Dec.  2019

Article Contents

# Reducing Uncertainties in Climate Projections with Emergent Constraints: Concepts, Examples and Prospects

Funds:

Agence Nationale de la Recherche (ANR) [grant HIGH-TUNE ANR-16-CE01-0010]

• Models disagree on a significant number of responses to climate change, such as climate feedback, regional changes, or the strength of equilibrium climate sensitivity. Emergent constraints aim to reduce these uncertainties by finding links between the inter-model spread in an observable predictor and climate projections. In this paper, the concepts underlying this framework are recalled with an emphasis on the statistical inference used for narrowing uncertainties, and a review of emergent constraints found in the last two decades. Potential links between highlighted predictors are explored, especially those targeting uncertainty reductions in climate sensitivity, cloud feedback, and changes of the hydrological cycle. Yet the disagreement across emergent constraints suggests that the spread in climate sensitivity can not be significantly narrowed. This calls for weighting the realism of emergent constraints by quantifying the level of physical understanding explaining the relationship. This would also permit more efficient model evaluation and better targeted model development. In the context of the upcoming CMIP6 model intercomparison a growing number of new predictors and uncertainty reductions is expected, which call for robust statistical inferences that allow cross-validation of more likely estimates.
摘要: 很多模式在对气候变化的很多响应上存在分歧，如气候反馈、区域变化、气候平衡态敏感性的强度等。观测涌现约束方法(以下称为“涌现约束”)是找到关于预报因子的多模式间预报离散性和气候预测的关系，来减少模式间预报的不确定性。本文回顾了在涌现约束这个框架下的一些基本概念，强调了用于缩小不确定性的统计推断，此外文章还对过去二十年间关于涌现约束的研究做了回顾。本文探索了重要因子之间的潜在联系，尤其是尝试缩小气候敏感度、云反馈和水循环的变化的不确定性。但涌现约束结果的不统一表明目前的方法还不能显著地缩小气候敏感度的不确定性范围。这要求通过对这个关系的物理理解的水平进行量化来加强涌现约束真实性。这可能也需要更有效率的模式评估和更有针对性地发展模式。在即将到来的CMIP6模式间比较中，我们希望看到更多的预报因子并且希望预报不确定性能缩小，这需要可靠的统计推断，以便对更有可能的估计进行交叉验证。
• Figure 1.  Idealized relationship between a predictor and a predictand. The 29 models (dots) are associated with randomly generated values of the predictor A ( x-axis, between 0 and 3). The predictand B, on they-axis follows the idealized relationship $y' = ax+b$, with a = 1 and b = 2, plus a random deviation $\Delta$ following a normal distribution with $\sigma$ = 2 [such as $y = y'+\Delta(y')$]. The dashed lines and blue shades represent the 90% prediction limits and the 90% confidence limits of the slope, respectively. The green distribution on the x-axis represents an idealized observed distribution of the predictor, assuming a normal distribution (here with $\mu$ = 1.98 and $\sigma$ = 0.3). Prior and posterior distributions of the predictand are represented as vertical lines in the left part, with the mode (circle), 66% (thick) and 90% (thin) confidence intervals. Black lines represent the prior distribution, red lines represent the posterior distribution obtained by a weighted average of the climate models through a Kullback–Leibler divergence, and blue lines are the distribution inferred using the slope and its uncertainties. In this randomly generated example, posterior estimates are sensitive to the way inference is computed.

Figure 2.  (a) Scatterplot of ECS versus deseasonalized covariance of marine tropical low-cloud reflectance $\alpha_c$ with surface temperature T in CMIP5 models (numbered in order of increasing ECS). Gray lines represent a robust regression line (solid), with the 90% confidence interval of the fitted values (dashed) estimated by a bootstrap procedure. The green line at the lower axis indicates the PDF of the αc variation with T inferred from observations. The vertical green band indicates the 66% band of the observations. The blue circle and horizontal band show the mode and the likely (66%) ECS range inferred from a linear regression procedure, respectively, taking into account uncertainties estimated by bootstrapping predictions with estimating regression models. (b) Posterior PDF of ECS (orange) obtained by a weighted average of the climate models, given the observations. The bars with circles represent the mode and confidence intervals (66% and 90%) implied by the posterior (orange) PDF and the prior (gray) PDF. Adapted from Brient and Schneider (2016)

Figure 3.  Relationship between modes and correlation coefficient (r) of 104 randomly generated emergent constraints, as per the example shown in Fig. 1. Thick lines, dashed lines and shades represent the average mode, the average 66% confidence interval and the standard deviation of the mode across the set of emergent relationships. Characteristics of the prior distributions are represented in black color. Posterior estimates using the slope inference or the weighting averaging are represented in blue and red, respectively, using an idealized observed distribution of the predictor as defined in Fig. 1. The PDF of correlation coefficients is shown as a thin black line on the x-axis. This figure shows that average modes and confidence intervals remain independent of the inference method, but the uncertainty of the mode value is larger for the weighting method.

Figure 4.  Probability density distributions of ECS. The black and gray density distributions show the original CMIP3 and CMIP5 model distributions. The 11 emergent constraints of ECS are shown as a normal distributions, with the mean (color dots) and standard deviation listed in Table 1. Unweighted and weighted density distributions aggregated over the 11 emergent constraints are shown as green full and dashed lines respectively. A kernel bandwidth of 1.0°C is used and weights are computed as the reciprocal of the variance.