Methods

In this section, some methodologies used in this study are introduced. To obtain the signals of IPO and global warming, the empirical orthogonal function (EOF) analysis is applied. In section 2.2.1 we briefly introduce the EOF analysis, and the diagnostics of IPO and global warming signal are described in section 2.2.2. To investigate the relationships between clouds and large-scale fields, the linear regression analysis is applied to obtain the monthly regression relationships, which are explained in section 2.2.3.

2.2.1 The Empirical orthogonal function analysis

The EOF analysis is a statistical approach commonly used in climate diagnostics.

The concept of EOF analysis is to decompose the data into orthogonal spatial patterns called EOF patterns or EOF modes, and maximize the inhomogeneity of variance explained by each pattern. By doing so, the patterns that can better describe the characteristics of the variations of the data will be highlighted. Each EOF pattern is accompanied by a time series called principle component (PC), which is the projection of the data on the EOF mode. In this study, EOF analysis is applied on SST to obtain the pattern that best explain the SST variation.

2.2.2 The diagnostics of IPO and global warming signal

Traditionally, the IPO is defined as the dominant mode of SST in the Pacific basin after the effect of anthropogenic forcing is removed from data and the high-frequency variability is smoothed out. During the past century, the anthropogenic climate change

dominants the observed variability, the leading EOF mode represents the global warming mode, and the IPO is then defined as the second EOF mode (Dai 2013; Dong and Dai 2015;

Parker et al. 2007).

In this study, we diagnose the CMIP5 “pre-industrial” simulations. Since the SST is not influenced by external forcing due to experimental design, the IPO is defined as the leading EOF mode of SST in Pacific basin, after a 13 year low-pass filter via fast Fourier transform algorithm is applied on the GCM outputs to remove high-frequency variations.

Variables are then regressed on the PC of leading EOF mode to obtain corresponding anomalous field of one standard deviation change in PC, the IPO index. In observation, the IPO is defined as the second EOF mode of global SST from 1920 to 2013, after a 13 year low-pass filter is applied on SST data. The vertical motion is then regressed on the corresponding PC to obtain corresponding anomalous field of one standard deviation change in PC.

The influence of global warming on large-scale fields and clouds is investigated in the CMIP5 “1% CO2” simulations. The EOF analysis is applied on global SST, and the leading EOF mode represents the global warming response, the correlation coefficient of the corresponding PC and global mean surface temperature is above 0.99 in all model after the PC is rescaled so that unit change in PC corresponding to one degree change of global mean temperature. Variables are then linearly regressed on the rescaled PC at each grid point to obtain the anomaly per degree change of global mean temperature.

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2.2.3 The monthly regression relationships and the multiple regression relationships

To investigate how cloud changes are related to variation of local SST or vertical motion on monthly time scale, a simple linear regression is applied. In this study, the monthly regression relationship refers to the linear regression between two monthly mean variables at each grid point, after the seasonal cycle is removed:

Cloud properties = ∝ × L + constant + error , where L is the large-scale variable, can be either SST or vertical motion at 500 hPa. The ∝ is the slope of the regression line of cloud properties and large-scale variables, obtained by minimizing the mean square error.

The purpose is to find the local relationship between large-scale fields and clouds.

By a simple linear regression, we can obtain the cloud anomaly accompanied by unit anomaly of SST or vertical motion departure from its climatology seasonal cycle at each grid point.

We examine the monthly regression relationship between clouds and large-scale fields in CMIP5 “pre-industrial” simulations and in observation. In “pre-industrial”

simulations, the linear regression is applied to the whole 500 years. In observation the linear regression is applied to the period of 2000~2010, when the CERES CREs data is available. To test whether the difference of monthly regression relationships between GCMs and observation are arise due to the unequal data length, the 500-year-long data of GCMs is cut into a set of 10-year-long chunks. The monthly regression relationships in each 10-year-long chunk (not shown) are roughly agree with those of the 500-year-long

data, suggest that the observation data is long enough to capture the feature of monthly regression relationships.

The multiple regression relationship is generated by multiple linear regression method, and is same as monthly regression relationship except for it has two independent variables: SST and vertical motion at 500 hPa, instead of one of them in the case of monthly regression relationship:

Cloud properties = ∝ × T + β × 𝜔₅₀₀+ constant + error, where the T and 𝜔₅₀₀ are the anomalies of SST and vertical motion at 500 hPa. The ∝ and β, which are called the SST coefficient and vertical motion coefficient in this study, respectively, obtained by minimizing the mean square error. The purpose is to combine the effect from SST and vertical motion.

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