the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 May 2025
Detecting ground ice in warm permafrost with the dielectric relaxation time from SIP observations
Abstract. The melting of ground ice poses significant hazards in permafrost regions, making effective detection methods essential. Conventional geophysical techniques like electrical resistivity, seismic surveys, or ground-penetrating radar alone often produce ambiguous results due to the overlap of material characteristics between frozen and unfrozen ground. This study addresses these limitations by using the dielectric relaxation time of ice as a unique indicator of ground ice. We developed a method to quantify relaxation time from Spectral Induced Polarization (SIP) data measured by the FUCHS III device. The method's effectiveness was demonstrated through synthetic data and two field surveys. SIP field measurements, ranging from 1.46 Hz to 40 kHz, were conducted on a retrogressive thaw slump and a pingo in Yukon, Canada. The extracted relaxation times were mapped to pseudo-depths obtained from single-frequency inversion. This study proposes a relaxation time range from 10 to 400 µs for ground ice, and the results demonstrate that this range can detect ground ice spectra in field studies. Comparison with observations in a borehole and an exposure of permafrost indicate that relaxation time is less ambiguous in detecting ground ice in warm permafrost than conventional methods such as electrical resistivity tomography.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-1801', Anonymous Referee #1, 16 Jun 2025
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AC1: 'Reply on RC1', Hosein Fereydooni, 12 Sep 2025
We are sincerely grateful to Anonymous Referee #1 for their thorough review and guidance to improve the manuscript. Below, we provide a point-by-point response to the issues they raised.
Reviewer 1 response
The Referee wrote: Line 52: Real part is resistance, which is different from resistivity. It is important to have the right terminology, especially in this (theory) section. You may wish to explain the relationship between resistance and resistivity after.
Response: The manuscript has been updated accordingly.
The Referee wrote: Table 1: Is this produced with Eq. 7? If so, it is not very clear to the reader.
Response: Clarified in manuscript.
The Referee wrote: Line 189: Are the ground electrodes Ag/AgCl? This type of electrodes is used in SIP surveys to avoid polarization. Please specify.
Response: The ground electrodes used in this study were made of stainless steel, selected for their low resistivity, good conductivity, and high mechanical strength, which ensures stable contact even in frozen or rocky terrain. Stainless steel electrodes have been shown to exhibit relatively low polarization effects and to provide stable, reliable measurements in geoelectrical surveys (LaBrecque and Daily, 2008). The electrode materials is now clarified in the text.
The Referee wrote: Line 213: It looks like you have accurate GPS coordinates of the electrodes used. Are these being used in your inversions?
Response: No, the GPS coordinates of the electrodes were not directly used in the inversions.
The Referee wrote: Figure 6: X and Y axis font is too small.
Response: The figure has been updated.
The Referee wrote: Methods and Results: There is not a great deal of detail about postacquisition data processing. You also don’t report any error metrics corresponding to inversion or ART results. I believe this needs to be addressed in order to contextualise the accuracy of the model results presented.
Response: The RMSE percentage for the real-part inversion and the absolute error in mrad for the imaginary part have been added to the manuscript.
The Referee wrote: Consequently, the error corresponding to your results could have an impact on which areas you can confidently categorize as “containing ground ice”.
Response: In this manuscript, the focus is on the ART (Apparent Relaxation Time) as the key indicator for ground ice. During data processing, every extracted relaxation time comes from spectra that were fitted with a multi-Cole-Cole model and must pass a predefined RMSE threshold (< 6%), meaning only those fits with acceptably low error are considered. As a result, all relaxation times reported as evidence for ground ice (or for its absence) have met this confidence criterion, ensuring that the ground ice categorization is robust and backed by reliable spectral fits.
The Referee wrote: Figure 11: Can you comment on the fact that relaxation time does not seem to change when ice content increases. It seems to be effective in picking up presence of ice but not disgusting between different levels of ice content.
Response: The relationship between relaxation time and varying ground ice content was not evaluated in this study and is therefore outside the scope of the current research. But as seen in Figure 11, the relaxation time exhibits a subtle increasing trend that may relate to increasing ground ice content, rising from approximately 25 to 35 microseconds.
