The Akita prefecture with a total area of 11636.32 km² (http://uub.jp/47/akita) locates in the northeast of Honshu which is the main island of Japan as shown in Figure 1. Its coordinates of the latitude and longitude are between 38˚52'23''N and 40˚30'40''N, and 139˚41'32''E and 140˚59'43''E (http://www.gsi.go.jp/KOKUJYOHO/CENTER/kendata/akita_heso.htm). The region has a coast with the Sea of Japan in the west and is bordered by four other prefectures: Aomori in the north, Iwate in the east, Miyagi in the southeast and Yamagata in the south (http://www.pref.akita.jp/koho/foreign/en/0010.html).

Akita prefecture is the typical climate of the Sea of Japan, winter is long and summer is short. Its four seasons are distinct. Winter is very cold with short frost-free period, and summer is hot with less sunshine and abundant rainfall, the annual rainfall is about 1800 mm (http://www.data.jma.go.jp/gmd/risk/obsdl/index.php). The warm and cold Tsushima currents result in significant amounts of snowfall in Akita prefecture during the winter, with annual snowfall around 377 cm. The general average thickness of the snow is 48 cm. And the maximum and minimum temperature during the snowy season are −4.82˚C and −11.26˚C, respectively. The terrain of Akita prefecture is high in east and low in west. There are the Ou Mountains in the east boundary, and the Dewa Mountains with basins in the central, and coastal plains in the western. Due to the Dewa Mountains run parallel cross the central region of the prefecture, the whole region has been divided into two big areas, their climates are different. There are often a lot of snow cover in inland and few snow cover in coastal area (http://www.jma-net.go.jp/akita/4season/4season.htm).

Due to sparsely populated and almost no industrial in the Akita prefecture, rice planting in agricultural production is very developed and ranked third in Japan. In addition, more than 70% is covered by forests in the whole prefecture. The majority forests are coniferous and deciduous, and account for around 54.71% and 41.48% of the forested area in the whole prefecture, respectively [13] .

Akita prefecture is selected as the study area in this work for the following three reasons:

First, Akita is the typical climate of the Sea of Japan, with abundant snowfall in winter. Because of the influence of the sea wind, coastal areas have relatively few snow cover on the ground and there are plenty of snow cover on the ground in inland area, which can help to clearly judge the SCD method is effective or not.

Second, Akita prefecture is a village with large area and high density of forests. Tree species are relatively simple, mainly are coniferous and deciduous forests. Hence, whether the SCD method can detect the snow pixels hidden by forest or not can be clearly evaluated.

Third, due to there are many mountains and large terrain variations in Akita, we can clearly evaluate whether the SCD method can detect the snow pixels in the large terrain variation regions or not.

The Moderate Resolution Imaging Spectroradiometer (MODIS) is a key instrument aboard the Terra satellite, which was launched on December 18, 1999. It collects data from 36 spectral bands at three spatial resolutions (250 m, 500 m and 1000 m), and the wavelength for viewing the entire earth’s surface ranges from 0.4 µm to 14.4 µm. Terra as a sun synchronous polar orbiting satellite, its orbit around the earth is timed so that it passes across the equator from north to south in the morning, and can provide global coverage data every 1 to 2 days.

MODIS has 44 standard data products. They can enable us to improve our understanding of global dynamics and processes occurring in the earth, oceans, and atmosphere, playing a major role in the development of predictive models of global climate change, the status of the melting ice and snow and agricultural production. MODIS products are organized into different processing levels. Level 0 product is raw digital number images. Level 1 product includes uncalibrated and calibrated radiance values. Level 2, 3 and 4 products have more processing and are derived from lower level products [14] .

MODIS data are selected in this study because of its high spatial, time and spectral resolution. It can not only monitor the sudden changing natural disasters in real-time, but also improve the observation ability for the earth complex systems and the identification ability for the earth’s surface. In addition, the satellite images covering the entire Akita prefecture can be obtained almost every day.

Digital Elevation Model (DEM) is a digital geographic dataset of elevations in xyz coordinates. It is typically used in extracting terrain parameters for geomorphology, creating relief maps, analyzing terrain in geomorphological, and in terrain correction [15] .

