The diurnal variation of rainfall over China associated with landfalling tropical cyclones (TCs) is investigated using hourly rain gauge observations obtained from 2425 conventional meteorological stations in China. Records between 12 h prior to landfall and 12 h after landfall of 450 landfalling TCs in China from 1957 to 2014 are selected as samples. The harmonic analysis shows an obvious diurnal signal in TC rainfall with a rain-rate peak in the early morning and a minimum in the afternoon. The diurnal cycle in the outer region (between 400- and 900-km radii from the storm center) is found to be larger than in the core region (within 400 km of the storm center). This could be attributed to the effect of land on the inner core of the storms as the diurnal cycle is distinct in the core region well before landfall. As the result of this diurnal cycle, TCs making landfall at night tend to have cumulative precipitation, defined as the precipitation cumulated from the time at landfall to 12 h after landfall, about 30% larger than those making landfall around noon or afternoon. Moreover, the radial propagation of the diurnal cycle in TC rain rate, which has been a controversial phenomenon in some previous studies with remote sensing observations, was not present in this study that is based on rain gauge observations. Results also show that the diurnal signal has little dependence on the storm intensity 12 h prior to landfall.
Numerous studies have revealed the existence of a diurnal cycle in tropical cyclones (TCs) over the oceans, with the diurnal cloudiness and convection peaking in the early morning and then diminishing until late afternoon (Gray and Jacobson 1977; Steranka et al. 1984; Kossin 2002; Dunion et al. 2014). This diurnal signal is important for TCs as it could influence the TC structure and intensity changes (Tang and Zhang 2016). Yaroshevich and Ingel (2013) found that TCs in the western North Pacific Ocean tend to intensify much faster at night than in daytime. Dunion et al. (2014) found a diurnal pulse of the TC cirrus canopy that began to form in the inner core near the time of sunset and propagated outward to several hundred kilometers away by the afternoon.
The mechanisms forcing the diurnal cycle in TCs have not been fully understood. Melhauser and Zhang (2014) examined the effect of the diurnal radiation cycle with five sensitivity experiments (normal diurnal cycle, daytime only, nighttime only, no radiation, and reverse diurnal cycle) on the pregenesis environment of Hurricane Karl (2010) and found that the development of Karl was suppressed in the daytime-only and no‐radiation experiments whereas the nighttime-only experiment accelerated the intensification of Karl. They indicated that during nighttime, strong radiative cooling at the cloud top destabilized the environment, favoring the enhancement/initiation of deep convection. However, Duran and Molinari (2016) found that the mean static stability changed little between evening and early morning in radiosonde data. This might be because the study of Melhauser and Zhang (2014) mainly focused on TC genesis and was based on model simulations, while Duran and Molinari (2016) concentrated on mature TCs using observations.
The radial propagation of the diurnal signal in TCs has been discussed in many previous studies (Steranka et al. 1984; Dunion et al. 2014; Wu et al. 2015; Leppert and Cecil 2016). Dunion et al. (2014) found that the “diurnal pulse” of low infrared brightness temperatures propagated radially outward with a speed of 5–10 m s−1, which was similar to that found by Steranka et al. (1984). With idealized numerical experiments, Navarro and Hakim (2016) also found a downward propagation along with the outward propagation of disturbances in the outflow layer, with a vertical wavelength of 5.6 km in the stratosphere, which was consistent with the upward energy propagation of inertia–gravity waves as the phase speed and group velocity are orthogonal. Wu et al. (2015) indicated that the diurnal cycle in rain rate has a similar outward propagation. They speculated that this propagation was also driven by gravity waves as the propagation speed was 10–20 m s−1. However, this propagation was not found in Leppert and Cecil (2016) based on data from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Precipitation Radar (PR). They thought that the outward-propagating signal was manifest near the cloud top but not through the deep precipitation layer. They also speculated that results in Wu et al. (2015) might be influenced by the precipitation data (TRMM Multisatellite Precipitation Analysis 3B42 product) they used, which were largely derived from infrared brightness temperatures.
