overesti-Distribution of the Annual Precipitation Ratio of Radar/Raingauge-Analyzed Precipitation to AMeDAS across Japan

Radar/Raingauge-Analyzed Precipitation (RA) represents 1 km-grid precipitation after 2006 created by combining radar precipitation and ground precipitation, i.e., Automated Meteorologi- cal Data Acquisition System (AMeDAS) of Japan Meteorological Agency along with ground data observed by other organizations. Although RA is slightly greater than ground precipitation, no earlier studies investigated the spatial distribution of this accuracy across Japan using 1 km grid data, as clarified in this study. We se lected hourly data of RA and AMeDAS located closest each other, for which miss rates were less than 10% in 2006−2010. We then investigated the distribution of the annual precipitation ratio (RA/ AMeDAS). The ratio diverged in the smaller annual precipitation, but converged to ca. 1.2 for larger annual precipitation. By setting the observational area of 46 radars across Japan using Thiessen method, we investigated the relation between the annual precip- itation ratio and the distance from the radar to AMeDAS station. We found only negative relation was statistically significant. As a possible reason for this relation, we considered that RA far from the radar is affected by the attenuating and shadowing effect of heavy rainfall near the radar.


Introduction
Radar/Raingauge-Analyzed Precipitation (RA) is the areal precipitation created by combining radar precipitation and ground precipitation. The radar can grasp the precipitation distribution, however, the observation is not always quantitatively accurate because it is remote sensing. A regional weather observation system in Japan, i.e., Automated Meteorological Data Acquisition System (AMeDAS) operated by Japan Meteorological Agency (JMA) can measure precipitation accurately, however, we can get only precipitation at about 1,300 stations (JMA 2017). A salient characteristic of RA is that we can obtain precipitation at a point where no rain gauge exists.
Until 2005, 20 radars of JMA had been used for producing RA, which measured the precipitation at the altitude of ca. 2,000 m (Shimpo 2001a). The frequency used was around 5,300−5,370 MHz. Since 2006, 26 C-band radars (frequency around 5,300− 5,400 MHz) of Ministry of Land and Infrastructure, Transport and Tourism (MLIT), Japan have been sequentially used for producing RA (Miyagi et al. 2013, Fig. 1). As for ground precipitation, only AMeDAS had been used until 2005, however, ground data observed by organizations other than JMA, distributed through online system, have been available since 2006 (Nagata and Tsujimura 2006). According to Kajihara (2007), the number of ground data available for processing RA is more than 9,300 as of October 2007. Thanks to these improvements and finer spatial resolution of radar data, we can use 1 km-grid RA since 2006 (Nagata and Tsujimura 2006). Shimpo (2001a) pointed out that RA is quantitatively affected by the distance from the radar. Regarding areas close to the radar, radar observations are rarely obstructed, so that large weight is assigned to the observed radar precipitation. Miyagi et al. (2013) mentioned that at the final phase of processing RA, the values of radar observation and ground observation are compared where ground station is located. When the radar observation is smaller than the ground observation, the value of the former is replaced by the latter, and it is fixed as the final value of RA at that grid point. When the radar observation is larger than the ground observation, the value of the former is adopted as the final value of RA at that grid point. Reflecting this feature, RA shows slightly larger values than ground observations. Earlier studies (Yamamoto 1991;Shimpo 2001b;Urita et al. 2011) have demonstrated that the overestimation is about 20%. Urita et al. (2011) spatially averaged RA and AMeDAS precipitation across Japan, respectively, from 1991 to 2009, and clarified that year-to-year variation showed good correspondence with the systematic overestimation of RA. However, they did not discuss the spatial distribution. Yamamoto (1991) compared the distribution of RA and AMeDAS precipitation. He prepared a nationwide distribution map of the monthly precipitation ratio of RA to AMeDAS (hereafter referred to as precipitation ratio) in September 1990 using 5 km-grid RA, however, he did not mention its geographical characteristics.
One reason we think it necessary to discuss the spatial distribution of the precipitation ratio is related to the results of Matsuyama and Izumi (2002). They analyzed 5 km-grid RA and AMeDAS precipitation in central Kyushu (southwestern Japan) from January 1996 to December 1998. They found that the monthly precipitation ratio was about 167% on average. The overesti- ig. 1. AMeDAS stations (colored dots) nearest to one of the 46 radars (squares with numbers) determined by Thiessen method (Thiessem 1911). Numbers respectively correspond to those of Table 1. Red numbers indicate that the annual precipitation ratio (RA/AMeDAS) is significantly correlated with the distance from the radar to AMeDAS station located in its observational area. tically distributed. According to Wijngaard et al. (2003), the significance level is set at 1%, and the time series is "useful" if one or zero tests reject the null hypothesis. It is considered "doubtful" if two tests reject it. A time series is considered "suspect" if three or four tests reject the null hypothesis. Wijngaard et al. (2003) suggested that we should not use "suspect" data for the analyses.
When we applied the homogeneity test to RA from 2006 to 2010 at 801 grid points (Fig. 1), we found no "suspect" data. "Doubtful" data were sparsely distributed in the northern part of Japan, however, the number was only 12 (Figure not shown).
Other 789 data were decided as "useful". Based on this preliminary evaluation, we used RA from 2006 to 2010 at 801 grid points in the following analyses.
We calculated the annual average precipitation from 2006 to 2010 (hereafter referred to as annual precipitation), then we produced respective maps of annual precipitation of both RA and AMeDAS. As for the annual precipitation ratio, we respectively calculated it from 2006 to 2010, then averaged the five values. We also made a histogram of the annual precipitation ratio and investigated the relation between the ratio and the annual precipitation itself.

