Can a Single Profile Reveal the Three-Dimensional Ocean Temperature Field in Its Surrounding Region? A Lightweight Deep Learning Proof of Concept

Abstract

The 3-D ocean temperature fields are fundamental to ocean dynamics, ecosystems, and climate, yet observing them at high resolution remains a major challenge. A critical gap exists between extensive satellite surface coverage and sparse subsurface in situ measurements—lacking the ability to map the 3-D context around individual profiles. This study introduces and validates a novel paradigm: directly inferring the synoptic 3-D ocean temperature field from a single vertical profile. We propose the profile-to-3D-field network (P3DFNet), a lightweight deep learning model that transforms an instantaneous profile into a 3-D field (∼100 km × 100 km, 0–1000 m); its efficient architecture enables near-real-time deployment on resource-constrained platforms. A key methodological contribution addresses an overlooked issue: conventional root-mean-square error (RMSE) is sensitive to depth-layer configuration, impeding fair cross-study comparisons. We argue for a domain-averaged perspective and propose volume-averaged RMSE (VARMSE) as a robust, discretization-invariant metric, using its squared form as the training loss for evaluation alignment. Developed using HYbrid Coordinate Ocean Model (HYCOM) reanalysis data from 1992 to 2008 for training and 2009 to 2010 for validation, P3DFNet outperforms climatology and neighbor estimations on a held-out HYCOM test set (2011–2012), achieving VARMSE reductions of 59% and 9% while extending the area below the neighbor's average error by 36%. Critically, this advantage is confirmed against independent in situ observations (2014–2024), where P3DFNet reduces error by 44% and 17% versus baselines. This work provides the first proof-of-concept for the profile-to-3D-field paradigm, demonstrating that a single profile contains recoverable information about its spatial context. By transforming point measurements into synoptic fields, this approach augments ocean observing systems and creates new opportunities for integrating sparse in situ data with satellite observations.