Role of the Kuroshio Current on the Diurnal Variation of the Early-Summer Meiyu-Baiu Rainband

Mechanism of the strong diurnal cycle of precipitation over the Kuroshio Current 19 (KC) during mid-June is investigated, when the climatological location of the 20 Meiyu-Baiu front overlaps the KC. Heating from the KC intensifies in the morning 21 when the temperature difference between the sea surface and the surface air (TDF) 22 maximizes. The diurnal cycle of precipitation, on the other hand, peaks in the 23 afternoon, consistent with previous studies. It is revealed that convective 24 precipitation (CP) due to convective instability is in phase with TDF, whereas 25 large-scale precipitation (LSP) caused by the cross-frontal circulation matures 26 later. Intensified convective instability via enhanced heating from the KC in the 27 morning hours (03–12 LST) increases the mean amount of CP as well as the 28 probability of stronger CP. Surface wind convergence is also strengthened during 29 the morning hours and helps sustain the convection. The diurnal cycle of LSP, 30 which peaks in the afternoon hours (12–15LST), covaries with the intensity of the 31 Meiyu-Baiu front and the assocaited cross-frontal circulation. The wind 32 convergence and deformation anomalies associated with the intensified thermal 33 heating over the KC during the morning hours intensifies the frontogenesis 34 function, which leads to the maximization of the frontal intensity in the afternoon. 35 The direct contribution of diabatic heating to the frontogenesis is relatively weak.


Introduction 40
The early-summer East Asian rainy season is characterized by a quasi-stationary 41 rainband elongated from the eastern China to Japan. This rainband, known as 42 Meiyu in China and Baiu in Japan, are frequently accompanied by heavy rainfall 43 events and exerts an enormous impact on local communities. In particular, intense 44 precipitation exceeding twice the amount in other months is observed during the 45 early summer (June) when the Meiyu-Baiu (MB) rainband is located over the East 46 China Sea (ECS) and is affected from beneath by warm sea surface temperature 47 (SST) (Sasaki et al. 2012). 48 The Meiyu-Baiu Front (MBF) draws a boundary between mid-latitude and 49 subtropical air masses and is characterized by a strong gradient of equivalent 50 potential temperature (Ninomiya 1984;Ninomiya and Akiyama 1992;Kodama 51 1993). The MBF exhibits multi-scale characteristics from meso-to large-scale 52 spatial distribution (Akiyama 1989;Akiyama 1990a, Ninomiya andAkiyama 1992;53 Ninomiya 2000) and diurnal to several-day temporal distribution (Akiyama 1990a;54 Ninomiya 2004). The MBF entails the meso-a to g scale clouds along the frontal 55 zone, constituting a cloud system family with a length scale of ~2000 km. The type 56 of precipitation depends on the position relative to the MBF. The southern side is 57 characterized by a higher ratio of convective rainfall, with more intense and deep 58 precipitation (Yokoyama et al. 2014). Convergence of equivalent potential 59 temperature flux accompanying the low-level jet stream in the MBF zone produces 60 convective instability, which plays a role of maintaining moist-neutral 61 stratification against the stabilizing effect of convection (Kodama 1992; Akiyama 62

Data 135
To evaluate the diurnal cycle of rain, 3-hourly precipitation on a 0.25° × 0.25° 136 resolution from the Tropical Rainfall Measuring Mission (TRMM) 3B42 product is 137 used. The optimally interpolated SST version 2.1 product (OISST v2.1) archived at 138 National Centers for Environmental Information, National Oceanic and 139 Atmospheric Administration (https://www.ncei.noaa.gov/oisst) is also used. The 140 spatial resolution of the OISST is 0.25° × 0.25° with a daily time step. Analysis of 141 the atmospheric fields is conducted using the latest reanalysis data, ERA5 142 (Hersbach et al. 2020), provided by the European Centre for Medium-Range 143 Weather Forecasts (ECMWF). The ERA5 reanalysis product is provided at an 144 hourly interval with a spatial resolution of 0.25° × 0.25° at 37 pressure levels. 145 Several improvements over the ERA-interim product are detailed in Hersbach and 146 Dee (2016). The most significant improvement for our study is that the horizontal 147 resolution is high enough to resolve mesoscale oceanic features. Precipitation data 148 from the ERA5 product is also used after a comparison with the TRMM 3B42 data 149 in order to classify precipitation into convective and large-scale types. East Asia 150 (109°-145°E, 20°-45°N; area shown in Fig. 1a)  The frontogenesis (FG) function is used to investigate diurnal variation of the MBF. 156 gradient is relatively weak due to cooling in the frontal precipitation zone 158 (Ninomiya 2004). Therefore, using equivalent potential temperature is more 159 appropriate than potential temperature to define the front. Thus, the equation of 160 FG suggested by Ninomiya (1984) is used. It can be written as follows: 161 (2e) 168 Here, ! represents equivalent potential temperature. The FG equation in 169 Ninomiya (1984) is multiplied with |∇ ! | to come up with the final equation in (1). 