Precipitation Diurnal Cycle in Germany Linked to Large-Scale Weather Circulations

: The precipitation diurnal cycle (PDC) varies with the season and location. Its link to large-scale weather circulations has been studied in di ﬀ erent regions. However, comparable information is lacking for Central Europe. Two decades of hourly precipitation data were combined with records of objective weather patterns over Germany, focusing on the general atmospheric wind directions (WD). The PDC is characterized by the frequency and the average amount of hourly precipitation. The precipitation frequency generally has two peaks: one in the morning and the other in the afternoon. The morning peak of the precipitation amount is small compared to that of the afternoon peak. Remarkably, WD has a prominent inﬂuence on the PDC. Days with southwesterly WD have a high afternoon peak and a lower morning peak, while days with northwesterly WD have a high morning peak and a lower afternoon peak. Furthermore, the seasonal variations of PDC are dominated by the seasonal frequency of WD classes. This study presents a general overview of the PDC in Germany with regard to its variation with seasonality, geographical location, elevation, and WD.


Introduction
Globally, the diurnal amplitude variation of the precipitation frequency exceeds 20% of the mean daily values [1]. The precipitation diurnal cycle (PDC) emerges from fluctuations in global radiation. This is evident, especially in the tropics, where solar forcing is at its maximum. The PDC in mid-and high latitudes is influenced by frontal systems and topography, among other factors [1][2][3]. The PDC and its temporal and spatial variations have been addressed on global and local scales using the vast amount of precipitation records available at high resolution. Studying and understanding the PDC are important because of its applications in atmospheric science and hydrology. It interacts with the changes in surface temperatures, cloud formation processes, and boundary layer development [4][5][6], and affects the trace gas concentrations [7]. PDC influences the risk of floods and must be taken into consideration in hydrological models and designs [8,9]. Furthermore, it aids in the development of numerical weather models, which struggle to improve their representation of the PDC [10][11][12]. Such a challenge has been studied recently [13][14][15][16], particularly because the accuracy of a climate model on a daily scale reflects its quality in properly representing the physical processes or in parameterizing them.

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How do PDC patterns vary with CTs over Germany? • How does seasonality and location within Germany influence such a variation?
Thus, we aim for an overview of the PDC across Germany linked to CTs and its dependence on seasonality and location. We also compare our findings with published work on the PDC, especially at nearby locations in Central Europe.

Data Sources and Analysis Tools
The data set used in this research consists of daily records of objective weather types and hourly precipitation measurements at 136 stations in Germany.
The classification of the large-scale weather types over Germany is performed on a daily basis by the German Meteorological Service (Deutscher Wetterdienst, DWD). The classification method uses results of the operational numerical weather analysis and forecast system of the DWD. One class out of 40 possible of objective weather classes over Central Europe is assigned to each day. Each class comprises three indices: wind index, cyclonality index, and humidity index. The direction of the air mass advection within each CT has more influence on the PDC than the pressure system type itself [3]; thus, we investigated only the influence of the wind index based on the horizontal wind components at 700 hPa. The daily wind index was assigned to one of the five wind direction classes (hereafter, WD), which are no prevailing direction (XX), northeasterly (NE), southeasterly (SE), southwesterly (SW), and northwesterly (NW). The classification process is explained in detail by DWD [40]. Full records of the objective weather types are available online [41].
The hourly precipitation measurements are provided via the DWD climate data center [42]. A full list of the available German weather stations is provided in the online document [43]. We limited this study to stations with 15 years or more of precipitation records between December 1995 and November 2017. Four types of precipitation measurement devices were used in the selected data set: pluviometers (52% of the total measurement period), NG200 (20%), Hellmann (18%), and Joss-Tognini [44,45] (9%). The hourly sums of precipitation below 0.2 mm might consist of dew aside from other sources of error, and these values were filtered out. The data set contained a total of 2,011,797 h of precipitation at 136 stations.
The stations were grouped by latitude, longitude, and elevation. Each parameter had three classes with~equal number of stations. Figure 1 shows the location of the 136 selected stations and their three elevation classes. Table 1 presents their number per class. Supplementary file provides their station names, IDs, and geographical coordinates. h of precipitation at 136 stations. The stations were grouped by latitude, longitude, and elevation. Each parameter had three classes with ~equal number of stations. Figure 1 shows the location of the 136 selected stations and their three elevation classes. Table 1 presents their number per class. Supplementary file provides their station names, IDs, and geographical coordinates.  We used R [46], RStudio [47], and packages reader [48], stringi [49], ggplot2 [50], lubridate [51], maptools [52], raster [53], reshape2 [54], and dplyr [55] for data filtering, analysis, and production of visual and statistical results.