The diurnal variation also exists in precipitation in TCs. Shu et al. (2013) found an early morning maximum and an evening minimum diurnal signal for landfalling TCs over the western North Pacific, and approximately 70% of rainfall days in TCs showed a significant diurnal cycle. Wu et al. (2015) found a similar morning rainfall peak as well and also indicated that as the radial distance from the TC center increases, the amplitude of the diurnal variation decreases, and the phase of the diurnal variation delays. By compositing TCs from all basins, Bowman and Fowler (2015) found that the diurnal amplitude in TC precipitation could be as large as 15% of the mean rain rate. All these studies were based on satellite-derived precipitation data, which could underestimate rainfall in the morning and overestimate rainfall in the afternoon (Yuan et al. 2012) and might also be influenced by other factors as speculated by Leppert and Cecil (2016). These could influence the composite diurnal cycle of TC rainfall.
Most of the previous studies have been mainly concerned about the precipitation diurnal cycle in TCs over oceans. Few studies have focused on the precipitation diurnal cycle in TCs after landfall, although it may have important implications for precipitation forecasts, such as the dependence of precipitation and storm intensity change on the time of day when the storm makes landfall. Different from the diurnal cycle over oceans, Jiang et al. (2011) found two peaks in the diurnal cycle of rain rate in TCs over land, with one in the early morning and the other in the afternoon. Bowman and Fowler (2015) found that when interacting with land, the diurnal cycle of TC precipitation tends to be weaker over land than over oceans. This might be affected by their method that averaged both the land and ocean portions of TC precipitation and/or might be partially due to the possible interference of different diurnal phases between land and ocean. Without considering the effects from TCs, Yu et al. (2007) reported that, climatologically, the maximum rainfall often occurs in the late afternoon over south and east China. As mentioned above, the TC rainfall over oceans tends to be at a minimum in the late afternoon. The characteristics of a possible diurnal variation in TC rainfall over land during and after landfall remain unknown.
The purpose of this study is to document the diurnal cycle of rainfall over land associated with landfalling TCs based on hourly rain gauge data from conventional stations in China. To achieve this goal, we decomposed the rain rate in terms of the Fourier harmonics and examined the variation of the diurnal cycle in the inner and outer regions of landfalling TCs. The remainder of the paper is organized as follows. Section 2 describes the rain gauge and TC best-track data and the harmonic analysis method used in this study. Results of the diurnal cycle in rain rate averaged in the TC primary circulation and the TC outer region, the radial propagation of the diurnal signal, a comparison of the precipitation diurnal cycles in TCs prior to and after landfall, and a comparison of the precipitation diurnal cycles in strong and weak TCs are discussed in section 3. Conclusions together with extended discussion are given in the last section.
2. Data and methodology
In this study, the hourly rain gauge data, defined as the cumulative precipitation of the preceding 59 min, during 1957–2014 from 2425 conventional stations in China, collected and quality controlled by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA), were utilized to extract rainfall associated with landfalling TCs. Prior to 2000, the rain gauge data were read from precipitation-recording graphs, with the precipitation automatically measured by siphon or tipping-bucket gauges, using a digitizing process to identify hourly precipitation after scanning those graphs. For years after 2000, the rain gauge data were collected from automatic precipitation recorders, with a temporal sampling interval of 1 min. The dataset is accurate to within 0.1 mm, and quality-control processes, including a climatological limit value test (to eliminate unusual observations based on the climatology data), a station extreme value test (to eliminate unusual observations based on the station data), and an internal consistency test (the hourly data were compared with manually checked daily rainfall data) were applied to this dataset.
Under TC conditions, there are some error sources in rain gauge data, including but not limited to splash, intermittent gauge halt, turbulence, reading error, overflow, and wind damage. These error sources except for reading errors likely lead to underestimates of rainfall. The largest error source is likely to be turbulence under high wind conditions, such as under the influence of TCs. The quality-control process could reduce the errors to some extent, and thus, the effect of errors in rainfall data on our analysis of the precipitation diurnal cycle in TCs in this study should not be a major concern.
