Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Knowledge of the spatial distribution characteristics of hydraulic parameters is essential for the management and protection of karst groundwater resources. In this study, we propose a workflow integrating the transition probability geostatistics (T-PROGS) and the discrete cosine transform (DCT) with the ensemble smoother with multiple data assimilation (ES-MDA) method to map the hydraulic conductivity of karst aquifers that usually follow a multimodal distribution. The priori parameter ensemble is constructed from the T-PROGS and transformed into an approximately Gaussian distributed coefficient field containing critical spatial structural features about the aquifer using DCT. The ES-MDA method is employed to update the DCT coefficients by assimilating the measurements. In addition, a postprocessing process based on cumulative distribution function (CDF) mapping is used to address the problem of parameters gradually tending to a Gaussian distribution after updating using the ES-MDA and the inappropriate selection of initial parameter values. In practice, the limited amount of available data makes it difficult to fully capture the spatial distribution of the parameters in the initial ensemble of a single realization. Therefore, we suggest a new strategy for structuring the initial ensemble by mixing samples from multiple realizations. We then apply the proposed approach to four single realization models and a combined multiple realizations model in a field hydraulic tomography investigation of a real karst aquifer. The computed results show that this method can effectively identify the characteristics of the spatial distribution of hydraulic conductivity in karst aquifers. Compared with an individual realization model, the uncertainty of the hydraulic conductivity estimated by the combined multiple realizations model is significantly reduced. Therefore, including more uncertainty of the aquifer in the initial ensemble is beneficial to improve the accuracy of the parameter estimation.