The Referee wrote: Line 298: Remove “the”?
Response: The manuscript has been updated.
The Referee wrote: Line 300: I would probably introduce RFE earlier, alongside the other equations in your methodology, not in the discussion.
Response: RFE has been introduced earlier in Section 2.5 (Detecting ground ice based on SIP measurements) in the revised manuscript.
The Referee wrote: Figure 12: Please mention what yellow and black outlines mean in figure caption.
Response: The manuscript has been updated.
The Referee wrote: Figure 13: As for figure 12, please explain the black outlines in the figure caption.
Response: The manuscript had been updated.
The Referee wrote: Line 312: Degree symbol.
Response: done.
The Referee wrote: Line 330: How was the threshold for the imaginary part determined?
Response: The threshold values for both the imaginary part and the RFE were chosen based on statistical analysis of the data to identify anomalously high signals that reliably indicate polarization effects linked to frozen ground conditions. This statistical cutoff ensures that only signals significantly above typical background variability are considered.
The Referee wrote: Section 6.2: I don't fully understand the logic behind figures 14 and 15. ART categorizes some data points as in the "contains ground ice region", Imaginary part does the same, and there is some overlap between the two. However, how do you know which one is correct? Is this based on the borehole data? Are you assuming everything below 0.6m depth (borehole log) has an above zero percentage of ground ice?
Response: The primary goal of Figures 14 and 15 is to compare non-inverted data for consistent analysis using defined criteria to categorize data points as ground ice. At the borehole location, ART results show strong agreement with the borehole visible ice, validating the method.
The Referee wrote: Line 367: I suggest you expand this is a short paragraph in your discussion. The section would be about the limitations of the SIP method, pathways for improvement and future research. I believe this would round up your narrative and provide prospects for future Studies.
Response: A separate section titled “Current limitations of using SIP for detecting ground ice” has been added to the discussion.
**The marked version of the manuscript is attached.
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AC1: 'Reply on RC1', Hosein Fereydooni, 12 Sep 2025
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RC2: 'Comment on egusphere-2025-1801', Anonymous Referee #2, 11 Aug 2025
In their preprint submitted to EGUsphere, “Detecting ground ice in warm permafrost with the dielectric relaxation time from SIP observations”, Fereydooni et al. (2025) introduce the Apparent Relaxation Time (ART) approach for detecting ground ice within warm and highly conductive permafrost by leveraging dielectric relaxation time derived from spectral induced polarization (SIP) measurements.
This is a complement approach to use SIP measurements for ground ice detection (without quantification or thermal characterization) in field scale. In addition, the authors present a great dataset of high-frequency SIP measurements of frozen ground, which is of high scientific interest by its own, demonstrate the field applicability of the ART approach for delineating subsurface zones containing ground ice, and compare the results to other established SIP data analysis frameworks.
Nevertheless, fundamental improvements and corrections are required before this draft is suitable for publication in The Cryosphere.
- Correct usage of terminologies, symbols and equations:
Please use the terms “impedance”, “apparent complex resistivity”, and “complex resistivity” correctly (see e.g. Binley and Slater, 2020. Resistivity and Induced Polarization, DOI: 10.1017/9781108685955). Instead of “apparent impedance” use “apparent complex resistivity”.
Use correct notation of complex symbols and indicate all complex valued parameters with $^*$. To indicate real and imaginary part, you can use $^{\prime}$ and $^{\prime\prime}$ instead of subscripts.
Note, that relaxation times from different model definitions are not equivalent (e.g. Limbrock and Kemna, 2024. Relationship between Cole–Cole model parameters in permittivity and conductivity formulation, DOI: 10.1093/gji/ggae300). In this study, a resistivity-based model is used to estimate relaxation times while reverence values for ice a given for a permittivity-based model. As exact relaxation time values are not used for further analysis (e.g. temperature estimates), this is not a big issue but should be mentioned.
Please use short subscripts for parameters and in equations. E.g. “app” or “a” ($\rho_a$) instead of “apparent”, “meas” or “m” instead of “measured”, in Eq. 10: “m” for “measured” or “d” for “data”, and “f” for forward response instead of “predicted”. Also, make sure that you follow the official Copernicus guidelines for mathematical notations and terminology (https://publications.copernicus.org/for_authors/manuscript_preparation.html#math).