In this work, American National Aeronautics and Space Administration (NASA) Shuttle Radar Topographic Mission (SRTM) DEM data with 90 m resolution are used to conduct the topographic correction across the study area. SRTM 90 m DEM is available for over 80% of the entire globe, including Japan, and its vertical error is reported to be less than 16 m. So far, the SRTM 90 m DEM data have 4 versions (http://srtm.csi.cgiar.org), and in this study, the latest version 4 is selected as the highest quality SRTM dataset. Currently, DEM data are distributed by the United States Geological Survey (USGS) free of charge and can be obtained from the National Map Seamless Data Distribution System website (http://srtm.csi.cgiar.org).

Automated Meteorological Data Acquisition System (AMeDAS) is a high-resolution surface observation network developed by the Japan Meteorological Agency (JMA). It is used for gathering regional weather data and verifying forecast performance. The AMeDAS snow depth data operated on November 1, 1974, and currently comprises 1300 stations throughout Japan. It is an automated measuring dataset, comprising a supersonic gauge measurement for snow depth. Hourly observation data (cm) of snow depth over 24 hour periods can be recorded (http://www.jma.go.jp/jma/kishou/know/amedas/kaisetsu.html). Akita Local Meteorological Observatory also operated AMeDAS data in 1974, and to date has deployed 13 observation stations across the entire prefecture (http://www.jma-net.go.jp/akita/yoho.htm).

In this work, AMeDAS snow depth data from the 6 observation stations which can observe snow and provide the snow depth record data are obtained from the JMA website (http://www.data.jma.go.jp/obd/stats/etrn/index.php). They are selected for conducting practical objective judgment and comparing with the SCD results from the proposed method.

Road Snow Information System (RSIS) is also an automated measured observation network developed by the Akita Construction Department Road Division used for gathering snow depth and snowfall data on the road surface and outside of the road across the entire Akita prefecture. In this system, snowfall sensor, frozen road detection sensor and workstation are combined online, and then snowfall and freezing information are collected in real-time. It is intended to give information for timely snow removal, anti-freezing agent spraying, and optimization and faster on the road surface management in winter. RSIS was operated in 1996, and currently comprises 31 observation stations throughout the whole Akita prefecture

(http://www.pref.akita.lg.jp/www/genre/0000000000000/1000000001048/index.html). It can record hourly observation data (cm) of snow depth over 24 hour periods.

In this work, in order to evaluate the effectivity of the proposed method for the SCD results, RSIS snow depth data from the 25 observation stations which can provide the long time and continuous observation record data obtained from the Akita Construction Department Road Division are selected.

The snow depth records of 31 observation stations have been selected, which are Furutoobe, Hakka, Nakataki, Towadaminami, Toroko, Yonaizawa, Tokko, Noshiro (RSIS), Hachimori, Showa, Takahi, Funagawa, Tateai, Kmagadai, Jinego, Omagari, Kariwano, Ota, Nangai, Tozawa, Yokote (RSIS), Jumonji, Akinomiya, Yuzawa (RSIS), Minase, Kazuno, Akita, Takanosu, Kakunodate, Yokote (AMeDAS) and Yuzawa (AMeDAS). Figure 2(a) shows the spatial geographic distributions of these 31 snow depth observation stations in the Akita prefecture. Figure 2(b) lists the detailed information of 31 snow depth observation stations, including the station ID numbers, data type, station name, station name abbreviation, latitude, longitude and start observation years.

In order to remove internal and external distortions and precisely identify the location of each pixel on the earth, the MODIS Swath Reprojection Tool (MRT Swath) is applied for geographic correction of image. The MRT Swath is developed by the Land Processes Distributed Active Archive Center (LP DAAC) for MODIS Level 1B products and Level 2 land product data, and can be obtained from the website of LP DAAC in USGS

(https://lpdaac.usgs.gov/tools/MODIS_reprojection_tool_swath). In this step, MOD03-Geolocation data are also used due to all projections requiring the corresponding additional inputs. During this process, format type of

output file is GeoTIFF, the resampling type is nearest neighbor, the projection type is geographic, and the output pixel size is 0.0045 degrees at 500 m spatial resolution [16] .

To remove those areas that do not belong to the study area and decrease the amount of calculations, the administrative regional boundary ShapeFile data of Akita prefecture are used to clip the acquired image after accomplished geographic correction. The clipped image is directly used for atmospheric correction in the next step.

