Diurnal Variation of Seasonal Precipitation over the CONUS: A Comparison of Gauge Observations with TRMM Data

Diurnal variation of precipitation is a fundamental periodic signal of local climate. Comprehensive study of diurnal variation of precipitation is helpful in studying the formation of local climate and validating satellite precipitation products. In this study, a comparison is drawn between precipitation gauge observations and Tropical Rainfall Measuring Mission (TRMM) 3B42 data on diurnal variation of precipitation. First, using the K-means clustering algorithm, stations with gauge observations and pixels with TRMM data are divided into different groups according to the diurnal variation of precipitation, respectively. In each group, the stations have similar diurnal variation of precipitation.)enmaps of diurnal variation of precipitation for gauge observations and TRMM data are obtained. According to these maps, the diurnal variation of precipitation over the contiguous United States (CONUS) presents seasonal variability in both gauge observations and TRMM data. In addition, the diurnal variation of precipitation shows clustered features in space. However, the spatial patterns of the obtained maps do not match, and the TRMM satellite data perform poorly in capturing the hourly precipitation event. Finally, the possible mechanism behind the prevailing nocturnal precipitation over the middle of the CONUS is discussed, with the prevailing nocturnal precipitation judged likely to be strongly related to the mountain-plains solenoid (MPS) circulation.


Introduction
Diurnal variation of precipitation is a periodic signal at subdaily scale and can be used to characterize local climate [1][2][3]. Driven by solar radiation and affected by heterogeneous underlying surface, it shows remarkable seasonal variability and regional difference. A comprehensive study of diurnal variation of precipitation can provide valuable clues for the mechanisms study of local climate [4,5].
At first, precipitation gauge observations were used to study the diurnal variation of precipitation [6][7][8][9][10][11]. Using hourly precipitation gauge observations from 588 weather stations, Yu et al. [7] analyzed the spatial pattern of diurnal variation of summer precipitation over China. e results show that the prevailing afternoon precipitation is over southern inland China and northeastern China, while the prevailing midnight precipitation is over most of the Tibetan Plateau and its east periphery. Although gauge observations have high accuracy, weather stations are far between. Moreover, diurnal variation of precipitation is various due to the heterogeneities in underlying surface [12,13]. Accordingly, gauge observations are not sufficient for the study of the spatial pattern of diurnal variation of precipitation.
Recently, the release of abundant satellite-based precipitation data has allowed the use of spatially continuous data to study the diurnal variation of precipitation [14,15]. For example, using Tropical Rainfall Measuring Mission (TRMM) data, Nesbitt and Zipser [14] compared the diurnal variation of precipitation over a land area with that over an ocean area and found that the amplitude of diurnal variation of precipitation over the ocean area was less than that over the land area. Although satellite precipitation products are usually adjusted by gauge observations, their performance still needs to be improved [16][17][18][19][20][21][22][23]. Previous studies [24][25][26] have also noted that satellite precipitation products perform poorly at capturing hourly precipitation, causing differences between gauge observations and satellite data in diurnal variation of precipitation.
Comparisons between gauge observations and satellite data on diurnal variation of precipitation have been drawn in previous studies [27,28]. For example, by selecting the south China coast as the study area, Zhou et al. [28] found that TRMM and Climate Prediction Center morphing technique (CMORPH) satellite precipitation data showed less morning rainfall and more afternoon rainfall than gauge observations. Differences between gauge observations and satellite data on diurnal variation of precipitation have been found in other areas as well [29,30]. In these studies [27][28][29][30], predefined regions have usually been used to compare gauge observations with satellite data in these studies with differences between gauge observations and satellite data evident for such region, but the actual spatial pattern of diurnal variation of precipitation from precipitation data remains unclear.
In this study, the K-means clustering algorithm is applied to mine the spatial pattern of diurnal variation of precipitation from gauge observations and satellite-based precipitation data. Furthermore, a comparison is drawn between gauge observations and satellite-based precipitation data about diurnal variation of precipitation. e objectives of this study are (1) to analyze the seasonal variability and spatial pattern of diurnal variation of precipitation and (2) to compare the diurnal variation of precipitation indicated by gauge observations with that indicated by satellite-based precipitation data. e diurnal variation of precipitation over the contiguous United States (CONUS) is chosen for study because of its long availability of historical gauge data, and the long availability of historical satellite-based precipitation data of TRMM product is used.

