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Empirical local synchrony range

v.empirical_synchrony_range(...) asks a diagnostic question: does focal-centered synchrony approach an empirical background clearly and persistently enough that a finite range can be resolved? It does not promise that such a range exists, and it is not the preferred general method for choosing an adaptive neighborhood.

The maximum distance in the input pair table is the discovery or observation support: where the diagnostic looked. It is not an estimated range. The verb does not estimate dispersal, a mechanistic correlation length, or a distance-decay kernel.

Relationship to the validated workflow

The experiment reuses v.local_synchrony_pairs(...) without changing its scientific semantics:

  • cold synchrony is exact Spearman dependence on joint lower-tail TMIN days, where both endpoints are at or below their own pair-valid median;
  • warm synchrony is exact Spearman dependence on joint upper-tail TMAX days, where both endpoints are strictly above their own pair-valid median;
  • pairwise Delta_S = S_cold - S_warm;
  • distance is great-circle distance in kilometers;
  • canonical undirected pairs are calculated once within each bounded input;
  • the self-pair is excluded before reduction.

v.empirical_synchrony_range(...) consumes that sparse relationship Dataset. It does not stack local maps, align overlapping landscapes, run a second convolution, or apply distance weights.

Empirical criterion

The default experiment uses 20 km annuli inside a 500 km discovery radius. For cold, warm, and Delta it retains annular median, IQR, count, and cumulative median. Cold and warm ranges are estimated separately.

Three empirical background definitions are retained for comparison:

  1. the median of the four most distant well-supported annular medians;
  2. the median of the corresponding three-shell median-smoothed profile;
  3. the median of the distant-pair reference distribution.

The first is the predeclared primary background. A candidate range is the outer edge of the first of three consecutive, well-supported annuli that:

  • are within an adaptive tolerance of the selected background;
  • have successive cumulative-median changes no larger than 0.01; and
  • are followed by at least 80% of supported annuli within twice the annular tolerance.

The annular tolerance is the larger of 0.03 and 1.5 robust standard deviations of the outer annular medians, capped at 0.10. A response with total supported profile range below 0.04 is recorded as flat/no identifiable focal signal. A candidate at or beyond 80% of the discovery radius, or a response with no qualifying candidate, is unresolved. The discovery boundary is never assigned as the range.

The returned same-neighbor comparison uses one neighbor set. When both tail ranges resolve,

R_common = max(R_cold, R_warm)
Delta_adaptive = median[S_cold(i,j) - S_warm(i,j), d(i,j) <= R_common]

Tail-specific range-based cold and warm summaries are also retained, but they are not subtracted to construct the pairwise-Delta reduction. These fields are diagnostic outputs, not a production recommendation.

Bounded real-data gate

The retained PRISM window is 2023-11-01 through 2024-01-30. Five representative CONUS pixels and 25 spatially balanced Colorado pilot sites were tested with 10, 20, and 40 km bins and 200, 300, 400, and 500 km discovery radii. The fixed 100 km control reproduced the validated Colorado baseline exactly, and manual annular counts and reductions passed.

The scientific scale-up gate is on HOLD:

  • zero of five representative pixels resolved a common range at the primary 500 km/20 km setting;
  • one of 25 Colorado pilot sites resolved a common range;
  • 96% of Colorado common ranges were censored or unresolved; and
  • zero of 25 Colorado sites had a common range stable between the 400 and 500 km primary-bin analyses.

These results do not show that synchrony has no spatial structure. They show that this deterministic kernel-agnostic criterion does not identify a stable scalar common range for this single winter window. R_common was therefore not promoted into a general adaptive-radius rule, and full-state and CONUS range-based maps were withheld instead of filling unresolved cells with 500 km.

Outputs and limitations

Evidence is under artifacts/empirical-synchrony-range/, including the pair checkpoints, annular pilot Dataset, representative curves, sensitivity tables, anisotropy diagnostic, figures, decision gate, performance record, provenance, and exact reproduction command.

The 25-site Colorado product is a bounded method pilot, not a statewide raster. The single winter window does not establish temporal stability. Directional sector estimates are frequently unresolved, so a scalar isotropic range is not validated. A future experiment should test longer discovery support or a different predeclared empirical criterion on independent temporal windows before considering a production-scale run.

For the less restrictive question “how does synchrony change with distance?”, use v.empirical_synchrony_decay(...). Return to the complete local synchrony workflow for the fixed-support, surface, decay, and landscape-change branches.