Stellar surface convection and magnetic activity imprint variability on high-precision radial-velocity (RV) measurements and currently limit the detection of low-mass exoplanets. For quiet, Sun-like stars, stellar granulation is among the dominant sources of RV variability on short timescales. Because spectral lines form at different depths in the photosphere, line-depth variations trace the balance between granules and intergranular lanes that drive convective RV shifts.

We model line-depth, shift, and width scale factors as tracers of granulation using MURaM simulations to characterise intrinsic line responses. Using singular value decomposition (SVD) of line-by-line properties, we find that a small number of modes explain nearly all the RV variance. The recovered feature vectors further reveal that individual line responses depend strongly on atomic properties. To extend the method to realistic data, we construct a subspace from the noise-free scale factors and project the scale factors with a realistic noise level into it. We then downweight lines with large uncertainties to obtain a noise-aware decorrelation basis. This framework performs robustly on synthetic spectra degraded to realistic signal-to-noise ratios explaining ~50% of the variance. It enables improved recovery of injected planetary signals, and a significant reduction in RV scatter in HARPS-N solar observations.