines, respectively. Note that the y axis of Figure 5c has a different scale from those of Figures 5a and 5b. have issues of larger amplitude and earlier timing (e.g., 2 h for the KF and SAS schemes, 3 h for the BMJ and TDK schemes) compared to the TMPA. This discrepancy has been considered a typical error in atmospheric models by previous modeling studies in East Asia [e.g., Koo and Hong, 2010] and other regions [e.g., Yang and Slingo, 2001; Wang et al., 2007; Jeong et al., 2013]. The KFtr scheme alleviates the excessive precipitation rate at the afternoon peak and delayed the afternoon peak by 1 2 h, which is much closer to the TMPA observation than other cumulus parameterization schemes. It should be noted that the use of 1 h WRF output without temporal interpolation leads to a slight phase shift without any changes in the amplitude (e.g., same phases for morning and afternoon peaks in the KF experiment, but 1 h delayed afternoon peak in the KFtr experiment; not shown). Due to the temporal consistency for observation and simulation, 3 h WRF output is used in the analysis instead of 1 h WRF output. CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,979

10 Figure 6. Spatial distribution of the local time (LST) of maximum precipitation rate in diurnal variation from the (a) TMPA observation and model simulations with the (b) KF, (c) SAS, (d) BMJ, (e) TDK, and (f) KFtr schemes. The blue colors represent local morning, and the red colors represent local afternoon. The separated analysis over land and ocean shows a distinct contrast in the diurnal variations of the total precipitation rate between land and ocean, indicating an afternoon peak over land and a morning peak over ocean. Excessive precipitation with an early afternoon peak over land is commonly found in the KF, SAS, BMJ, and TDK schemes, whereas the KFtr scheme results are comparable to the observed precipitation rate and timing. Figures 5b and 5c show that the early afternoon peaks over land from all the simulations are mainly caused by the diurnal variation of convective precipitation, indicating that the phase biases are due to a close connection to the unrealistically early onset and immediate response of deep convection caused by surface heating over land. A minor peak in the early morning at around 0500 LST mostly results from the diurnal variation of total precipitation rate over ocean and partly from nonconvective precipitation over land. The variations of convective precipitation rate over land are larger than those over ocean, whereas the fluctuation of nonconvective precipitation rate over land is comparable to that over ocean. The spatial distributions of the local time of maximum precipitation rate from the TMPA observation and five sensitivity simulations are shown in Figure 6. Consistent with the previous studies, the precipitation rate from the TMPA observation peaks in the late afternoon ( LST) over most of the land area and in the early morning ( LST) over ocean. The early morning peaks appear over the eastern flank of the Tibetan region possibly due to a high orography, as shown by Dai and Trenberth [2004] and Koo and Hong [2010]. The land-sea contrast of peak time is more distinctive in the model simulations. In other words, the maximum precipitation evidently occurs in the early afternoon ( LST) over land and in the early morning ( LST) over ocean, which is earlier than in the observed peaks. The differences in peak time over land are considerable among the schemes, but those over ocean are not as large as over land. Compared to the KF scheme, the simulated diurnal peak in the BMJ and TDK schemes occurs approximately 1 2 h earlier over most of the land area. The SAS scheme shows the diurnal peak later locally than the KF scheme (e.g., southern China). The peak time from the KFtr schemes is delayed by approximately 1 2h compared to that of the KF scheme; therefore, the timing of the afternoon peak from the KFtr scheme is very close to that of the observation. Given the comparison of diurnal variation in precipitation and the timing of maximum precipitation rate, the best performance is obtained with the KFtr scheme. This result suggests that a modulation of the afternoon peak time in the precipitation diurnal cycle could be achieved by controlling the trigger function. CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,980