Hourly Precipitation Gauge Observations.
e precipitation gauge observations used in this study are derived from the hourly precipitation data (HPD) network (version 1). e HPD precipitation data set provides hourly precipitation amount of USA from 1948 to 2017, with local solar time (LST), sourced the NOAA/NWS Fischer-Porter (F&P) in situ network of precipitation gauges. is network consists of approximately 2,000 stations that are a subset of the NWS Cooperative Observers Program (COOP) network. e data set was compiled and released by the National Centers for Environmental Information (NCEI) and can be freely requested at ftp://ftp.ncdc.noaa.gov/pub/data/hpd/ auto/v1/beta/. A quality control procedure has been applied to the data set based on a paradigm established [31][32][33].
For this research, precipitation gauge observations were extracted from January 1, 2002, to December 31, 2016. e locations of the 1,243 chosen stations, those found to have less than 5% missing data, are shown in Figure 1.

TRMM Precipitation Data: 3B42 Data.
e TRMM is a joint mission between the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA). e TRMM satellite was launched in 1997 to monitor and study tropical precipitation [34,35]. e satellite carries three precipitation-relevant instruments: a precipitation radar (PR), TRMM microwave image (TMI), and visible and infrared scanner (VIRS). e TRMM 34B2 precipitation product (version 7) with 3-hour temporal resolution and 0.25°spatial resolution is used here, which can be downloaded from Google Earth Engine (https://explorer.earthengine.google.com/#index).
is product is a multisatellite data set and is created by blending the passive microwave data collected by the TMI, the Special Sensor Microwave Imager, the Advanced Microwave Scanning Radiometer for Earth Observing System, the Advanced Microwave Sounding Unit B, and the IR data [35,36].
To allow comparison with precipitation gauge observations, TRMM grid data were first extracted for each of the 1,243 precipitation gauge stations' locations, dating from January 1, 2002, to December 31, 2016. e extracted data were then interpolated into hourly precipitation data using a B-spline interpolation method. Local solar time (LST) was used to calculate hourly rainfall frequency.

Representation of Diurnal Variation of Precipitation.
Precipitation frequency was used to research diurnal variation of precipitation in this study, as in previous studies [37][38][39]. First, hourly precipitation frequency was calculated as times of measurable precipitation amounts (i.e., ≥0.1 mm h −1 ) for each hour, expressed as a 24-dimensional vector corresponding to 24 hours in a day. en hourly precipitation frequency was normalized using the following formula [40]: where D (h) represents the normalized precipitation frequency at time h and P (h) represents the original precipitation frequency at time h.

Mining the Spatial Pattern of Diurnal Variation of
Precipitation. e K-means clustering algorithm is applied to mine the spatial pattern of the diurnal variation of precipitation, as previously used to mine the spatial pattern of diurnal rainfall variation over China by Zhu et al. [39]. e K-means clustering algorithm aims to partition n observations into K clusters such that each observation belongs to the cluster having the nearest distance. e number of clusters (K values) must be determined in advance. To identify an ideal K number, various K values ranging from 2 to 31 were used for clustering, after which the average distance from every point to its corresponding cluster center was calculated. e average distance decreased with increases in cluster number and the decreased values of average distance were also declining with the increase of the cluster number. A slight drop in average distance caused cluster number to be larger than the "true" number of clusters, so the clusters do not need to be divided any more [41]. Finally, the 20 K clusters were selected as the ideal K number in this study.
A large enough cluster number can lead to clusters that have similar diurnal variation of precipitation. Such clusters should be merged manually. Peak time is the most interesting information in the study of diurnal variation of precipitation. erefore, the merging criteria used here are as follows: Clusters were merged if their peak times of diurnal variation fell into any of six periods: from 0300 LST to 0600 LST (early morning), from 0700 LST to 1000 LST (morning), from 1100 LST to 1400 LST (midday), from 1500 LST to 1800 LST (afternoon), from 1900 LST to 2200 LST (evening), and from 2300 LST to 0200 LST (midnight). For the diurnal variation of precipitation with multiple peaks, clusters were merged only if all peak times were similar. e merging criteria are the same as mentioned above. It should be noted that only if the amplitude of diurnal variation was larger than 0.2, then it was deemed to be a peak.

