Quantifying the potential of using SMAP soil moisture variability to predict subsurface water dynamics

Nayak, Aruna Kumar; Xu, Xiaoyong; Frey, Steven K.; Khader, Omar; Erler, Andre R.; Lapen, David R.; Russell, Hazen A. J.; Sudicky, Edward A.

doi:https://doi.org/10.5194/hess-2023-309

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https://doi.org/10.5194/hess-2023-309

Preprints

15 Jan 2024

| 15 Jan 2024

Status: a revised version of this preprint was accepted for the journal HESS and is expected to appear here in due course.

Quantifying the potential of using SMAP soil moisture variability to predict subsurface water dynamics

Aruna Kumar Nayak, Xiaoyong Xu, Steven K. Frey, Omar Khader, Andre R. Erler, David R. Lapen, Hazen A. J. Russell, and Edward A. Sudicky

Abstract. Advances in satellite Earth observation have opened up new opportunities for a global monitoring of soil moisture (SM) at fine to medium resolution, but satellite remote sensing can only measure the near-surface soil moisture (SSM). As such, it is critically important to examine the potential of satellite SSM measurements to derive the water resource variations in deeper subsurface. This study compares the SSM variability captured by the Soil Moisture Active and Passive (SMAP) satellite and the Soil Water Index (SWI) derived from SMAP SSM with subsurface SM and groundwater (GW) dynamics simulated by a high resolution fully-integrated surface water - groundwater model over an agriculturally-dominated watershed in eastern Canada across two spatial scales, namely SMAP product grid (9 km) and watershed (~4000 km²). SMAP measurements compare well with the hydrologic simulations in terms of SSM variability at both scales. Simulated subsurface SM and GW storage show lagged and smoother characteristics relative to SMAP SSM variability with an optimal delay of ~1 days for the 25‒50 cm SM, ~6 days for the 50‒100 cm SM, and ~11 days for the GW storage for both scales. Modelled subsurface SM dynamics agree well with the SWI derived from SMAP SSM using the classic characteristic time lengths (15 days for the 0‒25 cm layer and 20 days for the 0‒100 cm layer). The simulated GW storage showed a slightly delayed variation relative to the derived SWI. The quantified optimal characteristic time length T_opt for SWI estimation (by matching the variations in SMAP-derived SWI and modeled root zone SM) is comparable to T_opt obtained in other agricultural regions around the world. This work demonstrates SMAP SM measurements as a potentially useful aid when predicting root zone SM and GW dynamics and validating fully integrated hydrologic models across different spatial scales. This study also provides insights into the dynamics of near surface–subsurface water interaction and the capabilities and approaches of satellite-based SM monitoring and high resolution fully-integrated hydrologic modelling.

Received: 29 Dec 2023 – Discussion started: 15 Jan 2024

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Aruna Kumar Nayak, Xiaoyong Xu, Steven K. Frey, Omar Khader, Andre R. Erler, David R. Lapen, Hazen A. J. Russell, and Edward A. Sudicky

Status: closed

RC1:
'Comment on hess-2023-309', Anonymous Referee #1, 13 Feb 2024

Overall comments:
This is an interesting study discussing the potential use of SMAP surface soil moisture (SM) in estimating deep layer SM. However, I feel the two results sections were not well connected, and there is a lack of linkage between the time lag and characteristic time length. There is also lack of an in-depth discussion on the underlying factors controlling the characteristic time length, a key parameter for the deep layer SM estimation. If the goal is to obtain high-resolution and high-quality deep layer SM variations, the authors should at least provide a brief discussion on the spatial heterogeneity in this parameter. Finally, even though the in-situ data were scarce, they can provide key information on this parameter, but they were not used in the analysis. Some specific comments were provided as below:
1. Evaluation using the in-situ data is an important part of the study. So I suggest moving the Table A1 into the main text.
2. Figs. A1 & A2: There is a mismatch between the model soil layers and in-situ SM observations. Please specify the soil depth of the in-situ data used for the comparison
3. Fig A7: First I suggest the authors using different legend for the layers at top 50cm, and below 50cm. And what explains the spatial heterogeneity in the optimal time lags? It would be good to provide more specific details on this, rather than a general discussion as shown in Lines 315-318.
Moreover, even though the in-situ data were very scarce, I would like to see a comparison of the optimal time lags derived from in-situ soil moisture data with the values derived from model simulations and SMAP surface SM. Are they comparable?
4. Fig. 7. The SMAP surface SM seems showing an early thaw onset compared to the model simulations. Why? Does this affect the above time lag analysis?
5. The characteristic time length T: how does this relate to the time lag shown in Section 4? I believe the time lag analysis should provide some useful information on this. Otherwise, what is the use of such analysis?
6. For the comparison between SWI and model simulations, why was the middle layer (i.e. 50cm) ignored?
7. Line 483-: how do these results compared to the point-scale analysis using in-situ SM data?
8. Line 517-518: I did not see any specific analysis on the relations between Topt and soil texture.