- Structure of Section 2 (Background):
Please reorganize this section and rename the subsections. Subsections 2.1 and 2.3 referrer to special media while 2.2 also is about ice polarization and 2.4 about interpretation depending on type of ground media.
- Improve figures:
Make sure that all labels and tick marks are big enough to read. Some figures are very crowdy and messy (mainly Figs. 2 and 6). Maybe you can use some additional subplot (e.g. for real and imaginary part) or different symbols and color-coding to improve readability. Also, avoid having multiple legends within a single subplot.
- Referencing style:
Use consistent referencing style for figures. Sometimes you used “Figure 12b” (e.g. line 303) and sometimes “Figure 10(b)” (e.g. line 270)
Additional inline comments:
L2: “electrical resistivity” is not a method. There is, e.g. “electrical resistivity tomography”.
L20: Olhoeft (1977) is not about ERT but about electrical properties in general and dielectric properties in particular.
L27: Huisman et al. (2016) is not about SIP application to frozen environments.
L29ff: There are also some approaches for spectral data analysis for ice content quantification, e.g. Mudler et al., 2022 or Zorin and Ageev, 2017 (DOI: 10.3997/1873-0604.2017043). An additional approach is the phase-frequency-effect after Maierhofer et al. (2024, DOI: 10.5194/tc-18-3383-2024).
L36: There are tools for full tomographic inversion for sEIT data, e.g. ResIPy or pyGIMLi.
L53: Impedance combines resistance R (instead of resistivity) and reactance X.
Eq. (1) and L56: Voltage and currant are also complex valued parameters here.
L61 and Eq. (3): This is the Debye-model and not the Cole-Cole model. Please cite with Debye, 1929: Polar molecules.
L67 and Eq. (6): This is the Pelton model (Pelton et al., 1978). When formulated for Z*, R_0 must be used instead of \rho_0. Alternatively, you have to use the formulation for \rho^*. Including the Cole-Cole exponent, it is based on the Cole-Cole model and not the Debye-Model.
L73 and L83: The following reference should be used for temperature-dependent relaxation time of ice: Auty and Cole (1952, DOI: 10.1063/1.1700726) or Evans (1965, DOI: 10.3189/S0022143000018840)
L121ff: Is this a realistic scenario, that frozen and unfrozen soil only differ in main relaxation time but have the same \rho_0 and m?
L126f: Please use the equation environment instead of inline equation. Introduce all parameters used (R1, C1, …).
L137: Use the $\pm$-symbol.
L137: Which standard deviation and which mean? Of all values of one spectrum? What is the "unit" of "3"? Or is it just a factor of three?
L138: What is excluded? A single data point from the spectrum at this frequency? Is a data point only excluded from the real or imaginary spectrum, where it exceeded the threshold or is a complex data point (real and imaginary part) also removed if it exceeds only the threshold value for the real or the imaginary part?
Eq. (9): Usually, the total response is the sum of the individual responses. Thus, a “+”-sign is missing.
L154 and Eq. (10): Is this RMSE also used for minimization within the least square method? Or is this a different RMSE?
L158f: Please give more details: Is the same factor applied to both, real and imaginary part? How big is this weighting? How is it defined/chosen?
L161: Accuracy of which results? The spectral fits?
Eq. (10): $i$ is already introduced as imaginary number $i=\sqrt{-1}$
Eq. (10) and following lines: Z* or \rho* are complex valued parameters. Why is only the magnitude used to calculate an RMSE?
Fig. 3: Dots do not represent measured data, but synthetic data to test the spectral inversion code. To my opinion, this figure is not needed and can be removed.
L191ff: This paragraph has many redundant sentences. Reduce it to a single sentence.
Fig. 4a: Scale in (a) way to small.
L244: “result” = Impedance Magnitude from Fig. 7a?
Fig. 7: Why different grid/mesh resolutions between (a) and (b)/(c)?
L268ff and Fig. 10: It looks like there is ground ice more or less everywhere in this figure. Is that realistic?
Fig. 11: Which data are shown here? From the field measurement presented in this study or from measurements at the core or borehole samples?
