Estimating components of covariance between two climate variables using model ensembles

Abstract

The seasonal mean of a climate variable is considered to consist of: (a) slow-external; (b) slow-internal; and (c) intraseasonal components. Using an Analysis of Variance-based method, the interannual variability of the seasonal mean from an ensemble of coupled atmosphere-ocean general circulation model realisations is separable into these components. Here, we propose a method for analysing the covariability of these components between pairs of climate variables. In particular, the method allows for an estimate of the covariability of the projected time series of the modes of variability of one climate variable with the time series of another. To illustrate this, the relationship between time series of the modes of variability of 500 hPa geopotential height and sea surface temperature is examined for an ensemble of coupled general circulation model realisations. The method is applicable to other atmospheric climate variables and datasets.

Assessment of Modes of Interannual Variability of Southern Hemisphere Atmospheric Circulation in CMIP5 Models

“…To compare the CMIP5 model modes of variability with the 20CR, all data must be mapped onto the same grid (e.g., Grainger et al 2008). CMIP5 500-hPa geopotential height data are mapped onto the 20CR 2.58 3 2.58 grid, while SST data are mapped onto the HadISST 28 3 28 grid.…”

“…The spatial truncation method of Zheng and Frederiksen (2004) is applied to the covariance matrices of the total internal and intraseasonal components. Covariance matrices are adjusted so that they are positive semidefinite using the method of Grainger et al (2008). The modes of interannual variability for each component are estimated using empirical orthogonal function (EOF) analysis.…”

Projections of Southern Hemisphere atmospheric circulation interannual variability

“…The associated time series thus defined are used to estimate covariances between the modes and other climate fields through further application of Eqs. (3-9); see Grainger et al (2011a) for further details. This method is applied here to estimate the covariance between the 500 hPa geopotential height S-mode, SI-mode and SE-mode associated time series and the corresponding components in the model grid point SST and SLP.…”

“…3.2) is able to be estimated through testing of likelihood ratios. Following Grainger et al (2011a), the monthly anomalies of the associated time series, p sym , and climate field anomalies, x sym ′, are respectively defined as and…”

A method for estimating and assessing modes of interannual variability in coupled climate models

“…The method for calculating the slow sst-height covariance patterns is analogous to the covariance methodology in Section 2, and is detailed by Grainger et al [11].…”