Citation: https://doi.org/10.5194/hess-2023-309-RC1
- AC1:
  'Reply on RC1', Xiaoyong Xu, 09 Apr 2024
  Overall comments:
  This is an interesting study discussing the potential use of SMAP surface soil moisture (SM) in estimating deep layer SM. However, I feel the two results sections were not well connected, and there is a lack of linkage between the time lag and characteristic time length.
  Response:
  Thank you for the comments. The two result sections quantify the potential of using SMAP soil moisture (SM) variability to predict subsurface water dynamics based upon two different approaches. The first one focuses upon the time lagged cross-correlation in SM variations between the near surface and deeper soil layers (e.g., Mahmood and Hubbard, 2007; Mahmood et al., 2012; Wu et al., 2002), which can be used to quantify if the subsurface SM variability could be approximated by delaying the temporal variations in Satellite/SMAP near surface SM (SSM). The second result section focuses upon the SWI approach, which tests if the subsurface water content variability can be estimated by smoothing the satellite/SMAP SSM time series with an exponential filter (e.g., Bouaziz et al., 2020; Ceballos et al., 2005; Ford et al., 2014; Paulik et al., 2014; Tian et al., 2020; Wagner et al., 1999). The results from the two approaches are linked in the following aspects: (i) both approaches indicates that the SMAP/satellite SSM variability is strongly linked to the deeper subsurface water content fluctuations and can be used to predict/infer subsurface SM and groundwater variability; (ii) both the time lag (e.g. Figure 7) and the characteristic time length (e.g. Figure 11) increase with the increasing soil depths. Note that since the time lag and the characteristic time length are applicable to the above two different approaches, an explicit/mathematical relationship between them cannot be quantified (which is also not needed).
  There is also lack of an in-depth discussion on the underlying factors controlling the characteristic time length, a key parameter for the deep layer SM estimation. If the goal is to obtain high-resolution and high-quality deep layer SM variations, the authors should at least provide a brief discussion on the spatial heterogeneity in this parameter.
  Response: As mentioned in the manuscript (Line 423-426), the soil properties have an important impact on the spatial variability of characteristic time length. We will provide a table to specify the impact of soil texture on the characteristic time length in the revision.
  Finally, even though the in-situ data were scarce, they can provide key information on this parameter, but they were not used in the analysis.
  Response: We have examined the cross-correlations between the in situ SSM (top 5 cm) and the in situ SM from the top 25 cm and top 100 cm depths at the four RISMA sites, indicating that the delay is less than 1 day between the variations of SSM and subsurface soil moisture at the point scale (see the attached results pls).
  Some specific comments were provided as below:
  Evaluation using the in-situ data is an important part of the study. So I suggest moving the Table A1 into the main text.
  
  Response: Table A1 will be moved to the main text in the revised manuscript.
  Figs. A1 & A2: There is a mismatch between the model soil layers and in-situ SM observations. Please specify the soil depth of the in-situ data used for the comparison
  
