The complexity of alluvial-pluvial fan depositional systems makes the detailed characterization of their heterogeneity difficult,yet such a detailed characterization is commonly needed for construction of reliable groundwater models.Traditional models mainly focus on using a single aquifer property to qualitatively or semi-quantitatively characterize the heterogeneity of aquifer,so that they are unable to quantitatively reflect the synthetic heterogeneity of all aquifer properties.In this paper,we propose the heterogeneity synthetic index (HSI) for quantitative characterization of synthetic heterogeneity of an aquifer.The proposed calculation process involves four steps:(1) estimation of the hydraulic conductivity of a sediment sample using the cloud-Markov model,(2) establishment of the sedimentary microfacies distribution model through the Markov chain,(3) characterization of the distribution model of hydrogeological parameters using the improved sequential simulation method according to the “facies-controlled modeling” technique,and (4) application of the entropy weight method to calculate the weight coefficient of the above aquifer properties.The HSI of an aquifer is calculated by superposition of these models according to the corresponding weight coefficient.This approach was applied to the Luancheng aquifer deposit in the southeast Hutuo River alluvial-pluvial fan in the North China Plain (NCP).The results have demonstrated that aquifer 3 which was formed in the middle Pleistocene has the strongest heterogeneity,with an HSI of 0.25-0.75.Aquifer 4 formed in the early Pleistocene shows an intermediate heterogeneity,with the HSI ranging 0.35-0.75.The weakest heterogeneity was found in aquifers 1 and 2 formed in the Holocene and late Pleistocene,with HSI values of 0.40-0.75 and 0.40-0.80,respectively.The heterogeneity of all the four aquifers is relatively strong in the radial direction of the Huai River alluvial-pluvial fan due to the abrupt change of microfacies.In contrast,in the radial direction of the Hutuo River alluvial-pluvial fan,the microfacies change mildly,and the continuity of hydrogeological parameters is better,which has resulted in weaker heterogeneity of the four aquifers in this direction.Findings suggest that the sedimentary environment has significant effects on the aquifer heterogeneity.Considering that there are many aquifer properties,HSI can quantitatively characterize the synthetic heterogeneity of the aquifer and describe the influence of each aquifer property on the synthetic heterogeneity of the aquifer according to its weight coefficient.Thus the HSI approach can be successfully used to deal with the spatial heterogeneity of aquifer and provide a foundation for studies on contaminant transport.