The diurnal cycle of East Asian summer monsoon precipitation simulated by the Met Office Unified Model at convection-permitting scales

A limited area convection permitting model (CPM) based on the Met Office Unified Model, with a 0.04° (4.4 km) horizontal grid spacing, is used to simulate an entire warm-season of the East Asian monsoon (from April to September 2009). The simulations are compared to rain gauge observations, reanalysis and to a lower resolution regional model with a 0.12° (13.2 km) grid spacing that has a parametrization of subgrid-scale convective clouds and precipitation. The 13.2 km simulation underestimates precipitation intensity, produces rainfall too frequently, and shows evident biases in reproducing the diurnal cycle of precipitation and low-level wind fields. In comparison, the CPM shows significant improvements in the spatial distribution of precipitation intensity, although it overestimates the intensity magnitude and has a wet bias over central eastern China. The diurnal cycle of precipitation over Mei-yu region, southern China and the eastern periphery of the Tibetan Plateau, as well as the diurnal cycle of low-level winds over both the Mei-yu region and southern China are better simulated by the CPM. Over the Mei-yu region, in both simulations and observations, the local atmospheric instability in the afternoon is favorable for upward motion and rainfall. The CPM receives more sensible heat flux from the surface, has a stronger upward motion, and overestimates water vapor convergence based on moisture budget diagnosis. All these processes help explain the excessive late afternoon rainfall over the Mei-yu region in the CPM simulation.


Introduction
The diurnal cycle of precipitation is an important aspect of our weather and climate. It is closely related to surface temperature, moist convection, the formation of clouds and boundary-layer development Yang and Slingo 2001). Furthermore, it is intimately connected with both regional and synoptic-scale dynamical and thermal conditions and thus provides a good test bed for weather and climate models (Dai and Trenberth 2004). On a global scale, the diurnal variations of precipitation are evident over much of the world's land and oceans, especially during the summer months. For example, there is a substantial nocturnal-precipitation maximum over the oceans, due to cloud-radiative interactions, the diurnal circulation between land and ocean (Dai and Deser 1999) and the evolution of deep convective systems, and a late-afternoon maximum of showery precipitation over most areas of land, due to solar heating on the ground (Dai 2001(Dai , 2006Dai et al. 2007; This paper is a contribution to the special issue on Advances in Convection-Permitting Climate Modeling, consisting of papers that focus on the evaluation, climate change assessment, and feedback processes in kilometer-scale simulations and observations. The special issue is coordinated by Christopher L. Castro, Justin R. Minder, and Andreas F. Prein. 1 3 Dai and Trenberth 2004). The diurnal cycle of precipitation associated with the East Asian summer monsoon (EASM) shows unique features due to complex interactions between surface heating, orography and the monsoon flow (Yu et al. 2004(Yu et al. , 2007a. The observed warm-season precipitation over contiguous China has distinct diurnal variations with considerable regional features (Yu et al. 2007a(Yu et al. , b, 2009Zhou et al. 2008;Yuan et al. 2010Yuan et al. , 2012Li 2017). Over inland areas of southern China, the summer rainfall peaks in the late afternoon (i.e., between 3 p.m. and 7 p.m., local solar time (LST), hereafter 1500 LST and 2000 LST; Yu et al. 2007a, b;Zhou et al. 2008;Jiang et al. 2017). On the eastern periphery of the Tibetan Plateau (TP), there is a large contribution from nocturnal rainfall (between 2200 LST and 0300 LST; Yu et al. 2007b;Zhou et al. 2008;Chen et al. 2010a). Along the Yangtze River valley, the geographical distribution of diurnal-cycle variation exhibits an eastward phase delayed in the timing of peak precipitation (Asai et al. 1998;Yu et al. 2007a, b;Chen et al. 2010a).
The diurnal cycle of precipitation in monsoon regions has been a rigorous test-bed for validating cumulus and other parametrizations in numerical models. Current state-ofthe-art climate models generally show poor performance in reproducing the diurnal cycle (Dai 2006;Flato et al. 2013;Yuan et al. 2013;Covey et al. 2016). Moreover, most general circulation models (GCMs) and regional circulation models (RCMs) are highly sensitive to cloud microphysics, boundary-layer, land-surface physics and cumulus-parametrization schemes Liang et al. 2004;Chen et al. 2010b;Zhang and Chen 2016). In particular, the cumulus-parameterization has been regarded as the single largest source of uncertainty in precipitation simulation Liang et al. 2004;Dai 2006;Brockhaus et al. 2008;Bukovsky and Karoly 2009;Hohenegger et al. 2009;Sun et al. 2016;Zhang and Chen 2016). Many long-standing model biases are related to the convection schemes, such as excessive light rainfall and too little heavy rainfall, errors in the timing of afternoon precipitation over land, and an inability to produce meso-scale convective systems (Yang and Slingo 2001;Dai 2006;Guichard et al. 2010;Stephens et al. 2010;Birch et al. 2014).
