Surrogate inference for threshold-derived environmental indices depends on null placement and seasonal event concentration

Abstract

Threshold-derived environmental indices convert native-resolution variables into event indicators and aggregated counts, but surrogate tests may impose their null constraints either before or after this transformation. We show that these choices define different inferential targets. A threshold--copula representation separates temporal dependence from the seasonal event-probability vector and makes seasonal concentration an explicit experimental coordinate. In a prespecified benchmark of 13,500 short-memory monthly trajectories, an index-resolution marginal-and-spectrum surrogate and a constrained native-resolution surrogate produced strongly asymmetric paired conclusions: 1084 trajectories rejected only at index resolution, compared with 16 only at native resolution. Holding the expected annual event count fixed while concentrating event probability within the seasonal cycle increased index-only discordance from 4.4\% to 16.2\%. In an independent experiment, equalizing monthly event probability reduced the corresponding rate from 15.9\% to 3.9\%; the mitigation persisted when monthly percentiles were estimated from an independent 30-year reference period. Native-resolution inference was calibrated under the benchmark null but had strongly mechanism-dependent sensitivity: the strongest prespecified history-feedback alternative had a 30.7\% detection rate under the fixed synthetic gate, with substantially lower sensitivity to a persistent-regime alternative. A Coupled Model Intercomparison Project Phase 6 Amazon dry-month case study was non-discriminating, illustrating why null placement and design-specific detectability should be reported together. The results provide a practical framework for surrogate inference on threshold-derived hydroclimatic and environmental indices.