  Response: The soil depth matching between the in situ SM and model simulations for the two soil depths (0-25 cm and 0 -100 cm) are provided in Line 185 – 188:
  0–25 cm: the simulated SM in the model’s top soil layer (0 -25 cm) against a depth-weighted average of in situ measurements in the top 25 cm soil (i.e., 5 cm and 25 cm depths at the RISMA sites, 10 and 20 cm depths at Metcalfe and Pleasant Valley, and 20 cm depth at Winchester stations, as shown in Table A1)
  0–100 cm: a depth-weighted average of simulated SM from the model’s three soil layers versus a depth weighted average of in situ measurements in the top 100 cm soil (i.e., 5, 20, and 50 cm depths at the RISMA sites; 10, 20, and 50 cm depths at Pleasant Valley, and 15 and 45 cm depths at WEBS stations, as shown in Table A1)
  .
  Fig A7: First I suggest the authors using different legend for the layers at top 50cm, and below 50cm. And what explains the spatial heterogeneity in the optimal time lags? It would be good to provide more specific details on this, rather than a general discussion as shown in Lines 315-318.
  
  Response: The same legend is used since it can facilitate the time lag comparison/variation across the different depths. As mentioned in the manuscript (Line 315-318), the soil properties have an important impact on the spatial variability of the time lag. We will be able to provide a table to specify the impact of soil texture on the time lag in the revision.
  Moreover, even though the in-situ data were very scarce, I would like to see a comparison of the optimal time lags derived from in-situ soil moisture data with the values derived from model simulations and SMAP surface SM. Are they comparable?
  Response: As mentioned above, we examined the cross-correlations between the in situ SSM (top 5 cm) and the in situ SM from the top 25 cm and top 100 cm depths at the four RISMA sites, indicating that the delay is less than 1 day between the variations of SSM and subsurface soil moisture at the point scale. The time lag is shorter than that derived from the model simulations and SMAP SSM for the SMAP grid or watershed scale. This is not surprising since the moisture dynamics in deeper subsurface layers exhibit a quicker response to the near-surface moisture content variability at the point scale (e.g., Mahmood and Hubbard, 2007; Mahmood et al. 2012).
  
  Fig. 7. The SMAP surface SM seems showing an early thaw onset compared to the model simulations. Why? Does this affect the above time lag analysis?
  
  Response: When comparing the SMAP surface SM (SSM) and the model SSM (Fig. 6), there is no difference between them in terms of the thaw onset. In figure 7, the SMAP SSM (top 5 cm) indicates a slightly earlier thaw onset than do the model simulated water content in deeper unsaturated/saturated zones (0‒25 cm, 25‒50 cm, and 50‒100 cm SM and GW storage). This is not surprising since this reflects a downward heat transfer and migration of thawing front. During a thawing/warming period, the soils typically have a downward temperature gradient (i.e., soil temperature decreases with increased soil depth), which causes a downward heat transfer and migration of thawing front. The thaw onset difference between different depths is consistent with (not against) the time lag analysis and the response time differences between satellite SSM and the subsurface water.
  The characteristic time length T: how does this relate to the time lag shown in Section 4? I believe the time lag analysis should provide some useful information on this. Otherwise, what is the use of such analysis?
  
  Response: The time lag is derived from the time lagged cross-correlation in SM variations between the near surface and deeper soil layers, and determines how the subsurface SM variability could be approximated by delaying/shifting the temporal variations in Satellite/SMAP near surface SM (SSM), while the characteristic time length determines how the subsurface water content variability can be estimated by smoothing the satellite/SMAP SSM time series with the exponential filter SWI. Since the time lag and the characteristic time length are applicable to two different approaches, an explicit/mathematical relationship between them cannot be quantified and is also not needed, although both the time lag (e.g. Figure 7) and the characteristic time length (e.g. Figure 11) increase with the soil depths. The time lag analysis can provide a quick approach for predicting/estimating deeper subsurface water changes by shifting the satellite/SMAP SSM time sequences, which can alleviate the need for integrated hydrologic modeling in some types of investigations (Line 490-500).
  For the comparison between SWI and model simulations, why was the middle layer (i.e. 50cm) ignored?
  