Precipitation Diurnal Cycle (PDC) Indicators
The precipitation measurements covered different time spans at different stations (ranging from 15 to 23 years). We calculated the long-term average of the hourly precipitation amount (P a ) and that of the hourly precipitation occurrence frequency (P f ) to prepare the comparable indicators for the PDC [56]. For each station, P a and P f are defined as: where P (h,d) is the precipitation amount at hour (h) and day (d). O (h,d) is the precipitation occurrence at h and d. It takes the value of 1 if a precipitation equal to or greater than 0.2 mm is recorded; otherwise, it takes the value of 0. N is the number of days over which the measurements are taken at the corresponding station, including the non-precipitation days.

PDC Variation with Season and Location
The PDC in Germany was characterized by two peaks in P f with a similar magnitude, one near dawn (hereafter morning peak) and the other in the late afternoon (afternoon peak) ( Figure 2, upper panel). This frequency pattern was observed in all elevation classes and at all locations. However, at high elevations, the precipitation frequency after the afternoon peak decreased more slowly than those at medium and low elevations. At the southern stations, the decrease in the frequency after the afternoon peak was equally weaker. The majority of the southern stations is elevated ( Figure 1); hence, separating these two effects is challenging. The PDC was equally characterized by two peaks in P a ; however, in most of the locations, the afternoon peak was more pronounced than the morning peak ( Figure 2, lower panel). The morning peak almost disappeared for the high elevations and southern stations.
The ranking of elevations and locations by hourly precipitation amounts corresponded to the ranking by frequency. More precipitation accumulated at high elevations and less in the northern and eastern stations.  Table 1 for the definitions of the classes; N-north, C-central, and S-south (a); W-west, C-central, and E-east (b); and H-high, M-medium, and L-low (c)).
The precipitation frequency was the highest in winter, followed by fall, spring, and summer ( Figure 3a). All seasons shared a comparable PDC ( ) with a morning peak and an afternoon peak. Both peaks had similar magnitudes in spring and winter, whereas the morning peak was higher than the afternoon peak in fall, and vice versa in summer.
Summer had the highest precipitation amount, while winter and spring had the lowest ( Figure  3b). Each season had a different PDC ( ): the afternoon peak was the strongest in summer, and had much lower magnitudes in spring, fall, and winter. The morning peak was clear in fall and spring, but weak in winter and summer.  Table 1 for the definitions of the classes; N-north, C-central, and S-south (a); W-west, C-central, and E-east (b); and H-high, M-medium, and L-low (c)).
The precipitation frequency was the highest in winter, followed by fall, spring, and summer ( Figure 3a). All seasons shared a comparable PDC (P f ) with a morning peak and an afternoon peak. Both peaks had similar magnitudes in spring and winter, whereas the morning peak was higher than the afternoon peak in fall, and vice versa in summer.
Summer had the highest precipitation amount, while winter and spring had the lowest (Figure 3b). Each season had a different PDC P a : the afternoon peak was the strongest in summer, and had much lower magnitudes in spring, fall, and winter. The morning peak was clear in fall and spring, but weak in winter and summer.

Precipitation Linked to Wind Direction (WD)
Before addressing the PDC pattern in different WD classes, we must first consider the occurrence of each WD class and the occurrence of precipitation within these classes.
The most common WD class was the SW, followed by the NW (Figure 4). Both comprised a total of 67.1% of the 8036 days between December 1995 and November 2017. The SW prevailed in all seasons, except in winter when the NW occurred more often. The NE and SE covered less than 14% of the total number of days. XX represented less than 20% of the days, with a slightly higher frequency in spring.

Precipitation Linked to Wind Direction (WD)
Before addressing the PDC pattern in different WD classes, we must first consider the occurrence of each WD class and the occurrence of precipitation within these classes.
The most common WD class was the SW, followed by the NW (Figure 4). Both comprised a total of 67.1% of the 8036 days between December 1995 and November 2017. The SW prevailed in all seasons, except in winter when the NW occurred more often. The NE and SE covered less than 14% of the total number of days. XX represented less than 20% of the days, with a slightly higher frequency in spring.