170 * (≡ ! ⁄ ) is diabatic heating excluding latent heat release so that * does not 171 account for the contribution of heating due to condensation. Near the surface over 172 the KC (say, 975 hPa), diabatic heating is primarily in the form of sensible heating, 173 part of which is offset by a radiative process (Sasaki et al. 2012). Therefore, 1 174 term near the surface can be understood as the effect of direct heating by the KC. 175 Frontogenesis by surface wind convergence produced by the KC is manifested in 176 2, which will be called the indirect effect of the KC. 3 and 4 terms 177 represent respectively the effect of stretching deformation (confluence) and 9 shearing deformation. These deformation terms are usually most prominent in 179 large-scale processes (Ninomiya 1984). 5 term denotes the tilting effect of the 180 front. The tilting effect tends to oppose changes due to deformations to maintain 181 the thermal wind balance (Lackmann 2012). 182

Results and Discussion 183
Shading in Fig. 1a depicts the TRMM precipitation (TRMM PR) pattern averaged in 184 June 7-23. This averaging period is determined by selecting when precipitation is 185 particularly intense over the KC in a climatological sense (see Fig. 1c  China Sea in the TRMM data are reasonably reproduced in the ERA5 product. In 218 contrast, noticeable difference is seen near Kyushu; TRMM PR shows precipitation 219 around Kyushu, but ERA5 TP is shifted slightly to the north. Despite some 220 differences, the two datasets commonly show localized peaks over the KC, 221 although TP significantly underestimates TRMM PR. Also, the seasonal march of 222 the precipitation zone during June seems adequately represented (Fig. 1d). 223 Figure 2 shows the diurnal cycle of rainfall (shading) and the temperature 224 difference between the sea surface and surface (10 m) air (TDF; contours) 225 averaged during the target period (June 7-23) along the cross frontal lines in Fig.  226 1a. With respect to the latitudinal position, TDF is maximized over the KC and 227 shows positive (ocean is warmer) values to the south and negative (ocean is colder) 228 values to the north. TDF is maximized over the KC at 09 LST, because atmospheric 229 temperature is significantly low in the morning while ocean temperature remains nearly the same during the course of a day. TRMM PR over the KC gradually 231 increases from 03 LST and shows a maximum around the noontime and then 232 decreases (Fig. 2a). Precipitation signal starts to migrate at 06 LST from the north 233 to the south of the KC in the afternoon. This southeastward migration signal is 234 consistent with that in Minobe and Takebayashi (2015). The daily change of TP 235 ( Fig. 2b) over the KC shows a similar pattern to the TRMM PR in that it gradually 236 intensifies from 03 LST and exhibits a weak precipitation pattern near midnight. 237 While the southeastward movement can also be found in the TP, its speed is 238 slower than that of the TRMM PR, taking three hours longer to reach the KC. 239 Although the southeastward propagation speed of TP is slightly lower and 240 the intensity over the KC is somewhat underestimated, it seems that the diurnal 241 variation of the TP is reasonable compared to that of the TRMM PR. Dividing TP 242 into the convective (CP) and the large-scale (LSP) components yields a better 243 understanding of the physical processes contributing to precipitation. The diurnal 244 variation of CP over the KC (Fig. 2c) is different from that of LSP (Fig. 2d). Since the 245 diurnal variation of CP is in phase with TDF, it seems that the air parcel near the 246 surface gains buoyancy due to intense direct heating from the warm KC, resulting 247 in increased convective instability and ultimately CP. A more detailed statistical 248 relationship between the two variables will be shown after the diurnal variation of 249 LSP is described. LSP, which lags TDF by about 6 hours, accounts for more 250 precipitation than CP. The southeastward propagating signal is also explained 251 primarily by LSP. Therefore, the intense precipitation that starts in the morning 252 hours ( Fig. 2a and d) seems associated with atmospheric circulation rather than a 253 convective process. Two types of precipitation are analyzed separately since their 254 mechanisms seem different. 255 The probability distribution of CP near the KC is illustrated in Fig. 3. This 256 joint probability distribution function (PDF) is obtained as follows. First, to 257 minimize the effect of synoptic disturbances, which depends more on the 258 propagation of individual systems than heating from the SST warm tongue, CP and 259 TDF are averaged over the target period (June 7-23) for every three hours ( and are binned at 0.016 mm hr $% and 0.07 K interval, respectively (see Fig. 3). 