11 Figure 7. Diurnal variations of (a) precipitation frequency (%) and (b) intensity per precipitation occurrence (mm h 1 ) over (left) the whole analysis domain, (middle) the land, and (right) the ocean. Simulated and observed diurnal variations are represented by solid and dotted lines, respectively. The precipitation amount is determined by how frequently the precipitation occurs and how strong the precipitation is when it occurs. Therefore, the diurnal variation of precipitation rate based on frequency and intensity needs to be assessed because the correct combination of frequency and intensity of precipitation is important for the precipitation rate to be simulated well in a physically reasonable manner [Trenberth et al., 2003]. The frequency of precipitation is determined as the percentage of times where measurable precipitation has a threshold value of 0.1 mm h 1,accordingtoDai et al. [1999] and Koo and Hong [2010], during JJA 2011 at a certain LST. The intensity of precipitation is defined as an averaged precipitation rate during the precipitating time that has measurable precipitation once the precipitation occurs. The multiplication of the frequency and the intensity of precipitation is regarded as the same as the precipitation rate. Figure 7 shows the composited diurnal variation of precipitation frequency and intensity from the TMPA observation and simulations over the whole analysis domain, land, and ocean. The diurnal variations in the frequency of observed precipitation over the whole domain, land, and ocean are substantially similar to that of the precipitation rate presented in Figure 5a. Likewise, the influence of the frequency in simulated precipitation is more predominant than its intensity in determining the diurnal variation of precipitation rate. The simulated precipitation from all the cumulus parameterization schemes exhibits higher occurrence frequency and much lower intensity per occurrence overall than TMPA observation does. Indeed, previous modeling studies have consistently reported this problem (i.e., the overestimation of frequency and the underestimation of intensity), attributing much of this discrepancy to cumulus parameterization being easily triggered [Sun et al., 2006; Evans and Westra, 2012]. This frequent occurrence of precipitation leads to the amplitude errors in the simulated precipitation amount. The maximum simulated frequency in the afternoon (except the KFtr scheme) is earlier than that in the observation, causing the phase error as well. The separated analysis over land and ocean shows that the peak time of the simulated frequency over land is the same (e.g., the KF and SAS schemes) or 1 h earlier (e.g., the BMJ and TDK schemes) compared to that of the observed frequency (1500 LST). However, the peak time of simulated intensity is out of phase (i.e., at least 3 h earlier CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,981

12 Table 2. Percentage Variance of Diurnal Variation in Precipitation Amount in Terms of the Frequency and Intensity of Precipitation Over Land and Ocean From the TMPA Observation and Model Simulations With Five Different Cumulus Parameterization Schemes Frequency Intensity Unit : % Land Ocean Land Ocean TMPA KF SAS BMJ TDK KFtr than the observation) with that of the observed intensity (1700 LST), which intensifies the phase error in the simulation over land. The relative contribution of the frequency and intensity of precipitation to the amount of precipitation can be measured by percentage variance, as demonstrated by Zhou et al. [2008] and Koo and Hong [2010]. The percentage variance is defined as the square of the correlation coefficient between the diurnal cycles of precipitation amount and frequency (or intensity). The percentage variance of diurnal variation in precipitation amount in terms of the frequency and intensity of precipitation from the TMPA observation and model simulations over land and ocean is described in Table 2. Consistent with the results in Figure 7, the diurnal variation of precipitation amount is significantly affected by precipitation frequency rather than its intensity in both the TMPA observation and model simulations. Additionally, the relative contributions of both frequency and intensity are overestimated in the model simulations compared with those from the TMPA observation. 