Spatial Aggregation Analysis.
Moran's index (Moran's I; ranges from −1.0 to +1.0) is used to analyze the spatial aggregation of diurnal variation of precipitation. A positive value of Moran's I means that the diurnal variation of precipitation is clustered in space, whereas a negative value means that diurnal variation is discrete in space and a value of zero means that diurnal variation is random in space. z-score indicates confidence level. For reference, the z-score for 95% confidence is larger than 1.96 or smaller than −1.96, and the z-score for 99% confidence is larger than 2.58 or smaller than −2.58.  Table 1.

Diurnal Variation of Precipitation of Gauge Observations.
In Figure 2(a), there are 6 types of diurnal variation of precipitation: no peak diurnal variation (not shown in the figures), morning peak diurnal variation, midday peak diurnal variation, afternoon peak diurnal variation, early night peak diurnal variation, and midnight peak diurnal variation. e stations having no peak diurnal variation of precipitation account for 46.8% of total stations (1,243). Stations having the other five types of diurnal variation of precipitation, morning peak, midday peak, afternoon peak, early night peak, and midnight peak, account for 22.2%, 14.2%, 5.6%, 10.2%, and 1% of total stations, respectively.
In Figure 2(b), there are 7 types of diurnal variation of precipitation. An early morning peak diurnal variation is more than that in Figure 2(a). 10.2% of total stations have no peak diurnal variation of precipitation. Stations having the other six types of diurnal variation account for 35.6% (morning peak), 3.4% (midday peak), 24.7% (afternoon peak), 14.1% (early night peak), 4.8% (midnight peak), and 7.2% (early morning peak).    Early-N is short for early night, and Early-M is short for early morning. 27.4% (morning peak), 11.8% (midday peak), 15% (afternoon peak), 7.6% (early night peak), and 5.4% (midnight peak). In Figure 2(d), 34.9% of stations have no peak diurnal variation and stations having the other five types of diurnal variation account for 19.3% (morning peak), 32.8% (midday peak), 5.2% (afternoon peak), 4.1% (early night peak), and 3.7% (midnight peak). ese results show that the spatial pattern of diurnal variation of precipitation of gauge observations presents seasonal variability. In Figure 2, the stations with different diurnal variation of precipitation present the spatial aggregation characteristics. e phenomenon is particularly obvious in summer (Figure 2(b)). It can be seen from Figure 2(b) that the prevailing high precipitation is mainly located in the central of the CONUS, while the prevailing afternoon precipitation is mainly distributed in the coastal region and the mid-west region of the CONUS. Table 2 summarizes Moran's I and the corresponding z-scores for the classified stations in Figure 2. All z-scores for the four seasons are much larger than 2.58, indicating that stations having similar diurnal variation of precipitation are significantly clustered in space. Figure 3 shows the curve of normalized hourly precipitation frequency corresponding to the diurnal variation of precipitation in Figure 2. e amplitudes of the curves in spring, autumn, and winter are comparable but they are much less than that in summer. ese results show that the amplitude of diurnal variation of precipitation of gauge observations presents seasonal variability. Similar conclusion was mentioned in a previous study (Dai et al., 1999).  Table 3.