The 6-hourly best-track data in the studied period were obtained from the Shanghai Typhoon Institute (STI) of CMA (downloaded from http://tcdata.typhoon.org.cn/en/zjljsjj_sm.html). To make better use of the hourly rain gauge data, the 6-hourly TC locations in the best-track data were linearly interpolated into hourly locations. We selected TC records from 12 h prior to landfall to 12 h after landfall as TC samples, and TC cases with records less than 12 h before or after landfall were eliminated from our analysis, resulting in 25 samples for each TC case. Thus, 450 landfalling TCs from 1957 to 2014 were selected, and the total sample number is 11 250 (25 samples multiplied by 450 TCs). Figure 1 shows the station locations and frequency distribution of all TC samples. The station density is much higher in south and east China than in central and west China, which provides more observations in areas where we are concerned about. In south and east China, the highest station density could reach 17 stations per square degree and the average station density is around 5 stations per square degree.
Each TC record was first converted to the local time (LT) by , where and are the LT and the UTC time, respectively; lon is the longitude of the TC center. This longitude conversion for time will result in more time assignments than the original hourly time assignments.
Following Bowman and Fowler (2015), we decomposed the rain rate in terms of the Fourier harmonics using the least squares regression to identify the diurnal signal:
where is the rain rate; is the LT, ; N is the maximum harmonic number, which is 24 in our study; M is the number of time bins, which is 48 in our study; and are the amplitudes of the cosine and sine terms of the kth harmonic, respectively; R0 is the daily mean rain rate, which is the average of the binned rain rate in our study; is the residual; and is the length of the day in the same units as . The amplitude and phase of harmonic k can be calculated by
The F test, with 2 and M − (N + 1) degrees of freedom, was used to detect whether the harmonics were significantly different from zero.
To filter the nonphysical high-frequency clutters, following Leppert and Cecil (2016), a three-point average (with weights of 0.25, 0.50, and 0.25) was utilized to remove high-frequency oscillations with a period less than an hour before Fourier analysis.
a. Diurnal cycle in TC rain rate over land
The observed rain rates were averaged between 0- and 500-km radii (Fig. 2a) and between 500- and 1000-km radii (Fig. 2b) from the TC centers to represent the rain rate in the TC primary circulation and the TC outer region, respectively. Note that only the stations with measurable rain rate (≥0.1 mm) were considered in this study and that samples with less than 20 stations inside the average area were eliminated from the analysis. After this elimination, all samples were averaged into 48 equally sized time bins based on their LTs with the results shown in Fig. 2 as the gray curves. The black curves in Fig. 2 indicate the smoothed diurnal variations. It shows a clear diurnal variation with the peak rain rate in the early morning (0200–0400 LT), especially for rain rates in the TC outer region, which is about 3 h earlier than that associated with TCs over oceans reported in previous studies (Steranka et al. 1984; Kossin 2002; Dunion et al. 2014). Moreover, the binned rain rate is much larger than that in previous studies, which could be a result of the complex interaction with land surface processes and topographic effects, and might also be partly related to the overall underestimate of rain rate derived from satellite observations when compared with the rain gauge observations (Zhou et al. 2008).
The diurnal and semidiurnal signals are shown in Fig. 2 in red and blue curves, respectively. Both are significantly different from zero at the 99% confidence level. The diurnal harmonic presents a peak in rain rate between 0200 and 0400 LT, which is about 3 h earlier than that over oceans reported in previous studies. This is different from the results of Jiang et al. (2011), who found double peaks in the diurnal cycle of rain rate in TCs over land, with one in the early morning, which is consistent with that in our study, and the other in the afternoon. This difference could be due to the different data used. Jiang et al. (2011) used the TRMM 3B42 product, which could overestimate afternoon rainfall and underestimate morning rainfall (Yuan et al. 2012). Yuan et al. (2012) also pointed out that the afternoon overestimation of rainfall is more prominent in mountainous regions, while the morning underestimation of rainfall is more prominent over plains. Because of this systematic bias, the TRMM 3B42 product might distort the rainfall diurnal cycle in TCs over land. The semidiurnal harmonics for landfalling TCs in Fig. 2 show two peaks in rain rate, one in the early morning and the other in the late afternoon, consistent with the climatological precipitation diurnal cycle over south and east China (Yu et al. 2007). The variance contributed by the diurnal (semidiurnal) signal is 34.56% (26.23%) and 78.41% (14.09%) in the TC primary circulation and the TC outer region, respectively. However, the precipitation variation amplitude, which was defined as the difference between the daily maximum and minimum rain rates as a percentage of the mean rain rate during a TC rainfall day, of the diurnal harmonic in the TC primary circulation is only 3.69% (Fig. 2a), while Shu et al. (2013) found that the precipitation variation amplitude could reach about 30% in the diurnal cycle of TC rainfall over oceans. This suggests that the precipitation diurnal cycle in TCs contributes more over oceans than over land within 500 km from the storm center, which is due to the weaker diurnal cycle between 0- and 400-km radii over land as shown in Fig. 3. But the precipitation variation amplitude of the diurnal cycle in the TC outer region is 35.84%, which is similar to results for TCs over oceans.
