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

Michel Mfeze

doi:doi:10.11648/j.wros.20261503.15

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

Michel Mfeze^*

Published in Journal of Water Resources and Ocean Science (Volume 15, Issue 3)

Received: 4 June 2026 Accepted: 16 June 2026 Published: 30 June 2026

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Abstract

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, R²), 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, R² ≈ 0.1376) with Kriging close behind. At Dibamba-Yassa (06 stations, 4 retained), Trend Surface performs best (RMSE ≈ 0.1225 m, R² ≈ 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.

Published in	Journal of Water Resources and Ocean Science (Volume 15, Issue 3)
DOI	10.11648/j.wros.20261503.15
Page(s)	106-142
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Deterministic Method, Geostatistical Method, Hydrography, LOO Cross-validation, MSL-LAT, Spatial Interpolation, Uncertainty, Vertical Reference

1. Introduction

The MSL-LAT differential is a fundamental requirement for marine mapping, navigation safety, and coastal/offshore engineering

[1]

. This offset governs bathymetric sounding reduction, under-keel clearance monitoring, and infrastructure levelling. It is not spatially uniform, governed by local hydrodynamic, bathymetric, and astronomical processes

[2]

. Accurate realisation of the LAT surface requires combining hydrodynamic model-derived estimates with tide gauge observations

[3]

Where geoid models are unavailable or of insufficient accuracy

[4]

, MSL is estimated from in-situ tide gauge data processed with specialised filters (Doodson X0, Godin, Demerliac)

[5]

. The MSL-LAT differential is then drawn from datasets such as the Admiralty Tide Tables (ATT)

[6]

, whose spatial coverage remains limited. This constraint is particularly critical along West African coasts: the tide gauge network is heterogeneous and sparse

[7, 8]

. Sea level datasets are limited in size and quality

[9, 10]

, with tidal regimes spanning microtidal (~0.76 m in Ghana) to macrotidal (>3.9 m in Guinea-Bissau)

[11]

. To address these coverage gaps, this study enriches the 106-station ATT database with 9 complementary stations drawn from internationally validated databases (GLOSS, PSMSL, UHSLC/JASL) spanning the northern West African coast from Cape Verde to Mauritania. Spatial interpolation is therefore indispensable for uninstrumented coastal sites in the Gulf of Guinea.

Interpolation reliability depends strongly on the spatial configuration, density, and distribution of reference stations, requiring both non-stationarity representation and robust uncertainty quantification

[12, 13]

Turner et al.

[14]

showed that tidal levels including LAT and MSL can vary significantly over short distances in estuarine settings, making interpolation method and station distribution critical factors. Orton et al.

[15]

found IDW and Kriging suitable for regional tide datum interpolation in well-gauged regions; their applicability to sparse Gulf of Guinea networks has not been systematically validated. Previous practice has relied on ad hoc nearest-neighbour assignments or graphical interpolation from Admiralty Tables, without spatial gradient correction or IHO M-3 uncertainty quantification

[16]

. In contrast, advanced methodologies such as hydrographic vertical separation surfaces (HyVSEPs)

[17]

, demonstrate achievable accuracy when network density and modelling tools are combined, highlighting the gap that persists in undersampled regions like the Gulf of Guinea. The vertical datum uncertainties arising from such simplified approaches can be substantial, compromising hydrographic survey quality and maritime safety

[18]

Existing methods fall into three families

[19]

: deterministic (NN, IDW, TIN, Spline), geostatistical (Kriging

[20]

), and hybrid approaches. Inter-method discrepancies can reach 0.5 m in certain regions

[11]

, incompatible with IHO S-44 hydrographic survey precision. Despite this methodological diversity, comparative evaluations remain rare in this specific context of African coasts although satellite altimetry offers complementary sea-level observations that can partially compensate for the sparse tide gauge coverage in the region

[21, 22]

These limitations raise several major operational questions: which interpolation method yields the most reliable estimates under sparse and heterogeneous data? What is the optimal number of neighbouring stations guaranteeing estimate convergence? How can total uncertainty, from data, interpolation processes, and modelling assumptions, be rigorously quantified and propagated?

