Abstract
Coastal sensor networks are limited less by sensing than by the radio: on our stations, one long-range uplink costs as much energy as seventy minutes of sampling. Periodic schedules therefore force a choice between battery life and the ability to see short events such as turbidity plumes. We present Tidal Memory, an event-triggered scheme in which every station and the shore server run the same compact predictor. A station transmits only when a reading would move the shared estimate by more than a threshold priced by its remaining energy, and the shore model treats each silence as a bounded observation rather than missing data. In a 214-day deployment of six stations in the Merrow Estuary, Tidal Memory sent 63.4% fewer uplinks than a 10-minute schedule while keeping reconstruction error within 4% of it, and recalled 94.1% of turbidity plumes against 71.3% for a periodic schedule with matched energy.
1Introduction
Estuaries change on two clocks. Tides move water level, salinity and temperature on a predictable twelve-hour rhythm, while rain, wind and dredging produce short events that matter most to managers: a turbidity plume can arrive and pass in under six hours. A monitoring station must report both, on a battery, through a radio that costs far more energy per message than the sensors do per sample.
The usual compromise is a fixed schedule. Sending every ten minutes captures events but drains a station in about five months; sending every thirty minutes lasts a season but blurs or misses the events (). We argue that most of what a station measures is already predictable on shore, and that the radio should carry only the part that is not.
This paper makes three contributions:
- A shared-predictor event gate whose threshold rises as the battery drains, so stations spend energy in proportion to surprise and remaining charge.
- A shore field model that treats silence as a bounded observation, which recovers most of the accuracy that event-triggered schemes usually lose.
- A 214-day, six-station deployment and an open dataset of every 1-minute sample, with a harness that replays all baselines on identical data.
2Background
Send-on-delta sampling transmits when a reading moves more than a fixed amount from the last sent value [1]. It is simple but treats the tide as change, so it spends most of its budget on predictable motion. Dual-prediction schemes keep a model on both ends of the link [2, 3]; ours extends them with an energy-priced threshold and with explicit use of silence on the receiving side. Gaussian-process reconstruction of coastal fields is well studied for complete data [4]; we adapt it to censored observations following [5].
3Method
3.1 Shared predictor
Each station keeps a tidal harmonic fit with four constituents (M2, S2, K1, O1) and a first-order residual model per variable. The shore server holds an identical copy that it updates only from received messages. Because both copies see the same inputs, they produce the same prediction at every minute, and a station always knows what the shore believes.
3.2 Energy-priced gate
At each sample the station computes the surprise of the reading under the shared prediction and transmits if it exceeds a threshold that depends on the normalised battery level b:
We use τ = 0.17 and κ = 2 throughout. A heartbeat of 6 bytes is sent after six hours of silence so the shore can tell a quiet station from a failed one.
3.3 Silence-aware field model
On shore, a spatio-temporal Gaussian process with a separable Matérn kernel fuses messages from all stations. A silent minute contributes a censored observation: the reading stayed within the gate's bound of the prediction. We approximate the resulting posterior with expectation propagation, which runs in real time for six stations on a single board computer.
4Deployment
Six stations were installed in the Merrow Estuary from 11 February to 13 September 2025 (). Each carries a multi-parameter probe, an STM32-class microcontroller, a sub-GHz radio at 20 dBm, two 18650 cells and a 2 W panel (). Stations logged every 1-minute sample to local flash, which lets us replay any policy on the same data. Two stations had outages: S2 was buried by mud for 8 days and S5 lost its radio for 7.
5Results
Table 1 reports the mean over stations. Tidal Memory comes within 4% of the 10-minute schedule's accuracy with 37% of its uplinks, and it is the most accurate method among those with a comparable budget. The threshold sweep in shows the same ordering at every budget we tested.
| Method | Uplinks / day | NRMSE | Plume recall | Lifetime |
|---|
Table 1. Main results, mean over six stations and four variables.
Removing silence modelling at an identical budget raises NRMSE from 0.081 to 0.109 (Table 2 on the project page), which is the largest single effect we measured. Radio use concentrates in storms ().
6Limitations
Fouling of a conductivity cell produces drift that the gate cannot distinguish from real change; S3 sent 18% more uplinks for 37 days until it was cleaned. Results come from one temperate estuary in one season. Lifetimes are projections from logged energy use, not measurements to depletion. Baselines were replayed, not deployed alongside. The spatial kernel assumes a fixed station layout. The project page lists these with figures ().
7Conclusion
When a station and the shore agree on what the water should do, silence becomes a measurement. That agreement lets a coastal network keep near full-rate accuracy at about a third of the radio cost. We are extending the gate to detect sensor drift so that fouling stops looking like change.
References
- Okonjo, R. and Lind, P. Send-on-delta reporting for low-power environmental sensors. Workshop on Field Sensing Systems, 2019.
- Albrecht, M., Duarte, C. and Sato, K. Dual prediction for long-lived sensor links. Journal of Embedded Telemetry, 12(3), 2021.
- Nwosu, F. and Haldane, J. Model-mirrored transmission in wireless monitoring networks. Sensing Systems Letters, 2022.
- Ferreira, L. and Whitlow, A. Gaussian-process mapping of estuarine salinity. Coastal Data Science, 7, 2020.
- Brandt, E. Expectation propagation for censored spatio-temporal data. Statistical Signal Processing Notes, 2023.
AAppendix: hardware and energy model
Average power is dominated by the radio. The table lists each part with its mean draw over the deployment under Tidal Memory.
| Part | Specification | Mean draw | Share |
|---|
Table A1. Station bill of materials and mean power. Unit cost per station was 214 EUR excluding the probe.
An uplink averages 1.24 J at 24-byte payloads, including radio wake-up at the slowest data rate. That is as much as the rest of the station uses in about seventy minutes. Lifetime projections divide 2 × 1,500 mAh at 3.2 V (9.6 Wh) by the logged daily energy with the panel disconnected.
Version history
- v2, camera-ready14 Sep 2026
Added the ablation of the tidal prior (Table 2). Corrected S5 uptime from 209 to 207 days; no result changed by more than 0.001 NRMSE.
- v1, preprint12 Mar 2026
Initial release with code v1.0.0 and the dataset.