In Korea, typhoons are becoming an essential issue as they cause huge damage and their occurrence frequency has increased since 2001. Many types of research and case studies related to the prediction of typhoon intensity and typhoon track are being conducted, especially with the help of numerical models. However, there is a lack of studies investigating the nonlinear behavior of typhoons, especially by using radar data, see however Lee et al. (2020, DOI: 10.1175/JAMC-D-18-0209.1). We perform such a detailed analysis of datasets of wind fields retrieved from radar in a multifractal framework. More precisely, we analyzed the difference of multifractality on each altitude depending on the different typhoon tracks and show that estimates of the multifractal parameters can be used to characterize the typhoon The radar dataset was collected depending on the category of the track of the typhoon. Track category 1: typhoon moving straight north from Jeju island to the Korean peninsula, and track category 2: typhoon making a curve northeastward as the typhoon passes Jeju island. Typhoon Khanun, Bolaven and Sanba (2012) are selected for track category 1. Tembin (2012) and Chaba (2016) are selected for track category 2. Then, the wind field of each typhoon case was calculated by using the dual-Doppler wind retrieval method and the analysis of each field was separately performed on its positive and negative parts. This large amount of space-time data was analyzed by calculating fractal dimension, the Trace Moments (TM, Schertzer and Lovejoy, 1987) and Double Trace Moment (DTM, Lavallée et al., 1992). The last two enable to quantify the mean fractality of the process with the help of its fractal co-dimension C1 and its multifractality index α, which measures how fast the intermittency evolves for higher singularities. It was possible to estimate the category of the tracks of the typhoon by calculating the fractal dimension of wind velocity components U and V (resp. East-West and South-North) before and after landfalling on Jeju island. Also, it was noted that the location of the typhoon center affects the decreasing trend of fractal dimension of positive V. Also, with the help of TM and DTM analysis, it was possible to verify the movement of the typhoon even with the same category of track moving north. The parameter C1 quantifies the mean sparseness of the field but the dependence on α of positive U showed the possibility of typhoon curving to the east. Also, the track category moving to the northeast, the dependence on α of negative U makes the difference of degree of curvature of the track. Moreover, it was possible to identify the location of the typhoon track according to the UM parameters. If the curvature degree at the altitudes of 2-5 km is large, the typhoon center is located more on the east side of the island.