To address these challenges, this study proposes an integrated framework for comparative evaluation of spatial interpolation methods applied to hydrographic vertical references, based on: (i) an enriched 115-port regional database spanning 20 countries; (ii) unified Java implementation of six algorithms (NN, IDW, TIN, Spline, Trend Surface, Kriging); (iii) systematic leave-one-out (LOO) cross-validation (MAE, RMSE, bias, R²); (iv) convergence analysis; (v) quadratic uncertainty decomposition; and (vi) application to three Cameroonian sites representative of principal hydrographic configurations in the Gulf of Guinea.

Beyond algorithmic comparison, this framework provides a decision-support tool for hydrographic services, enabling objective method selection, transparent reliability evaluation, and guidance for tide gauge network densification strategies. By establishing an explicit link between method performance and spatial data configuration, this study contributes to improving the reliability and harmonisation of vertical reference systems in undersampled coastal regions, in service of maritime safety and the blue economy

[23]

2. Materials and Methods

2.1. Regional Hydrographic Context of the Gulf of Guinea

The Gulf of Guinea presents a semi-diurnal mesotidal regime; M₂ accounts for >96% of sea-level variance in the Wouri Estuary

[5, 24]

. Mean tidal range varies from microtidal at Takoradi (0.76 m) and Lagos (0.78 m) to mesotidal in Cameroon and Nigeria, peaking at Calabar (≈2.09 m) and Douala (≈1.62 m)

[25]

. These spatial contrasts reflect the influence of seasonal upwelling and regional hydrodynamic forcing documented across the Gulf of Guinea

[26]

Nine complementary stations from GLOSS/ PSMSL/ UHSLC provide spatial anchoring for the northern domain. Dakar hosts one of Africa's longest sea level records

[8, 27, 28]

. Palmeira and Nouakchott document sea level rise of 4.51 and 20.08 mm/year respectively

[29]

. Δᵢ values are derived from FES2014 harmonic model with estimated uncertainty ±0.10-0.15 m.

2.2. Spatial Interpolation Database

The database comprises 115 ports across 20 West African countries (Figure 1, Table 1). 106 are from the Admiralty Tide Tables

[6]

; 9 complementary stations from GLOSS/PSMSL/UHSLC. Each entry Pᵢ includes coordinates (ϕᵢ, λᵢ, WGS84), MSL-LAT differential Δᵢ, and tidal regime Ti.

P_{i} = {N_{i}, C_{i}, S_{i}, ϕ_{i}, λ_{i}, Δ_{i} {, T}_{i}}

(1)

Where

N_{i}

is the number,

C_{i}

is the country,

S_{i}

is the station/port,

ϕ

ᵢ and λᵢ are geodetic coordinates (latitude and longitude respectively in WGS84, decimal degrees), Δᵢ is the observed MSL-LAT differential (m), and

T_{i}

is the tidal regime classification (microtidal/mesotidal/macrotidal). The full dataset is provided in Table 1.

The Gulf of Guinea network has inter-station spacings of 20-200 km

[9]

. Major ports are 200-500 km apart; local densifications exist around Bonny-Calabar, Douala-Kribi, and Guinea-Bissau islands.