b. Propagation of precipitation diurnal cycle
As mentioned in the introduction, whether the radial propagation of the diurnal cycle in TC rain rate exists is still controversial. Leppert and Cecil (2016) suggested that the radially propagating diurnal signal of precipitation detected by Wu et al. (2015) was a result of infrared brightness temperatures and not necessarily precipitation. In this study, we used the rain gauge data to examine the existence of this propagation.
Figure 3 presents the diurnal variations of the annularly averaged rain rates. To better compare the results for each annulus, rain rates were calculated as the percentage anomaly relative to the annulus average rain rates. Note that samples with less than 5 stations in the average annulus are eliminated, and after that, the total station number from all the samples averaged in an annulus varies from 33 057 in the innermost annulus to 48 223 in the outermost annulus. The variations in the core region within 400 km from the TC center are irregular as compared with those in the outer region between 400- and 900-km radii. An obvious early morning maximum (0200–0400 LT) and an afternoon minimum (1400–1600 LT) could be identified in the outer region. The amplitude in the outer region could reach 20% in the diurnal cycle, with the highest amplitude larger than 23%, which is similar to the results for TCs over oceans found in Shu et al. (2013). All diurnal harmonics in the outer region contribute over 50% to the total variance, which is about 20% higher than the largest contribution in the TC core region (Fig. 4a). These results strongly suggest that the diurnal signal in Fig. 2a is mainly contributed by the rain rate between 400 and 500 km from the storm center and that the diurnal signal appears to be much larger in the outer region than in the core region in TCs after landfall. Moreover, the diurnal variation in rain rate tends to have two obvious peaks between 900 and 1000 km from the TC center, one in the early morning and the other in the afternoon, which is similar to the diurnal variation of summer precipitation over central eastern China largely independent of TCs (Yu et al. 2007). However, the semidiurnal harmonic is statistically significant at the 99% confidence level only in the area beyond 900 km from the storm center, where the influence of TCs is very weak (Figs. 4a,b). Meanwhile, the diurnal harmonic is distinct and statistically significant at the 99% confidence level in all annuli between 400- and 1000-km radii, which is consistent with the results in Leppert and Cecil (2016). This indicates that the diurnal signal in the outer region revealed above is mainly contributed by TCs.
Figure 4c shows the phase and amplitude of the diurnal harmonics as a function of radial distance from the storm center. Consistent with the results in Wu et al. (2015), the diurnal amplitude decreases radially outward in the outer region (500–1000 km from the storm center). Meanwhile, the peak time delays as the radial distance from the TC center increases in the outer region, which is also consistent with Wu et al. (2015). It seems that the diurnal variations extend gradually outward. Previous studies speculated that the radial propagation of the precipitation diurnal cycle might be caused by gravity waves with a propagation speed of 10–20 m s−1 (Steranka et al. 1984; Dunion et al. 2014). However, Fig. 4c shows that the peak time delays by about 6 h from 300 to 900 km from the storm center, which implies a propagation speed of around 30 m s−1, larger than the propagation speed of gravity waves. This indicates that for TCs over land, the radial propagation of the diurnal cycle in rain rate may not be controlled by gravity waves.