L294ff: Maierhofer et al. (2022) is looking into full spectral responses. Here you refer to Maierhofer et al. (2024). I think the reason why this is not perfectly differentiate ground ice from other materials is the fact that even the high frequency used in that study (75 Hz) is not within the range of ice polarization relaxation. But not that only single frequencies are used.
Figs. 7, 9, 12 and 13: Why are you using a frequency of 40 kHz as reference? From your spectral responses (e.g. Fig. 6), it would be more convenient to use the peak frequency of the imaginary part (something between 1 kHz and 3 kHz).
Figs. 12 and 13: Maybe the interpretation can be improved, if for ART three different colors are used to distinguish between relaxation times below and above ice-relaxation.
L312: “0C” -> “0 °C”
L321: Just for clarification: Both are directly extracted from the measured spectra without inversion? Because the imaginary parts shown in the previous figures are data from inversion.
L322: Do not introduce parameters within the equation itself.
L330 and L342: Why these threshold values?
Fig. 14a: Often, conductivity or resistivity values are log-normal distributed (log values instead of linear values). Therefore, you can try this as well to get closer to a normal distribution. Later in Fig (c) a log-distribution is used!
L343f: Do you have an independent validation that provides a "true" distribution of ground ice as reference? Here, it is assumed that the ART results are more reliable. Why?
L348: SIP is not a relatively new method, but not that well established as other methods for ground ice characterization.
L350: The issue of manual layout configurations depends on the device not on the method itself.
L355: The abbreviation “SIP” is already introduced.
L365: There are already tools available to properly invert SIP data as mentioned before.
Citation: https://doi.org/10.5194/egusphere-2025-1801-RC2 -
AC2: 'Reply on RC2', Hosein Fereydooni, 12 Sep 2025
We are sincerely grateful to Anonymous Referee #2 for their thorough review as well as for their detailed feedback and guidance to improve the manuscript. Below, we provide a point-by-point response to the issues they raised.
Reviewer 2 response
The Referee wrote: Correct usage of terminologies, symbols and equations: Please use the terms “impedance”, “apparent complex resistivity”, and “complex resistivity” correctly (see e.g. Binley and Slater, 2020. Resistivity and Induced Polarization, DOI: 10.1017/9781108685955). Instead of “apparent impedance” use “apparent complex resistivity”.
Response: The manuscript has been updated.
The Referee wrote: Use correct notation of complex symbols and indicate all complex valued parameters with $^*$. To indicate real and imaginary part, you can use $^{\prime}$ and $^{\prime\prime}$ instead of subscripts.
Response: The manuscript has been updated.
The Referee wrote: Note, that relaxation times from different model definitions are not equivalent (e.g. Limbrock and Kemna, 2024. Relationship between Cole–Cole model parameters in permittivity and conductivity formulation, DOI: 10.1093/gji/ggae300). In this study, a resistivity-based model is used to estimate relaxation times while reverence values for ice a given for a permittivity-based model. As exact relaxation time values are not used for further analysis (e.g. temperature estimates), this is not a big issue but should be mentioned.
Response: Thank the reviewer for highlighting the distinction between relaxation times derived from different Cole–Cole model definitions. The manuscript has been updated by adding more explanation about it.
The Referee wrote: Please use short subscripts for parameters and in equations. E.g. “app” or “a” ($\rho_a$) instead of “apparent”, “meas” or “m” instead of “measured”, in Eq. 10: “m” for “measured” or “d” for “data”, and “f” for forward response instead of “predicted”. Also, make sure that you follow the official Copernicus guidelines for mathematical notations and terminology (https://publications.copernicus.org/for_authors/manuscript_preparation.html#math).
Response: The manuscript has been updated.
The Referee wrote: Structure of Section 2 (Background): Please reorganize this section and rename the subsections. Subsections 2.1 and 2.3 referrer to special media while 2.2 also is about ice polarization and 2.4 about interpretation depending on type of ground media.