[7]	Wöppelmann, G., Marcos, M. Vertical land motion as a key to understanding sea level change and variability. Reviews of Geophysics. 2016, 54(1), 64-92. https://doi.org/10.1002/2015RG000502 View Article
[8]	Intergovernmental Oceanographic Commission (IOC/UNESCO). Global Sea Level Observing System (GLOSS) Implementation Plan 2022. Paris: IOC/UNESCO; 2022. Available from: https://doi.org/10.25607/OBP-1851 View Article

[9]	Woodworth, P. L., Hunter, J. R., Marcos, M., Caldwell, P., Menendez, M., Haigh, I. D. Towards a global higher-frequency sea level dataset. Geoscience Data Journal. 2017, 3, 50-59. https://doi.org/10.1002/gdj3.42 View Article
[10]	Intergovernmental Oceanographic Commission. Manual on Sea Level Measurement and Interpretation, Volume V: Radar Gauges. Paris: IOC/UNESCO; 2017. Available from: https://doi.org/10.25607/OBP-1037 View Article

[12]	Lloyd, C. D. Local Models for Spatial Analysis, 2nd ed. Boca Raton, FL: CRC Press; 2010.
[13]	Chilès, J. P., Delfiner, P. Geostatistics: Modeling Spatial Uncertainty, 2nd ed. Hoboken, NJ: Wiley; 2012.

[21]	Guo, J., Hwang, C., Chang, X., Liu, Y. Improved inversion of tide gauge positions from satellite altimetry. Geophysical Research Letters. 2021, 48(5), e2020GL091997. https://doi.org/10.1029/2020GL091997 View Article
[22]	Kemgang Ghomsi, F. E., et al. Sea level variability in Gulf of Guinea from satellite altimetry. Scientific Reports. 2024, 14(1), 5061. https://doi.org/10.1038/s41598-024-55170-x View Article

[5]	Mfeze, M. Harmonic Modeling of Tidal Fluctuations in the Wouri Estuary: A Unified Analysis for Accurate Tide Prediction at the Port Authority of Douala. Journal of Geosciences and Geomatics. 2025, 13(1), 1-22. https://doi.org/10.12691/jgg-13-1-1 View Article
[24]	L. Djeumeni Noubissie, "Sea level variations in the Gulf of Guinea and coastal risks: focus on the Wouri estuary" (in French), Ph.D. dissertation, Université Toulouse III - Paul Sabatier & Université de Douala, 2024.

[8]	Intergovernmental Oceanographic Commission (IOC/UNESCO). Global Sea Level Observing System (GLOSS) Implementation Plan 2022. Paris: IOC/UNESCO; 2022. Available from: https://doi.org/10.25607/OBP-1851 View Article
[27]	Holgate, S. J., et al. New data systems and products at the Permanent Service for Mean Sea Level. Journal of Coastal Research. 2013, 29(3), 493-504. https://doi.org/10.2112/JCOASTRES-D-12-00175.1 View Article
[28]	Wöppelmann, G., et al. Dakar sea-level records: 200 years of tide gauge data for sea-level research. SONEL/PSMSL Technical Report; 2008.