Determination of the observational (representative) area of 46 radars
In Section 3, we discussed the relation between the annual precipitation ratio and the distance from the radar to AMeDAS station. For this purpose, we determined the observational (representative) area of each radar by Thiessen method (Thiessen 1911). This method divides a certain area by combining perpendicular bisectors using the locations of the radars obtained from JMA (2018) and MLIT (2018). We could not find the official data concerning the coverage of each radar. Actually, the coverage will change according to the weather condition at the boundary of multiple radars. However, we think that Fig. 1 is not far from the actual observational area of each radar.
After determining observational area of each radar, we adopted Mann-Kendall rank statistic (Kendall 1938), a robust method, to confirm the relation between the annual precipitation ratio and the distance from the radar to AMeDAS station.

General characteristics, and comparison with previous studies
Figures 2a and 2b respectively show the annual precipitation of RA and AMeDAS. Both maps show that precipitation is large in the Pacific side of western Japan and Hokuriku regions (around radars 17−20 in Fig. 1), which is consistent with the general characteristics of its distribution (e.g., Nishina 2014). RA precipitation is slightly greater than that shown by AMeDAS, however, their respective distribution characteristics are roughly consistent. Figure 2c displays the annual precipitation ratio. It is distributed between 1.2 and 1.4 at almost all stations across Japan (see Fig. 3). From Fig. 2c, we perceive that the Pacific side of western Japan shows relatively smaller ratio, whereas northern Japan and other areas show relatively larger ratios. The ratio is considered to be related to the annual precipitation itself, however, this is a subjective judgement. The characteristic will be further discussed below.
Using the data presented in Fig. 2, we produced a scatter diagram between the annual precipitation of AMeDAS and the annual precipitation ratio (Fig. 3a). The ratios converge to ca. 1.2 where the annual precipitation increases to 5,000 mm/y, although they diverge where the annual precipitation is smaller. The histogram of the annual precipitation ratio is displayed in Fig. 3b. Most of the ratio is distributed between 1.2 and 1.4, which shows almost identical characteristics of the previous studies (Yamamoto 1991;Shimpo 2001b;Urita et al. 2011).
Even a smaller change of the denominator affects the ratio because the precipitation ratio is a fraction. This is expected to be the reason for the greater divergence found in the smaller precipitation in Fig. 3a. For example, Matsuyama and Izumi (2002) depicted mation of 67% was greater than previously reported (about 20%, Yamamoto 1991;Shimpo 2001b). Therefore, it is possible that the precipitation ratio of Matsuyama and Izumi (2002) is regional, and that there is much room for discussing the nationwide distribution of the precipitation ratio.
In this study, we clarified the spatial distribution of the annual precipitation ratio over a long period across Japan, and investigated the relation between the distance from the radar and the annual precipitation ratio. Note that the analysis is limited to the grid points where AMeDAS stations are located, and overall evaluation of the characteristics of RA is beyond the scope of this study. Still, such analysis and discussion are effective to increase the reliability of RA itself. Additionally, these analysis and discussion will contribute to applied studies such as those of the water balance in the basin using RA (Matsuyama and Izumi 2012), and the validation of reproduced precipitation by meso-scale models using RA (e.g., Kato and Aranami 2005).

