| 18 Aug 2026
Application of Sparse Sensing for Stream Nutrient Monitoring Programs
Abstract. Existing stream nutrient (i.e., nitrogen or phosphorus) monitoring approaches often exhibit low sampling frequency and associated high uncertainty due to financial and maintenance constraints. Data-driven Sparse Sensing (DSS) offers an alternative approach to estimate concentration data at high resolution using fewer measurements. DSS transforms stream data from training locations into a reduced-dimension space and identifies optimal sampling times. These optimal measurements are used to reconstruct high-resolution concentration data at target locations. In this study, we used the DSS framework to estimate stream nutrient concentrations and loads (nitrate nitrite as NOx and total phosphorus as TP) across the US Midwest region, with additional analyses in other hydrologic regions to examine regional variability in optimal sampling times. The modeling approach was designed to address key issues in nutrient monitoring programs, including determining the required size and length of training data and establishing data selection procedures. The base model predicted NOx and TP concentrations and loads with good accuracy (NSE > 0.5, load error < ±4 % for NOx; NSE >0.45, load error < ±10 % for TP) using only 40–60 samples per year (~10–15 % of total measurements). Optimal sampling times were concentrated in spring and early summer in the Midwest but varied across regions. Findings indicated that DSS requires only 2–3 years of training data from either 10–15 regional monitoring locations (NOx and TP) or the target location itself (NOx). This study demonstrates that DSS can be integrated into nutrient monitoring programs to generate high-resolution stream data, estimate loads, and support resource-efficient management decisions.
I read with interest this paper on distributed sensing for nutrient monitoring. I think the distributed sensing is an elegant method that hydrologists and monitoring programme managers should be more aware of. It is a follow-on from the GRL (2025) paper from the authors. In essence, it identifies the optimal sampling times from SVD of high resolution historical data—sampling at those times in the future can reconstruct the full resolution. The overarching aim is to replace daily sampling with ~40-60 strategically chosen samples per year.
This paper made several useful incremental contributions from previous papers on the topic by the group. Notably, it investigates the (1) data requirements for DSS implementation (2) regional transferability (Midwest, Mid-Atlantic, S. Atlantic Gulf), (3) compares historical vs regional training and (4) flow only vs flow and concentration training. Its key result is that regional information is highly transferable, and a monitoring network containing roughly 10-15 nearby stations and 2-3 years of data can generate a useful low-dimensional representation of nutrient dynamics (Sections 3.1.5 and 3.2.1-3.2.3). Much of the rest of the text is largely elaboration of the 2025 framework.
While the data requirement analysis is valuable, the concept was demonstrated and results compared benchmark load estimation models, these contributions are hidden in the current narrative. Crucially, the title of the article does not highlight the key contributions of the article and the issues that are being addressed. Readers unfamiliar with DSS are unlikely to know what the motivations are to use the method. I would suggest expanding and highlighting sensitivity/regional analysis in the text and the title, which is the main contribution of the manuscript. Th empirical sensitivity analysis is thorough but would be strengthened by a more rigorous treatment of uncertainty (e.g. uncertainty bounds, sensitivity to extremes years), non-stationarity, and experimental design theory.
The discussion section is currently too limited for HESS and similar journals in terms of the wider literature on monitoring network optimisation, adaptive sampling, experiment design, optimal sensor placement, hydrologic similarity/regionalisation, information theory, etc. A discussion on the operational constraints for field sampling will also be highly relevant. The conclusions are also too descriptive and limited to the current study, rather than tying the findings with previous literature or a broader theoretical framework.
The current text mirrors greatly to the 2025 GRL paper. Although the figures and nothing is copied substantially verbatim, the structure and arguments are very similar. The introductions basically had the same flow. The main addition is a longer discussion of compressed sensing and practical monitoring needs. I suggest bringing in the motivation for the analysis done in this study early and highlight why it is needed. The methodology section is essentially the same. I suggest on focusing on extra analytical methods or metrics that was not used in the previous paper. The results sections’ narrative structures are also nearly identical—I suggest varying it to highlight the most novel findings.
The discussion section contains several arguments that are restated from the previous study. It may be useful to separate findings that confirm the earlier work from those that genuinely extend it. This would make the contribution of the present manuscript clearer.
Finally, I was not entirely convinced by the citation to Kratzert et al. (2019). The paper is on LSTM/ML flow prediction in ungauged catchments. Currently, I don’t see the link between the two methods.