First signals of an a-priori, source-model-free transferability predictor: the target field's spatial roughness

Estimating whether a source will transfer to a target usually needs a trained source model: LEEP, LogME,Task2Vec and even "source-free" methods all require a forward pass. We ask a simpler question — can ascalar computed from the target field alone, before any transfer, predict transfer success? We test thetarget field's spatial roughness (a graph-Laplacian measure of how far the field is from harmonic,mean|Lv|/mean|v−mean|), computed from its own grid and blind to any transfer fit. On 31environmental fields (temperature, humidity, precipitation, soil moisture, radiation, ...), roughness predictsmeasured cross-domain transfer R² at Spearman ρ = −0.86 (p = 6×10⁻¹⁰): smooth fields (temperature,humidity) transfer well, rough/discontinuous fields (precipitation) transfer poorly. The relationship is notnew to geostatistics — spatial autocorrelation has long predicted within-field interpolation error — but toour knowledge it has not been used as a source-model-free, data-intrinsic, a-priori predictor of cross-domain transfer, and it is mechanistically exact for harmonic transfer (roughness is precisely the quantitythat transfer assumes small). We also report a methodological caution: a fit-derived distance on the samedata correlates at −0.95 but is circular; the fit-blind roughness independently recovers −0.86, evidencing areal, non-circular signal. In a complementary field→field setting (200 same-grid transfers, donor fieldvarying), the donor↔recipient roughness match predicts transfer beyond recipient difficulty (partialSpearman −0.34, p < 10⁻⁶) and survives controlling for physical relatedness (−0.28 among cross-familypairs) — a first signal of a structural-similarity (distance) law. Scope is honest and narrow (n = 31 grid→field, n= 200 field→field; one environmental family; single-run R²); coarser confounds (spatial scale, dynamic range)and non-environmental domains remain for the follow-up.