5. Impacts of Trigger Function on Diurnal Variation of Precipitation 5.1. Comparison Between the KF and KFtr Schemes From the comparisons of the diurnal variation in precipitation, the KFtr scheme with a modified trigger function produces a better performance, especially in the phase of the afternoon peak, compared to the KF scheme. This is well matched with the previous study over another region (e.g., South Africa in Pohl et al. [2014]). In this section, the impact of trigger function on the diurnal variation of precipitation during the EASM period is investigated through a comparison of the KF and KFtr schemes. To determine whether convection is initiated by the trigger function of the KF scheme, the summation of a parcel temperature (T LCL ) and temperature perturbation (δt vv ) is compared with an ambient temperature (T ENV ) at the lifting condensation level (LCL). Convection can be triggered if this summation is warmer than the ambient temperature (i.e., T LCL + δt vv > T ENV ), while the parcel is negatively buoyant when it is colder than its environment. In the KF scheme, the temperature perturbation is defined as a function of grid-resolvable vertical velocity at the LCL, because convection tends to be favored by vertical motion based on Fritsch and Chappell [1980], as shown in equation (1). In the KFtr scheme [Ma and Tan, 2009], however, the temperature perturbation takes into account the effect of moisture advection. The KFtr scheme employs temperature perturbation composed of horizontal and vertical components in a temperature anomaly with an accompanying weighting coefficient to reflect the effect of moisture advection (equation (2)). δt vv ¼ c 1 wg 1=3 (1) δt vv ¼ R h δt vvh þ R v δt vvv (2) v M q M Minðv M q M Þ h;v R h;v ¼ Maxðv M q M Þ h;v Minðv M q M where c 1 is a unit number ( C s 1/3 cm 1/3 ) and w g is the vertical velocity at the LCL. δt vvh and δt vvv are the temperature horizontal and vertical anomalies, respectively. R h and R v are the normalized horizontal and vertical moisture advections from 0 to 1, respectively. Preliminary results in the case simulation of a tropical cyclone by Ma and Tan [2009] showed that the KFtr scheme reduces convective precipitation by approximately 10% by eliminating convective instability under weak synoptic forcing, while it has an insignificant influence on nonconvective precipitation (i.e., negligible differences compared with those of KF). In this study, the modified trigger function in the KFtr scheme leads to a significant reduction of convective precipitation by 24.2% and an enhancement of nonconvective precipitation by 11.2%, and thereby a decrease of total precipitation by 13.0% compared to the results from Þ h;v CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,982

13 Figure 8. Comparisons of the local time (LST) for maximum convective and nonconvective precipitation in simulated diurnal variation from the (a and b) KF and (c and d) KFtr schemes. The color scale is the same as that in Figure 6. the KF scheme. Pohl et al. [2014] pointed out that the improvement of diurnal variation in precipitation over South Africa is due to the larger contribution of nonconvective precipitation in the KFtr scheme, while the convective precipitation still peaks in the early afternoon. In contrast to the results of Pohl et al. [2014], the delayed afternoon peak from the KFtr scheme of this study is affected by not only the delayed timing of the afternoon peak in convective precipitation, but also the shift from the early morning peak to the nighttime peak in nonconvective precipitation (see Figure 8), contributing to the better performance in simulating the diurnal variation of precipitation. In addition, the effects of improved diurnal variation of precipitation on seasonal mean precipitation and large-scale circulation patterns, one of EASM components, are examined. Previousstudieshaveshownthat the cloud resolving models reproducing realistic diurnal cycles of precipitation have difficulties in reproducing the large-scale features of the mean climate of precipitation [Dirmeyer et al., 2012;Cash et al., 2015]. Since the EASM precipitation is a complex phenomenon with a various spatiotemporal scales, the improvement of diurnal variation of precipitation might not be linked directly with better simulation of mean precipitation. Comparing to mean precipitation from the KF scheme (Figure 2), the adjusted triggering function and improved diurnal variation of precipitation in the KFtr scheme do not deteriorate seasonal mean precipitation. Also, little differences are found in the large-scale circulation patterns between the KF and KFtr simulations (not shown here) Sensitivity of Temperature Perturbation on the Diurnal Variation of Precipitation Each term consisting of the trigger function (i.e., parcel temperature, temperature perturbation, and ambient temperature at LCL) is compared between the KF and KFtr schemes. The magnitude of temperature perturbation CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,983