  Response: In the study, given the scarcity of in situ soil moisture measurements, it is not practical to determine the characteristic time length T (model-independent) using in situ data. Therefore, the classic T values (15 days for 0-20/25 cm soil layer and 20 days for 0-100 cm soil layer, as proposed by Wagner et al., 1999) are selected. As such, the calculated SWI is entirely independent of the model simulations so that we can compare the SWI to the modeled subsurface soil moisture (in Section 5.1). Since the widely-used/classic T value for the 0-50 cm soil layer is not evident (to the best of our knowledge), the 0-50 cm SWI comparison was not provided in Section 5.1. However, this will not impact the assessment of SWI results. Since the SWI for the 0-25 cm and the 0 -100 cm layers show very good agreement with the model simulations, it is expected that the SWI for the 0-50 cm layer is also in very good agreement with the model simulations. In addition, the optimal T analysis for the 0-50 cm SWI is provided in Figure 11.
  Line 483-: how do these results compared to the point-scale analysis using in-situ SM data?
  
  Response: See our above reply to Q3
  
  Line 517-518: I did not see any specific analysis on the relations between Topt and soil texture.
  
  Response: As mentioned in the manuscript (Line 423-426), the spatial variability of Topt is related to the soil texture. We will provide a table to specify the impact of soil texture on the characteristic time length in the revision.
  
  Citation: https://doi.org/10.5194/hess-2023-309-AC1
RC2:
'Comment on hess-2023-309', Anonymous Referee #2, 26 Feb 2024

This study conducted a thorough analysis, comparing SMAP soil moisture and the Soil Water Index (SWI) with both in situ measurements and simulations from HydroGeoSphere. The paper is commendably well-written and organized. However, discerning novelty and originality proves challenging, as the primary focus seems to be on the comparison and testing of various T values. I would have expected the paper to explore novel methodologies, see references below, beyond the conventional exponential filter method already utilized for SMAP. A more convincing exploration of alternative approaches would enhance the overall contribution of the study.
Li, M.; Sun, H.; Zhao, R. A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing. Remote Sens. 2023, 15, 5361. https://doi.org/10.3390/rs15225361
Stefan, V.-G.; Indrio, G.; Escorihuela, M.-J.; Quintana-Seguí, P.; Villar, J.M. High-Resolution SMAP-Derived Root-Zone Soil Moisture Using an Exponential Filter Model Calibrated per Land Cover Type. Remote Sens. 2021, 13, 1112. https://doi.org/10.3390/rs13061112

Citation: https://doi.org/10.5194/hess-2023-309-RC2
- AC2: 'Reply on RC2', Xiaoyong Xu, 09 Apr 2024
  
  This study conducted a thorough analysis, comparing SMAP soil moisture and the Soil Water Index (SWI) with both in situ measurements and simulations from HydroGeoSphere. The paper is commendably well-written and organized. However, discerning novelty and originality proves challenging, as the primary focus seems to be on the comparison and testing of various T values. I would have expected the paper to explore novel methodologies, see references below, beyond the conventional exponential filter method already utilized for SMAP. A more convincing exploration of alternative approaches would enhance the overall contribution of the study.
  Li, M.; Sun, H.; Zhao, R. A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing. Remote Sens. 2023, 15, 5361. https://doi.org/10.3390/rs15225361
  Stefan, V.-G.; Indrio, G.; Escorihuela, M.-J.; Quintana-Seguí, P.; Villar, J.M. High-Resolution SMAP-Derived Root-Zone Soil Moisture Using an Exponential Filter Model Calibrated per Land Cover Type. Remote Sens. 2021, 13, 1112. https://doi.org/10.3390/rs13061112
  Response: Thanks for the comments. Although the authors agree that exploring other approaches (e.g., data assimilation and machine learning) would be also very useful for quantifying the potential of using SMAP soil moisture (SM) variability to predict subsurface water dynamics, the authors feel that the novelty of using a fully-integrated groundwater (GW)-surface water (SW) model for this type of study should be acknowledged and appreciated. Although the analysis methods used for quantifying the connections between satellite/SMAP soi moisture measurements and modelling results in this study have been widely used previously, fully-integrated groundwater (GW)-surface water (SW) models have not yet been used for this type of study. How a fully-integrated GW-SW model deals with soil moisture, GW, and runoff/streamflow is different from land surface models which are widely used previously. As stated in the manuscript (~Line 80-85), fully-integrated GW-SW model present better ability to reproduce realistic root zone SM and GW dynamics than surface-water models used in previous studies. Hence, these models are well suited to help expand our understanding of connections between satellite/SMAP SM and the variably-saturated subsurface flow regime. Therefore, the use of a fully-integrated groundwater (GW)-surface water (SW) model HydroGeoSphere (HGS) and the examination of the connections between SMAP soil moisture and the HGS simulations in this study has provided a novel exploration for this field. The specific novelty points and advances are discussed in Section 6.1 (Line 465-525). The authors have also been exploring other approaches (e.g., data assimilation and machine learning) for this type of study. Some preliminary results were presented on conferences (e.g., X Xu, SK Frey, AK Nayak, Assimilation of SMAP Soil Moisture for Advancing Integrated Groundwater-Surface Water Modeling, AGU Fall Meeting 2022; AK Nayak, X Xu, SK Frey, Improving Physically-Based Hydrologic Predictions With Deep Learning, AGU Fall Meeting 2023). The detailed analysis results will be presented in separate manuscripts that are in preparation.
  