Due to advances in scientific computing, numerical meshes can now be refined to the point where the parametrization of convection can be switched off for many climate and climate-change applications (Prein et al. 2015). When the horizontal grid spacing is 4 km or less (Weisman et al. 1997), it becomes realistically possible to run RCMs with "explicit" convection. Such models are usually called "convection-permitting" models (CPMs), or "convectionresolving" models, and presumably have a better representation of small-scale physical processes, such as those due to moist-processes, complex terrain and land-atmosphere coupling, than coarser RCMs. CPMs show improvements in the simulation of the diurnal cycle of precipitation and the representation of convection (Guichard et al. 2004;Pearson et al. 2013;Ban et al. 2014;Prein et al. 2017a). Improvements are also evident in the simulation of precipitation frequency, intensity and precipitation histograms , both light and extremely heavy precipitation , the Madden-Julian oscillation (Miura et al. 2007;Benedict and Randall 2009;Sato et al. 2009), and even the doldrums over tropical Atlantic (Klocke et al. 2017). CPM is useful for providing improved projections of future changes in hourly precipitation extremes (Kooperman et al. 2013;Fosser et al. 2015Fosser et al. , 2017Kendon et al. 2014;Liu et al. 2017;Prein et al. 2017b, c) and changes in precipitation histograms . One major weakness of CPMs is the overestimation of rainfall amount over certain regions (Weisman et al. 1997;Holloway et al. 2012;Birch et al. 2014), but that was not an issue over North America Liu et al. 2017).
CPMs have been demonstrated that they are useful tools in regional climate modeling and projection. A present-day and future climate simulations using a CPM with a horizontal grid-spacing of 2.2 km over the Alps showed that both extreme day-long and hour-long precipitation events intensified with temperature as constrained by the Clausius-Clapeyron relation, along with a better simulation of the precipitation diurnal cycle (Ban et al. 2014(Ban et al. , 2015. A continental-scale CPM simulation of the West African monsoon (WAM) shows better simulations of storm structures, and the diurnal cycle of rainfall intensity (Marsham et al. 2013). Stein et al. (2015) studied the effect of reducing model-grid spacing to 4 or 1.5 km over WAM region, and validated model cloud structures against satellite retrievals from CloudSat. They found that, compared with simulations using a coarser-resolution regional model, the CPM showed improvements in the representation of thin-anvil cirrus and mid-level clouds. In addition, the accurate representation of the diurnal cycle of convection and the ability to trigger convection is key to improving the model performance over the WAM (Birch et al. 2014). The diurnal cycle of precipitation over the maritime continent is improved when the gridresolution is increased from 12 to 4 km (Birch et al. 2016). CPM simulations of the present and future climates over North America have also been done and found to produce realistic characteristics of convection and precipitation Liu et al. 2017;Prein et al. 2017a).
The monsoon rainfall over East Asia is a useful test bed for climate modeling. But the performances of limited area CPMs in simulating precipitation diurnal cycle remain unknown. In this study, we aim to: (1) evaluate the performance of a limited area CPM in reproducing the diurnal cycles of precipitation frequency, intensity and amount, and their geographical distribution over East Asia and understand what aspects or factors are improved in a CPM, over a low-resolution version of the same model with parametrized convection; (2) quantify the model performance in reproducing the diurnal cycle of large-scale circulation associated with diurnal variations of precipitation.
The remainder of this paper is organized as follows. The model and experiment design, description of the observation and reanalysis datasets, and analysis methods are described in Sect. 2. In Sect. 3, we evaluate the performance of the two high resolution regional model simulations in reproducing the summer mean precipitation characteristics, and investigate how well the CPM simulates the diurnal cycle of precipitation and the associated large scale circulation compared to a convection-parametrized model. Finally, a summary and a discussion are given in Sect. 4.

Model and experiment design
Two season-long simulations were performed using regional configurations of the Met Office Unified Model (MetUM; Cullen 1993;Brown et al. 2012): a convection-permitting version with an angular grid spacing of 0.04° (corresponding to approximately 4.4 km, in the model's rotated-pole coordinate system) and a 20-s time step; a lower-resolution (convection-parameterized) simulation, with a grid spacing of 0.12° (13.2 km) and a 60-s time step. Both simulations have the spatial domain shown in Fig. 1 (big blue box). The overall configuration of the convection-permitting model is similar to that described in Pearson et al. (2010) and Lean et al. (2008), who tested the implications for convection over the United Kingdom. The regional configuration used the Met Office Global Atmosphere version 6.1 (GA6.1; Walters et al. 2017), which (at the time of running) was the version of the Unified Model used operationally by the Met Office for global weather and climate prediction. The domains for both simulations were identical (Fig. 1). Since the continental CPM simulation is computationally very expensive, we performed simulations that cover the warm seasons of 2009, which is regarded as a normal monsoon year. The duration of the simulations was from 1st April to 30th September in 2009. Further details of the model grids are summarized in Table 1.
In the convection-parametrized (13.2 km) simulation, the convection scheme is based on the Gregory-Rowntree scheme (Gregory and Rowntree 1990) with closure based on the convective available potential energy (CAPE) River and Yellow River) are shown here for regional averaging. The big blue box indicates the integration domain used in the convectionpermitting simulation (4.4 km) and convection-parametrized simulation (13.2 km) and a relaxation timescale of 30 min. In the convectionpermitting simulation, "explicit" convection was achieved by increasing the closure time scale of the parametrized convection for high CAPE, such that the parameterization of deep convection is effectively switched off. The parameterization of shallow cumulus, which is basically the same as Gregory-Rowntree scheme, with some modifications following Grant et al. (2001), is active in both two simulations.
The regional models derive their lateral-boundary conditions hourly from a global-model simulation using the GA6.1 configuration with a resolution of 0.2°. We use the analyses provided by the European Centre for Medium-Range Weather Forecast (ECMWF) to re-initialize the global driving-model on a six-hourly forecast cycle, thus constraining the nested simulations to be reasonably close to the re-analyzed atmospheric state. The sea surface temperature (SST) is updated daily from Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA; Donlon et al. 2012). The model uses a terrain-following hybrid height coordinate (η), which is described in detail in Davies et al. (2005).

