Statistical Review of Annual Precipitation at Seoul in 1778-2015

1. Introduction
Rainfall data is useful for evaluating the results of climate variation and for applying socio-economic impacts on natural disasters. Bluestine pointed out Korean rain gauge (Chukwookee) was the first measurement of rainfall event in the 15th Century. According to Annals of the Joseon-Dynasty (listed under the UNESCO’s Memory of the World in 1997; Joseon Wangjo Sillok), King Se-Jong invented the rain gauge in May and commanded daily measurements through organized observation networks in September of 1441. Unfortunately, rain measurement recordings temporally quitted upon the invasion of Japan in 1592, and restarted in 1770. These rainfall records were in The Daily Records of Royal Secretariat (DRRS, Seungjeongwon Ilgi) of Joseon Dynasty in 1770-1894 (designated as UNESCO World Documentary Heritage in 2001) and Records of Daily Reflections (RDR, Ilseongnok) of Joseon Dynasty in 1785-1910 (designated as UNESCO World Documentary Heritage in 2011). Thus, precipitation recording data using Korean rain gauge remains only between 1770 and 1907.
The earliest Korean rain gauge measurement data was constructed by Wada (1917) and analyzed by Arakawa (1956). There are three versions of Korean rain gauge dataset in Korea after the year of 1945: Hahn (Hahn, 1970), Juhn (Jhun and Moon, 1997), and KAMC (a research product from the Korean Academy of Meteorology and Climate, 2010). A brief explanation of data will follow in section 2. The aim of this paper is (1) to compare two datasets: Hahn and Jhun, (2) to check the normality dataset  1778-1907, and (3) to analyze data using time series analysis in 1778-2015.

2. Data
This study is to compare two dataset: Hahn and Jhun. As mentioned earlier, there are three versions of dataset. First, Hahn’s version derives from DRRS and RDR. He edited monthly precipitation amount by using interpolation of 1770-1907 for the purpose of treating missing data. Second, Jhun’s version is based on the previous data but differently interpreted in terms of units. He edited monthly precipitation amounts excluding winter seasons of 1777-1907. Additionally, the KAMC version includes daily precipitation data edited by the Local Government Report (LGR) of Joseon Dynasty in 1892-1907.
  In this paper, to compare between two dataset (Hahn and Juhn), annual precipitation measurement except for winter seasons (December-February) is employed through statistical analysis of 1778-2015.

3. Statistical Procedure
(Step-1) To assure the quality of climate data, regarding WMO regulations (WMO, 2011), statistical value is calculated only when values are at least 80% of recorded.
(Step-2) To check the similarity between two samples, T-test is used. First is to investigate similar distribution of data between Hahn and Jhun in 1778-1907. Second is to compare between Period-1 (1778-1907) and Period-2 (1908-2015)
(Step-3) To test the normality of each data-set, two methods of study are applied: Shapio-Wilk normality test for quantitative and frequency analysis (e.g., histogram, boxplot) for qualitative. This is to compare characteristics of data with outliers and without outliers.
(Step-4) To analyze integrated period (1778-2015) dataset, power spectrum analysis is employed. This is to investigate the cycle of occurrence concerning heavy rain or severe drought of Seoul.

4. Analysis and Discussion
Dataset of winter season (D-J-F, 64.1%) is less than 80% of the years recorded. In winter, the data of Period-1 would be inaccurate due to the difficulty of converting the measurements of snow and ice into liquid water. Data from Period-2 does not include 15 months of meteorological data because of the Korean War. The missing periods are the following: November 1950 - November 1951, May and August of 1952.
To find the similarity of two datasets, T-test is employed between Hanh and Jhun. Samplings of spring and fall seasons show significantly small p-value (0.0058 and 0.0075, respectively). Therefore, the two datasets cannot accept similar distribution. However, summer seasons show large p-value (0.3568). Statistically, the two samples are similar in their distribution. Additionally, with employment of T-test, Period-1 and Period-2 dataset are similar in distribution: 1.4682 in t-statistic, and 0.1434 in p-value.
Due to the sophisticated frequency distribution of precipitation, 1778-2015 dataset can be divided into normal and erratic state. According to the definition of drawing boxplot, outlier is more than ‘third quartile (Q3) + 1.5  interquartile (Q3-Q1)’ and less than ‘first quartile (Q1) - 1.5  (Q3-Q1)’. In this study, erratic case is assumed as outliers. A few small erratic cases are contaminating the large number of dataset of normal distribution. For instance, outliers are generated from heavy rain events associated with tropical cyclones and mid-latitude cyclones activities after 1908. Moreover, although there are no authorized meteorological records before 1907, there exist the many records of death and property disasters in Annals of the Joseon-Dynasty.
In spite of the similar of the two periods, a bunch of cycles are not exactly identical. As seen in Fig. 1, Period-1 displays 3-, 9-, 22-, 36-, 47-year cycles; Period-2 has 4-, 16-, 42-, 66-year cycles; and integrated period has 3-, 17-, 21-, 43-year cycles in rainfall events. These differences are due to the lack of homogeneity - movement of site location, change of operational measurements, climate variation associated with urbanization. In future studies researchers should consider these differences and tune them in order to predict the cycle of occurrence with accuracy.

Acknowledgements
This study has been supported under the Research and Development for KMA Weather, Climate, and Earth System Services of Korea Meteorological Administration in 2016.

REFERENCES
Korean Academy of Meteorology and Climate, 2010: A comprehensive planning study for the restoration of meteorology and climate in the Joseon Dynasty based on historical records (in Korean). RACS 2010-5002, 544pp.
Jhun J. G., and Moon, B. K., 1997: Restorations and analyses of rainfall amount observed by Chukwookee (in Korean). J. Korea Meteor. Soc. 33, 4, 691-707.
Hahn S, 1970: On the precipitation records in Seoul for 200 years long. Annual Review Korean National Committee IUGG 1970, 9-21.
WMO, 2011: Guide to Climatological Practices. WMO-NO 100.