Maximum Covariance Analysis
Also known as: MCA, Singular value decomposition, SVD analysis, Covariance analysis
Maximum covariance analysis (MCA) is a statistical technique that identifies coupled patterns of variability between two spatially distributed fields (e.g., sea surface temperature and precipitation). Unlike EOF analysis which focuses on variance in a single field, MCA identifies spatial patterns that are maximally correlated between two different fields.
Key highlights
- Focuses on covariance between two fields rather than variance within a single field; reveals coupled modes
- More interpretable than EOF analysis for understanding interactions between distinct components
- Quantifies degree of coupling through singular values; stronger coupling means higher singular value
- Extends naturally to analysis of lagged relationships (one field leads/lags the other)
Intuition
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How it works
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When to use it
Use MCA to identify coupled variability between two fields, to find teleconnections between distant variables (e.g., tropical SST and extratropical precipitation), to understand predictability based on coupling strength, and to reduce complexity in coupled systems.
Strengths & limitations
- Focuses on covariance between two fields rather than variance within a single field; reveals coupled modes
- More interpretable than EOF analysis for understanding interactions between distinct components
- Quantifies degree of coupling through singular values; stronger coupling means higher singular value
- Extends naturally to analysis of lagged relationships (one field leads/lags the other)
- Results depend on choice of two fields; different field pairs give different results
- MCA modes are not orthogonal in time; temporal overlap/lag structure can complicate interpretation
- Dominated by linear relationships; nonlinear coupled modes are not captured
- Significance of MCA modes must be assessed; not all modes represent significant coupling
Common pitfalls
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Applications
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Frequently asked
How is MCA different from EOF analysis?
EOF focuses on variance within a single field. MCA focuses on covariance between two fields. MCA reveals which patterns in field 1 are most tightly linked to patterns in field 2.
Can MCA show causality?
No. MCA shows correlation/covariance between patterns, not causality. To infer causality, you need additional tools (e.g., Granger causality, lagged regression) or physical reasoning.
What do singular values represent?
Singular values quantify the covariance explained by each MCA mode. Larger singular values indicate stronger coupling; a singular value of zero means no correlation.
Can I use MCA with lags?
Yes. Lagged MCA computes covariance between field 1 at time t and field 2 at time t+lag. This reveals whether patterns in field 1 lead/lag patterns in field 2.
Sources
- 1.Bretherton, C. S., Widmann, M., Dymnikov, V. P., Wallace, J. M., & Blade, I. (1992). The effective number of spatial degrees of freedom of a time-varying field. Journal of the Atmospheric Sciences, 49(11), 1063-1083.
- 2.Newman, M., Sardeshmukh, P. D., & Penland, C. (2016). Relative Contributions to Subseasonal Predictability: Bridging Medium-Range and Climate Time Scales. Journal of Climate, 29(15), 5629-5647.
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Cite this page
ScholarGate. (2026, June 3). Maximum Covariance Analysis. ScholarGate. https://scholargate.app/meteorology/maximum-covariance-analysis