Description of the observation and reanalysis datasets
Surface hourly rain gauge data from 2420 stations in 2009 are used in this study, which were obtained from the National Meteorological Information Center (NMIC) of the China Meteorological Administration ). Most of the stations are located in eastern China where the distribution is relatively dense (Fig. 1). The precipitation measurements were made by siphon or tipping-bucket rain gauges and were collected automatically by computers. The data has been quality controlled by NMIC . Given that annual precipitation over most of China occurs mainly between June and August (JJA; Zhou and Yu 2005;Zhou et al. 2008), and the diurnal cycle is strongest in summer (Dai et al. 2007;Zhou et al. 2008;Chen et al. 2010a), we focus on the summer season in this paper. The Modern-Era Retrospective analysis for Research and Applications, Version 2 reanalysis datasets (MERRA2; Gelaro et al. 2017) were used to reveal the diurnal cycle of large-scale circulations. These included hourly surface latent and sensible heat flux, and three-hourly vertical velocity, zonal and meridional wind components, specific humidity, geopotential height and air temperature. The results based on MERRA2 data are broadly comparable with those from the Japanese 55-year Reanalysis Projects (JRA55; Ebita et al. 2011) and ECMWF interim reanalysis (ERA-Interim, hereafter ERAIM; Dee et al. 2011). Thus in the following section, most of the results are shown by using MERRA2 because of the high temporal and spatial resolution.

Analysis methods
Following previous studies Yu and Li 2016;Chen and Dai 2018), in our analysis, the precipitation frequency (F) is defined as the percentage of all hours during the period which had measurable precipitation (> 0.1 mm h − 1 ), the precipitation intensity (I) is defined as the average precipitation rate over all the precipitating hours, and the precipitation amount (A) is defined as the accumulated precipitation amount over a given time period. We calculated the F, I, and A at each grid point during the period of June to August in 2009.
To characterize the diurnal cycle of precipitation A, F and I, we first used the hourly precipitation data over all days during the studying period to derive a composite diurnal cycle of precipitation A, F and I, then used T max to denote the local solar time of the maximum in the composite diurnal cycle of precipitation A, F and I over central eastern China (97.5°E-122.5°E, 18.0°N-41.0°N).
The results of Chen and Dai (2018) show that the estimated F and I are highly sensitive to the data spatial resolution. Moreover, they highlighted the need to have similar resolutions when comparing observations and models. To enhance the comparability between the observation and our model simulations, we first averaged the station data within each convection-parametrized model grid (0.12° grid) to produce a gridded precipitation dataset, then masked out the grids which did not contain stations. We also averaged the 0.04° CPM data onto the 0.12° grid without spatial interpolation. After these procedures, we computed the precipitation F and I, and their diurnal cycles.
For observations, we further checked the differences between calculating the precipitation F and I at the original scattered 2420 rain gauge locations and from the new 0.12° observational gridded precipitation dataset (contains 2260 grid points with non-zero values), we found the estimated F and I are highly consistent (figures are not shown). For all quantitative comparisons between models and observations (such as the pattern correlation coefficients, the root mean square errors, and the diurnal cycle), we used the new gridded precipitation dataset. For visual clarity, when plotting maps of the spatial distributions of rainfall, we applied the iterative improvement objective analysis method (Cressman 1959) to fill the small gaps by using NCAR Command Language (http://www.ncl.ucar.edu/Docum ent/Funct ions/Built -in/ obj_anal_ic.shtml ), the influencing radius array was set up to (/0.24°, 0.12°/). When comparing the differences between the model simulations and MERRA2 reanalysis, all variables that are derived from the model simulations are averaged onto the same grid as the MERRA2 reanalysis.
Based on the different underlying surface types and diurnal features, four sub-regions are defined similar to those by Zhou et al. (2008). These domains are marked in Fig. 1, and correspond to the upper Yangtze River valley, the-lower Yangtze River valley (hereafter the "Mei-yu region"), southern China and the regions between the Yangtze River and the Yellow River. We use local solar time (LST) to study the diurnal variation of precipitation characteristics, and use Beijing Standard Time (BST) to reveal the diurnal cycle of large scale atmospheric circulation in our analysis.
The composite diurnal cycle of precipitation A, F and I over each sub-region is normalized as where R(h) is the original, and D(h) is the rainfall after normalization by the daily mean R (Yu et al. 2007a;Yuan et al. 2013).
To understand the relationship between local atmospheric instability and the afternoon rainfall peaks, we examined the moist static energy (MSE) in both reanalysis and model simulations. The MSE is the sum of the sensible heat, latent heat and geopotential contents of a parcel: where c p and L v denote the specific heat of air and the latent heat of water vaporization, respectively. T is the air temperature, q is the specific humidity, g is the gravitational acceleration and z is the geopotential height. An MSE profile decreasing with altitude indicates an unstable atmosphere. MSE analysis is widely used in studying instability associated with rainfall (Pu and Cook 2012;Neupane and Cook 2013;Lau and Kim 2017). The diurnal variations in MSE are mainly contributed by the temperature ( c p T ) and moisture components ( L v q ), the changes of geopotential are negligible (Pu and Cook 2012;Neupane and Cook 2013), thus we mainly focus on the c p T and L v q components of the MSE changes.
