Status: this preprint is open for discussion and under review for Geoscientific Instrumentation, Methods and Data Systems (GI).
Bias corrections and prediction intervals for time-series measurements with fouling and calibration drift
Timothy O. Hodsonand Gregory E. Schwarz
Abstract. Environmental time-series measurements are subject to systematic errors from fouling and calibration drift, requiring operators to routinely check, clean, and recalibrate their sensors. Information from these checks can then be used to estimate bias corrections and prediction intervals for the measurements. If the checks are exact, the corrections and intervals have direct solutions. More realistically, the checks are noisy, and the error state is estimated with a Kalman smoother. Check information can also be pooled across sensors in a monitoring network to improve estimates for newly deployed sensors. The method relies on checks that operators already perform, and its computation and storage demands are modest, so it integrates readily into existing monitoring programs.
Received: 06 Jul 2026 – Discussion started: 17 Aug 2026
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The manuscript, Bias corrections and prediction intervals for time-series measurements with fouling and calibration drift, by Hodson and Schwarz presents a framework for handling measurement errors in environmental monitoring. A downloadable computer code with the framework has also been made and is cited in the manuscript.
The manuscript is mathematically dense and including appendices contains about 100 equations. I have not checked all of them but found no errors in the ones I did scrutinize.
The content of the manuscript is clearly appropriate for GI journal, and I have no objections to the manuscript being published after a moderate revision outlined below.
Abstract: The abstract needs thorough revision. As it is written now, it reads like a background section and it is not clear from the abstract what the manuscript contains, what contributions are presented, and what the results are.
Introduction: The background of the introduction is very, very short. In my opinion it would be appropriate if several papers with examples of environmental monitoring (with relevance to the presented methodology) were discussed and cited and similarly it would be appropriate with some sort of summary of the present methodology for time-series calibration and a clear exposition of what the novel contributions of this work are.
Regarding the positioning of the manuscript in the research literature, it is a little odd that the most recent paper cited is from 2010. As such this is not a problem, but it underlines the need for a more thorough introduction to the manuscript.
Equation 19. The assumed error model contains a linear term. Is this enough to adequately model the sensors or is there a risk that higher-order terms would be required?
The manuscript contains a demonstration section, but it is rather short and difficult to match with the manuscript. With fouling errors being an integral part of the presented framework I would have assumed a more detailed discussion and data examples in this demonstration. I would expect that the authors have made tests on both numerous synthetic data sets and other real-world data. However, there is no mention of such.
Further, there is no discussion section in the manuscript putting the framework into a broad context, e.g., what are the pitfalls with this method? There are a few comments here and there in the text, but in my opinion, it would be appropriate with a more thorough discussion.
Environmental sensors gradually develop errors during the course of a deployment. Operators routinely check, clean, and recalibrate each sensor, but current practice treats the checks as error-free and reports no uncertainty for the corrected data. We present a statistical method that quantifies uncertainty in both the checks and the corrections, combines information across a sensor network to improve estimates for new sensors, and is efficient enough for routine use.
Environmental sensors gradually develop errors during the course of a deployment. Operators...
The manuscript, Bias corrections and prediction intervals for time-series measurements with fouling and calibration drift, by Hodson and Schwarz presents a framework for handling measurement errors in environmental monitoring. A downloadable computer code with the framework has also been made and is cited in the manuscript.
The manuscript is mathematically dense and including appendices contains about 100 equations. I have not checked all of them but found no errors in the ones I did scrutinize.
The content of the manuscript is clearly appropriate for GI journal, and I have no objections to the manuscript being published after a moderate revision outlined below.
Abstract: The abstract needs thorough revision. As it is written now, it reads like a background section and it is not clear from the abstract what the manuscript contains, what contributions are presented, and what the results are.
Introduction: The background of the introduction is very, very short. In my opinion it would be appropriate if several papers with examples of environmental monitoring (with relevance to the presented methodology) were discussed and cited and similarly it would be appropriate with some sort of summary of the present methodology for time-series calibration and a clear exposition of what the novel contributions of this work are.
Regarding the positioning of the manuscript in the research literature, it is a little odd that the most recent paper cited is from 2010. As such this is not a problem, but it underlines the need for a more thorough introduction to the manuscript.
Equation 19. The assumed error model contains a linear term. Is this enough to adequately model the sensors or is there a risk that higher-order terms would be required?
The manuscript contains a demonstration section, but it is rather short and difficult to match with the manuscript. With fouling errors being an integral part of the presented framework I would have assumed a more detailed discussion and data examples in this demonstration. I would expect that the authors have made tests on both numerous synthetic data sets and other real-world data. However, there is no mention of such.
Further, there is no discussion section in the manuscript putting the framework into a broad context, e.g., what are the pitfalls with this method? There are a few comments here and there in the text, but in my opinion, it would be appropriate with a more thorough discussion.