The study area image with precise latitude and longitude is obtained after the above processing. However, this image still continues the properties of MODIS Level 1B product data. That is, the MODIS Level 1B product has been calibrated, but its reflectance only represents the apparent reflectance at the top of atmosphere, and not the real ground surface reflectance. In order to return real ground surface reflectance of the target area and eliminate the atmosphere scattering and absorbance impacts from water vapor, carbon dioxide, ash and smoke dust in the atmosphere which are the primary factors for generating error in the SCD, the geographically corrected and study area clipped image should be atmospheric corrected.

The Second Simulation of a Satellite Signal in the Solar Spectrum (6S) code model is applied for atmospheric correction in this study. It is a basic Radiative Transfer (RT) code used for the calculation of Look Up Tables (LUTs) in the MODIS atmospheric correction algorithm. It can accurately simulate and calculate the parameters of the study target, background, topography, weather, spectrum and sensor conditions, thus can obtain the relationship between the apparent reflectance from atmosphere and the real surface reflectance from ground [17] , [18] .

This atmospheric correction can be calculated online, and obtained from the website of the MODIS Land Surface Reflectance Science Computing Facility, 6S Vector Code (http://6s.ltdri.org).

Table 1 lists the detailed parameters of the 6S code atmospheric correction with MODIS images from the Terra satellite acquired on April 2, 2014, 10:00 AM (‎Japan Standard Time (JST)).

After the all above processing, the equations of real ground surface reflectance and the apparent reflectance from the top of the atmosphere can be obtained with three atmospheric correction coefficients x_a, x_b, and x_c as shown in Equations (1) and (2).

where the measured radiance is the apparent reflectance from the top of the atmosphere and acr is the real ground surface reflectance.

The study area Akita prefecture is a mountainous region with rugged terrain. Reflected brightness changes caused by irregular topography can lead to the inconsistency phenomenon of the reflectance from similar or identical ground surface features, which results in the accuracy reduction in process of the SCD. In order to reduce the impact of the inconsistency phenomenon and improve the accuracy of the SCD, topographic correction is conducted for the atmospheric corrected image in the study region.

Before the topographic correction, the SRTM 90 m DEM data are conducted to be resampled by the geographic projection and cut with the administrative regional boundary ShapeFile data of Akita prefecture at 500 m resolution. Then, image registration in pixel level is conducted for matching the study area image. Finished the all above steps, the obtained SRTM 90 m DEM data are applied for topographic correction.

In this work, topographic correction method developed by Dubayah [19] and a shadowing function algorithm developed by Hapke [20] are adopted for the study region [21] .

The MODIS imagery of the real ground surface reflectance in the study region can be obtained after completion of the above pre-processing operations.

In order to analyze the spectrum distribution of the ground surface substances in bands 1 and 3 within the study area, the spectrums of the ground surface substances in accordance with clear day conditions of Akita prefecture are searched and produced from the relevant spectral libraries. Figure 4 shows the ideal standard reflectance spectrums of the various representative ground surface substances in Akita prefecture, such as snow, soil, deciduous, conifer, grass and water.

From Figure 4, it can be seen that the reflectance spectrums of different substances can be clearly distinguished in the visible red band 1, blue band 3 and green band 4 (0.545 - 0.565 µm). In these three bands, the reflectance of snow is the highest, followed in order by soil and other vegetation (deciduous, conifer and grass). Vegetation has much lower reflectance because of the strong chlorophyll absorption among these three wavelengths. The reflectance of water is only 5%, which is the smallest in all of the substances. Due to green vegetation shows a small reflectance peak in band 4, there may be some difficulties during the identification of mixed snow and green vegetation pixels. Therefore, the visible bands 1 and 3 are selected to detect and distinguish snow pixels from other ground surface substances in this work.

In order to investigate the snow cover distribution at different periods in the study area, we selected 5 types of typical snow cover distribution situations images from May 2012 to April 2014 on clear days as the training images and are shown in Figure 5.

Figure 5 shows the true color images composited by MODIS images of the Terra satellite at 500 m spatial resolution in different periods. The winter of Akita prefecture is from the late December to early February, so the whole study area is almost covered by snow as shown in Figure 5(a). The white area represents snow cover, its brightness increased with the snow cover becoming thicker. The deep green area represents the bared vegetation, because the snow cover on the branches are blown down by the strong sea wind, which lead to some of the forest is exposed. On the other hand, there is no snow cover over the Tazawa Lake and shows black colors because it keeps ice-free all the year round.