Figure 5 displays the radius–time plots of the standardized mean TC rain rate. The rain rate at each LT is standardized by the daily averaged standard deviation of rain rate in each annulus. While the propagation speed of the afternoon minimum is similar to that of the diurnal signal in Fig. 4c, the phase of the early morning peak seems invariant. On the other hand, the amplitude of the early morning peak increases in the radial direction, while that of the afternoon minimum changes less. We can see from Fig. 3 a gradual increase in the amplitude of the semidiurnal harmonic as the radial distance increases, which would enlarge the diurnal morning peak and flatten the afternoon minimum. Thus, the outward-propagating signal of the diurnal harmonic in Fig. 4c is most likely a result of the enhancement in the semidiurnal harmonic as the influence from TCs weakens as the radial distance increases. This could support the conjecture in Leppert and Cecil (2016) that the outward-propagating signal is manifest near the cloud top but not through the deep precipitation layer.
c. Stratification by time relative to landfall
To evaluate the diurnal variations for samples prior to and after landfall, we consider samples from 12 h prior to landfall to the time at landfall as the before-landfall group and samples from the time at landfall to 12 h after landfall as the after-landfall group. As mentioned above, samples with less than five stations in the average annulus are eliminated. The sample mean station number in the innermost annulus and the outermost annulus is 8.43 and 11.22, respectively, in the before-landfall group and 8.96 and 13.47, respectively, in the after-landfall group.
Figures 6 and 7 display the diurnal and semidiurnal cycles in rain-rate percentage anomaly associated with samples prior to (Fig. 6) and after (Fig. 7) landfall. Their amplitudes and phases are shown in Fig. 8. In the after-landfall group, the diurnal cycle is less distinct within 400 km from the storm center, which is similar to the uncategorized results shown in Fig. 3. However, the diurnal cycle in the before-landfall group is distinct among all annuli up to 1000 km from the storm center, except for the innermost annulus. Although the variance contribution of the semidiurnal cycle is larger than the diurnal cycle in Fig. 6c, the smoothed diurnal variation shows that the early morning peak is larger than the afternoon peak. This means that when the inner core region is over ocean, the diurnal cycle in rain rate is more like that in storms over oceans in both the inner and outer regions as shown in previous studies. The high-frequency oscillations in rain rate within 400 km from the storm center as seen in Fig. 3 could be mainly a result of the samples after landfall. Moreover, the diurnal variation tends to be larger in the before-landfall group than in the after-landfall group. But the phases of diurnal harmonics are not statistically different between 400- and 900-km radii, where the diurnal harmonics are significant in both the before-landfall group and the after-landfall group.
The amplitudes of the diurnal harmonic show peaks between 600- and 700-km radii in both the before-landfall group and the after-landfall group and decrease as the radial distance increases in the outer region (Fig. 8a). The amplitudes of the diurnal harmonic in the core region are lower than that in the outer region in the before-landfall group, which is consistent with the results in Leppert and Cecil (2016) except that they showed that the diurnal amplitudes vary little in the outer region. Note that the weakening of the diurnal harmonic is accompanied by the strengthening of the semidiurnal harmonic (Figs. 6 and 7). We speculate that the decrease in the diurnal amplitude in the outer region may be partially due to the amplification of the semidiurnal variation.
d. Stratification by storm intensity 12 h prior to landfall
In this study, the storm intensity is the maximum sustained near-surface wind speed in the best-track data from the STI of CMA, and the 6-hourly intensities were linearly interpolated into hourly intensity. Based on the intensity 12 h prior to landfall, we divided the samples into strong and weak storms with a criterion of median intensity, which is roughly 30 m s−1. Figure 9 shows the radius–time plot of rain-rate percentage anomaly, respectively, in weak storms (Fig. 9a) and strong storms (Fig. 9b). The diurnal signals are not distinct in the inner region (within 400 km from the storm center) in both weak storms and strong storms, which is consistent with results shown in Fig. 5. Although its amplitude in strong storms is slightly larger than that in weak storms, the diurnal signal shows little dependence on storm intensity, which is consistent with results in some previous studies (Bowman and Fowler 2015; Leppert and Cecil 2016).