Precipitation Linked to Wind Direction (WD)
Before addressing the PDC pattern in different WD classes, we must first consider the occurrence of each WD class and the occurrence of precipitation within these classes.
The most common WD class was the SW, followed by the NW (Figure 4). Both comprised a total of 67.1% of the 8036 days between December 1995 and November 2017. The SW prevailed in all seasons, except in winter when the NW occurred more often. The NE and SE covered less than 14% of the total number of days. XX represented less than 20% of the days, with a slightly higher frequency in spring.  The percentage of wet days (days with precipitation equal to or exceeding 0.2 mm) differed among the WD classes and seasons ( Figure 5). Half the days in the WD classes NW and SW were wet days (47.6 and 48.0%, respectively). The NW WD class in winter and autumn and the SW WD class in spring and especially in summer had the highest percentages of wet days. The annual mean percentages of the other WD were less than 26% (25.9%, 20.9%, and 17.0% for the XX, NE, and SE, respectively). Interestingly, the WD class SE had the lowest percentage in winter and a much higher percentage in summer.
Atmosphere 2019, 10, x FOR PEER REVIEW 7 of 17 The percentage of wet days (days with precipitation equal to or exceeding 0.2 mm) differed among the WD classes and seasons ( Figure 5). Half the days in the WD classes NW and SW were wet days (47.6 and 48.0%, respectively). The NW WD class in winter and autumn and the SW WD class in spring and especially in summer had the highest percentages of wet days. The annual mean percentages of the other WD were less than 26% (25.9%, 20.9%, and 17.0% for the XX, NE, and SE, respectively). Interestingly, the WD class SE had the lowest percentage in winter and a much higher percentage in summer. The comparison of wet hours per wet day revealed that the differences between the WD classes were negligible ( Figure 6). XX had the highest annual mean value with 4.9 wet hours per wet day. NE had ~1 h less than the smallest annual mean. The NW and the SW scored higher averages than the remaining classes only in winter.  The comparison of wet hours per wet day revealed that the differences between the WD classes were negligible ( Figure 6). XX had the highest annual mean value with 4.9 wet hours per wet day. NE had~1 h less than the smallest annual mean. The NW and the SW scored higher averages than the remaining classes only in winter. The percentage of wet days (days with precipitation equal to or exceeding 0.2 mm) differed among the WD classes and seasons ( Figure 5). Half the days in the WD classes NW and SW were wet days (47.6 and 48.0%, respectively). The NW WD class in winter and autumn and the SW WD class in spring and especially in summer had the highest percentages of wet days. The annual mean percentages of the other WD were less than 26% (25.9%, 20.9%, and 17.0% for the XX, NE, and SE, respectively). Interestingly, the WD class SE had the lowest percentage in winter and a much higher percentage in summer. The comparison of wet hours per wet day revealed that the differences between the WD classes were negligible ( Figure 6). XX had the highest annual mean value with 4.9 wet hours per wet day. NE had ~1 h less than the smallest annual mean. The NW and the SW scored higher averages than the remaining classes only in winter.   WD classes had different occurrence frequencies and different percentages of wet days, but no significant differences in wet hours per wet day. The WD classes with a western component (SW and NW) were more frequent ( Figure 4) and also had a higher percentage of the precipitation days ( Figure 5). This was reflected in the average precipitation amount accumulated within each WD seasonally and throughout the year (Figure 7). On average, and regardless of the season, approximately 576 mm of precipitation per year was recorded for the SW and NW classes. This value corresponds to 77% of the annual amount. XX was linked to 14% of the yearly precipitation amount, while the NE and the SE combined were responsible for less than 10%. The SW recorded higher precipitation amounts in spring, summer, and fall than the remaining WD classes. Meanwhile, the NW led in the winter precipitation amount. WD classes had different occurrence frequencies and different percentages of wet days, but no significant differences in wet hours per wet day. The WD classes with a western component (SW and NW) were more frequent ( Figure 4) and also had a higher percentage of the precipitation days ( Figure  5). This was reflected in the average precipitation amount accumulated within each WD seasonally and throughout the year (Figure 7). On average, and regardless of the season, approximately 576 mm of precipitation per year was recorded for the SW and NW classes. This value corresponds to 77% of the annual amount. XX was linked to 14% of the yearly precipitation amount, while the NE and the SE combined were responsible for less than 10%. The SW recorded higher precipitation amounts in spring, summer, and fall than the remaining WD classes. Meanwhile, the NW led in the winter precipitation amount. The WD classes occurred in different frequencies across the seasons, and the complex interactions between the WD classes, seasonality, and location within Germany must be considered when addressing the PDC, especially for the most common WDs, because the amount of precipitation associated with these classes also differed between seasons.