From Figure 5(b), it can be seen that some of snow cover began to melt in March, but there are still snow cover in most of the study area. In fact, all of snow cover distributed in the mountain and basin areas of inland but not in the coastal area. It is because that the snow cover in coastal area was blown to the inland by strong sea wind. Therefore, the bared soil in the coastal area shows the dark brown. In addition, there is also no snow cover on the Hachirougata Choseichi in the southeast of Oga Peninsula.

In May, the weather of the whole study area warms into spring, most of snow cover has been melted, and there is only snow cover on the top of mountains in inland as shown in Figure 5(c). The dark brown area is the bared land with the buds of green vegetation like grass, and the dark green area is the forest. Meantime, the Tazawa Lake on the satellite images begins to show the blue color due to the strong light of sun.

With the study area entering into the late June, almost all of snow cover has been melted due to the continuous high temperature of summer. There is only still a little snow cover on the peak of Mt. Chokaizan which locates in the southwest corner of the Akita prefecture as shown in Figure 5(d). It is because that the altitude of Mt. Chokaizan is 2236 m and the temperature on the top of the mountain is much lower. Other places across the whole study area have a large area of the vegetation and the bared land has become the agricultural land. They show the bright green color from the satellite images.

In October, the study area enters into the alternate season of summer and autumn. Due to the continuous high temperature of summer in July, August and September, there is not any snow cover even on the Mt. Chokaizan as shown in Figure 5(e). At this time, the forest is still lush and shows dark green. And due to the harvest of the crops, the agricultural land turns into bared land again. But the brightness on the satellite images is higher than before because only weeds are left.

Based on the above analysis, we conclude that when the reflectance value of one pixel is greater than the soil, this pixel will be judged as the snow pixel. From Figures 6(a)-(e), the largest reflectance values of soil pixels in visible bands 1 and 3 are 0.458 and 0.60, respectively. Therefore, in this work, the threshold values are determined as greater than 0.458 in band 1 and greater than 0.60 in band 3.

A 2-dimensional scatter plot density distribution can further illustrate the pixel distributions of various substances in the study area. Figure 6 shows the 2-dimensional scatter plot density distributions of the above 5 types of training images in visible red band 1 and blue band 3. Figures 6(a)-(e) are the 2-dimensional scatter plot density distributions across the whole study area which represent that there are all snow cover and not melted situation, at 10:20:00 AM on the December 29, 2012, there are mostly snow cover and less melted situation, at 10:35:00 AM on the March 7, 2014, there are less snow cover and mostly melted situation, at 10:50:00 AM on the May 9, 2013, there are only snow cover on the top of the Mt. Chokaizan, at 10:25:00 AM on the June

27, 2012, and there are no snow cover situation, at 10:30:00 AM on the October 8, 2012, respectively. The density distribution location of each substance in the 2-dimensional scatter plot is marked in these 5 types of different figures.

From Figure 6, it is obvious that snow pixels decreased from (a) to (d) until it disappeared in (e). The reflectance values of images from (a) to (e) also decreased along with the snow pixels decreasing in the MODIS visi- ble red band 1 and blue band 3. Combining with the composited true color images in Figure 5, from Figure 6(a), it can be seen that there are only 3 types substances which are snow, vegetation (conifer and deciduous forest) and water. Due to all of the study area are almost covered by snow in winter, the pixels are mainly snow and the distributions of the pixels mainly locate at the top right part of the whole 2-dimensional scatter plot density distribution figure. With the weather warming, the snow began to melt and some of bared lands in the coastal region gradually appeared. The whole 2-dimensional scatter plot density distribution figure shows some soil pixels which located in the lower part of the snow and vegetation mixed pixels in the visible blue band 3 from Figure 6(b) and Figure 6(c). In Figure 6(d), due to there is only still a little snow cover on the peak of Mt. Chokaizan, the snow pixels still exist at the top right part of the whole 2-dimensional scatter plot density distribution figure. And due to the bared land has become the agricultural land, the soil pixels in the 2-dimensional scatter plot also disappeared and became into the vegetation pixels again. In Figure 6(e), there is not any snow cover across the whole study area, all of substances pixels become relative clearness. There are only three kinds of substances pixels which are soil, vegetation and water pixels. In addition, the reflectance of soil pixels became the biggest in the absence of snow pixels.