No.	Country	Station	$ϕ_{i}$ (°)	$λ_{i}$ (°)	$Δ_{i}$ (m)	$T_{i}$ ¹
Stations from Admiralty Tide Tables
1	Angola	Enseada Cabinda	-5.5500	12.2000	1.10	Micro
2	Angola	Soyo (Santo Ant.)	-6.1167	12.3667	1.10	Micro
3	Angola	Porto de Luanda	-8.7500	13.2500	1.10	Micro
4	Angola	Porto Amboim	-10.7333	13.7167	1.10	Micro
5	Angola	Porto Lobito	-12.3333	13.5667	1.10	Micro
6	Angola	Porto de Benguela	-12.5667	13.4167	0.92	Micro
7	Angola	Baia dos Elefantes	-13.2167	12.7333	1.10	Micro
8	Angola	Baia de Santa M.	-13.3500	12.6500	1.10	Micro
9	Angola	Namibe	-15.2000	12.1500	1.10	Micro
10	Angola	Porto Alexandre	-15.8000	11.8500	1.10	Micro
11	Angola	Baia dos Tigres	-16.6000	11.8167	1.10	Micro
12	Atlantic Is.	Ascension Island	-7.9167	-14.0333	0.70	Micro
13	Atlantic Is.	Saint Helena Is.	-15.9167	-5.7000	0.50	Micro
14	Benin	Cotonou	6.3473	2.4105	0.93	Micro
15	Cameroon	Rio Del Rey Ent.	4.5000	8.8500	1.41	Micro
16	Cameroon	Man O War Bay	3.9667	9.3670	1.20	Micro
17	Cameroon	Entrance Bimbia	4.0667	9.1170	1.10	Micro
18	Cameroon	Tiko-Bimbia R.	4.0500	9.2170	1.20	Micro
19	Cameroon	Cap Cameroun	3.9000	9.4500	1.40	Micro
20	Cameroon	Douala	4.0333	9.7000	1.62	Micro
21	Cameroon	Manoka	3.9167	9.6000	1.42	Micro
22	Cameroon	Malimba	3.5333	9.3833	1.32	Micro
23	Cameroon	Kribi	2.9167	9.9333	1.00	Micro
24	Congo	Pointe Noire	-4.7886	11.8329	0.96	Micro
25	DR Congo	Bulabemba	-6.0500	12.4500	1.00	Micro
26	Eq. Guinea	Pagalu (Annobon)	-1.4167	5.6333	0.80	Micro
27	Eq. Guinea	Bata	1.8667	9.7667	1.02	Micro
28	Eq. Guinea	Rio Benito	1.5667	9.6333	0.96	Micro
29	Eq. Guinea	Cogo-Rio Muni	1.0833	9.7000	1.49	Micro
30	Eq. Guinea	Malabo	3.7500	8.7833	1.16	Micro
31	Eq. Guinea	Bahia de Luba	3.2833	8.5833	1.02	Micro
32	Gabon	Libreville	0.3833	9.4500	1.29	Micro
33	Gabon	Pointe Owendo	0.2886	9.5101	1.45	Micro
34	Gabon	Port Gentil	-0.7149	8.7852	1.45	Micro
35	Gabon	Cap Esterias	0.6167	9.5000	1.40	Micro
36	Gabon	Cap Lopez	-0.6827	8.8580	1.23	Micro
37	Ghana	Takoradi	4.8869	-1.7401	0.76	Micro
38	Ghana	Sekondi	4.9534	-1.7369	0.98	Micro
39	Ghana	Accra	5.5599	-0.1964	0.98	Micro
40	Ghana	Tema	5.6579	0.0260	0.88	Micro
41	Guinea-Conakry	Rio Nunez App.	10.6638	-14.5844	2.65	Meso
42	Guinea-Conakry	Port Kamsar	10.6638	-14.5845	3.03	Meso
43	Guinea-Conakry	Conakry	9.5102	-13.7158	2.07	Meso
44	Guinea-Bissau	Varela	12.2865	-16.5949	1.33	Micro
45	Guinea-Bissau	Cacheu	12.2746	-16.1632	1.60	Micro
46	Guinea-Bissau	Ilheu de Caio	12.2794	-16.1655	1.90	Micro
47	Guinea-Bissau	Ponta Biombo	11.7407	-15.9516	2.33	Meso
48	Guinea-Bissau	Bissau	11.8600	-15.5767	2.89	Meso
49	Guinea-Bissau	Jabada	11.9467	-15.3477	3.34	Meso
50	Guinea-Bissau	Porto Gole	11.9668	-15.1347	3.95	Meso
51	Guinea-Bissau	Bolama	11.5772	-15.4798	2.88	Meso
52	Guinea-Bissau	Sanincha	11.8599	-15.5767	2.90	Meso
53	Guinea-Bissau	Bubaque	11.3000	-15.8272	2.54	Meso
54	Guinea-Bissau	João Vieira	11.1333	-15.6318	2.59	Meso
55	Guinea-Bissau	Cacine	11.1318	-15.0233	3.31	Meso
56	Ivory Coast	Abidjan Entrance	5.3327	-4.0296	0.74	Micro
57	Liberia	Monrovia	6.3440	-10.7930	0.90	Micro
