Rapid estimation of global sea surface temperatures from sparse streaming in situ observations

TL;DR

This paper presents S-DEIM, a model-free method to reconstruct high-resolution sea surface temperatures from sparse in situ observations by coupling instantaneous empirical interpolation with an RNN-learned kernel. Trained on NOAA OISST data, S-DEIM significantly improves over DEIM and Q-DEIM, achieving roughly 40% lower reconstruction error and 91% of estimates within ±1°C, while remaining robust to sensor placement and enabling real-time performance. The approach hinges on estimating the S-DEIM kernel vector from past observations via RNNs (RC and LSTM), addressing the underdetermined reconstruction problem where r < m. The work demonstrates practical utility for rapid nowcasting and offers avenues for extending to moving sensors and multi-fidelity data integration.

Abstract

Reconstructing high-resolution sea surface temperatures (SST) from staggered SST measurements is essential for weather forecasting and climate projections. However, when SST measurements are sparse, the resulting inferred SST fields are rather inaccurate. Here, we demonstrate the ability of Sparse Discrete Empirical Interpolation Method (S-DEIM) to reconstruct the high-resolution SST field from sparse in situ observations, without using a model. The S-DEIM estimate consists of two terms, one computed from instantaneous in situ observations using empirical interpolation, and the other learned from the historical time series of observations using recurrent neural networks (RNNs). We train the RNNs using the National Oceanic and Atmospheric Administration's weekly high-resolution SST dataset spanning the years 1989-2021 which constitutes the training data. Subsequently, we examine the performance of S-DEIM on the test data, comprising January 2022 to January 2023. For this test data, S-DEIM infers the high-resolution SST from 100 in situ observations, constituting only 0.2% of the high-resolution spatial grid. We show that the resulting S-DEIM reconstructions are about 40% more accurate than earlier empirical interpolation methods, such as DEIM and Q-DEIM. Furthermore, 91% of S-DEIM estimates fall within $\pm 1^\circ$C of the true SST. We also demonstrate that S-DEIM is robust with respect to sensor placement: even when the sensors are distributed randomly, S-DEIM reconstruction error deteriorates only by 1-2%. S-DEIM is also computationally efficient. Training the RNN, which is performed only once offline, takes approximately one minute. Once trained, the S-DEIM reconstructions are computed in less than a second. As such, S-DEIM can be used for rapid SST reconstruction from sparse streaming observational data in real time.

Figures (10)

• Figure 1: Schematic framework for S-DEIM. In the offline stage, we use high-fidelity data to train the RNN. This pretrained RNN is then used in real-time reconstruction to obtain the S-DEIM estimate from sparse in situ observations.
• Figure 2: Three POD modes generated using the training dataset.
• Figure 3: Mean and standard deviation of relative reconstruction error for an increasing number of modes $m$. The mean and standard deviation are taken over the snapshots in the test dataset.
• Figure 4: Relative reconstruction error with $r=100$ sensors and $m=300$ modes. (a) CPQR sensor placement. (b) Randomly placed sensors.
• Figure 5: The PDF of the difference $\Delta T$ between the reconstructed SST and the truth for Q-DEIM and S-DEIM. For S-DEIM, $\Delta T$ is concentrated around $0^\circ$C, with $91\%$ of reconstructions falling within $\pm 1^\circ$C. For Q-DEIM, $\Delta T$ exhibits heavier tails and only $51\%$ are within $\pm 1^\circ$C.