AbstractDecadal‐scale unforced climate variability associated with low‐frequency ocean (or coupled) modes can be identified within the time‐evolving sea surface temperature (SST) pattern. We seek to find a relationship between 12 well‐known climate modes of variability (El Niño–Southern Oscillation, Pacific Decadal Oscillation, Atlantic Multidecadal Oscillation, etc.), which are reflected in the SST pattern, and decadal trends in downwelling shortwave radiation at Earth's surface (surface solar radiation, surface shortwave radiation [SSR]). The analysis is performed using the pre‐industrial control runs (piControl) of 57 models from the Coupled Model Intercomparison Project—Phase 6. We find that regional SSR trends occur during periods when a climate mode is transitioning and show a mirroring pattern (opposite sign SSR trends) when the mode transitions in the opposite direction. Unforced trends in clear‐sky SSR are mostly driven by SST‐induced water vapor changes, while all‐sky SSR trends show a complex spatial structure with trends of different signs in different regions. Unforced SSR trends are generally weaker in simulations with climatological SSTs. The role of natural aerosols as another potentially relevant factor for SSR variability is briefly addressed and we find that constantly higher aerosol loads result in increased variability for clear‐sky conditions, but not for all‐sky conditions. The results from this study suggest that all‐sky dimming and brightening in different parts of the world are enhanced rather than suppressed by internal variability related to an SST‐pattern with the exception of India and China, where both effects are present. A practical application can be the planning of photovoltaic energy facilities given areas where internal variability is generally smaller or affects SSR in opposite directions.