4. Conclusions and discussion
We have documented the diurnal variation in TC rain rate over land associated with landfalling TCs using rain gauge observations in China. The diurnal variation in rain rate shows a weak early morning maximum (0200–0400 LT) and afternoon minimum (1400–1600 LT) within 500 km from the storm center. Different from TCs over oceans, the diurnal variation in rain rate over land associated with landfalling TCs appears to be larger in the outer region between 400 and 900 km from the storm center than in the inner region within 400-km radius. Further analysis shows that the precipitation diurnal cycle in the before-landfall group is distinct in both the inner region and the outer region, while that in the after-landfall group is only distinct in the outer region. This suggests that the high-frequency oscillations within 400 km from the storm center are mainly due to the samples with most of their inner core regions over land.
The radial propagation of the precipitation diurnal cycle is not clear in landfalling TCs. Although the phase of the diurnal harmonic delays as the radial distance increases in the outer region of landfalling TCs, the variation of the diurnal amplitude in the radial direction decreases rapidly. The outward-propagating diurnal phase results from the enhancement in the semidiurnal harmonic, which becomes more pronounced in the outer region as the influences by TCs become weaker as the distance from the storm center increases. Moreover, the translational speed of a TC could affect the precipitation diurnal cycle in TCs as the station number of every annulus might be different between fast-moving TCs and slow-moving TCs. Further studies with high temporal resolution of TC information may help classify any differences in the precipitation diurnal cycle between fast- and slow-moving TCs.
Results from this study imply a diurnal variation of more than 60% in land precipitation in the outer region of landfalling TCs, and the percentage exceeds 30% in the inner region for TCs before landfall (Figs. 6 and 7). This strongly suggests that the diurnal variation should be considered in precipitation forecasts for landfalling TCs. Konrad (2001) found that TCs make landfall more frequently during the evening and midmorning hours than at other times of day over the eastern United States. However, this tendency is not obvious for TCs making landfall over China (Fig. 10b). Nevertheless, cumulative precipitation, defined as the precipitation cumulated from the time at landfall to 12 h after landfall, does have a distinct variation as a function of landfall LT, both in the inner region and in the outer region (Fig. 10a). Storms making landfall around noon and afternoon have cumulative precipitation about 30% less than storms making landfall at night. This variation should be considered an important factor in precipitation forecasts for landfalling TCs.
Precipitation in the region between 400 and 900 km from the storm center is not completely induced by TCs but also often results from interactions with other synoptic systems, in particular for TCs after landfall. Without considering the details of the interactions between TCs and other synoptic systems, we have shown an obvious diurnal signal in rain rate over land, which is consistent with results found for TCs over oceans in previous studies except for the different diurnal phases. Note that the diurnal phase, which is dominant in the outer region, differs greatly from the mean summer conditions in regions often affected by TCs in China. This suggests that interactions with nearby synoptic weather systems may affect the intensity of the precipitation diurnal cycle in TCs, but the diurnal variation discussed in this study is dominated by TCs, and the effect by other synoptic systems might be secondary. This could be explained as the composite analysis could reduce the impacts from other synoptic systems because these impacts are more random than effects from rain from TC themselves. The explanation for inconspicuous diurnal variation in the TC core region, which differs from TCs over oceans reported in previous studies, needs further investigation. Future studies with well-designed numerical experiments using cloud-resolving models may help elucidate the detailed physical mechanisms behind these results. Nevertheless, this is the first study that has documented the diurnal variation of rain rate over land associated with TCs making landfall over China with rain gauge observations. The results may be useful for verification of rainfall prediction for landfalling TCs by numerical weather prediction models and also may help improve the statistical rainfall prediction schemes for landfalling TCs.
The authors are grateful to three anonymous reviewers for their constructive review comments and suggestions, which helped improve the manuscript. This study has been supported in part by the National Basic Research and Development Project (973 Program) of China under Contract 2015CB452805 and in part by the National Natural Science Foundation of China under Grant 41375068. The authors thank the National Meteorological Information Center (NMIC) of China Meteorological Administration (CMA) for providing access to the rain gauge data and Dr. Jing Xu for her suggestions and discussions.