To better understand the large scale circulation dominating the late afternoon rainfall (from 1400 LST to 2000 LST) over the Mei-yu region, we perform a moisture budget analysis following previous studies (Seager et al. 2010;Chou and Lan 2012;Lin et al. 2014;Ma and Zhou 2015;. The moisture budget equation is: where P and E denote precipitation and evaporation, q is specific humidity and ⇀ V is wind vector. δ is a residual term including transient eddies (Trenberth and Guillemot 1995;Zhou and Yu 2005), and contributions from surface processes and model interpolation bias (Seager et al. 2010;Peng and Zhou 2017). " <> " denotes a vertical mass integration through the whole troposphere (Eq. 4), where g is gravitational acceleration, p s is surface pressure and p T is the pressure of the tropopause, taken as 100 hPa. The component of t ⟨q⟩ in Eq. 3 is the time derivative of vertically-integrated specific humidity, which indicates the is the convergence of integrated moisture flux. Each component on the right side of Eq. 3 is calculated by using the hourly output from regional simulation, and three-houly MERRA2 reanalysis. The 3-h variables (corresponding to the MERRA2 time interval) are then averaged to calculate the climatological summer mean late afternoon rainfall over the Mei-yu region.

Summer mean precipitation amount, frequency and intensity
The results for the summer mean precipitation A, F and I from the rain gauges and model simulations are shown in Fig. 2. In the observations, there is an evident monsoon rainband stretching from the southwest to the northeast, with several centers located in the eastern periphery of the TP (100°E-107°E, 27°N-33°N), the coastal areas over southern China (110°E-120°E, 22°N-27°°N) and the Mei-yu region (112.5°E-122.5°E, 27°N-33°N). The convection-permitting (CPM 4p4) and convection-parametrized (hereafter, "largescale model", LSM 13p2) simulations both show large-scale patterns that resemble the rain-gauge observations. Compared with rain gauge observation, the CPM 4p4 and LSM 13p2 have pattern correlation coefficients (PCCs) of 0.56 and 0.63, and root mean square errors (RMSEs) of 3.48 and 3.00 mm day − 1 , respectively. The LSM 13p2 realistically simulates the magnitude of precipitation A, except that the pattern is too uniform. In the observations, the spatial distribution of precipitation A is obviously affected by the underlying surface and uneven regional distribution, but these phenomena are less pronounced in the results of LSM 13p2. In contrast, the CPM 4p4 reasonably reproduces the locations of the three rainfall centers along with an overestimation of precipitation A magnitude. The precipitation A is above 12.0 mm day − 1 over southeastern China and the Mei-yu region in CPM 4p4, compared to 7.0-10.0 mm day − 1 in rain-gauge data.
In the observations, the large-scale features of the JJAmean precipitation F are similar to precipitation A. Figure 2d shows that the precipitation F is about 15% in the eastern periphery of TP, about 12% over the Mei-yu region and southeastern China in the observations. The LSM 13p2 simulation could reproduce the spatial distribution of precipitation F (with a PCC value of 0.74), but it produces too frequent rainfall, overestimates the magnitude, with a precipitation F higher than 20% over most regions (resulting in a relatively large RMSE of 19.15%; Fig. 2f). Improvements are seen in CPM 4p4 as evidenced by the three centers of precipitation F and the magnitude (with a PCC of 0.64 and a RMSE of 3.19%). One evident weakness of CPM 4p4 is the underestimation of the precipitation F over the Sichuan basin (the eastern part of region 1) and the coastal region over southern China (around 110°E, 22°N).
In rain-gauge observations, there are several local maxima in rainfall intensity over southern China (3.0-4.0 mm h − 1 ), and over the region between the Yangtze and the Yellow Rivers (112.5°E-122.5°E, 33°N-40°N). The observed south-China maximum is missing in the LSM 13p2 simulation, but it could reproduce the precipitation I center over the region between the Yangtze and the Yellow Rivers. Overall, the precipitation I was underestimated by

Diurnal cycle of precipitation amount, frequency and intensity
To identify the spatial distribution of the diurnal cycle, the LST of the maximum in the composite diurnal cycle of precipitation A, F and I are shown in Fig. 3. In rain gauge observations, the eastern periphery of the TP shows nocturnal rainfall (2100 LST to 0300 LST; Fig. 3a), which is due to concurrent peaks in both the precipitation F (Fig. 3d) and I (Fig. 3g). Southern China is dominated by the afternoon rainfall (on average the peak rainfall occurs around 1500 LST). The regions between the Yangtze and the Yellow Rivers see two peaks around 0600 LST and 1800 LST in both precipitation A and I. The observed features are poorly simulated by the LSM 13p2, including too early an afternoon peak (around 1300 LST) over eastern China (Fig. 3f), and the evident biases in reproducing the diurnal variation of precipitation A (Fig. 3c) and I (Fig. 3i). The CPM 4p4 shows superiority in the simulation of the nocturnal rainfall peak over the eastern periphery of the TP and the afternoon a-c Precipitation amount; d-f precipitation frequency; and g-i precipitation intensity from a, d, g 2420 rain gauge observations; b, e, h CPM 4p4 simulations; c, f, i LSM 13p2 simulations peak over southern and northern China (Fig. 3b). The weaknesses of CPM 4p4 simulation lie in the spurious afternoon rainfall (around 1500 LST) over the eastern periphery of TP, and an hour earlier peaktime of the afternoon rainfall over southern China. Nonetheless, in comparison with LSM 13p2, the CPM 4p4 is superior at reproducing the diurnal cycle of precipitation F, including the later afternoon rainfall over southeastern China and the nocturnal rainfall over the eastern periphery of TP which is in a good agreement with the rain gauge observation (Fig. 3e). We further divided eastern