PDC with WD
Regardless of the other variables, the WD classes showed different diurnal precipitation patterns, especially the SW and the NW (Figure 8). The SW circulations were associated with a higher afternoon peak in both frequency and precipitation amount. The exact opposite was observed for the NW circulations, where higher frequencies and larger precipitation amounts were observed in the morning. The SW days generally ended up with higher precipitation frequencies and amounts than the start of the day. Contrariwise, the NW had a generally lower precipitation toward the end of the day. XX showed a slightly higher morning peak in the precipitation frequency, but a higher afternoon peak in the precipitation amount. The remaining WDs did not demonstrate large diurnal variations; however, the SE (NE) showed an increase (decrease) in both frequency and amount by the end of the day. The WD classes occurred in different frequencies across the seasons, and the complex interactions between the WD classes, seasonality, and location within Germany must be considered when addressing the PDC, especially for the most common WDs, because the amount of precipitation associated with these classes also differed between seasons.

PDC with WD
Regardless of the other variables, the WD classes showed different diurnal precipitation patterns, especially the SW and the NW (Figure 8). The SW circulations were associated with a higher afternoon peak in both frequency and precipitation amount. The exact opposite was observed for the NW circulations, where higher frequencies and larger precipitation amounts were observed in the morning. The SW days generally ended up with higher precipitation frequencies and amounts than the start of the day. Contrariwise, the NW had a generally lower precipitation toward the end of the day. XX showed a slightly higher morning peak in the precipitation frequency, but a higher afternoon peak in the precipitation amount. The remaining WDs did not demonstrate large diurnal variations; however, the SE (NE) showed an increase (decrease) in both frequency and amount by the end of the day. Some interesting differences in the PDC are associated with the WD across Germany (Figure 9). The frequency peak for the SW at southern stations is delayed until midnight, while the precipitation amount peaks around 19:00. which is considerably later than for the central and northern stations. In contrast, the afternoon peak of frequency for the NW at southern stations is weaker than those for the northern and central stations. The precipitation frequency and amount increase as we move from north to south across Germany in all the WD cases. Some interesting differences in the PDC are associated with the WD across Germany (Figure 9). The frequency peak for the SW at southern stations is delayed until midnight, while the precipitation amount peaks around 19:00. which is considerably later than for the central and northern stations. In contrast, the afternoon peak of frequency for the NW at southern stations is weaker than those for the northern and central stations. The precipitation frequency and amount increase as we move from north to south across Germany in all the WD cases.
A decrease in the hourly precipitation frequency and amount in the SW is observed as we move from west to east, while a slight increase is found in both values for the NE. The remaining WD classes do not show clear differences with latitude and longitude. The general PDC of the SW is observed for the western and central stations. However, the precipitation frequency stabilizes after the afternoon peak only in the case of the eastern stations. The morning peak of in the eastern stations also disappears in the SW cases. Seasons seem to have more influence on the PDC patterns than geographical location. The frequency and the amount of summer precipitation are the largest for the SW (Figure 10), while in A decrease in the hourly precipitation frequency and amount in the SW is observed as we move from west to east, while a slight increase is found in both values for the NE. The remaining WD classes do not show clear differences with latitude and longitude. The general PDC of the SW is observed for the western and central stations. However, the precipitation frequency stabilizes after the afternoon peak only in the case of the eastern stations. The morning peak of P a in the eastern stations also disappears in the SW cases.
Seasons seem to have more influence on the PDC patterns than geographical location. The frequency and the amount of summer precipitation are the largest for the SW (Figure 10), while in winter, the NW records the highest rain frequency and amount. A higher peak for the SW (NW) in the afternoon (morning) prevails in all seasons. The morning peak in the precipitation frequency occurs at the same time for the SW and NW in all seasons, except for winter, where the SW morning peak appears a few hours later. The morning peaks in the precipitation amount differ by season and WD class. It is clear for spring and fall in SW and NW, has a weak magnitude in summer, and disappears in winter. Only in the case of the NW is the precipitation amount high from the early morning until 06:00, then it starts to drop.
XX generally has less precipitation frequency in winter and summer than in spring and fall. In winter, the peaks of XX disappear, and the morning hours have a generally higher frequency of rain than the evening hours. The PDC for XX is strong for the precipitation amount in the summer, weaker in spring and autumn, and almost disappears in winter.
The PDC is also weak for both the SE and NE, where the NE has a higher frequency than the SE, especially in the morning hours of winter, spring, and fall. The SE has only an increase in the precipitation amount that appears in the late afternoons of spring and summer. the afternoon (morning) prevails in all seasons. The morning peak in the precipitation frequency occurs at the same time for the SW and NW in all seasons, except for winter, where the SW morning peak appears a few hours later. The morning peaks in the precipitation amount differ by season and WD class. It is clear for spring and fall in SW and NW, has a weak magnitude in summer, and disappears in winter. Only in the case of the NW is the precipitation amount high from the early morning until 06:00, then it starts to drop. XX generally has less precipitation frequency in winter and summer than in spring and fall. In winter, the peaks of XX disappear, and the morning hours have a generally higher frequency of rain

