Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require $O(10^5)$ model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only $O(10^2)$ model runs and can accommodate internal climate variability. The approach consists of three stages: (i) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (ii) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (iii) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate-emulate-sample (CES) approach in a perfect-model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties.
翻译:气候模型中的参数通常是人工校准的,只是利用现有数据中的一小部分。这排除了最佳校准和量化不确定性的最佳方法。传统的巴伊西亚校准方法对气候模型来说过于昂贵,在内部气候多变性的情况下,这些参数也不健全。例如,Markov连锁的Monte Carlo(MCMC)方法通常需要O(10美5美元),并且对内部变异性噪音敏感。我们在这里展示了一种模型校准和不确定性量化参数的方法,模型的校准和不确定性量化参数只需要O(10美2)美元模型运行,并且能够容纳内部气候变异性。这种方法由三个阶段组成:(一)校准阶段使用全方位卡尔曼的变异体来校准模型,通过尽量减少模型和数据统计数据的不匹配;(二)模拟阶段模仿参数对数据地图,使用模型运行模型的校准方法进行培训;(三) 通常通过对GGPOPO的精确度模型运行和精确度参数进行抽样阶段,对Bayesian的远端分布进行模拟,通过对GPPRO的精确度进行取样进行精确的精确度分析。我们用模型对模型进行模拟的校验测测测算。我们用模型进行了一种标准的校验测算。我们用这个模型的精确测测测算的方法,用一个标准的精确度方法来计算。