14 Figure 9. Diurnal variations of (a) amount, (b) frequency, (c) intensity of total precipitation, (d) frequency of convective initiation, and (e) convective and (f) nonconvective precipitation from the sensitivity simulations with temperature perturbation in the trigger function of the KF and KFtr schemes. KF_dt0.1 and KF_dt0.01 represent the simulations with the decreased temperature perturbation by 0.1 and 0.01 times in the KF scheme, respectively. KFtr_dt10 means the simulation with the increased temperature perturbation by 10 times in the KFtr scheme. The solid and dotted lines indicate the model simulation and TMPA observation, respectively. in the KFtr scheme is found to be approximately one tenth smaller than that of the KF scheme (not shown), suggesting that the magnitude of temperature perturbation might modulate the phase of the afternoon peak in the diurnal variation of precipitation. Therefore, additional sensitivity simulations are performed with a decrease in the temperature perturbation of the KF scheme by 0.1 and 0.01 times and with an increase in the KFtr scheme by 10 times. Figure 9 shows the diurnal variations of the amount, frequency, and intensity of total precipitation, frequency of convective initiation satisfied by the trigger function, and convective and nonconvective components of precipitation from the sensitivity simulation based on the change of temperature perturbation. As the temperature perturbation decreases in the KF scheme, the afternoon peak in total precipitation tends to be delayed and the precipitation rate tends to be reduced, which becomes similar to the diurnal variation of precipitation from the KFtr scheme (Figure 9a). This phenomenon is also confirmed in the sensitivity simulation from the KFtr scheme in the way that the increased temperature perturbation in the KFtr scheme causes the earlier afternoon peak. Through the modulation of temperature perturbation in trigger function, the precipitation frequency bias could be alleviated, while the precipitation intensity bias could not be resolved (Figures 9b and 9c). The decreased temperature perturbation can lead cumulus convection not to be easily triggered. As shown in Figure 9d therefore, the decreased temperature perturbation reduces the frequency of convective initiation for the afternoon peak, and it delays the timing of convective initiation (e.g., from 1400 LST in the KF experiment to 1800 LST in the KF_dt0.01 experiment). It affects directly the diurnal variations in the convective precipitation, resulting in the delayed afternoon peak with the reduced precipitation rate (see Figure 9e). Nonconvective precipitation is simulated more in the late afternoon when the convection is more suppressed (Figure 9f), producing a larger contribution of nonconvective precipitation to total precipitation. Due to the increased nonconvective precipitation in the late afternoon, the delayed afternoon peak in total precipitation is shifted to later. In summary, the magnitude of temperature perturbation and the associated change in the triggering condition have an effect on the frequency of convective initiation, which plays a significant role in determining the phase CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,984

15 of afternoon peak of precipitation. An appropriate trigger function should be used to correctly simulate the diurnal variation of precipitation in the further improvement of cumulus parameterization schemes. 6. Summary and Conclusion This study aims to compare the reproducibility of diurnal variation in precipitation simulated by various cumulus parameterization schemes during the EASM period and to compare the simulated results by mainly focusing on the timing of the diurnal variation of precipitation. Simulated diurnal variation of precipitation over the East Asia region during JJA 2011 is examined using five different cumulus parameterization schemes (i.e., KF, SAS, BMJ, TDK, and KFtr) in WRF v3.6. Simulated seasonal mean precipitation from all cumulus parameterization schemes reproduces the overall pattern of observed precipitation well, but the small details of precipitation patterns are different in each cumulus parameterization. The KF and KFtr schemes can capture strong precipitation over the central area of the Korean peninsula. The BMJ and TDK schemes show similar spatial patterns of precipitation with smoothed local maxima. All the cumulus parameterization schemes in this study tend to underestimate the heavy precipitation and overestimate the light precipitation over land and overestimate the light precipitation over the Northwest Pacific below 30 N. The overestimation over land is remarkable in the SAS scheme because of the large contribution of convective precipitation to total precipitation. It is worthwhile mentioning that the KFtr scheme alleviates the overestimated precipitation and high