China into four sub-regions based on distinct diurnal features. The diurnal cycles of summer precipitation A, F and I from rain gauge data, CPM 4p4 and LSM 13p2 are shown in Fig. 4. Region 1 (the Upper Yangtze river-valley) is dominated by nocturnal rainfall (there is a large peak in rainfall around 0200 LST), which is clearly seen in the diurnal cycles of precipitation A, F and I (Fig. 4a, e, i). The CPM 4p4 performs reasonably well at reproducing the nocturnal rainfall over region 1, but it also has a spurious afternoon rainfall (around 1500 LST). Region 2 (Mei-yu region; Fig. 4b, f, j) and Region 3 (southern China; Fig. 4c, g, k) are dominated by the afternoon peak around 1600 LST in both precipitation A and F. The CPM 4p4 reproduces the afternoon rainfall peaks in Region 2 and Region 3, and also reproduces the secondary rainfall peaks in the early morning (around 0600 LST) over Region 3. By contrast, the LSM 13p2 has a 4-h earlier shift (until 1200 LST) in the timing of the afternoon rainfall peak. Region 4 (Fig. 4d, h, l) shows semi-diurnal rainfall peaks (with two peaks, of comparable magnitude: one in the early morning, the other in the afternoon). The peak around 0600 LST is mainly contributed by the precipitation F, the other peak after 1600 LST is primarily dominated by the precipitation I. The CPM 4p4 reproduces the afternoon Fig. 4 Mean diurnal cycle of summer mean precipitation amount (first column), frequency (second column) and intensity (third column) (normalized according to Eq. 1) averaged over the four sub-regions (outlined in Fig. 1) from rain gauge data (OBS; black line), CPM 4p4 (red line) and LSM 13p2 (blue line). The unit of x-axis is LST in hours peak but has an earlier shift of 2 h, along with an overestimation of the amplitude. The LSM 13p2 shows relatively low skill in reproducing the double diurnal peak over this region: it rains too frequently and too weakly, starts to rain too early in the afternoon, and has a rapid reduction in rainfall at sunset (around 1800 LST; Fig. 4d, h). Overall, CPM 4p4 performs better than LSM 13p2 in reproducing the characteristics of the diurnal cycle in all four sub-regions.

The diurnal cycle of large scale atmospheric circulations
The diurnal variation of wind fields over EASM, including the low-level wind, sea-land breeze, and surface wind, are fundamental circulation systems that modulate the diurnal cycle of rainfall (Yu et al. 2007b(Yu et al. , 2009Chen et al. 2009Chen et al. , 2010aChen et al. , 2013Chen et al. , 2016. We examine the performance of models in reproducing the large scale circulation patterns by showing the diurnal evolution of the horizontal low-level (at 850 hPa) winds and equivalent potential temperature (EPT) in  (Fig. 5c, g,  k), the winds are towards the TP and bring the warm and moist air mass to the upper Yangtze River valley. In addition, there exists an intense upward motion to the eastern periphery of the TP (Fig. 6c, g, k). This large-scale circulation is favorable for the nocturnal rainfall, until the intense upward motion becomes weaker and reverses to a descending motion at 0800 BST over the upper Yangtze River valley (Fig. 6a, e, i). The circulation pattern is consistent with the diurnal variation of rainfall (see the positive standardized rainfall from 2000 LST to 0800 LST; Fig. 4a). On the contrary, the Meiyu region is dominated by a descending motion at 2000 BST ( Fig. 6c, g, k). At 0200 BST, the low-level winds exhibit a clockwise rotation and become a southerly flow (Fig. 5d, h, l). In the morning (0800 BST), there exists a descending motion to the eastern periphery of the TP, and the low-level wind converges over the Mei-yu region (Fig. 5a, e, i). The LSM 13p2 produces a relatively stronger upward motion, with a value of − 8.4 × 10 − 2 Pa s − 1 at 500 hPa pressure level over the Mei-yu region (Fig. 6i), compared with the value of − 6.2 × 10 − 2 Pa s − 1 in MERRA2 (Fig. 6a) and − 5.0 × 10 − 2 Pa s − 1 in CPM 4p4 simulation (Fig. 6e). This is consistent with excessive rainfall over the Mei-yu region in LSM 13p2 in the morning (Fig. 6i).
In the afternoon (1400 BST), the low-level southwesterly weakens over southern China and the Mei-yu region, and the EPT of the air mass increases (Fig. 5b, f, j). In addition, the atmospheric conditions become unstable (higher EPT air near the surface and lower EPT air in the mid troposphere) and intense upward motions develop over the Mei-yu region (to the east of 115°E, Fig. 6b) which are consistent with the afternoon rainfall peak over the Mei-yu region (Figs. 4b,  6b). The upward motion over the Mei-yu region is relatively more intense in CPM 4p4 (Fig. 6f) compared with MERRA2 reanalysis (Fig. 6b). We further checked the low level (at 850 hPa) wind speed and direction bias in both simulations (Fig. 7). There exists a systematic bias in both LSM 13p2 and CPM 4p4 simulations: the low-level southwesterly is stronger in both simulations. The wind biases in both models are more evident during the night-time and morning (at 0200 BST, Fig. 7d, h; at 0800 BST, Fig. 7a, e), when the low-level southwesterly flow intensifies. In the LSM 13p2 simulation, the wind speed is more than 4 m s − 1 stronger than observed (Fig. 7h, e). The stronger winds bring moist-warm air from the South China Sea to the lower Yangtze River valley and, moreover, remain strong throughout the day. The excessive nocturnal wind speeds, are associated with enhanced upward motion over the Meiyu region (Fig. 6), and may explain why the LSM 13p2 has excessive night-time and morning rainfall over the Mei-yu region. Compared with LSM 13p2 simulations, the CPM 4p4 performs better at reproducing the clockwise rotation of lowlevel large-scale circulation. The wind speed bias is reduced during night-time (at 0200 BST; Fig. 7d) and morning-time (at 0800 BST; Fig. 7a), and the meridional wind is more realistic over the Mei-yu region (Fig. 7a, d), this is consistent with the nocturnal rainfall being better simulated by CPM 4p4.