Discussion
Westerly circulations are frequent over northern Europe because of the jet stream. These circulations are projected to occur more frequently in the future in most climate models [36,37]. They are of particular interest because they represent the dominant path and direction of humidity transport in this area [58]. Our results show that the NW and the SW are the most common WD classes. The NW is more frequent in winter, while the SW is the dominant WD class in summer. This can be explained by the different influences of the polar and subtropical jet streams. In winter, the polar jet stream lies over Scandinavia and Northern Germany and frequently advects cold air from the NW. In summer, the subtropical jet streams lie over the Mediterranean and bring warm air from the SW to Germany. The precipitation frequency and amount across all seasons and stations are generally the largest for the NW and SW. They have a bimodal PDC with a peak in the precipitation occurrence frequency in the morning and another peak in the afternoon. The morning peak is higher (lower) than the afternoon peak in the case of the NW (SW). Apart from the observed peaks, the NW (SW) ends with lower (higher) precipitation frequency and amount than the beginning of the day.
The precipitation frequency in each hour is determined by convective and stratiform precipitation occurrences. The probability of each type must be considered to explain the PDC patterns of the two most important WDs. Short (long) event durations are reported to be more frequent in the afternoon (morning) in China [59] and the UK [60], which implies that convective (advective) precipitation processes are generally intensified in these periods. In Lausanne, Switzerland, convective rain represents only 11% of the total rain duration, but up to 40% of the total rain amount [27]. Accordingly, we assume herein that the stratiform type dominates the precipitation occurrence in all WD classes, despite the fact that we did not classify rain into convective and stratiform. However, summer season, afternoon hours, and their combination produce conditions that support convective precipitation occurrence, especially in the case of the SW flow. Conversely, the reduced solar energy in winter, cold night hours until the morning, and the existence of snow cover suppress the convection process in this season.
Another important aspect that contributes to the PDC of the NW and the SW is the predominant origin of the air masses. When the SW is dominant over Germany, the air parcels move from the areas of higher solar energy input in the south into areas where less solar energy input is available. The opposite happens in the case of the NW. Cold fronts are reported to have a typical direction toward the south and southeast in the US, while warm fronts typically move toward the north and northeast [61]. A similar pattern might apply to Germany. However, this has not been reported so far.
We attribute the morning peak in stratiform precipitation mainly to the radiative cooling of the earth's surface and cloud tops when clouds exist. This initiates and intensifies the condensation process at lower levels in the form of fog and low clouds. This process has been reported and explained in the western Washington state [62], Scotland [63], Japan [64], California [65], and China [66], and is especially intense in windless nights in the south of Poland [3]. The morning peak in Sweden is attributed to the cold temperatures of the surface near the sea [56]. The morning radiative cooling is more efficient in producing precipitation in the case of the NW because of the cold air advection compared to the warm air in the case of the SW. The morning peak is observed, despite filtering precipitation records below 0.2 mm. The threshold aims to remove records of dew/frost, which might amplify the observed morning peak frequency.
The contribution of convection to the early morning precipitation has been addressed in several studies, where the early morning peak was attributed at least partially to factors such as the interaction between the accumulated humidity at low levels over the night hours and the complex topography [67] or proximity to water bodies [68][69][70]. However, the morning peak, which is intensified in winter and in northern circulations, suggests that stratiform rain is the dominant type in this peak. A previous study in Austria [23] pointed out that the morning peak cannot be strictly linked to orography because it is observed in both plain regions and mountain areas. Our results support this finding because the morning peak occurs in all areas across Germany. However, the morning peak is most prominent in the case of the NW. In this case, the air parcels are relatively cold compared to the other WD cases, which means that the radiative cooling effect has higher potential and efficiency in initiating the precipitation. The afternoon peak is mainly caused by the convection mechanism. The warm and moist air coming from the Mediterranean in the case of the SW causes instability and raises the possibility of a convective precipitation in the afternoon. This high peak in the precipitation frequency for the SW appears at all locations and in all seasons and is especially intense in summer. Contrariwise, less convection is expected in the case of the NW because of the cold air advection and the higher stability of the air masses. Additionally, clouds are formed during the night and remain until sunrise by radiative cooling in the case of the NW. They reduce the amount of solar energy that reaches the ground and hinder the afternoon convective process [60], leading to a lower afternoon peak.
The effect of elevation on the PDC is hard to separate from the effect of latitude in Germany because high-elevation stations are concentrated mostly in the Alps, while stations to the north are below 100 m a.s.l. (Figure 1). The southern high-elevation stations receive precipitation with higher frequency and amounts than the lower stations to the north. This applies to all WD classes, except for the NW, where no difference between the northern and southern stations is detected. In the case of the NW flows, a reduction of humidity is supposed when precipitating clouds move from the sea over the whole of Germany.
Lower precipitation frequency and amount were observed in the eastern stations only on the SW days, while the remaining WD classes showed similar observations in the east and west of Germany. The reduced precipitation in the eastern regions in the case of the SW flow can be explained by the fact that precipitation is formed usually over the Alps, and while moving to the northeast, the air is dried out. The foehn effect might also contribute because the area in the southeast of Germany falls within the leeward side of the Alps considering the SW. This is similar to the reported effect of foehn on the area south of the Alps in the case of the northern WDs [38]. The frequency afternoon peak is delayed on the SW days for both eastern and southern stations because precipitation initiates in the afternoon over the central Alps and takes time until midnight on average to peak in the southern and eastern stations. A similar effect is reported for Poland, where the Carpathians delay the precipitation peak to late night and early morning, and the warm fronts witness a delayed afternoon peak [3]. This can be explained by the strength of the frontal system, which makes it intense and resistant to the radiative cooling, pushing the convection process to continue further into the late night and early morning. However, this effect is reported for the NW situations in the south of Poland. In our case, it was observed only in the SW situation. The Alps are reported to have a higher amplitude of the PDC than the regions north and east of the Alps [23]. We were not able to identify the geographical extent to which the Alps influence the amplitude of the PDC. However, at least for the SW situations, the convection cells move toward the regions north and east of the Alps. Consequently, the precipitation frequency increases in the evening hours after the afternoon peak at the southern stations, remains stable at the eastern stations, and decreases at all other locations. This also causes the delay in amount afternoon peak which appears in southern and eastern stations in the case of SW.
Other local factors may play a role in altering the PDC discussed previously. Such factors include urban heat island, land use, availability of nearby water bodies, and availability of condensation nuclei. However, on the scale addressed across the whole of Germany, they should be negligible, and a further analysis is beyond the scope of this paper.