convective rain ratio over land produced by the KF and SAS schemes. The semidiurnal cycle with a 12 h interval over land and the diurnal cycle with a 24 h interval over ocean are commonly found in all simulations, consistent with those from the TMPA observation. Spectral analysis also shows that the semidiurnal cycle is responsible for the variation of convective precipitation over land. In the comparisons of the diurnal variation of precipitation, most of cumulus parameterization schemes reproduce the afternoon peak, while the relatively weak morning peaks are not clearly simulated especially in the TDK and BMJ schemes. The simulated afternoon peaks also have issues of larger amplitude and earlier timing compared to those of the TMPA. The separated analysis of precipitation amount into frequency and intensity indicates that the frequency of simulated precipitation determines the diurnal variation of precipitation rate rather than its intensity. The frequent occurrence of simulated precipitation leads to the amplitude and phase errors of the precipitation amount, and the peak time of simulated intensity intensifies the phase error in the simulation over land. The KFtr scheme provides slightly better results, because it alleviates the excessive precipitation rate and the overestimated precipitation frequency at the afternoon peak and delayed the afternoon peak by 1 2 h, which is much closer to the TMPA observation than other cumulus parameterization schemes. There is a better performance in the diurnal variation of precipitation from the KFtr scheme than from the KF scheme not only in terms of the delayed initiation of convection by the modified trigger function, but also the increase of nonconvective precipitation. The reason why the concept of trigger function in the KFtr scheme works better for simulating diurnal variations of precipitation is that the temperature perturbation based on moisture advection in the KFtr scheme is much smaller than that based on vertical motion in the KF scheme. It implies that the magnitude of temperature perturbation would be a crucial factor to determine the timing of diurnal peaks. Therefore, additional sensitivity simulations based on the change of temperature perturbation in the KF and KFtr trigger function are performed to determine the impact of trigger function on the diurnal variation of precipitation. As the temperature perturbation in trigger function decreases, the afternoon peak in total precipitation tends to be delayed later with a reduced precipitation rate. The modulation of temperature perturbation in trigger function could improve the diurnal variation of precipitation frequency, but not that of precipitation intensity. The magnitude of temperature perturbation and the associated change in triggering condition have an effect on the frequency of convective initiation, which plays a significant role in determining the phase of afternoon peak of precipitation. Only the modulation of the trigger function in cumulus parameterization schemes alone will probably neither bring all the answers nor solve all problems. Nevertheless, the findings of this study are useful for partly understanding the reasons for the typical biases in the simulated diurnal variation of precipitation, and for suggesting a plausible direction for the further development of cumulus parameterization scheme. Given the relatively insignificant effect of the modulation of trigger function on the precipitation intensity, it might be worth to explore other aspects or advanced approaches for improving the representation of diurnal CHOI ET AL. DIURNAL CYCLE OF PRECIPITATION 11,985

16 variation of precipitation. For example, the varying entrainment with height of the lifting condensation level [Stratton and Stirling, 2012], the prescribed variations in entrainment and detrainment [Hohenegger and Steven, 2013], an entraining CAPE-dependent diagnostic closure for the cloud base mass flux [Bechtold et al., 2014], and/or a cold-pool dynamics [Schlemmer and Hohenegger, 2014] possibly contribute to the improvement of diurnal variation of simulated precipitation. Acknowledgments This work has been carried out through the R&D project on the development of global numerical weather prediction systems of the Korea Institute of Atmospheric Prediction Systems (KIAPS) funded by the Korea Meteorological Administration. The RA2 and TMPA products were obtained freely from the CISL Research Data Archive ( and from the Goddard Space Flight Center Distributed Active Archive Center (ftp://disc2.nascom.nasa.gov/data/trmm/ Gridded/3B42_V7/), respectively. 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