A bias-corrected projection for the changes in East Asian summer monsoon rainfall under global warming

Abstract

Projecting regional rainfall changes in a warmer climate attracts ongoing attention. However, large uncertainty still exists in multi-model projection. In this study, we introduce a bias-corrected method to correct the multi-model projection of changes in East Asian summer monsoon (EASM) rainfall based on the historical and RCP8.5 runs of 25 models from phase 5 of Coupled Model Intercomparison Project. Firstly, the total rainfall changes are separated into the thermodynamic component due to increased specific humidity and the dynamic component due to circulation changes. The thermodynamic component is corrected using the observed present-day rainfall and the increase rate of specific humidity based on the wet-get-wetter mechanism. On the other hand, the dynamic component with the circulation changes is corrected based on a “spatial emergent constraint” method, which is further validated by the perfect model approach. Together, these corrections give an integrated projection for EASM rainfall changes under global warming. Such an approach can improve the signal-to-noise ratio of projection effectively, from the original 0.73 of the multimodel mean to around 1.9. The corrected projection of EASM rainfall changes shows a pronounced increase in southern China, the northwest Pacific and a belt from northern China to northeastern China, and a weak increase in other EASM regions.

Appendix: Spatial emergent constraint and Ensemble pattern regression method

The spatial emergent constraint with the ensemble pattern regression method used in this study was first developed in Huang and Ying (2015), extending the original emergent constraint for regional-mean changes, to constrain the future changes with apparent spatial pattern. The main steps are introduced here.

We indicate the historical climatology of model i by $H_{i}$ and the future climatology by $F_{i}$. The future change $C_{i}$ is defined as $C_{i} = F_{i} - H_{i}$. We suppose that there is a perfect projection of future change $C_{real}$, which is the same in all models, and the difference between the $C_{real}$ and the MMM change $\bar{C} = N^{ - 1} \mathop \sum \nolimits_{i = 1}^{N} C_{i}$ is the common change bias $\bar{C}^{\prime} = \bar{C} - C_{real}$. For the individual change bias $C_{i}^{\prime \prime }$, this is defined as $C_{i}^{\prime \prime } = C_{i} - \bar{C}$ and the total change bias of a model i is $C_{i}^{\prime } = \bar{C}^{\prime} + C_{i}^{\prime \prime }$. An identical decomposition method can be applied to the $H_{i}$. The historical climatology $H_{i}$ consists of the observed climatology $H_{obs}$, the common historical bias $\bar{H}^{\prime } = N^{ - 1} \mathop \sum \nolimits_{i = 1}^{N} H_{i} - H_{obs}$ and the individual historical bias $H_{i}^{\prime \prime } = H_{i} - \bar{H}$.

Next, we need to build up the spatially correlated mode between the historical bias and the change bias. EOF analysis is a common method to decompose a signal into a time series and spatial pattern. However, here we apply an intermodel EOF analysis to the $H_{i}^{\prime \prime }$ of all the model and get the spatially orthogonal modes ${\text{EOF}}_{j}$, $j = 1, \ldots ,M$ and corresponding principal coefficients ${\text{PC}}_{ij}$. For a specific $H_{i}^{\prime \prime }$, this can be represented as $H_{i}^{\prime \prime } = \sum\nolimits_{j = 1}^{M} {{\text{EOF}}_{j} } {\text{PC}}_{ij}$. The truncation of $M\,{\text{EOFs}}$ depends on the representation of the EOF modes for the historical bias $H_{i}^{\prime \prime }$ and $\bar{H}^{\prime}$, and influences the results of the correction. Multivariant linear regression analysis is performed on PCs and individual change bias $C^{\prime\prime}$. The estimation of $C^{\prime\prime}$ can be calculated by the regression pattern $\hat{b}$ and PCs:

$$\hat{C}_{i}^{\prime \prime } = \sum\limits_{j = 1}^{M} {\hat{b}_{j} } {\text{PC}}_{ij} .$$

(2)

Because the PCs are linearly independent, the regression pattern $\hat{b}$ equals the simple linear regression result of $C^{\prime\prime}$ onto PCs mode by mode. This simplifies the procedure of regression.

The estimation of the common change bias $\bar{C}^{\prime}$ is based on a hypothesis that the relationship between $\bar{C}^{\prime}$ and the common historical bias $\bar{H}^{\prime}$ is the same as the relationship between the modes of ${\text{EOF}}_{j}$ and $\hat{b}_{j}$. First, we project the $\bar{H}^{\prime}$ onto ${\text{EOF}}_{j}$ and represent the $\bar{H}^{\prime}$ by the expansion coefficient $e_{j}$:

$$\bar{H}^{\prime} = \mathop \sum \limits_{j = 1}^{M} {\text{EOF}}_{j} e_{j} .$$

(3)

We replace the PCs in Eq. (2) by the expansion coefficient $e_{j}$ and estimate $\bar{C}^{\prime}$:

$$\widehat{{\bar{C}^{\prime}}} = \mathop \sum \limits_{j = 1}^{M} \hat{b}_{j} e_{j} .$$

(4)

Finally, we can correct the MMM change $\bar{C}$ as $\bar{C}_{C} = \bar{C} - \widehat{{\bar{C}^{\prime}}}$. The individual change in model i$C_{i}$ can also be corrected as the correction for common bias in MMM. We then just need to substitute the common historical bias $\bar{H}^{\prime}$ in Eq. (3) with the total historical bias $H_{i}^{'} = H_{i} - H_{obs}$:

$$H_{i}^{'} = \mathop \sum \limits_{j = 1}^{M} {\text{EOF}}_{j} e_{ij} .$$

(5)

The expansion coefficient $e_{ij}$ for $H_{i}^{\prime }$ can replace the $e_{j}$ in Eq. (4):

$$\hat{C}_{i}^{\prime } = \sum\limits_{j = 1}^{M} {\hat{b}_{j} } e_{ij} .$$

(6)

The individual change in model i is corrected as $C_{Ci} = C_{i} - \hat{C}^{\prime}_{i}$.