MUSE: virtual tide gauge reference estimates and error budgets for coastal index validation at ungauged coastlines

Prasetyo Wibowo 

Multi-dimensional coastal indices such as mangrove health indices aggregate tidal-range, mean higher-high water (MHHW), and tidal-anomaly sub-scores. Validating these sub-scores requires in situ tide gauges that low-data coastlines lack within 100 km. Global tide models such as EOT20 give accurate coastal tidal constituents but no tidal-anomaly metrics or per-source error terms for a composite-index budget. Such metrics would capture weather-band non-tidal variability driving coastal flooding and ecosystem exposure.
We present MUSE (MUlti-Source tidal Estimation) as a virtual tide gauge combining University of Hawai’i Sea Level Center (UHSLC) harmonic analysis from nearby stations with EOT20 constituents through a basin-friction-aware inverse-distance-weighted ensemble. MUSE adds tidal-anomaly metrics from the UHSLC residual and per-source error components that EOT20 lacks.
Seven complementary tests assess the protocol at five pilot and three development sites across four continents. They comprise leave-one-station-out cross-validation (LOO-CV), four baselines, a Diebold–Mariano test, sensitivity, subsample analysis, bootstrap confidence intervals, and adversarial tests. MUSE returns finite anomaly standard-deviation estimates while the EOT20 anomaly is zero by construction, with LOO-CV root-mean-square errors of 0.020 to 0.095 m. A worked example indicates that this error term carries 63 to 90% of an illustrative index’s variance at the four coherent sites, a component no model-only budget supply. EOT20 alone is most accurate for range and MHHW at every site when extracted at the validation stations, with root-mean-square errors of 0.01 to 0.26 m for range and 0.01 to 0.11 m for MHHW. The independent Bitung gauge check passes two gates and fails two. Four sites pass the 0.50 m tidal-range threshold and pass/fail is consistent with a post-hoc station-coherence explanation rather than with station count, although eight sites limit confirmation. At the five sites where spatial-block cross-validation is testable both the station-level and block-level evaluations fail the 0.50 m gate. MUSE complements EOT20 by completing index error budgets rather than improving tidal-range accuracy.