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             \author[1]{Kazunari  Ishida}

             \affil[1]{  Hiroshima Institute of Technology}

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\date{\small \em Received: 7 December 2013 Accepted: 5 January 2014 Published: 15 January 2014}

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\begin{abstract}
        


One of the serious fears  for Japanese society  is  contamination of radioactive substances  due to the huge  earthquake and subsequent  Fukushima No. 1 nuclear power  plant disaster. This paper proposes a detection method to identify  diffusion sources of radioactive small particles in the air based on  publicly available data, which are composed of  air dose rate,  amount of  rain, wind speed,  and direction.  Air dose rate is  observed on each public monitoring point. The nearest weather  observation station for each public monitoring point concerning  air dose rate is also identified to analyze the relationship between  air dose rate and weather conditions. This method focuses on all  cases of continuous rainfall duration, because various sizes of  spike concerning air dose rate on a public monitoring point are  observed among the cases. Each spike starts when rainfall begins  and the spike disappears when rainfall continues. This is because  rainfall cleans up radioactive particles in the atmosphere. The  method confirms  a  statistically significant difference of increase  rate of air dose rate between each pair among rainfall cases. It  also identifies an existence range of direction of diffusion sources  based on significance tests of correlation coefficients. 

\end{abstract}


\keywords{radioactive small particles, air dose rate, weather condition, earthquake debris, incineration plant}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
fter the huge earthquake in Japan on  {\ref March 11, 2011}, radioactive substance derived from the Fukushima No. 1 nuclear power plant could affect the world's environment and society. Japanese people were concerned about contaminated food, wood, resources, and goods due to air and water pollution in terms of radioactive substance. According to the nature blog news on December 21, 2012, one of the most interesting articles on social media is an academic article concerning the biological effect of the crippled Fukushima nuclear power plant \hyperref[b0]{[1]}. Worldwide attention on this article means that the crippled nuclear power plant and diffusion of radioactive substance from the plant are a major concern and threat against our environment.\par
The Japanese government has a warning system, called SPEEDI (System for Prediction of Environmental Emergency Dose Information) \hyperref[b1]{[2]}, which is supposed to predict the radiation spread based on information concerning power plant, weather conditions, and geographic area in terms of dose rate. SPEEDI is intended to detect a serious accident at a nuclear power Author: Faculty of Applied Information Science, Hiroshima Institute of Technology, Japan. e-mail: plant; however, it is not intended as a secondary diffusion from contaminated goods, water, and other items. In order to specify a radiation level, the Japanese government provides information collected from monitoring points in Japan \hyperref[b2]{[3]}. This paper analyzes the relationship between radiation level and weather conditions toward development of a detection system to identify sources or origins of spreading radioactive substance. 
\section[{II.}]{II.} 
\section[{Diffusion of Radioactive Substance}]{Diffusion of Radioactive Substance}\par
Many researchers have been trying to clarify the environmental and social effects of radioactive substance. Yasunari et al. \hyperref[b3]{[4]} estimated the amount of radioactive substance on and inside soil in Japan. Koyama drew a contamination map around Shizuoka prefecture due to the Fukushima No. 1 nuclear power plant \hyperref[b4]{[5]}. Hayashi researched the contamination of wood in forests \hyperref[b5]{[6]}. The Forestry Agency of Japan provides questions and answers concerning handling wood products because the products might be contaminated \hyperref[b6]{[7]}.\par
The Ministry of Agriculture of Forestry and Fisheries provides information concerning the limitation of export of Japanese products to other countries, and inspection of agricultural products and fisheries products with respect to cesium 137 contamination \hyperref[b7]{[8]}. The Ministry of Land, Infrastructure, Transport, and Tourism of Japan provides a report on the result of inspection of drainage and sewage sludge with respect to radiation levels \hyperref[b8]{[9]}. The Ministry of Health, Labor, and Welfare provides information concerning inspection results of water supply with respect to cesium 137 contamination \hyperref[b9]{[10]}.\par
According to these reports, agricultural and fisheries products and water supply contain a thousand times contamination of radioactive substance compared to that before the Fukushima nuclear power plant disaster. The clean association of Tokyo 23 waste reports that ashes contain radioactive substance continuously after the disaster. In addition, burning earthquake debris derived from the northeast regions in Japan is another significant concern of spreading radioactive particles because burning earthquake debris could make secondary spreading contamination worldwide, as much as the primary spreading contamination \hyperref[b10]{[11]}  \hyperref[b11]{[12]}. 
\section[{III.}]{III.} 
\section[{Open Data Analysis}]{Open Data Analysis}\par
