Global Climate Model tuning (calibration) is a tedious and time‐consuming process, with high‐dimensional input and output fields. Experts typically tune by iteratively running climate simulations with hand‐picked values of tuning parameters. Many, in both the statistical and climate literature, have proposed alternative calibration methods, but most are impractical or difficult to implement. We present a practical, robust, and rigorous calibration approach on the atmosphere‐only model of the Department of Energy's Energy Exascale Earth System Model (E3SM) version 2. Our approach can be summarized into two main parts: (a) the training of a surrogate that predicts E3SM output in a fraction of the time compared to running E3SM, and (b) gradient‐based parameter optimization. To train the surrogate, we generate a set of designed ensemble runs that span our input parameter space and use polynomial chaos expansions on a reduced output space to fit the E3SM output. We use this surrogate in an optimization scheme to identify values of the input parameters for which our model best matches gridded spatial fields of climate observations. To validate our choice of parameters, we run E3SMv2 with the optimal parameter values and compare prediction results to expertly‐tuned simulations across 45 different output fields. This flexible, robust, and automated approach is straightforward to implement, and we demonstrate that the resulting model output matches present day climate observations as well or better than the corresponding output from expert tuned parameter values, while considering high‐dimensional output and operating in a fraction of the time.