the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note: Removing dynamic sea-level influences from groundwater-level measurements
Todd C. Rasmussen
Gabriel C. Rau
Abstract. The sustainability of limited freshwater resources in coastal settings requires an understanding of the processes that affect them. This is especially relevant for freshwater lenses of oceanic islands. Yet, these processes are often obscured by dynamic oceanic water levels that change over a range of time scales. We use regression deconvolution to estimate an Oceanic Response Function (ORF) that accounts for how sea-level fluctuations affect measured groundwater levels, thus providing a clearer understanding of recharge and withdrawal processes. The method is demonstrated using sea-level and groundwater- level measurements on the island of Norderney in the North Sea (Northwest Germany). We expect that the method is suitable for any coastal groundwater system where it is important to understand processes that affect freshwater lenses or other coastal freshwater resources.
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Patrick Haehnel et al.
Status: final response (author comments only)
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RC1: 'Comment on hess-2023-54', Jonathan Kennel, 18 Jun 2023
This Technical Note introduces the Ocean Response Function which is an application of regression deconvolution using tidal levels as a basis for inputs. It can be used to remove the ocean signal from the water level data. It is well written and presents the underlying study well.
Moderate concern:
- In terms of the scientific significance could you describe the difference between the ocean response function and river response function as you see it? Perhaps you might describe how you see them different or similar. Some rivers also have strong tidal effects due to ocean levels or cyclical forcing resulting from dam operations. Does each stressor (barometric, evapotranspiration, pumping, precipitation, Earth tides, river stage, lake levels, ocean tides, anthropogenic loading/unloading, seismic, …) require a separate methods paper when the underlying method is the same but the input varies? Is the key point that for this ocean tide example that the response can be approximated as linear time invariant over the time frame of analysis.
Minor concerns:
- Lines 85:88 “It is recommended to perform the deconvolution using the first differences of the measurements, leading to Eq. 5 becoming ∆y = β ∆X. This removes the effect of persistent trends in the data and therefore avoids a bias in the regression (Rasmussen and Crawford, 1997; Butler Jr. et al., 2011). “ It is also possible to prefilter data or include a background trend term(s) in the regression equation. I would probably not include the difference formulation as a recommendation, but can mention why you did it. In general if appropriate data is available the analysis can be done on non-differenced data. It also avoids the correction required in line 89.
- The term “corrected” is used throughout. While this is commonly used and has been defined before, it suggests that the raw water level is in error. I prefer, the water level with the ___ component(s) removed.
- With different length maximum lags you are comparing response functions based on different time periods, you may want to say this or highlight the applicable analysis length. It might not be important with long datasets and relatively short lags, but in shorter length datasets it may be important. Also if the relationship isn’t strictly LTI it can be an issue.
- Perhaps mention how ocean tides and barometric pressure are spatially variable. What is the influence of the tide monitoring location and weather monitoring location. Is it important for this study?
- 162:163 “Tidal data were downsampled to hourly intervals for subsequent analysis.” Readers may be interested in how - dropping non-matching values or other decimation procedure.
- 183:184 “The precipitation response of BS3 and NY-10 is discernible in mid-August 2019, where groundwater levels increase despite a lack of change in sea levels.” Did you calculate a response function for these? If not why not?
- 187 “Periodic and aperiodic sea-level fluctuations” consider simplifying to “Sea-level fluctuations”
- How reproducible are the response functions when calculated for different portions of the dataset?
- The ocean tide data also includes a barometric related component which may be worth mentioning more directly. This could influence the analysis when barometric pressure and ocean tides were used as it now ends up having correlated data.
- In the ocean response functions, did you compensate for salt water density? Might be worth mentioning if you did or didn’t and how it might affect the response function numbers.
- A key aspect of this is the linear time invariant assumption. I think you should mention this in the applicability portion of the conclusions.
- There is no interpretation of the responses. Given that the ocean tides can be considered similar to other surface water bodies - it is likely very similar to a river response function analysis (Brookfield et al, 2017). Interpreting temporal variations in river response functions: an example from the Arkansas River, Kansas, USA
Figure suggestions:
Figure 4: Were ocean levels converted to freshwater head for the comparison? If the goal of this figure is to highlight the signal with the ocean response removed, you may want to make this the focus by using a smaller vertical range for these. Right now they are somewhat obscured by the large y-axis range. I’m not sure it is necessary to repeat the ocean levels and precipitation on each facet and I would probably just have them in separate facets. This also improves readability by not having dual axes. A subset of the total time can also be helpful.
Figure 5: Perhaps you want to comment on the oscillations in the response function – what frequency and the potential causes – method related, noise related.