264 Since the KC warm tongue area is set as the target, average TDF is ~0.4 K, meaning 265 that heat flux, on average, is from the ocean to the atmosphere. 266 Figure 3 shows that CP tends to intensify as TDF increases. Both the upper 267 and lower 10 percentiles and the median of CP increase almost linearly with TDF 268 when TDF is in the range of -0.5 K and 1.2 K. TDF lower than -0.5 K does not result 269 in much weaker precipitation. When TDF is higher than 1.7 K, CP tends to decrease. 270 The upper 10% line is steeper than the others, indicating that not only the mean 271 amount of CP but also the probability of stronger CP are enhanced as TDF 272 increases. To examine the diurnal dependency of CP, joint PDFs are obtained by 273 separating the morning (03-12 LST) and afternoon (15-00 LST) hours. The color 274 contours in Fig. 3 show the differences between the two PDFs. The red contours 275 show that CP are more intense in the morning and the blue contours depict a 276 weakening of CP in the afternoon; the joint PDFs indicate a clear difference in the CP intensity between the morning and the afternoon hours. Also, intensity of CP in 278 the morning tends to be more widely spread with increased mean and extreme 279 values compared with that in the afternoon. 280 The oceanic front is known to cause surface wind convergence through the 281 mechanisms mentioned earlier: PAM and VMM. During June, PAM is a dominant 282 mechanism causing surface wind convergence above the KC (Sasaki et al. 2012;Xu 283 et al. 2018). VMM is not a primary cause of surface wind convergence in this 284 season, since convergence is produced over the region of strongest SST gradient 285 slightly off the KC warm tongue (Liu et al. 2013). Meanwhile, PAM develops 286 localized surface low-pressure just above the KC warm tongue, which results in 287 wind convergence by friction in the marine atmospheric boundary layer (MABL). 288 Correlation between wind convergence and pressure can be shown by applying 289 the Laplacian operator to surface pressure, which acts as a high-pass filter 290 removing large-scale structures such as monsoon or synoptic storms (Minobe et al. 291 2008). 292 Figure 4 shows the daily variation of (a) 1000-hPa wind convergence and (b)  293 the Laplacian of SLP. The overall structure of the diurnal variation of surface wind 294 convergence resembles that of CP with a maximum at 09 LST, which is coherent 295 with the enhanced surface heating and is nearly twice the amount of CP at 18 LST. 296 Surface wind over the KC responds quickly to changes in heating from the surface. 297 Southeastward propagation of the core is also seen in wind convergence. The 298 diurnal variation of the Laplacian of SLP seems to partly explain surface wind 299 convergence above the KC but no propagation of the core is observed. Thus, it can 300 be interpreted that low pressure develops above the KC in response to enhanced surface heating during the early morning. Then, surface wind convergence due to 302 friction in the MABL can mechanically raise air triggering condensation. 303 The interpretation above based on PAM is not entirely satisfactory for the 304 following reasons. Theoretical models for PAM suggested by Minobe et al. (2008) 305 and others (e.g., Takatama et al. 2012;Takatama et al. 2015) assume stationarity. 306 In reality, however, pressure gradient, Coriolis force, and frictional force will 307 change in time within the MABL even if all other physical processes are neglected. 308 This model is adequate when it is applied to fields averaged over a month or 309 longer (Takatama et al. 2015). Further, the relative amplitude of the diurnal cycle 310 of surface wind convergence is stronger than that of SLP Laplacian, which implies 311 that other mechanisms, possibly including moist process, should also be 312 considered. If PAM, instead of convective instability, is the leading cause of surface 313 wind convergence and the onset of precipitation, LSP rather than CP is expected to 314 correlate closely with surface wind convergence. This, however, is not true 315 because the diurnal variation of wind convergence is strongly in phase with CP but 316 not with LSP (Fig. 2). As will be described later, variation of LSP is found to 317 coincide with front and frontal circulation rather than convective instability. Thus, 318 surface wind convergence over the KC seems to have occurred to compensate for 319 the rising air due to convective instability rather than friction associated with 320 cyclonic circulation. It is suggested that surface wind convergence over the KC 321 represents a response to convection rather than serving as a mechanical cause for 322 precipitation, at least during the morning hours. 