  Citation: https://doi.org/10.5194/hess-2023-309-AC2

Status: closed

RC1:
'Comment on hess-2023-309', Anonymous Referee #1, 13 Feb 2024

Overall comments:
This is an interesting study discussing the potential use of SMAP surface soil moisture (SM) in estimating deep layer SM. However, I feel the two results sections were not well connected, and there is a lack of linkage between the time lag and characteristic time length. There is also lack of an in-depth discussion on the underlying factors controlling the characteristic time length, a key parameter for the deep layer SM estimation. If the goal is to obtain high-resolution and high-quality deep layer SM variations, the authors should at least provide a brief discussion on the spatial heterogeneity in this parameter. Finally, even though the in-situ data were scarce, they can provide key information on this parameter, but they were not used in the analysis. Some specific comments were provided as below:
1. Evaluation using the in-situ data is an important part of the study. So I suggest moving the Table A1 into the main text.
2. Figs. A1 & A2: There is a mismatch between the model soil layers and in-situ SM observations. Please specify the soil depth of the in-situ data used for the comparison
3. Fig A7: First I suggest the authors using different legend for the layers at top 50cm, and below 50cm. And what explains the spatial heterogeneity in the optimal time lags? It would be good to provide more specific details on this, rather than a general discussion as shown in Lines 315-318.
Moreover, even though the in-situ data were very scarce, I would like to see a comparison of the optimal time lags derived from in-situ soil moisture data with the values derived from model simulations and SMAP surface SM. Are they comparable?
4. Fig. 7. The SMAP surface SM seems showing an early thaw onset compared to the model simulations. Why? Does this affect the above time lag analysis?
5. The characteristic time length T: how does this relate to the time lag shown in Section 4? I believe the time lag analysis should provide some useful information on this. Otherwise, what is the use of such analysis?
6. For the comparison between SWI and model simulations, why was the middle layer (i.e. 50cm) ignored?
7. Line 483-: how do these results compared to the point-scale analysis using in-situ SM data?
8. Line 517-518: I did not see any specific analysis on the relations between Topt and soil texture.

