## 3 Methods and Data
### L-Band PALSAR for Volume Mapping  
In the first step of the study, a simple relationship analysis was performed between the biophysical parameters collected from field observations by the Chiba Prefectural Government and the L-band backscattering intensity data collected by the Advanced Land Observing Satellite (ALOS) Phased Array L-band Synthetic Aperture Radar (PALSAR) provided by the Japan Aerospace Exploration Agency (JAXA). This step involved extracting the biophysical parameters (volumes) of the forested areas and  
Figure 2: Overall flowchart of the methodology. mapping them for the whole of Japan. The use of SAR for detecting forest parameters works because the radar waves are longer than the optical waves, so the radar beam penetrates through the top layer of canopy and scatters from the stems and branches of the trees when using L-band radar [19, 20, 21, 22, 23]. A number of studies have been conducted to develop models related to those studies' specific regions of interest. Those studies confirm that the backscattering signature correlates with forest parameters and that SAR images can be used to extract information related to forest biomass. While most of the papers present and acknowledge the possibility of extracting forest parameters using the L-band SAR information, some studies show difficulties in data interpretation [24], mostly due to distortions caused by local topography, which is also one of the challenges for this work. To meet this topography challenge for the analysis, Chiba Prefecture was selected due to its relatively flat terrain, which limits this critical and fundamental topography problem when utilizing SAR imagery [25]. The 25 m PALSAR Global Mosaic (PGM) image used in this study was converted from the provided Digital Number (DN) values to the backscattering intensity information, also known as backscattering coefficients, using Equation (1). The PALSAR specification is in ascending Fine Beam Dual (FB) mode characterized by a 34.3 degree of off-nadir angle, calculated as:  
\[\sigma^{0}=10\times\log_{10}(\text{DN}^{2})+\text{CF} \tag{1}\]  
where \(\sigma^{0}\) is the backscattering intensity represented in decibel units (dB) and CF is the calibration factor for the data obtained, depending on the observation period and polarization [26]. The image is already processed for ortho-rectification and slope correction [27], so further analysis uses these data directly without any additional correction. A statistical analysis for formulating relationships among the field observation data of the forest stand characteristics and the remotely sensed microwave satellite data was carried out. The process analyzes the relationships between SAR backscattering intensity (\(\sigma^{0}\)) and the stand characteristics (volume) for the 25 m pixel spacing PALSAR image. The PALSAR image used here is the mean value of the years 2009 and 2010, to minimize local variations from such things as precipitation. Using the vegetation continuous field data [14], the sample plots were selected from an area of less than 70% forest cover to avoid uncertainties associated with scattering, as [PERSON] and [PERSON] [28] explain that attenuation of the radar beam is caused by high dense forested areas, resulting in lower backscattering values compared to the peak areas (70%-75% forest cover), and causing difficulties when interpreting the actual forest trend. Using the result, the model function was applied to the 50 m PALSAR mosaic product (which can be downloaded free from the JAXA web page [29]) to obtain volume information for the forests across Japan. The 50 m PALSAR data were selected because of the spatial coverage and availability (it is freely available and covers the whole of Japan). The equation obtained from the relationship analysis was assumed to be acceptable to apply to the downscaled data, because several papers confirm an increase in accuracy and higher correlations when the pixel spacing is reduced [30,31].