Diffusion factors of radioactive airborne particles are analyzed with open data concerning air dose rate, rainfall, wind speed, and wind direction. A set of three incineration plants in Kitakyushu city were employed as safe spreading origins of radioactive airborne particles because the Japanese Ministry of Environment approved the burning earthquake debris contaminated by radioactive substance derived from the Fukushima No. 1 power plant accident.\par
A monitoring post (MP) of the Yahata common building for government offices in Kitakyushu city was employed for analysis because it was the closest monitoring post from the incineration plants. Employing an original geo-coding database, which has the same function of Google geo-coding API, the nearest weather observation station for each MP is automatically identified in terms of the name of the stations, which contains prefecture and region names. The weather station information is publicly provided by Japan's meteorological agency. 
\section[{a) Near Consistent Wind with Rainfall}]{a) Near Consistent Wind with Rainfall}\par
In case A, consistent wind with rainfall flows from the plants to the near MP. When wind flows from an exact direction in terms of the set of incineration plants, many radioactive airborne particles are transferred from the diffusion origin. At the same time, rainfall starts, and the particles are starting to drop around MP.\par
Figure \hyperref[fig_0]{1} illustrates trajectories of air dose rate, rainfall, wind speed and consistency. The former three values are rescaled between 0 and 1, based on the minimum and maximum values. The maximum and minimum air dose rates are 0.082 and 0.054 micro sievert per hour. The max and min amount of rainfall are 18 and 0 mm per hour. The max and min wind speeds are 5.7 and 1.7 meter per second. Wind consistency is defined by (cos(d) + 1)/2, where d is the difference between the origin's correct direction and wind direction. The range is between 0 and 1. The unit of xaxis is the time period where the unit is an hour. Table  {\ref I} summarizes the maximum and minimum values of dose rate and the three factors. The correlation coefficients between dose rate and the other factors, which are rainfall, wind speed and consistency, are -0.09178, -0.58939, and 0.865703, respectively.\par
According to correlation coefficients, wind consistency is the most important factor on increasing the dose rate because the coefficient is 0.986 and is close to 1.0. Start of rainfall is another factor for increasing dose rate; however, continuous rainfall leads to decrease of the rate because rainfall cleans all particles in the air. This is the reason for the low or correlation coefficient between dose rate and rainfall, which is -0.09178. Wind speed multiplies the effect of wind consistency on dose rate. In case B, inconsistent wind with rainfall flows from the plants to the near MP. When wind flows different angles from the diffusion origin, the maximum air dose rate, which is 0.065, is not very high compared to the minimum rate 0.0585 (Fig. \hyperref[fig_1]{2}). In this case, the wind consistency is between 0.095492 and 0.383, which is quite low compared to case 1. Table  {\ref II} summarizes the maximum and minimum values of dose rate and the three factors. The correlation coefficients between dose rate and the other factors, which are rainfall, wind speed and consistency, are -0.42046, -0.2712, and 0.13966, respectively. In case C, long-term consistent wind before rainfall flows from the plants to the near MP. When consistent wind blows long term before rainfall, air dose rate reaches high value, which is 0.091333 in this case. A big spike on dose rate is observed at time period 9, when small rainfall starts (Fig. \hyperref[fig_2]{3}). The maximum dose rate is achieved when rainfall reaches the maximum level. Table  {\ref III} summarizes the maximum and minimum values of dose rate and the three factors. The correlation coefficients between dose rate and the other factors, which are rainfall, wind speed and consistency, are -0.12168, -0.17734, and 0.58694, respectively. Based on the observations described in subsection A, B, and C, this paper proposes a method to identify diffusion sources of sparse radioactive small particles based on air dose rate, amount of rainfall, wind direction, and speed. It is difficult to measure radioactive small particles with monitoring points managed by the Ministry of Education and Culture, Sports, Science and Technology of Japan, because they are intended to measure high dose rate due to the serious effect of the severe nuclear power plant accident. However, they are able to detect the small particles when rainfall starts because it brings the particles to the ground from the air. Hence, based on the amount of increase, this method identifies diffusion sources with wind direction and speed.\par
Radioactive small particles contribute increase of air dose rate when rain falls. Hence, this method determines all durations of effective rainfall in terms of continuous rainfall. In the early stage of rainfall, radioactive small particles in the atmosphere have begun to drop on the ground, and they contribute an increase of air dose rates of monitoring points. When rainfall has continued long term, the dose rates are going to return to the normal rates because there are no more small particles in the air. Hence, the effective rainfall duration is defined as duration between the beginning of rainfall and the time period of returning to the normal air dose rate.\par
