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 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 model runs and can accommodate internal climate variability. The approach consists of three stages: (a) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (b) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (c) 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.

中文翻译：

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理想化 GCM 中对流参数的校准和不确定性量化

气候模型中的参数通常是手动校准的，仅利用可用数据的一小部分。这排除了最佳校准和不确定性量化。允许不确定性量化的传统贝叶斯校准方法对于气候模型来说过于昂贵；在存在内部气候变率的情况下，它们也不稳健。例如，马尔可夫链蒙特卡罗 (MCMC) 方法通常需要模型运行并且对内部可变性噪声敏感，这使得它们不适用于气候模型。在这里，我们展示了一种模型校准和不确定性量化的方法，它只需要模型运行并且可以适应内部气候变化。该方法包括三个阶段：(a) 校准阶段使用集合卡尔曼反演的变体通过最小化模型和数据统计之间的不匹配来校准模型；(b) 模拟阶段使用高斯过程 (GP) 模拟参数到数据的映射，使用在校准阶段运行的模型进行训练；(c) 采样阶段通过使用 MCMC 对 GP 模拟器进行采样来近似贝叶斯后验分布。我们证明了这种校准模拟样本 (CES) 方法在完美模型设置中的可行性和计算效率。使用理想化的环流模型，我们根据模型生成的合成数据估计简单对流方案中的参数。CES 方法生成参数的概率分布，这些概率分布是贝叶斯后验的良好近似，其计算成本通常只是获得它们所需的一小部分。从这个近似后验采样允许生成具有量化参数不确定性的气候预测。