Conclusions
The hourly measurements of precipitation were combined with the general WD in the upper atmospheric levels taken from the synoptic weather pattern over Germany for the period 1995-2017. These records were used to study the diurnal variation of the precipitation frequency and amount in Germany. The combined effects of the WD at the upper levels, seasonality, and geographical location were investigated. Our main conclusions regarding the PDC are as follows: • Precipitation occurs most frequently in winter and least in summer. However, the precipitation amount is the highest in summer and the lowest in winter and spring.
• The more continental eastern part of Germany witnesses lower values of precipitation frequency and amount than the rest of Germany. Southern high-elevation stations receive higher precipitation frequencies and amounts than the others.

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The PDC generally has a bimodal distribution with one morning peak in the precipitation frequency and another afternoon peak. The morning peak in the precipitation amount is small compared to the afternoon peak. The pattern of the PDC shows only small differences with location and elevation.

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The PDC shows clear differences between the two most frequent WDs. The SW days have a high afternoon peak and a lower morning peak. The NW days have a high morning peak and a lower afternoon peak. This applies to both precipitation frequency and amount.

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The SW days end with higher levels of both precipitation frequency and amount than the early morning. The opposite applies for the NW.

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The PDC differences between seasons are dominated by the frequency of each WD per season.
Our findings highlight, for the first time, the importance of weather circulations in controlling the PDC of the precipitation occurrence and amount in Germany. Future research needs to consider the influence of advection and convection preferably over long periods of measurements. The heavy and extreme precipitation occurrence and amount over the hours of the day considering large-scale weather circulations are of special interest for hydrologists and weather forecasters.