323 The two precipitation types also show markedly distinct spatial patterns 324 (see supplementary Fig. S1). Contrary to CP, which shows a local maximum over the KC warm tongue, the distribution of LSP is much broader along the MBF. As 326 shown in Fig. 2d, LSP explains a larger fraction of the MB precipitation than CP 327 does. In order to understand total precipitation, therefore, it is necessary to 328 analyze the diurnal variation of LSP in addition to that of CP. The intensity of the 329 front is chosen as a crucial variable explaining the diurnal variation of LSP. Many 330 previous studies explained precipitation through cross-frontal ageostrophic 331 circulation accompanying a large-scale atmospheric motion (e.g., Ninomiya 1984Ninomiya , 332 2004 here. 336 Figure 5 shows the diurnal variation of the front intensity and the FGs at 337 975 hPa (see the Method section for definitions). During mid-June, the MBF is 338 located about 3 degrees north of the KC (Fig. 5a, and shading in Fig. 1c). The 339 strength of the front is not uniform throughout the day but is maximized at 15 LST; 340 this is coherent with the diurnal variation of LSP. An intense front accompanies 341 ageostrophic circulation with an upward motion to the south of the front. FG1 is 342 maximized about three hours earlier than the front at the same latitude. 343 Quantitatively, however, FG2 and FG3 explain a much larger fraction of frontal 344 variation than the diabatic component (FG1). Frontogenesis driven by FG2 and FG3 345 continues until the frontal intensity is maximized in the afternoon (Fig. 5c and d). 346 It should be noted that FG2 and FG3 are located about 2-300 km south of the front. 347 Since the equation for the tendency of the frontal intensity is given in the form of 348 the total derivative, frontogenesis terms do not coincide directly with the local change in frontal intensity, as shown by a comparison between Fig. 5a and Fig. 5c  350 or 5d. Distance between the location of frontogenesis and the front (see Fig. 5) 351 seems to be due to advection by prevailing southwesterlies, which is the main 352 direction of surface wind during mid-June. FG2 is the product of wind convergence 353 and frontal intensity. The local maximum of FG2 results from the enhanced surface 354 wind convergence in the morning (Fig. 4a), which in turn is the imprint of 355 enhanced heating over the KC. Thus, adiabatic process (FG2) is at least as 356 important as diabatic process (FG1) in the discussion of the influence of the KC on 357 the atmospheric frontogenesis. FG3 also shows a daily variation similar to that of 358 FG2. FG3 is mainly controlled by the confluent deformation (see also 359 supplementary Fig. S2), which shows a diurnal variation similar to that of surface 360 wind convergence. 361 Shading in Fig. 6 shows the vertical structure of anomalous patterns of front 362 intensity (Fig. 6a)  the KC, south of the front, and further north of the KC near the surface. The local 372 peak of CC above the KC appears to be the result of convection caused by direct heating from the surface, which matches the local maximum of CP shown in Fig. 2c. 374 The lower-tropospheric cloud to the north of the KC seems like fog generated by 375 radiative cooling in the morning. This cloud covers a large area but does not 376 accompany precipitation (Fig. 2a). Cloud located to the south of the front appears 377 to be caused by the frontal circulation. The altitude of this cloud anomaly is higher 378 than those at the other two locations. The TRMM PR (Fig. 2a) and LSP (Fig. 2d), 379 located further north of the KC in the morning, appear to be caused by this frontal 380 circulation. 381 The vertical structure shows that the contribution of FG2 to frontogenesis is 382 most significant, followed by FG3. FG2 shows a peak below 900 hPa just above the 383 KC, which is apparently due to low-level wind convergence arising from a direct 384 influence of the KC as discussed earlier. Near 29°N, north of the KC, the vertical 385 structure of FG2 is characterized by frontogenesis at 850 hPa and frontolysis at 386 500 hPa. They are associated respectively with convergence and divergence of 387 wind, which occurs due to the mid-tropospheric ascending branch of the frontal 388 circulation to satisfy the mass continuity. Similar to FG2, FG3 also results in 389 frontogenesis at a slightly higher latitude than the KC. Meanwhile, FG1 causes 390 frontolysis despite that diabatic heating from the surface is vigorous in the 391 morning, which indicates that the directions of gradient of equivalent temperature 392 (∇ ! ) and diabatic heating (∇ * ) are opposite to each other. The FG4 is smallest in 393 magnitude. FG5 causes frontolysis near the positive front anomaly. The negative 394 relation between FG5 and the front can also be found in the climatological mean 395 (Fig. S3). 396 In the afternoon (Fig. 7; 12-15  circulation moves over the KC with a higher altitude, making a taller cloud than in 401 the morning (red contours in Fig. 7a). Although the height of the cloud is tall, 402 precipitation at this time is classified as LSP (Fig. 5d) rather than CP (Fig. 5c), 403 because the role of frontal circulation is more important than convective process 404 near the surface. Besides, the fact that the afternoon TDF is weaker than in the 405 morning supports that this deep cloud is triggered by a dynamic forcing. To the 406 north of the KC, fog near the surface seems to have disappeared by strong solar 407 insolation in the afternoon. Although FG1, FG2, and FG3 all contribute to the 408 frontogenesis, frontolysis by FG5 is more significant in the afternoon. Thus, the 409 intensity of the front weakens gradually until midnight. 410