Diurnal Variation of Precipitation of TRMM Data.
In Figure 4(a), there are 6 types of diurnal variation of precipitation: no peak diurnal variation, midday peak diurnal variation, afternoon peak diurnal variation, early night peak diurnal variation, midnight peak diurnal variation, and two peaks with one peak in the morning and the other in the afternoon. For these stations, 24.2% of stations have no peak diurnal variation, and stations having the other five types of diurnal variation account for 3.4% (midday peak), 24.7% (afternoon peak), 13.8% (early night peak), 26.1% (midnight peak), and 7.8% (two peaks). Figures 4(b) and 4(c) have the same types of diurnal variation of precipitation as in Figure 4(a). In Figure 4(b), 9.1% of stations have no peak diurnal variation of precipitation and stations having the other five types of diurnal variation account for 1.2% (midday peak), 57.5% (afternoon peak), 0.6% (early night peak), 30.0% (midnight peak), and 1.6% (two peaks-one in the morning and the other in the afternoon). In Figure 4(c), 55.8% of stations have no peak diurnal variation of precipitation and stations having the other five types of diurnal variation account for 2.1% (midday peak), 22.3% (afternoon peak), 3.1% (early night peak), 10.8% (midnight peak), and 5.9% (two peaks-one in the morning and the other in the afternoon).
In Figure 4(d), stations having no peak diurnal variation of precipitation account for 47.1% and stations having the other five types of diurnal variation account for 10.8% (morning peak), 1.6% (midday peak), 4.2% (afternoon peak), 32% (midnight peak), and 4.3% (two peaks-one in the morning and the other in the afternoon). e result shows that the spatial pattern of diurnal variation of precipitation of TRMM data also presents seasonal variability.
Compared with spatial pattern of diurnal variation of precipitation in Figure 2, the spatial pattern of Figure 4 is more clustered in all seasons than the spatial pattern in Figure 2. It can be seen from Figure 4 that the diurnal variation of precipitation with day peak occurs mostly in the west and the east of the CONUS, whereas the diurnal variation of precipitation with night peak occupies the middle area of the CONUS. In the southeastern CONUS, the diurnal variation of precipitation with afternoon peak is predominant over this area in spring, summer, and autumn. Table 4 summarizes Moran's I and corresponding z-scores for the diurnal variation of precipitation in Figure 4. Moran's I indexes in Table 4 are larger than those in Table 2 in four seasons. e result indicates that the spatial pattern of diurnal variation of precipitation of TRMM data also is significantly clustered in space.
Similarly, Figure 5 shows the curve of normalized hourly TRMM precipitation frequency. e amplitudes of the curves in spring, autumn, and winter are comparable and are less than that in summer. In addition, a new diurnal variation of precipitation, with one peak in morning and the other in the afternoon, appears in four seasons. e results show that the amplitude of diurnal variation of precipitation of TRMM data presents seasonal variability.

Difference of Diurnal Variation of Precipitation between Gauge Observations and TRMM Data.
According to the classification of diurnal variation of precipitation in Figure 2 (gauge observations), this study calculated the normalized hourly TRMM precipitation frequency for each type of diurnal variation of precipitation (shown in Figure 6). As shown in Figure 6, stations that had prevailing afternoon precipitation in gauge observations still had an afternoon peak in TRMM data. However, stations that had other types of diurnal variation of precipitation in gauge observations had different types of diurnal variation of precipitation in TRMM data.
Similarly, according to the classification of diurnal variation of precipitation in Figure 4 (TRMM data), this study calculated the normalized hourly gauge precipitation frequency for each type of diurnal variation of precipitation (shown in Figure 7). e curves in Figure 7 show that stations that had an afternoon peak in TRMM data still had an afternoon peak in gauge observations but that stations that had other types of diurnal variation of precipitation had different types of diurnal variation of precipitation in gauge observations.
In general, precipitation gauge observations can be regarded as the true value, and TRMM data should be the same as gauge observations in theory. However, as shown in Figures 6 and 7, except for prevailing afternoon precipitation, diurnal variation of precipitation in gauge observations was largely inconsistent with TRMM data, indicating that TRMM data can well capture prevailing afternoon precipitation but performs poorly at capturing hourly precipitation at other times. A study by Kotsifakis et al. [42] also pointed out that version 7 of the TRMM 3B42 precipitation data can hardly captain the characteristics of 3-hour, 6-hour, 12-hour, 24-hour, and 48-hour precipitation.
e result obtained in this study further confirms the conclusion that the TRMM 3B42 data performs poorly in captaining the characteristics of hourly precipitation.