58	Liberia	Balfu Bay	5.1529	-9.2901	0.73	Micro
59	Liberia	Sinoe Bay	5.2901	-8.8153	0.91	Micro
60	Namibia	Walvis Bay	-22.9500	14.4833	0.98	Micro
61	Namibia	Luderitz	-26.3167	15.0167	0.94	Micro
62	Nigeria	Warri	5.5499	5.7671	1.04	Micro
63	Nigeria	Forcados River	5.3700	5.4399	0.97	Micro
64	Nigeria	Opobo River	4.5147	7.5284	1.10	Micro
65	Nigeria	Kwa Ibo River	4.6660	7.9884	1.13	Micro
66	Nigeria	Bonny Town	4.4383	7.1592	1.48	Micro
67	Nigeria	Bonny River Bar	4.4296	7.1956	1.43	Micro
68	Nigeria	No 2 Buoy	4.3833	8.4000	1.10	Micro
69	Nigeria	Bakassi Bank	4.4500	8.4000	1.22	Micro
70	Nigeria	Jamestown	4.4833	8.1170	1.48	Micro
71	Nigeria	James Island	4.8667	8.1170	1.34	Micro
72	Nigeria	Calabar	4.9667	8.3170	2.09	Meso
73	Nigeria	Inikoi Island	4.8500	8.3833	1.60	Micro
74	Nigeria	Lagos Bar	6.5255	3.3785	0.78	Micro
75	Nigeria	Badagry Creek	6.4244	3.2440	0.61	Micro
76	Nigeria	Jamestown (2)	5.0167	8.3833	1.48	Micro
77	Nigeria	James Island (2)	5.5187	5.7498	1.54	Micro
78	Nigeria	Ogidigbe	5.5558	5.1822	0.97	Micro
79	Nigeria	Forcados	5.3456	5.3463	0.82	Micro
80	Nigeria	Akassa	4.3222	6.0625	0.98	Micro
81	Nigeria	Bonny River	4.4769	7.1744	1.48	Micro
82	Nigeria	Ford Point	4.8027	7.0018	1.52	Micro
83	Nigeria	Port Harcourt	4.8478	6.9650	1.46	Micro
84	Nigeria	Sapele	5.8964	5.6715	0.91	Micro
85	Nigeria	Apapa	6.4574	3.3644	0.88	Micro
86	Nigeria	Youngtown	4.4544	6.9905	0.59	Micro
87	Nigeria	Koko	5.9993	5.4460	0.56	Micro
88	Nigeria	Madagho	5.6019	5.2301	0.86	Micro
89	Nigeria	Rugged Point	5.5827	5.3727	0.75	Micro
90	Sao Tome & Pr.	Ilha do Principe	1.6000	7.2500	1.20	Micro
91	Sao Tome & Pr.	Ilha do Sao Tome	0.2167	6.7500	1.20	Micro
92	Sierra Leone	Freetown	8.4844	-13.2344	1.77	Micro
93	Sierra Leone	Shenge Point	7.9007	-12.9408	1.65	Micro
94	Sierra Leone	Sheather Rock	7.7513	-12.7971	1.68	Micro
95	Sierra Leone	Bonthe	7.5312	-12.5014	0.92	Micro
96	South Africa	Port Nolloth	-29.2500	16.0833	1.09	Micro
97	South Africa	Lamberts Bay	-32.0833	18.3333	0.85	Micro
98	South Africa	Saint Helena Bay	-32.7333	17.8333	0.90	Micro
99	South Africa	Saldanha	-33.0323	17.9214	0.99	Micro
100	South Africa	Schrywershoek	-33.0615	18.0419	0.98	Micro
101	South Africa	Cape Town	-33.9242	18.4127	0.98	Micro
102	South Africa	Simons Town	-34.1929	18.4379	1.00	Micro
103	South Africa	Hermanus	-34.4166	19.2453	1.02	Micro
104	South Africa	Mossel Bay	-34.1837	22.1267	1.17	Micro
105	South Africa	Knysna	-34.0309	23.0226	1.06	Micro
106	Togo	Lome	6.1284	1.2213	1.15	Micro
Complementary Stations - GLOSS / PSMSL / UHSLC² - ATT²
107	Senegal	Dakar	14.6333	-17.4500	0.82	Micro
108	Mauritania	Nouakchott	18.0830	-15.9800	0.97	Micro
109	Mauritania	Nouadhibou (Port-Etienne)	20.9000	-17.0500	1.00	Micro
110	Gambia	Banjul	13.4500	-16.5700	1.05	Micro
111	Ivory Coast	Abidjan (GLOSS)	5.2500	-4.2500	0.74	Micro
112	Cameroon	Port Sonara (Limbe)	4.0050	9.1250	1.20	Micro
113	Congo	Pointe Noire (GLOSS)	-4.7830	11.8330	0.96	Micro
114	Sao Tome & Pr.	Sao Tome (PSMSL)	0.0167	6.5167	1.20	Micro
115	Cape Verde	Palmeira (Sal)	16.7550	-22.9300	0.65	Micro