Summary 411
In this study, causes of the strong diurnal cycle of precipitation over the KC in mid-412 June were analyzed. Precipitation peaks in the afternoon, as addressed in many 413 earlier studies. Heating from the KC, however, is maximized during the morning. 414 This temporal gap was explained by separating the convective and large-scale 415 components of ERA5 total precipitation. Although there are some differences from 416 the satellite observation (TRMM PR), the ERA5 product reasonably reproduces the 417 essential features of precipitation such as the localized peak over the KC, afternoon 418 maximization, and the seasonal migration of the Meiyu-Baiu rainband. 419 The convective component (CP) is in phase with temperature difference 420 between the sea surface and the atmosphere 10 m above (TDF), which is explained 421 by the intensified convective instability triggered by enhanced heating from the KC 422 during the morning hours (03-12 LST). The intensity of CP in the morning tends to 423 be more widely distributed with increased mean and extreme values compared to 424 that in the afternoon. The enhanced surface wind convergence is also observed 425 during the morning hours, which sustains the convection. The diurnal cycle of 426 large-scale component (LSP), however, is quite different from that of TDF, and 427 shows a peak in the afternoon. The vertical structure near the front reveals that 428 the diurnal cycle and the location of LSP are well explained in terms of the 429 ageostrophic circulation encircling the front in the meridional direction. An intense 430 front and an accompanying upward motion to the south, which trigger LSP, are 431 observed during the afternoon. Calculation of the frontogenetic functions reveals 432 that the contribution of the adiabatic terms (FG2-FG5) exceeds the diabatic term 433 (FG1). In particular, terms associated with wind convergence (FG2) and shear deformation (FG3) show the largest contributions. Positive FG2 anomaly develops 435 from the early morning until the afternoon, when the front intensity is maximized. 436 The vertical structure of FG2 shows a strong signal, which is confined below 850 437 hPa over the KC. The spatio-temporal distribution of FG2 is dominated by the near-438 surface wind convergence, which is an imprint of the enhanced heating in the 439 morning over the KC. 440 This study focused on the diurnal cycle of precipitation over the KC. 441 However, the Gulf Stream (GS) is another region of a strong diurnal signal. The 442 diurnal cycle over the GS peaks several hours earlier than the KC (Minobe and 443 Takebayashi 2015). Hence, the lag between TDF and precipitation is expected to be 444 smaller. Since a salient front is not seen over the GS, it is suggested that the MBF, 445 which takes several hours to intensify fully, is a possible explanation for the 446 difference. 447

Data Availability 448
The data (ERA5) employed in the present study is publicly available at the ECMWF 449 website (ecmwf.int).    TP averaged from June 7 to 23. Black and blue contours represent respectively SST 604 (K) and 200-hPa zonal wind (at the contour levels 30, 33, 36, and 39 m s -1 ). 605 Shading in (c) and (d) shows sub-seasonal variation of the TRMM PR and TP along 606 the dashed lines crossing the KC in Fig. 1a. The red semi-transparent shading 607 represents the location of atmospheric front defined by the gradient of equivalent 608 potential temperature exceeding 5 K 100 km ⁄ . Blue contours in (c) represent 1000-609 hPa wind convergence (at 2´10 -6 s -1 interval from ±1´10 -6 s -1 ) with dashed 610 contours for negative and solid contours for positive values. 611 613 Figure 2. The diurnal cycle (shading; mm hr -1 ) of (a) TRMM PR, (b) TP, (c) CP, and 614 (d) LSP during the target period (June 7-23) along the cross frontal lines shown in 615 Fig 1a. Red contours represent temperature difference (K) between the sea surface 616 and 10 m air above it. 617 618 Figure 3. The joint PDF of CP and TDF near the KC (shading). The thin black lines 620 represent the 10 and 90 percentiles of CP with the median in thick black line for 621 each TDF bin. The color contours represent differences in the joint PDF between 622 the morning (03-12 LST) and the afternoon (15-00 LST). The red contours show 623 that the cases are more frequent in the morning and the blue contours in the 624 afternoon. Details for the calculation of the joint PDF can be found in the main text. 625