SBDM v1.0: A scaling-based discretization method for the Geographical Detector Model

Abstract. Geographical Detector Model (GDM) can be used to assess the affinity between potential environmental factors and the response variables. If environmental factors entered are continuous, the first step for application of GDM is to discretize the continuous variable into category strata with an appropriate discretization method. Many one-dimensional discretization methods have been arbitrarily applied to GDM but failed to obtain the optimal strata of environmental factors, resulting in an inaccurate model output. In this paper, we present the Scaling-Based Discretization Method (SBDM) as a novel discretization method that can be used to obtain the optimal strata for GDM. The SBDM takes the power of determinant as a criterion function through upscaling and downscaling processes to obtain the optimal discretization. The software was tested with two case studies: (1) The distance to river was discretized with SBDM to reveal the effect of rivers on the sand cover ratio in the Maowusu (Mu Us) Sandy Land, northern China. The SBDM obtained more accurate information for the influence of rivers on the sand cover ratio than the results from Priori Knowledge discretization method. (2) Seven environmental factors were discretized using SBDM to detect potential associations between these factors and NDVI spatial pattern in Xinjiang, north-western China. Then we compared the q values from SBDM with the values from four commonly used one-dimensional discretization methods, demonstrating that for all considered factors, SBDM gets a larger q value than other methods. Collectively, SBDM offers a new way for data discretization that accurately reveals the relationship between controlling factors and response variables.