To further quantify the improvements in the diurnal cycle of low-level wind in CPM 4p4, Fig. 8 shows hodograph plots of low level (850 hPa) wind vectors over the Mei-yu region (Fig. 8a) and southern China (Fig. 8b). It is clear that the diurnal cycle of low level wind over both the Mei-yu region and southern China exhibits an inertial oscillation, the wind speed becomes larger during the night-time (from 2300 BST to 0200BST) and is minimal in the afternoon (between 1400 BST to 1700 BST). Both the LSM 13p2 and CPM 4p4 could simulate the wind direction and the inertial oscillation over the Mei-yu region and southern China, but LSM 13p2 overestimates the meridional wind over the Mei-yu region (Fig. 8a) and has a stronger wind speed over southern China (Fig. 8b). The CPM 4p4 performs better at reproducing the cycle of low level wind, in terms of both wind speed and wind direction over Mei-yu region and southern China. Based on previous studies (Du and Rotunno 2014;Du et al. , 2015aShapiro et al. 2016), it is hypothesized that the improvement results from either a better representation of pressure gradient forcing or the turbulent mixing in CPM, but the details warrant further study.

Diurnal variation of rainfall along the Yangtze River valley
The Hovmöller diagrams of rainfall diurnal variation over the Yangtze River valley (averaged between 27°N and 33°N) are shown in Fig. 9. There is an obvious eastward delay in the phase of the diurnal cycle along the Yangtze River valley (Fig. 9a). A prominent feature of summertime precipitation over the upper Yangtze River valley is that it occurs nocturnally. In addition, the rainfall maximum shows a 6-h delay (until around 0600 LST in the early morning) between the upper and middle Yangtze River valley (e.g., between 100°E and 108°E). This phase-shift comes from the diurnal clockwise rotation of the low tropospheric circulation (Chen et al. 2010a). The "eastward-delayed diurnal phase transition" phenomenon is not evident to the east of 110°E where there is diurnally-synchronous rainfall over the lower reaches of the Yangtze River valley (i.e., the "Mei-yu" region), with the precipitation peaking around 1600 LST in the afternoon. The LSM 13p2 reproduces the nocturnal rainfall over the upper Yangtze River valley, but it has a spurious peak in the early afternoon (around 1400 LST; Fig. 9b). Due to the dependence on the convection scheme, rainfall often occurs in the morning to the east of 110°E in LSM 13p2 and thus shows an early-shifted phase compared with the rain gauge observation. For locally-forced convection, this sort of error is similar to those reported in previous studies and is typical of models with parametrized convection (Dai 2006;Guichard et al. 2010;Stephens et al. 2010). The CPM 4p4 successfully reproduces the nocturnal rainfall over the upper Yangtze River valley, but has a spurious afternoon rainfall (around 1500 LST; Fig. 9b). Relative to the LSM 13p2, the CPM 4p4 has a closer resemblance to the rain gauge observations, in terms of the phase of the diurnal cycle, over the areas to the east of 110°E that are dominated by the late afternoon rainfall. The weakness of CPM 4p4 is the overestimation of the magnitude of late afternoon rainfall over the Mei-yu region, and the afternoon precipitation in the middle of Yangtze River valley (around 105°E-110°E).
To understand the relationship between local atmospheric instability and afternoon rainfall peaks over the Mei-yu region, the vertical profile of MSE (calculated using Eq. 2) over Mei-yu region is investigated. The profiles of MSE anomalies (solid line; defined as the anomalies of the MSE profiles at each time, compared to the daily mean MSE profile for JJA in 2009) at every 0200 BST (blue) and 1400 BST (red) averaged for the Mei-yu region, and its temperature ( c p T ; dashed lines) and moisture components ( L v q ; dotdashed lines) are shown in Fig. 10. In reanalysis (Fig. 10a,  b), the afternoon rainfall over the Mei-yu region is associated with an anomalous higher MSE profile (red solid line in Fig. 10a, b), which has enhanced instability below 700 hPa, compared to the daily mean, and neutral above that level. The development of MSE gradients in the lower-troposphere in the afternoon is favorable for an upward motion and rainfall; in particular, compared to ERAIM and LSM 13p2, the MSE profile has larger positive perturbations in the lower troposphere in CPM 4p4, indicating the existence of more intense motions in the model.
In the afternoon, the c p T term is largest near the surface and decreases with the altitude below 750 hPa in both reanalysis and models simulations, due to the daytime warming from the land surface. The diurnal variation of L v q term is relatively smaller and negative near the surface (around 975 hPa) and becomes largest at lower troposphere (between 950 and 850 hPa). An anomalous profile of this shape is consistent with the occurrence of strengthened vertical transport of specific humidity by upward motions in the afternoon. Although there is also rainfall at night over the Meiyu region, the MSE anomalies are stable and therefore are not favorable for the initiation of nocturnal convection (blue solid line in Fig. 10a, b). This suggests that the nocturnal rainfall over the Mei-yu region is likely to be contributed to by large-scale circulations, e.g., moisture convergence or down-stream advection of MCSs, and is less related to local surface-driven process than the afternoon rainfall.