Response: The structure of this section has been revised as follows: 2.1 Ice; 2.2 Mixed media; 2.3 Interpretation of impedance measured in heterogeneous frozen ground; 2.4 Relaxation time of ice and frozen ground; 2.5 Detecting ground ice based on SIP measurements
The Referee wrote: Improve figures: Make sure that all labels and tick marks are big enough to read. Some figures are very crowdy and messy (mainly Figs. 2 and 6). Maybe you can use some additional subplot (e.g. for real and imaginary part) or different symbols and colorcoding to improve readability. Also, avoid having multiple legends within a single subplot.
Response: The figures have been updated.
The Referee wrote: 1.Referencing style: Use consistent referencing style for figures. Sometimes you used “Figure 12b” (e.g. line 303) and sometimes “Figure 10(b)” (e.g. line 270).
Response: The manuscript has been updated to use a consistent referencing style, following the format “Fig. 12b.”
The Referee wrote: L2: “electrical resistivity” is not a method. There is, e.g. “electrical resistivity tomography”.
Response: The manuscript has been updated.
The Referee wrote: L20: Olhoeft (1977) is not about ERT but about electrical properties in general and dielectric properties in particular.
Response: The manuscript has been updated.
The Referee wrote: L27: Huisman et al. (2016) is not about SIP application to frozen environments.
Response: The manuscript has been updated.
The Referee wrote: L29ff: There are also some approaches for spectral data analysis for ice content quantification, e.g. Mudler et al., 2022 or Zorin and Ageev, 2017 (DOI: 10.3997/1873-0604.2017043). An additional approach is the phase-frequency-effect after Maierhofer et al. (2024, DOI: 10.5194/tc-18-3383-2024).
Response: The manuscript has been updated.
The Referee wrote: L36: There are tools for full tomographic inversion for sEIT data, e.g. ResIPy or pyGIMLi.
Response: While some tools exist for inverting parts of SIP data, most are limited to inverting either the Cole-Cole model or individual frequency data separately. What is needed is a tool that can simultaneously invert multiple frequency components to satisfy the full spectral response and reproduce impedance spectra accurately. Packages like Pygimli show promising progress but are not yet fully reliable for complex field measurements. ResIPy uses individual frequency inversion (like what we did in this study) and does not ensure reproduction of spectra in each cell after inversion. Therefore, although some software packages and studies perform partial SIP data inversion, none currently provide a complete, robust inversion solution for all parts of SIP data in typical field conditions.
The Referee wrote: L53: Impedance combines resistance R (instead of resistivity) and reactance X.
Response: The manuscript has been updated.
The Referee wrote: Eq. (1) and L56: Voltage and currant are also complex valued parameters here.
Response: The manuscript has been updated.
The Referee wrote: L61 and Eq. (3): This is the Debye-model and not the Cole-Cole model. Please cite with Debye, 1929: Polar molecules.
Response: The manuscript has been updated.
The Referee wrote: L67 and Eq. (6): This is the Pelton model (Pelton et al., 1978). When formulated for Z*, R_0 must be used instead of \rho_0. Alternatively, you have to use the formulation for \rho^*. Including the Cole-Cole exponent, it is based on the Cole-Cole model and not the Debye-Model.
Response: The manuscript has been updated.
The Referee wrote: L73 and L83: The following reference should be used for temperaturedependent relaxation time of ice: Auty and Cole (1952, DOI: 10.1063/1.1700726) or Evans (1965, DOI: 10.3189/S0022143000018840)
Response: The manuscript has been updated.
The Referee wrote: L121ff: Is this a realistic scenario, that frozen and unfrozen soil only differ in main relaxation time but have the same \rho_0 and m?
Response: Its totally right, those are used to show how the different relaxation time values can be captured in the SIP spectra, just as an example to show relaxation time features…
The Referee wrote: L126f: Please use the equation environment instead of inline equation. Introduce all parameters used (R1, C1, …).
Response: The manuscript has been updated.
The Referee wrote: L137: Use the $\pm$-symbol.
Response: The manuscript has been updated.
The Referee wrote: L137: Which standard deviation and which mean? Of all values of one spectrum? What is the "unit" of "3"? Or is it just a factor of three?
Response: It is a factor of 3 and the manuscript has been updated.
