the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Apr 2023
Measurement Error Proxy System Models: MEPSM v0.2
Abstract. Proxy system models (PSMs) are an essential component of paleoclimate data assimilation and for testing climate field reconstruction methods. Generally, current statistical PSMs consider the noise in the output (proxy) variable only, and ignore the noise in the input (environmental) variables. This problem is exacerbated when there are several input variables. Here we develop a new PSM, the Measurement Error Proxy System Model (MEPSM), which includes noise in all variables, including noise auto- and cross-correlation. The MEPSM is calibrated using a quasi-Bayesian solution, which leverages Gaussian conjugacy to produce a fast solution. Another advantage of MEPSM is that the prior can be used to stabilize the solution between an informative prior (e.g. with a non-zero mean) and the maximum likelihood solution. MEPSM is illustrated by calibrating a proxy model for δ18Ocoral with multiple inputs (marine temperature and salinity), including noise in all variables. MEPSM is applicable to many different climate proxies, and will improve our understanding of the effects of predictor noise on PSMs, data assimilation, and climate reconstruction.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2023-643', Anonymous Referee #1, 01 Dec 2023
This work proposes a proxy system model, which incorporates both prior information and generalized noise in all variables. This can be useful for paleoclimate data assimilation. The results look reasonable. The reviewer suggests this paper can be accepted after some minor revisions.
- I recommend the author to restructure Section 2.1, the existing methods/theories should be distinguished from the proposed methodology. The increment unique to this work needs to be clear.
- Because this paper has many symbols, I suggest all the symbols like those around Line 60 should be documented in Table 1, rather than being described in the text near the equations.
- On line 122, better use “Hadamard product” instead of “Hadamard multiplication”.
- Line 45, “exapands”=>”expands”
- Line 255, “incoporates”=> “incorporates”
Citation: https://doi.org/10.5194/egusphere-2023-643-RC1 -
RC2: 'Comment on egusphere-2023-643', Anonymous Referee #2, 22 Apr 2024
Overview
Proxy system models (PSMs) translate climate signals to proxy measurements and make the direct comparison between climate model simulations and proxy observations possible. They are also known as "forward data models" in contrast to "inverse models" that translate proxy measurements to climate signals. Since the forward process is natural (climate affects proxy formation; not the other direction), and the solution of an inverse process could be non-unique, PSMs have become a key component in paleoclimate data assimilation frameworks that bridges climate model simulations and proxy observations.
Existing statistical PSMs usually yield output with uncertainties, assuming the input climate signals are noiseless. This study proposes a new PSM framework that considers noises not only in the output, but also in the input. The comparison against existing PSMs may improve our understanding of the impact of the input noise on PDA reconstructions. I find the topic of this study to be important, and the proposed approach is noteworthy. The manuscript overall maintains a fine quality, although there are instances where the writing seems informal, and several places require clarification regarding the details. Furthermore, a major concern of mine is that while an application example is presented and some differences are compared, it is still unclear, at least not straightforward enough, on how the new PSM framework shows improvement compared to the traditional ones in terms of proxy data modeling accuracy. Therefore, I think a major revision is necessary. A few specific comments are listed below.
Specific comments- The idea of introducing prior noises is understandable. However, the setup of the current PDA projects applies an ensemble prior that samples potential prior errors as the input for the traditional statistical PSMs, which eventually can take into account the impact of the prior noises. In this ensemble prior setting, does the proposed new PSM framework show significant advantage? More discussions are needed.
- L31: What does "a" represent here; noise? Also, the word "unobservable" requires some clarification to readers not familiar with the method, as it is used many times in the manuscript. Does it mean the real signal without noise?
- L32: "Appendix 1" --> "Appendix A".
- Code availability: "Easy to read" --> "Intuitive"
- Conclusions: While I appreciate the author's theoretical work, overall it seems to me that the manuscript lacks a convincing validation. The author states that the next step is to apply the proposed PSM to different proxy types and to incorporate it into PDA projects. However, in my opinion, more tests and validations, e.g., real-world data modeling tests on more sites, and perhaps even a pseudoproxy DA experiment if the author would like to make concrete connections to PDA applications, are actually needed for this study to clearly show that this new PSM indeed works. The analyses in Figs. 1-4 and Table 2 show only the differences, which may not necessarily be the improvements.
Citation: https://doi.org/10.5194/egusphere-2023-643-RC2
Model code and software
Mattriks/MeasurementErrorModels.jl: MEPSM v0.2.0 Matt Fischer https://doi.org/10.5281/zenodo.7793741
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