Data
The precipitation data used in this study were RA and AMeDAS after January 2006, which extended the period of the data used in Urita et al. (2011). Since June 2003, RA is available at every 30 minute, but we used the data every hour on the hour. Total grid points of 1 km-grid RA on land are 382,428.
We used AMeDAS station data with hourly temporal resolution. The total station numbers of AMeDAS differ from year to year. In 2006 they were 1,376, but 1,296 in 2013. According to JMA (2014), data processing system of JMA has changed after March 2008, and observed data at meteorological observatories and AMeDAS stations are processed in a lump with the unit of precipitation changed to 0.5 mm/h. Also, wireless automatic rain gauges (wireless robot rain gauges) were abandoned until 2010. All these affect the difference of the station numbers of AMeDAS between 2006 and 2013.

Study period and selected grid points
First, we selected the grid points of RA that are nearest the AMeDAS stations. We then used these data to calculate the monthly precipitation for each month after January 2006, along with counting the misses recorded in the month. In March 2011, the Great East Japan Earthquake occurred bringing about many misses in AMeDAS data, especially around the eastern part of Tohoku district (northern Japan). For that reason, we set the study period of January 2006 through December 2010.
According to JMA (1990), when we estimate monthly precipitation from daily precipitation, we can ignore the misses only if the estimated precipitation of the missing days is less than 10% of the total monthly precipitation including the estimated precipitation of the missing days. In this study, we calculated the monthly precipitation from hourly precipitation. The criteria for this case are not described in JMA (1990), therefore, we followed the criteria presented above. When both RA and AMeDAS data were available simultaneously, and when the available data pairs were more than 90% of the total data in a month, we adopted them for analysis. Finally, the total number of grid points of RA and AMeDAS stations was 801 (Fig. 1).

Homogeneity test
According to Miyagi et al. (2013), major changes were introduced to the processing system of RA such as the usages of 26 MLIT C-band radars and 5-minute rainfall intensity of the radars since 2006. Because these major changes are considered to affect the quality of RA, we performed the homogeneity test of Wijngaard et al. (2003) in advance.
It is composed of four tests, i.e., (1) standard normal homogeneity test (Alexandersson 1986), (2) Buishand range test (Buishand 1982), (3) Pettitt test (Pettitt 1979), and (4) Von Neumann ratio test (Von Neumann 1941). The four tests suppose under the null hypothesis that monthly precipitations are independent and iden-monthly precipitation ratio (average of ca. 1.67) in central Kyushu from January 1996 through November 1998. The ratio, however, jumped to ca. 5 in December 1998 because monthly precipitation of AMeDAS in this month is smaller than 50 mm.
The annual precipitation ratio calculated by Fig. 6 of Matsuyama and Izumi (2002) was estimated to be 1.46. In this regard, the results obtained in this study is slightly different, i.e., the ratio in central Kyushu (spatial average of 32.5°N−33.5°N, 130.5°E− 131.5°E) is calculated as 1.26 that is smaller than 1.46 (Fig. 2c). As a reason for this discrepancy, the differences of the spatial resolution and the study period are considered which should be confirmed by further analyses.