Both the LSM 13p2 and CPM 4p4 simulations could reproduce the diurnal cycle of MSE profile (Fig. 10c, d). In the afternoon, LSM 13p2 and CPM 4p4 show enhanced vertical transport of humidity (red dot-dashed line in Fig. 10c, d).
The L v q term in CPM 4p4 (red dot-dashed line in Fig. 10d) is about twice large at its peak than that in LSM 13p2 (red dot-dashed line in Fig. 10c), suggesting that the vertical transport in CPM 4p4 is more vigorous which is consistent with the excessive rainfall in the model. In addition, the near surface value of the c p T term in CPM 4p4 is also larger than LSM 13p2 (the red dashed line in Fig. 10d, c). Both of these two factors are consistent with the more unstable atmospheric conditions in CPM 4p4, which is favorable for upward motion and afternoon rainfall over the Mei-yu region.
To further explore the reason why the CPM 4p4 overestimate the late afternoon (1400 LST to 2000 LST) rainfall over the Mei-yu region, we compare the variation of upward motion in the afternoon (Fig. 11a-c) and surface sensible heat flux (Fig. 11d) derived from the MERRA2 reanalysis and model simulation. In the afternoon, the atmosphere near the surface in CPM 4p4 receives more surface sensible heat flux than those in LSM 13p2 and MERRA2 (Fig. 11d), leading to a more unstable atmosphere. At the same time, the upward motion in CPM 4p4 becomes intense (Fig. 11b) and is stronger than those in MERRA2 (Fig. 11a) and LSM 13p2 (Fig. 11c), which is consistent with the excessive precipitation in CPM 4p4. The more unstable atmosphere and enhanced upward motion in CPM 4p4 provide a favorable dynamical background for the overestimation of afternoon rainfall.
We further perform a moisture budget analysis to understand the water vapor supply for the afternoon rainfall (Fig. 11e). The evaporation rates are calculated from the latent heat fluxes derived from MERRA2 and model simulations. The late afternoon rainfall in CPM 4p4 (0.54 mm h − 1 ) is about twice as much as in the observations (0.30 mm h − 1 ; Fig. 11e). The convergence of water vapor into the Mei-yu region is 0.07 mm h − 1 in the late afternoon, and the evaporation term is 0.22 mm h − 1 in MERRA2 (Fig. 11e), demonstrating that the late afternoon rainfall over the Meiyu region results from convective instabilities triggered by local heating. In CPM 4p4 from the contributions of local evaporation (0.18 mm h − 1 ) and large-scale convergence (0.23 mm h − 1 ) are comparable. The CPM 4p4 overestimates the convergence, compared to MERRA2 and LSM 13p2. Hence, one possible reason for the excessive rainfall in the CPM simulation, is that the convergence of the moisture flux is too large (0.23 mm h − 1 ) during the late afternoon compared with the MERRA2 reanalysis (0.07 mm h − 1 ) and LSM 13p2 (0.13 mm h − 1 ). This excess vapor water is then readily converted to rainfall because the model atmosphere has already been rendered too convectively unstable by a local surface-driven process (Fig. 11b, d).

Summary
In this study, we have used rain gauge observations, reanalysis, and two high resolution regional model simulations (one convection-permitting, and one with parametrized convection), to evaluate, for the first time in the literature, the ability of a season long limited area CPM continuous simulation to reproduce the precipitation characteristics of the EASM, including the spatial distributions of summer mean precipitation A, F and I, as well as the diurnal cycle of precipitation. The performances of the models in the simulation of rainfall diurnal cycle are explained in the context of large-scale circulation variations. The main conclusions are summarized as follows: 1. The spatial distributions of summer mean precipitation A, F and I derived from CPM 4p4 show a relatively stronger resemblance to rain gauge observations, compared with LSM 13p2 simulations. The LSM 13p2 overestimate precipitation F but underestimate precipitation I over most parts of central eastern China. These biases are consistent with excessively frequent light-rainfall being produced by the model's convection scheme. By contrast, the CPM 4p4 could reasonably reproduce the precipitation F and I both in magnitude and spatial distribution, except for an overestimation of precipitation I and A over the EASM region. 2. The spatial distribution of diurnal rainfall cycle over eastern China indicates that there is an obvious regional dependence: nocturnal rainfall dominates the diurnal cycle over the eastern periphery of the TP; rainfall peaks in the afternoon over eastern and southern China. The CPM 4p4 model successfully reproduces the night-time rainfall over the eastern periphery of the TP but merges with a spurious afternoon rainfall peak in this region. The CPM 4p4 reasonably reproduces the afternoon peaks over southern China, whereas the LSM 13p2 produces most of its rainfall 3 h earlier (at around local time noon each day). Because the LSM 13p2 rains preferentially around local time noon, it is unable to replicate the observed spatial distributions of the diurnal-cycle phase. This is particularly obvious for the diurnal cycles of precipitation F, for which LSM 13p2 produces a spatial homogeneous distribution of phase with no clear evolution of phase between central and eastern China, and an intensity which has a nocturnal peak throughout What's more, the LSM 13p2 always produces morning rainfall to the east of 110°E, thus shows an early-shifted phase compared with the rain gauge observation. The CPM 4p4 could reasonably capture the late afternoon rainfall (around 1600 LST) over the Mei-yu region, but it overestimates the magnitude of precipitation. 