Possible Mechanism behind Prevailing Nocturnal
Precipitation. Prevailing nocturnal precipitation over the middle of the CONUS has been explained by the mountainplains solenoid (MPS) circulation in previous studies [6,[43][44][45]. e obtained results of this study can provide valuable clues for studying the mechanism of diurnal variation of precipitation.
As shown in Figures 2 and 4, prevailing nocturnal precipitation occurs mostly in the middle of the CONUS.
is phenomenon is more obvious in summer than in other seasons. Taking six stations with prevailing nocturnal precipitation in summer as an example (shown in Figure 8), the possible mechanism behind the prevailing nocturnal precipitation is discussed.     Figure 8(b). As can be seen, the six stations are mainly distributed in the transitional area, from mountain area to plain area. Figures 8(c) and 8(d) show the curves of normalized hourly precipitation frequency for gauge observations and TRMM data, respectively. As shown in Figure 8(c), the diurnal variation of precipitation at Stations A, B, and C has an early night peak, whereas early morning precipitation predominates at Stations D and E and the diurnal variation of precipitation at Station F has a morning peak. e peak time of diurnal variation at these six stations presents eastward delay from Station A to Station F. is phenomenon can also be found in TRMM data (Figure 8(d)).
For MPS circulation, the cold air mass over mountains flows along the slope of mountains to the plains due to the stronger surface cooling on the mountains compared to that on the plains at night [39,46]. en the downward movement of cold air mass lifts the warm air mass at the downslope of mountains, which causes atmospheric instability and leads to prevailing nocturnal precipitation [47]. As the enhanced cooling air mass in deep night, it will strengthen the propagation of flow from mountaintop to plains.
en the further warm air mass is lifted, causing  prevailing nocturnal precipitation. e nocturnal rain belt moves accordingly, causing a time-delay pattern of rainfall peaks along the slope of macroterrain.
However, Seo et al. [48] and Seo et al. [49] also found anomalous propagation of the prevailing nocturnal precipitation over the middle of the CONUS using radarrainfall data. However, in their study, the anomalous propagation of the prevailing nocturnal precipitation was attributed to wind turbines' interference in radar observations. Wind turbines are clustered to form wind farms at night, leading to prevailing nocturnal precipitation in radar observations.
It should be noted that the mechanism of diurnal variation of precipitation is complicated [50][51][52]. e formation of diurnal variation of precipitation is affected by many factors, such as solar radiation, complex terrain, multiscale  Table 3: e percent of different types of diurnal variation in Figure 4 (unit: %).      atmospheric circulations, and transfer of water vapor [17,27,29]. However, one dominant factor in an area usually leads to a peculiar diurnal variation of precipitation. For example, the prevailing day precipitation is usually caused by surface solar heating [37,53], whereas prevailing midnight precipitation and the prevailing early morning precipitation are usually related to complex terrain or sea-breeze circulations [53,54]. is study focuses on spatial and seasonal patterns of diurnal variation of precipitation, comparing the diurnal variation of precipitation in gauge observations with that in satellite data. e mechanism study for diurnal variation of precipitation is a vast topic beyond the scope of this study, which focuses on analyzing the possible mechanism behind the prevailing nocturnal precipitation over the middle of the CONUS. Detailed mechanisms for diurnal variation of precipitation over the CONUS require further study, but the results of this study can provide valuable clues for the studies of the mechanism involved.

Conclusion
Diurnal variation of precipitation is a fundamental periodic signal of local climate. e study of diurnal variation of precipitation is helpful in studying the formation of local climate and validating satellite precipitation products. Precipitation gauge observations and satellite-based precipitation data were both used to study the diurnal variation of precipitation in previous studies. However, the diurnal variation of precipitation obtained from gauge observations is usually inconsistent with that obtained from satellite-based data due to the poor performance satellite-based precipitation data. Besides, predefined regions have usually been used to compare gauge observations with satellite data in these studies with differences between gauge observations and satellite data, but the actual spatial pattern of diurnal variation of precipitation from precipitation data remains unclear.
In this study, a comparison was drawn between precipitation gauge observations and TRMM data concerning diurnal variation of seasonal precipitation. e following conclusions were drawn: (1) Diurnal variation of precipitation over the CONUS presents seasonal variability. (2) Diurnal variation of precipitation shows clustered features in space but with significant differences in spatial pattern between mapped gauge observations and mapped TRMM data. (3) TRMM data can capture the prevailing afternoon precipitation well but perform poorly at capturing hourly precipitation at other times. (4) Prevailing nocturnal precipitation over the middle of the CONUS seems to be related to MPS circulation.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.