The Referee wrote: L138: What is excluded? A single data point from the spectrum at this frequency? Is a data point only excluded from the real or imaginary spectrum, where it exceeded the threshold or is a complex data point (real and imaginary part) also removed if it exceeds only the threshold value for the real or the imaginary part?
Response: We applied the 3$\sigma$ rule to both the impedance magnitude and the phase angle values. Any data points identified as outliers were excluded specifically at the corresponding frequencies for both the real and imaginary parts. Data points at other frequencies were retained for the fitting process. The manuscript has been updated.
The Referee wrote: Eq. (9): Usually, the total response is the sum of the individual responses. Thus, a “+”-sign is missing.
Response: We utilized the two Cole-Cole model (Multiplicative Case) by Pelton et al., 1978.
The Referee wrote: L154 and Eq. (10): Is this RMSE also used for minimization within the least square method? Or is this a different RMSE?
Response: Yes, we used it to evaluate the fitted spectra.
The Referee wrote: L158f: Please give more details: Is the same factor applied to both, real and imaginary part? How big is this weighting? How is it defined/chosen?
Response: The device provides separate uncertainties for the real and imaginary parts. We use these to assign inverse weights so that lower error, stronger signal points have more influence. The same method is applied to both components, but actual weights differ based on each part’s reported uncertainty and value, ensuring balance while reducing the impact of noisier data. Additional explanation has been added to the manuscript.
The Referee wrote: L161: Accuracy of which results? The spectral fits?
Response: Yes, the RMSE percentage (< 6%) quantifies the accuracy of the spectral fits obtained from the Cole–Cole model to the measured complex impedance spectra. It expresses the deviation between measured, and model predicted impedance magnitudes, averaged over all frequencies for each dataset.
The Referee wrote: Eq. (10): $i$ is already introduced as imaginary number $i=\sqrt{-1}$
Response: The manuscript has been updated.
The Referee wrote: Eq. (10) and following lines: Z* or \rho* are complex valued parameters. Why is only the magnitude used to calculate an RMSE?
Response: Because the goal is to quantify overall amplitude misfit, the RMSE is calculated on the magnitude, which combines real and imaginary parts into a single measure and avoids scale/unit differences between them. Additional explanation has been added to the manuscript.
The Referee wrote: Fig. 3: Dots do not represent measured data, but synthetic data to test the spectral inversion code. To my opinion, this figure is not needed and can be removed.
Response: The figure has been updated. We prefer to keep it as an illustration.
The Referee wrote: L191ff: This paragraph has many redundant sentences. Reduce it to a single sentence.
Response: The manuscript has been updated.
The Referee wrote: Fig. 4a: Scale in (a) way to small.
Response: The figure has been updated.
The Referee wrote: L244: “result” = Impedance Magnitude from Fig. 7a?
Response: The inversion result at each frequency includes the real part, imaginary part (phase angle), and impedance magnitude; depending on the discussion, we used the relevant ones—e.g., all in Fig. 7 show such inversion results.
The Referee wrote: Fig. 7: Why different grid/mesh resolutions between (a) and (b)/(c)?
Response: The figure 7a mesh resolution has been updated.
The Referee wrote: L268ff and Fig. 10: It looks like there is ground ice more or less every where in this figure. Is that realistic?
Response: Yes, in winter we expect some ground ice to be present at shallow depths throughout most areas within the pingo.
The Referee wrote: Fig. 11: Which data are shown here? From the field measurement presented in this study or from measurements at the core or borehole samples?
Response: shows data from the borehole drilled near the pingo apex as part of the field study presented in this paper. Specifically, it displays (a) relaxation time and (b) apparent resistivity measured at the borehole location (“electrode 22”), thus representing data obtained from direct field measurements at the core/borehole site within this study.
The Referee wrote: L294ff: Maierhofer et al. (2022) is looking into full spectral responses. Here you refer to Maierhofer et al. (2024). I think the reason why this is not perfectly differentiate ground ice from other materials is the fact that even the high frequency used in that study (75 Hz) is not within the range of ice polarization relaxation. But not that only single frequencies are used.
Response: The reference to Maierhofer et al. has been updated accordingly. Later in our paper, we present figures demonstrating that analyzing the entire spectral response rather than single frequencies provides more reliable and detailed information, improving the ability to distinguish ground ice from other materials.
