Development of a digital depth model for reef environments incorporating the heterogeneity of crowdsourced bathymetric data

Reef channels contain alternating shoals and deep troughs, densely distributed submerged reefs, and abrupt bathymetric transitions. Crowdsourced bathymetry (CSB) in these settings is heterogeneous: observations cluster along navigable tracks, remain sparse over shoals and reefs, and vary in measurement quality. Conventional Kriging may not adequately represent these characteristics, which can limit the recovery of terrain detail and bathymetric boundaries in digital depth models (DDMs). To address the heterogeneous sampling and error characteristics of CSB, we formulated an integrated Kriging framework tailored to heterogeneous crowdsourced bathymetry. First, we examined four features relevant to interpolation: spatial sampling patterns, observation quality, within-track dependence, and local systematic differences among bathymetric data sources. Second, we designed a track-aware, spatially balanced reference-point selection scheme. The neighborhood around each target location was divided into eight directional sectors, the search extent was expanded progressively, and contributions from the same original sounding batch and track segment were restricted. Third, we constructed Unified MFOK, a unified bias-shrinkage multi-factor optimized Kriging model. It combines Matérn 3/2 spatial covariance, location-specific observation-error variation, approximate within-segment dependence, and optional local source-difference correction in a generalized Kriging system with explicit unbiasedness constraints. Under track-aware selection, internal validation selected β=0 in all 15 Hawaiian region-by-support combinations, so the optional correction did not contribute to those predictions. When each workflow used the β value selected by its own internal validation, the track-aware workflow yielded a lower Unified MFOK root-mean-square error (RMSE) in 13 of the 15 combinations. The mean relative reduction was 14.95%, and the 95% confidence interval excluded zero in 10 combinations. The transfer-region experiment indicates that both the proposed method and the source-difference shrinkage mechanism can be effective in regions with more diverse source compositions, providing initial evidence for the cross-region applicability of the proposed method, although a single transfer region cannot establish universal cross-region performance. In addition, local error diagnostics at ten representative locations in the main study area showed that the proposed method reduced pointwise RMSE from 10.493 to 7.403 m, further indicating favorable error behavior across varied local terrain and observation conditions. Taken together, these results indicate that, within the data extent and spatial support conditions adopted in this study, the method can reduce the influence of CSB heterogeneity on DDM construction and improve the accuracy and stability of DDM construction.