Spatial Interpolation of Hydrographic Vertical References in the Gulf of Guinea: Hierarchical Ranking of Geostatistical and Deterministic Methods by LOO Cross-validation

The accurate determination of the offset between Mean Sea Level (MSL) and Lowest Astronomical Tide (LAT) is very important for marine and coastal navigation, mapping, and engineering (reduction of bathymetric soundings to LAT, under-keel clearance, and nearshore/offshore infrastructure levelling). The MSL value is obtained from either a local geoid model or from temporary in-situ tide gauge data processed using specialised filters. For many ungauged ports along the Gulf of Guinea, sources like Admiralty Tide Tables (ATT) provide insufficient spatial coverage, necessitating spatial interpolation from regional reference gauges. The low density, heterogeneity, and discontinuity of tide gauge observations impose the use of rigorously evaluated spatial interpolation methods. This study proposes an integrated methodological framework comparing six interpolation techniques: Nearest Neighbour (NN), Inverse-Distance Weighting (IDW), Triangulation (TIN), Spline, Trend Surface, and Kriging. The comparison is based on a regional database of 115 reference ports (106 from the ATT, and nine complementary stations from GLOSS, PSMSL, and UHSLC/JASL networks) spanning 20 West African coastal countries. Three representative Cameroonian test sites are selected: the Rio del Rey Shelf (Betika), the Wouri Estuary (Dibamba-Yassa), and the isolated southern coast (Batanga). The approach combines a unified software implementation, exhaustive comparison and leave-one-out (LOO) cross-validation (MAE, RMSE, bias, R 2 ), convergence analysis and quadratic decomposition of uncertainty components. Results indicate that the optimal interpolation method varies with local reference station density and spatial configuration. At Betika (18 reference stations, 9 retained), IDW yields the best cross validation performance (RMSE ≈ 0.2295 m, R 2 ≈ 0.1376) with Kriging close behind. At Dibamba-Yassa (06 stations, 4 retained), Trend Surface performs best (RMSE ≈ 0.1225 m, R 2 ≈ 0.2833), followed by Kriging (RMSE=0.1439 m). At Batanga (2 stations only), method comparison fails, illustrating problem degeneration under extreme undersampling. In all cases, interpolation variance σᵢ² accounts for more than 95% of the total error budget, with 95% confidence intervals reaching ±3.6 m to ±4.9 m. The convergence analysis shows that a minimum of 5-7 stations is required to stabilise estimates. The main finding is that network densification is the primary lever for improvement, well ahead of algorithmic optimisation. The study provides validated point estimates for the three sites and a transparent protocol for tidal datum estimation in data sparse coastal regions of the Gulf of Guinea.