Parameter	Dibamba-Yassa	Betika	Batanga
Geographic Coord. (WGS84)	Lat=03°56'26" N	Lat=04°16'27" N	Lat=02°48'48" N
Geographic Coord. (WGS84)	Lon=009°49'14" E	Lon=008°23'07" E	Lon=009°49'00" E
Water Depth (LAT)	5.0 m	21.5 m	30.0 m

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Model	Variogram formula $γ (h)$
Spherical	$c_{0} + c [1.5 (\frac{h}{a}) - 0.5 {(\frac{h}{a})}^{3}], h \leq a; c_{0} + c, h > a$
Exponential	$c_{0} + c [1 - \exp (- \frac{h}{a})]$
Gaussian	$c_{0} + c [1 - \exp (- {(\frac{h}{a})}^{2})]$
Matern 3/2	$c_{0} + c [1 - (1 + \sqrt{3} \frac{h}{a}) \exp (- \sqrt{3} \frac{h}{a})]$
Matern 5/2	$c_{0} + c [1 - (1 + \sqrt{5} \frac{h}{a} + \frac{5 h^{2}}{3 a^{2}}) \exp (- \sqrt{5} \frac{h}{a})]$

Metric	Formula	Interpretation
MAE	$\frac{1}{N} \sum_{t = 1}^{N} ‖ e_{t} ‖$	Mean Absolute Error: mean absolute deviation between observed and estimated values.
RMSE	$\sqrt{\frac{1}{N} \sum_{t = 1}^{N} e_{t}^{2}}$	Root Mean Square Error: strongly penalises large and outlying errors.
R²	$1 - \frac{\sum_{t = 1}^{N} [Z (x_{t}) - {\hat{Z}}_{(- t)} (x_{t})]^{2}}{\sum_{t = 1}^{N} [Z (x_{t}) - \overset{̀}{Z}]^{2}}$	Coefficient of Determination: proportion of variance explained (Z̄=mean of observations).
Bias	$\frac{1}{N} \sum_{t = 1}^{N} e_{t}$	Systematic Bias: tendency to consistently under- or over-estimate values.

Parameter	Value
Available stations (100 km radius)	18
Retained stations (CV	9
Inter-station distances (km)	12.2 - 133.0 (mean ≈ 78.3)
Spatial extent (lat × lon)	≈ 1.73° × 2.25°
Spatial variance σ² (m²)	0.0611 (σ ≈ 0.25 m; CV=18.8%)
Station density / 1,000 km²	0.347
Mean MSL-LAT of 18 stations (m)	1.31
MSL-LAT range (m)	1.02 (Bahia de Luba) - 2.09 (Calabar)

