Bayesian retro- and prospective assessment of CMIP6 climatology in Pan Third Pole region

Abstract

Pan Third Pole (PTP) region includes Tibet Plateau (TP), Central Asia (CA) and Southeast Asia (SEA) and it is one of the places on earth that are most sensitive to climate change. Meanwhile, PTP origins a series of large rivers such as Yangtze River, Yellow River and Lancang-Mekong River, which feed millions of people downstream. Therefore, climate change in PTP has significant impact on livings and water supply of local residents. In this study, 16 model predictions from the Coupled Model Inter-comparison Project Phase 6 (CMIP6) and Climate Research Unit (CRU) observations are used to evaluate historical precipitation and temperature climatology changes in PTP region for the far (1901–1930), middle (1941–1970) and near history (1981–2010) respectively. In addition, Bayesian model averaging (BMA) approach is applied to obtain the multi-model weighted average prediction and the BMA values are further used to assess the climate variabilities in the near (2021–2050), middle (2046–2075) and far future (2071–2100) under four SSP-RCP scenarios. Results indicate that temperature is significantly underestimated by most CMIP6 models in TP especially IPSL-CM6A-LR and CanESM5 whereas precipitation is overestimated for CA and TP. Most CMIP6 models do not predict precipitation very well in SEA, the difference of annual total precipitation between the highest estimation from UKESM1-0-LL and the lowest estimation from CAMS-CSM1-0 is about 800 mm. Overall, BMA prediction is more reliable compared with individual models. In addition, Pan Third Pole region is projected to be warmer and wetter in the future and the trend is stronger under SSP5-8.5 scenario. The BMA predicted temperature uncertainty is larger for high latitude CA region whereas precipitation uncertainty is higher for low latitude SEA region.

Appendix

1.1 Taylor diagram equation

In Taylor diagram, the correlation coefficient, standard deviation and RMSD have the following relationship (Eq. 6):

$${E}^{\prime 2}={\sigma }_{M}^{2}+{\sigma }_{r}^{2}-2{\sigma }_{M}{\sigma }_{r}R$$

(6)

where R is the correlation coefficient between the model and reference data. ${E}^{\prime}$ is the centered RMSD and ${\sigma }_{M}^{2}$ and ${\sigma }_{r}^{2}$ are the variances of the model and reference data respectively. In this study, spatial patterns of annual mean temperature and annual total precipitation climatology from CMIP6 and CRU observations are evaluated with Taylor diagram.

1.2 Expectation Maximization algorithm

The Expectation Maximization (EM) algorithm is iterative and alternates between two steps, the E (or expectation) step, and the M (or maximization) step by using a latent variable z. In the E step, z is estimated given the current estimates of the model weight w_k and σ_k (Eq. 7). The superscript j refers to the jth iteration of the EM algorithm and is a normal density with mean M_k,s and standard deviation . In the M step, the weight w_k and standard deviation σ_k are calculated with the current estimate of z_k,s (Eqs. 8 and 9). Where n is the number of observations for distinct values of locations. The E step and M step are iterated to convergence.

$${z}_{k,s}^{j}=\frac{{w}_{k}^{j-1}p({y}_{s}|{M}_{k,s},{\sigma }_{k}^{j-1})}{\sum _{k=1}^{K}{w}_{k}^{j-1}p({y}_{s}|{M}_{k,s},{\sigma }_{k}^{j-1})}$$

(7)

$${w}_{k}^{j}=\frac{1}{n}\sum _{s}{z}_{k,s}^{j}$$

(8)

$${\sigma }_{k}^{2\left(j\right)}=\frac{\sum _{s}{z}_{k,s}^{j}{({y}_{s}-{M}_{s})}^{2}}{\sum _{s}{z}_{k,s}^{j}}$$

(9)