The Referee wrote: Figs. 7, 9, 12 and 13: Why are you using a frequency of 40 kHz as reference? From your spectral responses (e.g. Fig. 6), it would be more convenient to use the peak frequency of the imaginary part (something between 1 kHz and 3 kHz).
Response: The purpose of using the 40 kHz frequency as a reference in Figs. 7, 9, 12, and 13 is to highlight the contrast between individual frequency results and those obtained by considering the whole spectral response. While the relaxation time (ART) captures the key information near the imaginary part’s peak frequency (around 1–3 kHz), most existing studies focus on results at the lowest and highest frequencies for practical and comparative reasons. By presenting the 40 kHz imaginary part data, we emphasize how interpretations based on a single high frequency differ from those using the full spectrum, illustrating the additional insights gained from broadband analysis and supporting the motivation for using relaxation time as a more comprehensive indicator.
The Referee wrote: Figs. 12 and 13: Maybe the interpretation can be improved, if for ART three different colors are used to distinguish between relaxation times below and above ice-relaxation.
Response: Since the purpose of this paper is not to interpret areas with relaxation times outside the ground-ice range, we prefer to keep those areas in the same color, simply indicating that they are not within the ground-ice relaxation time range, without making further interpretation.
The Referee wrote: L312: “0C” -> “0 °C”
Response: The manuscript has been updated.
The Referee wrote: L321: Just for clarification: Both are directly extracted from the measured spectra without inversion? Because the imaginary parts shown in the previous figures are data from inversion.
Response: Yes, its true.
The Referee wrote: L322: Do not introduce parameters within the equation itself.
Response: The manuscript has been updated.
The Referee wrote: L330 and L342: Why these threshold values?
Response: The threshold values for both the imaginary part and the RFE were chosen based on statistical analysis of the data to identify anomalously high signals that reliably indicate polarization effects linked to frozen ground conditions. This statistical cutoff ensures that only signals significantly above typical background variability are considered,
The Referee wrote: Fig. 14a: Often, conductivity or resistivity values are log-normal distributed (log values instead of linear values). Therefore, you can try this as well to get closer to a normal distribution. Later in Fig (c) a log-distribution is used!
Response: We used a linear scale in Fig. 14a to show the actual data distribution, as most imaginary-part values fall between 0 and 200 Ωm, making the spread in this range clearer than a log-scale.
The Referee wrote: L343f: Do you have an independent validation that provides a "true" distribution of ground ice as reference? Here, it is assumed that the ART results are more reliable. Why?
Response: As mentioned in the manuscript, based on the spectra from the short survey and previous studies on the relaxation time (range) of ground ice, we defined four criteria for an SIP spectrum to be considered as indicative of ground ice (see the Interpretation of impedance measured in heterogeneous frozen ground section). As also noted in different parts of this manuscript, ERT results can be ambiguous because they are based solely on the resistivity of subsurface materials, while relaxation time is a unique feature that is independent of material resistivity. Furthermore, the borehole log also supports the reliability of the ART results.
The Referee wrote: L348: SIP is not a relatively new method, but not that well established as other methods for ground ice characterization.
Response: The manuscript has been updated.
The Referee wrote: L350: The issue of manual layout configurations depends on the device not on the method itself.
Response: The manuscript has been updated.
The Referee wrote: L355: The abbreviation “SIP” is already introduced.
Response: The manuscript has been updated.
The Referee wrote: L365: There are already tools available to properly invert SIP data as mentioned before.
Response: While some tools exist for inverting parts of SIP data, most are limited to inverting either the Cole-Cole model or individual frequency data separately. What is needed is a tool that can simultaneously invert multiple frequency components to satisfy the full spectral response and reproduce impedance spectra accurately. Packages like Pygimli show promising progress but are not yet fully reliable for complex field measurements. ResIPy uses individual frequency inversion (like what we did in this study) and does not ensure reproduction of spectra in each cell after inversion. Therefore, although some software packages and studies perform partial SIP data inversion, none currently provide a complete, robust inversion solution for all parts of SIP data in typical field conditions.
** The marked version of the manuscript is attached.
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