Rank	Method	Score	σₜ (m)	Level
1	IDW	0.370	±2.479	AccepTable
2	Kriging	0.358	±2.479	AccepTable
3	TIN	0.219	±2.483	Limited
4	Trend	0.069	±2.488	Limited
5	NN	-0.125	±2.493	Limited
6	Spline	-0.149	±2.494	Limited

Method	NN	IDW	TIN	Trend	Spline	Kriging
NN	1.000	0.893	0.896	0.722	0.923	0.712
IDW	0.893	1.000	0.768	0.837	0.890	0.785
TIN	0.896	0.768	1.000	0.692	0.815	0.721
Trend	0.722	0.837	0.692	1.000	0.845	0.597
Spline	0.923	0.890	0.815	0.845	1.000	0.640
Kriging	0.712	0.785	0.721	0.597	0.640	1.000

Component	Value (m²)	Share in σ_t² (%)
σᵢ² (interpolation variance, spatial configure)	6.0827	≈ 96%
σd² (data source quality -IDW)	0.0527	≈ 1%
σd² (data source quality -NN)	0.1225	(reference)
σm² (model specification -all methods)	0.0098	< 1%
σ_t (IDW)	±2.479 m	-
CI₉₅ (IDW)	±4.859 m	-

Parameter	Value
Available stations (68 km radius)	6
Minimum inter-station distance (km)	11.8
Maximum inter-station distance (km)	65.8
Mean inter-station distance (km)	37.0
Spatial extent (lat × lon)	≈ 0.52° × 0.48°
Spatial variance σ² (m²)	0.0209 (σ ≈ 0.145 m; CV=10.6%)
Station density / 1,000 km²	1.766
Mean MSL-LAT of 6 stations (m)	1.36
MSL-LAT range (m)	1.20 (Tiko-Bimbia River) - 1.62 (Douala)

Rank	Method	Score	σₜ (m)	Level
1	Trend	0.539	±2.117	Good
2	Kriging	0.431	±2.118	AccepTable
3	NN	0.423	±2.119	AccepTable
4	TIN	0.352	±2.119	AccepTable
5	Spline	0.245	±2.121	Limited
6	IDW	0.224	±2.121	Limited

Method	NN	IDW	TIN	Trend	Spline	Kriging
NN	1.000	0.624	0.512	0.830	0.780	0.654
IDW	0.624	1.000	0.959	0.695	0.681	0.972
TIN	0.512	0.959	1.000	0.709	0.701	0.978
Trend	0.830	0.695	0.709	1.000	0.988	0.813
Spline	0.780	0.681	0.701	0.988	1.000	0.810
Kriging	0.654	0.972	0.978	0.813	0.810	1.000

Component	Value (m²)	Share in σₜ² (%)
σᵢ² (interpolation variance, spatial configure)	4.4610	> 95%
σd² (data quality - Trend Surface)	0.0150	≈ 1%
σd² (data quality - NN)	0.0211	(reference)
σm² (model specification - all methods)	0.0058	< 1%
σₜ (Trend Surface, 6 stations)	±2.117 m	-
CI₉₅ (Trend Surface, 6 stations)	±4.149 m	-
σₜ (Trend Surface, dedicated validation - 4 stations)	±1.834 m	-
CI₉₅ (Trend Surface, dedicated validation)	±3.595 m	-

Parameter	Value
Number of available stations	2 (Kribi and Malimba)
Distances to site (km)	17.3 (Kribi, south); 93.4 (Malimba, north)
Mean distance to site (km)	55.4
Spatial extent (lat × lon)	≈ 0.62° × 0.55°
MSL-LAT of stations (m)	1.00 (Kribi); 1.32 (Malimba)
Spatial variance σ² (m²)	≈ 0.0256 (n=2, statistically non-significant)
Station density / 1,000 km²	≈ 0.302
Coefficient of variation CV (%)	13.8 (uninterpreTable with n=2)

Component	Value (m²)	Share in σₜ² (%)
σᵢ² (interpolation variance)	5.5826	> 98%
σd² (data source quality -NN)	0.1447	≈ 2%
σm² (model specification)	0.0032	< 0.1%
σₜ	±2.375 m	-
CI₉₅	±4.662 m	-