Eight cases of effective rainfall duration are extracted from one month dataset concerning a monitoring post of Yahata common building for government offices in Kitakyushu city and Yahata weather station. Figure  {\ref 4} illustrates air dose rate, rainfall, and coefficient of wind direction and speed. In order to illustrate the values in a figure, air dose rate and rainfall are rescaled between 0 and 1 based on the minimum and maximum values, respectively. The minimum and maximum values of air dose rate are 0.0578 and 0.091333, respectively. The values of rainfall are 0 and 41, respectively. Coefficient of wind direction and speed ?"¨?"¨?"¨(w) is defined as the following formula: 1 where s is wind speed, ?"¨ is wind direction at a monitoring point, and ? is direction to a diffusion source from the monitoring point.\par
North, east, south, and west winds are 0, 90, 180, and 270 on wind direction (?"¨), respectively. On one hand, when wind is from a diffusion source (?"¨=?), w 0approaches to 1 from 0.5. On the other hand, when wind flow is the opposite direction (?"¨=?+180), w approaches to 0 from 0.5. When wind speed (s) is slow, w approaches to 0.5.\par
According to Fig.  {\ref 4}, when heavy rainfall is observed, high air dose rate per hour is observed, e.g., (c5) in Fig.  {\ref 4}. On the other hand, when light rainfall is observed, low air dose rate per hour is observed, e.g., (c6) in Fig.  {\ref 4}. In order to measure the amount of radioactive small particles in the air without the effect of different amounts of rainfall, the method evaluates increase of air dose rate per rainfall of one millimeter per hour. Hence, the method can compare the amount of radioactive small particles among different cases of effective rainfall duration.\par
Figure  {\ref 5} shows increase of air does rate per unit of rainfall. Table IV and Fig.  {\ref 5} show effective rainfall duration, average, and standard deviation of increase of air dose rate. The increase of air dose rate is defined by the difference between a value of each time period and the minimum value among all eight cases. The cases are numbered in descendant order in terms of average of increase of air dose rate.\par
In order to discuss statistically significant differences of average of increase of air dose rate, three groups (group A of case 1 and 2, group B of case 3, 4, and 5, and group C of case 6, 7, and 8) are separated based on a statistical test of population variance with significance level of 5\%. In each group, there is no significant difference on each pair of two cases based on a statistical test of difference of population mean with significance level of 5\%. However, concerning three pair of cases among the different groups, there are significant differences between case 3 and three cases (case 6, 7, and 8), in terms of Welch's t-test with a significance level of 5\%.  In order to identify the existence range of diffusion source, correlation between unit increases of air does rate and coefficient of wind direction and speed is calculated for ? from 0 to 359 with step one degree. Figure \hyperref[fig_4]{6} illustrates the correlation and ?, which is direction to a diffusion source from the monitoring point. According to a statistical test of popular correlation, the range between 76 and 113 is a significant range, where correlation is equal or greater than 0.8340, where F is greater than 13.7450, and it is the boundary of critical region of significance level of 1\%. For significance level of 5\%, the range between 64 and 137 is significant range, where correlation is equal or greater than 0.7068, where F is greater than 5.9874. The maximum direction is 92 degrees, where the maximum correlation is 0.8881. All coefficients of wind direction and speed are depicted in Fig. \hyperref[fig_4]{6}. The scatter diagram is illustrated in terms of coefficient of wind direction and speed and increase of air dose rate in Fig. \hyperref[fig_5]{7}.     
\section[{Conclusion}]{Conclusion}\par
This paper proposed a statistical method to find diffusion sources of radioactive substances. Diffusion of radioactive substance could be a major concern worldwide. In section II, this paper summarized the contamination derived from the Fukushima No. 1 nuclear power plant in Japan. A set of three incineration plants in Kitakyushu city were employed as safe spreading origins of radioactive airborne particles because the Japanese Ministry of Environment approved the burning earthquake debris contaminated by radioactive substance derived from the Fukushima No. 1 power plant accident. Data concerning air dose rate and weather conditions were analyzed on the nearest MP of the spreading area. The detection method identifies contamination sources of radioactive substances in the air based on open data, which are composed of air dose rate, amount of rain, wind speed, and direction. This method focuses on all cases of continuous rainfall duration because of the various sizes of spike concerning air dose rate on a public monitoring point. Each spike starts when rainfall begins while the spike disappears when rainfall continues because rainfall cleans up radioactive particles in the atmosphere. The method confirms a statistically significant difference of increased rate of air dose rate between each pair among rainfall cases. It also identifies a range of direction from a monitoring point to diffusion sources based on significance tests of correlation coefficients.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{45}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 4 :Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Figure 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{IV} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}Table IV :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{V} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table V :}\end{figure}
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