Figure 6: I don’t think I would highlight the pumping times with the grey boxes in A. It makes it seem like this is actual data. If you include it, I would clearly annotate on the figure to say inferred.
HESS questions
- Does the paper address relevant scientific questions within the scope of HESS? Yes
- Does the paper present novel concepts, ideas, tools, or data? The tools, concepts, and ideas are well developed previously, data and the relationships are new for this site.
- Are substantial conclusions reached? Yes/No
- Are the scientific methods and assumptions valid and clearly outlined? Yes
- Are the results sufficient to support the interpretations and conclusions? Yes
- Is the description of experiments and calculations sufficiently complete and precise to allow their reproduction by fellow scientists (traceability of results)? Yes
- Do the authors give proper credit to related work and clearly indicate their own new/original contribution? Yes
- Does the title clearly reflect the contents of the paper? Yes
- Does the abstract provide a concise and complete summary? Yes
- Is the overall presentation well structured and clear? Yes
- Is the language fluent and precise? Yes
- Are mathematical formulae, symbols, abbreviations, and units correctly defined and used? Yes
- Should any parts of the paper (text, formulae, figures, tables) be clarified, reduced, combined, or eliminated? See comments
- Are the number and quality of references appropriate? Yes
- Is the amount and quality of supplementary material appropriate? The supplementary data and code are good. I don’t know that the appendix B is necessary.
Citation: https://doi.org/10.5194/hess-2023-54-RC1 - AC1: 'Reply on RC1', Patrick Hähnel, 09 Oct 2023
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RC2: 'Comment on hess-2023-54', Rachel Housego, 15 Sep 2023
This manuscript applies a linear regression deconvolution to remove ocean-driven water fluctuations from groundwater heads observed at different three different locations and depths across the barrier island. After removing the ocean-driven forcing the residual groundwater fluctuations are used to understand recharge and pumping responses on the island. Overall, I think the paper is well-written, the figures are easy to interpret and it was interesting to see how well the timing of the fluctuations in the corrected time series did coincide with the pumping schedule. I think some of the methods and conclusions would benefit from adding some additional context about what is unique about applying these functions in a coastal setting to further differentiate it from other papers manuscripts that have applied similar techniques. With some additional clarification I think this manuscript will make a nice contribution to HESS. See specific comments below.
A lot of work (although not yet applied in coastal settings) has been done using transfer function noise models, which is also a convolution-based method for groundwater time series analysis but presumes a fixed shape of the response function. I think it would be worth citing some of this work and noting the difference in the methods.
Collenteur, R. A., Bakker, M., Caljé, R., Klop, S. A., & Schaars, F. (2019). Pastas: open source software for the analysis of groundwater time series. Groundwater, 57(6), 877-885.
Neglecting wave set-up likely causes an issue in removing the oceanic effects on water levels, especially during surges. For more see the following papers and references therein.
da Silva, P. G., Coco, G., Garnier, R., & Klein, A. H. (2020). On the prediction of runup, setup and swash on beaches. Earth-Science Reviews, 204, 103148.
Stockdon, H. F., Holman, R. A., Howd, P. A., & Sallenger Jr, A. H. (2006). Empirical parameterization of setup, swash, and runup. Coastal engineering, 53(7), 573-588.
How does the ORF behave in the frequency domain? Is it consistent with what is known about how ocean driven water table fluctuations propagate through the subsurface, e.g. longer wave periods propagate faster and attenuate less?
How sensitive are the ORF parameters to the storm? There is only one in the data set, if it is removed how different is the maximum time lag at each well? I think it may be possible that the maximum time lag is heavily influenced by the intensity and duration of the surges in the data set and if a more extreme event was measured that parameter may be different.
Would there be any benefit to applying the tidal constituents and the moving-averaged trend as separate drivers/would the residual be different if you took that approach?
What concerns are there for overfitting and aliasing with this approach?
Would the generated ORF function have the ability to forecast future groundwater levels based on ocean water level time series? Under what environmental conditions would this not work as well?
Line 235-245 I think this is presented as being too generally applicable to all coastal environments however some field studies have shown non-linear responses to ocean forcing, developing skewness and asymmetry in the water table fluctuations that I do not think this method would be able to remove.
E.g. Raubenheimer, B., Guza, R. T., & Elgar, S. (1999). Tidal water table fluctuations in a sandy ocean beach. Water Resources Research, 35(8), 2313-2320.
Citation: https://doi.org/10.5194/hess-2023-54-RC2 - AC2: 'Reply on RC2', Patrick Hähnel, 09 Oct 2023
Patrick Haehnel et al.
Patrick Haehnel et al.
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