Parameter	Dibamba-Yassa	Betika	Batanga
Context	Wouri Estuary (<20 m)	Rio del Rey Shelf (20-50 m)	Isolated open coast
Available / retained stations	6 / 4	18 / 9	2 / 2
Distance range (km)	16.9 - 50.4	12.2 - 133.0	17.3 - 93.4
Spatial extent (lat × lon)	≈ 0.52° × 0.48°	≈ 1.73° × 2.25°	≈ 0.62° × 0.55°
Density (st./1,000 km²)	1.766	0.347	0.302
Spatial σ (m) / CV (%)	0.145 / 10.6	0.25 / 18.8	0.16 / 13.8 (n.s.)
Retained method	Trend Surface (kopt=4)	IDW (kopt=9)	NN (default, kopt=1))
MSL-LAT offset (m)	1.571	1.147	1.00
Best RMSE (m)	0.1225 (Trend)	0.2295 (IDW)	0.320 (all)
Best R²	0.2833 (Trend)	0.1376 (IDW)	-3.000 (all)
σₜ / CI₉₅ (m)	±1.834 / ±3.595	±2.479 / ±4.859	±2.375 / ±4.662
Performance level	Good	AccepTable (moderate)	Unusable
Relative confidence (0-3)	2	1-2	0

Rank	Dibamba-Yassa (RMSE, m)	Betika (RMSE, m)	Batanga (RMSE, m)
1	Trend (0.1225)	IDW (0.2295)	All (0.320)
2	Kriging (0.1439)	Kriging (0.2343)	-
3	NN (0.1454)	TIN (0.2706)	-
4	TIN (0.1571)	Trend (0.3095)	-
5	Spline (0.1746)	NN (0.3501)	-
6	IDW (0.1777)	Spline (0.3562)	-
RMSE range	0.1225 - 0.1777 (0.055 m)	0.2295 - 0.3562 (0.127 m)	0 (degeneration)

Site	σᵢ² (m²)	σd² (m²)	σm² (m²)	σₜ (m)	Share σᵢ² (%)
Dibamba-Yassa (4 st.)	4.4610	0.015 - 0.032	0.006	±1.834	> 95%
Betika (9 st.)	6.0827	0.053 - 0.123	0.010	±2.479	≈ 96%
Batanga (2 st.)	5.5826	0.145	0.003	±2.375	> 98%

Site	Context	Reliability	Operational Recommendation
Dibamba-Yassa	Complex estuary (<20 m)	Good	Trend Surface suitable for operational use. In-situ validation by temporary tide gauge (≥15 days) recommended for critical applications.
Betika	Shelf (20-50 m)	Moderate to accepTable	Offshore surveys with conservative vertical margin ≈ ±4.9 m. Densify network to south of site.
Batanga	Isolated open coast	None	Use discouraged without dedicated tide gauge campaign. Nearest station value for indicative use only.

ATT	Admiralty Tide Tables
BLUE	Best Linear Unbiased Estimator
CI	Confidence Interval
GCV	Generalised Cross-Validation
GLOSS	Global Sea Level Observing System
IDW	Inverse-Distance Weighting
IHO	International Hydrographic Organization
JASL	Joint Archive for Sea Level
LAT	Lowest Astronomical Tide
LOO	Leave-One-Out
LOOCV	Leave-One-Out Cross-Validation
MAE	Mean Absolute Error
MSL	Mean Sea Level
NN	Nearest Neighbour
PSMSL	Permanent Service for Mean Sea Level
RMSE	Root Mean Square Error
TCARI	Tidal Constituent and Residual Interpolation
TIN	Triangulated Irregular Network
TPS	Thin-Plate Spline
UHSLC	University of Hawaii Sea Level Center
UTM	Universal Transverse Mercator
WGS84	World Geodetic System 1984

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