3. The diurnal cycle of precipitation is highly correlated with the diurnal cycle of large scale circulation. Both the LSM 13p2 and CPM 4p4 simulations reproduced the diurnal clockwise rotation of the low level atmospheric circulations recorded by MERRA2, but the magnitude of the southwesterly wind was overestimated in both simulations. At 2000 BST, the winds are towards the TP, bringing the warm and moist air mass and there exists an intense upward motion over the upper Yangtze River valley in both MERRA2 and model simulations, the large-scale circulation is favorable for the nocturnal rainfall. After that the low-level wind exhibits a clockwise rotation and reaches its minimum over the Mei-yu region and southern China in the late afternoon (around 1700 BST). Over those two regions, there is a clear inertial oscillation of low level wind fields in MERRA2 reanalysis and both two simulations. In LSM 13p2, the southwesterly jet is too strong during the night time and early morning (from 2000 BST to 0800 BST). This is accompanied by overly rapid ascent over the Yangtze River valley, which leads to the spurious nocturnal and morning rainfall in these regions. Compared with LSM 13p2 simulations, the CPM 4p4 has a better performance in reproducing the low-level wind fields in both wind direction and wind speed over the Mei-yu region and southern China. 4. Excessive afternoon rainfall over the Mei-yu region in the CPM 4p4 simulation is related to the interactions between biases in local atmospheric stability and biases in large-scale moisture convergence. In the observations and the simulations, the local atmospheric state in the afternoon over the Mei-yu region is conducive to vertical motion and the production of convective rainfall. However, in CPM 4p4, the lower troposphere receives more sensible heat flux from the surface, and the MSE profile becomes more unstable for atmosphere below 850 hPa and whilst showing relatively little change in atmospheric stability above this level. Stronger intense upward motion is also found, which is consistent with the excessive late afternoon rainfall (0.54 mm h − 1 ) in CPM 4p4, compared with MERRA2 and LSM 13p2. In observation, the moisture budget analysis indicates that the late afternoon rainfall (0.30 mm h − 1 ) over the Meiyu region is mainly contributed by the local evaporation (0.22 mm h − 1 ), compared with a minor contribution from large-scale convergence of water vapor transport (0.07 mm h − 1 ). The CPM 4p4 overestimate the convergence of water vapor transport (0.23 mm h − 1 ), and the atmosphere in CPM 4p4 converts the moisture from local evaporation and convergence of water vapor transport to precipitation readily, compared with MERRA2 and LSM 13p2. Both the enhanced unstable atmosphere and more convergence of water vapor help explain the excessive late afternoon rainfall over the Mei-yu region in the CPM 4p4 simulation.

Discussion
Since the added value of CPMs is often found at fine temporal and spatial scales, as well as the extreme events, such as mesoscale convective systems (Feng et al. 2016;Prein et al. 2017a, c), heavy downpours Mahoney et al. 2012;Ban et al. 2014;Zhu et al. 2018) and hourly precipitation extremes (Kendon et al. 2014;Ban et al. 2014Ban et al. , 2015Chen et al. 2016;Prein et al. 2017b), more high quality observational datasets over EASM at high temporal and spatial resolution (including precipitation, surface temperature and other atmospheric variables) are needed, to make a robust evaluation on the performances of CPMs. In addition, the diurnal cycle of large-scale circulations is known to modulate the diurnal cycle of precipitation over East Asia. For instance, during the warm-season there is a close relationship between the southwesterly low level jet (LLJ) and heavy rainfall over northern Taiwan (Chen et al. 2005) and in the middle and lower reaches of Yangtze River valley (Luo and Chen 2015;Chen et al. 2017) that has been reported for synoptic scale aspect. Recent studies (Du et al. , 2015a have elucidated the diurnal cycle of LLJ in terms of the classical theories of Blackadar (1957) and Holton (1967). It has been shown that the LLJ undergoes forced-damped quasi-diurnal oscillations due to the diurnal variations of turbulent mixing in the boundary layer and large-scale gradients in geopotential height. For example, turbulent frictional effects are largest in the afternoon (due to surface-driven vertical mixing), and smallest in the early morning. The ability of a model to represent these variations may play a significant role in simulating the diurnal cycle and mean-state of the LLJ. In this study, we show evidences that the CPM 4p4 has some added values in simulating the low-level wind over southern China and Mei-yu region, further studies are needed to understand the added values in CPM, in particular the relationship between the diurnal cycle of convection and large-scale circulations.
Long-duration CPM simulations could be useful for understanding the climatological effects of propagating mesoscale convective system (MCS) triggered in the lee of mountains. Globally, MCS is a major cause of extreme precipitation and is a common feature downstream of high topography such as the Rockies and the TP (Carbone et al. 2002;Wang et al. 2004Wang et al. , 2012Chen et al. 2013;Feng et al. 2016). However, most state-of-the-art climate models can not adequately simulate the organized MCS (Bukovsky and Karoly 2011;Kooperman et al. 2014), in comparison to , here P and E indicate precipitation and evaporation, respectively. "− dq/dt" denotes the changes of local moisture storage, the "conv(qU)" denotes convergence of integrated moisture flux, "residual" indicates the residual term CPM (Prein et al. 2017a, c). The TP is the highest and largest plateau in the world, previous studies have shown that eastward-propagating MCSs over EASM strongly influence the downstream rainfall and its diurnal cycle (Chen et al. 2013Luo et al. 2014;Luo and Chen 2015), but there are only limited efforts devoted to the CPM simulation of synoptic scale. CPM modeling of MCSs over the TP and their eastward propagation deserves further study.