Relation between the annual precipitation ratio and the distance from the radar to AMeDAS station
In this section, we investigated the relation between the annual precipitation ratio and the distance from the radar to AMeDAS station. For most radar observational areas, both positive and negative Mann-Kendall rank statistics including zero are found ( Table 1). The numbers of positive sign, zero, and negative sign are respectively 18, 3, and 25, most of which are not significant at the 5% level. Among 46 radars, 3 and 6 radars respectively show the significant relations at the 1% and 5% levels. The noteworthy fact is that all these 9 radars show the negative relations (Table 1), i.e., negative relation is, in some cases, not a noise but a significant signal. In some radars, distance from the radar to AMeDAS station is important factor to explain the distribution of the annual precipitation ratio. Figure 4 is an example of the distribution of the annual precipitation ratio at Nagano radar observational area (No.23 in Fig.  1 and Table 1) where the largest negative value of Mann-Kendall rank statistic was observed (Table 1). From this figure, we perceive that the ratio gradually decreases from the radar, however, we also find the anisotropic characteristic that the ratio is slightly larger in the eastern part. As a candidate to determine this distribution, the highest elevation of Nagano radar among 46 radars (1924.4 m, Table 1), rows of mountain ranges shaped in an arc that show the north-south direction around the radar, and large concavo-convex topography around the radar will be considered. Figure 5 displays the relation between the distance from the radar to AMeDAS station and the annual precipitation ratio at Nagano radar observational area. We find the negative correlation between them as speculated from Fig. 4.
The 9 radars showing statistically significant Mann-Kendall rank statistic (Table 1) are likely to be located in the central part of Japan, however, they are distributed throughout Japan (Fig.  1). The inspections on the relations between Mann-Kendall rank statistic and elevation of the radar, number of AMeDAS stations, spatially-averaged AMeDAS precipitation in radar's observational area, and spatially-averaged annual precipitation ratio revealed that none of them were statistically significant.
We did not clarify factors determining the statistical significance of Mann-Kendall rank statistic between the distance from the radar and the annual precipitation ratio, along with their geographical distribution, however, we can show possible candidate for the negative correlation. According to JARS (2001), C-band radars used for radar observations in this study attenuate because of absorption and scattering with the intensification of precipitation. When a radar captures heavy precipitation near the radar, it cannot fully capture other precipitation behind the heavy one, if these events occur simultaneously (Fig. 6b). Nagata and Tsujimura (2006) mentioned that at the final phase of processing RA, the ground precipitation is substituted to the value of corresponding grid point if the ground precipitation is larger than the radar precipitation where ground station is located (see Section 1). Now, we consider the situation of Fig. 6. In Fig.  6a, heavy precipitation from cloud X is quantitatively observed well, however, precipitation from cloud Y is underestimated by the radar due to the attenuation by precipitation from cloud X in Fig. 6b. In this case, the precipitation ratio at station G2 will be underestimated. We think the attenuation of the radar observation by heavy precipitation is one of the possible reasons that the annual precipitation ratio was negatively correlated with the distance from the radar ( Table 1). Note that this hypothesis is limited to the grid point where ground precipitation is available. As an other candidate for the negative correlation, the effect of orographic precipitation is considered as well (Shimpo 2001a), i.e., precipitation is only observed at the ground but it is not observed by the radar because the altitude of precipitating clouds is too low to be captured by the radar.
To clarify these hypotheses, further analyses are necessary, because this study is based on the annual precipitation data alone. Investigations of each precipitation event are necessary. Also, we should investigate factors affecting the precipitation ratio other than the distance from the radar to AMeDAS station. They are the      Table 1. Precise information on 46 radars. Also tabulated are number of AMeDAS stations in the observational area of the radar determined by Thiessen method (Thiessen 1911), arithmetic-mean annual precipitation of AMeDAS, arithmetic-mean annual precipitation ratio (RA/AMeDAS), and Mann-Kendall rank statistic on the relation between the annual precipitation ratio and the distance from the radar to AMeDAS station, along with its p-value. JMA: Japan Meteorological Agency MLIT: Ministry of Land and Infrastructure, Transport and Tourism, Japan *: Significant at the 5% level **: Significant at the 1% level height of radar beam, the anisotropic characteristics of the observation (Fig. 4), the effect of multiple radars that observe same grid points, and so on.

Conclusions
From 2006 to 2010, we investigated the distribution of the annual precipitation ratio of RA to AMeDAS at 801 AMeDAS stations throughout Japan. We confirmed that RA overestimated AMeDAS precipitation in most areas. The annual precipitation ratio diverged in the smaller annual precipitation, but it converged to ca. 1.2 in the larger annual precipitation. We also clarified the relation between the distance from the radar to AMeDAS station and the annual precipitation ratio. Both positive and negative correlations including zero were found, however, statistically significant relation is limited to negative one at 9 radar observational areas, based on Mann-Kendall rank statistic. Yamamoto (1991) reported that the precipitation ratio tends to decrease when the precipitation amount is large. Because this precipitation ratio is expected to change according to seasons, the same analyses of this study on monthly and/or seasonal precipitation are necessary. This is our future work.  6. Schematic diagram explaining why the annual precipitation ratio is negatively correlated to the distance from the radar to AMeDAS station, drawn by referring to Shimpo (2001a). (a) Observation of heavy precipitation (thick dashed lines) from cloud X near the radar (R). G1 is AMeDAS station. Solid arrows are transmissions from the radar, whereas dashed arrows are receptions at the radar. (b) Same as (a) but for heavy precipitation from cloud Y far from the radar (R) behind heavy precipitation from cloud X. G2 is AMeDAS station other than G1. Gray dashed lines represent the attenuation.