Citation: https://doi.org/10.5194/hess-2023-309-RC1
- AC1:
  'Reply on RC1', Xiaoyong Xu, 09 Apr 2024
  Overall comments:
  This is an interesting study discussing the potential use of SMAP surface soil moisture (SM) in estimating deep layer SM. However, I feel the two results sections were not well connected, and there is a lack of linkage between the time lag and characteristic time length.
  Response:
  Thank you for the comments. The two result sections quantify the potential of using SMAP soil moisture (SM) variability to predict subsurface water dynamics based upon two different approaches. The first one focuses upon the time lagged cross-correlation in SM variations between the near surface and deeper soil layers (e.g., Mahmood and Hubbard, 2007; Mahmood et al., 2012; Wu et al., 2002), which can be used to quantify if the subsurface SM variability could be approximated by delaying the temporal variations in Satellite/SMAP near surface SM (SSM). The second result section focuses upon the SWI approach, which tests if the subsurface water content variability can be estimated by smoothing the satellite/SMAP SSM time series with an exponential filter (e.g., Bouaziz et al., 2020; Ceballos et al., 2005; Ford et al., 2014; Paulik et al., 2014; Tian et al., 2020; Wagner et al., 1999). The results from the two approaches are linked in the following aspects: (i) both approaches indicates that the SMAP/satellite SSM variability is strongly linked to the deeper subsurface water content fluctuations and can be used to predict/infer subsurface SM and groundwater variability; (ii) both the time lag (e.g. Figure 7) and the characteristic time length (e.g. Figure 11) increase with the increasing soil depths. Note that since the time lag and the characteristic time length are applicable to the above two different approaches, an explicit/mathematical relationship between them cannot be quantified (which is also not needed).
  There is also lack of an in-depth discussion on the underlying factors controlling the characteristic time length, a key parameter for the deep layer SM estimation. If the goal is to obtain high-resolution and high-quality deep layer SM variations, the authors should at least provide a brief discussion on the spatial heterogeneity in this parameter.
  Response: As mentioned in the manuscript (Line 423-426), the soil properties have an important impact on the spatial variability of characteristic time length. We will provide a table to specify the impact of soil texture on the characteristic time length in the revision.
  Finally, even though the in-situ data were scarce, they can provide key information on this parameter, but they were not used in the analysis.
  Response: We have examined the cross-correlations between the in situ SSM (top 5 cm) and the in situ SM from the top 25 cm and top 100 cm depths at the four RISMA sites, indicating that the delay is less than 1 day between the variations of SSM and subsurface soil moisture at the point scale (see the attached results pls).
  Some specific comments were provided as below:
  Evaluation using the in-situ data is an important part of the study. So I suggest moving the Table A1 into the main text.
  
  Response: Table A1 will be moved to the main text in the revised manuscript.
  Figs. A1 & A2: There is a mismatch between the model soil layers and in-situ SM observations. Please specify the soil depth of the in-situ data used for the comparison
  
  Response: The soil depth matching between the in situ SM and model simulations for the two soil depths (0-25 cm and 0 -100 cm) are provided in Line 185 – 188:
  0–25 cm: the simulated SM in the model’s top soil layer (0 -25 cm) against a depth-weighted average of in situ measurements in the top 25 cm soil (i.e., 5 cm and 25 cm depths at the RISMA sites, 10 and 20 cm depths at Metcalfe and Pleasant Valley, and 20 cm depth at Winchester stations, as shown in Table A1)
  0–100 cm: a depth-weighted average of simulated SM from the model’s three soil layers versus a depth weighted average of in situ measurements in the top 100 cm soil (i.e., 5, 20, and 50 cm depths at the RISMA sites; 10, 20, and 50 cm depths at Pleasant Valley, and 15 and 45 cm depths at WEBS stations, as shown in Table A1)
  .
  Fig A7: First I suggest the authors using different legend for the layers at top 50cm, and below 50cm. And what explains the spatial heterogeneity in the optimal time lags? It would be good to provide more specific details on this, rather than a general discussion as shown in Lines 315-318.
  
  Response: The same legend is used since it can facilitate the time lag comparison/variation across the different depths. As mentioned in the manuscript (Line 315-318), the soil properties have an important impact on the spatial variability of the time lag. We will be able to provide a table to specify the impact of soil texture on the time lag in the revision.
  Moreover, even though the in-situ data were very scarce, I would like to see a comparison of the optimal time lags derived from in-situ soil moisture data with the values derived from model simulations and SMAP surface SM. Are they comparable?
  Response: As mentioned above, we examined the cross-correlations between the in situ SSM (top 5 cm) and the in situ SM from the top 25 cm and top 100 cm depths at the four RISMA sites, indicating that the delay is less than 1 day between the variations of SSM and subsurface soil moisture at the point scale. The time lag is shorter than that derived from the model simulations and SMAP SSM for the SMAP grid or watershed scale. This is not surprising since the moisture dynamics in deeper subsurface layers exhibit a quicker response to the near-surface moisture content variability at the point scale (e.g., Mahmood and Hubbard, 2007; Mahmood et al. 2012).
  
  Fig. 7. The SMAP surface SM seems showing an early thaw onset compared to the model simulations. Why? Does this affect the above time lag analysis?
  
  Response: When comparing the SMAP surface SM (SSM) and the model SSM (Fig. 6), there is no difference between them in terms of the thaw onset. In figure 7, the SMAP SSM (top 5 cm) indicates a slightly earlier thaw onset than do the model simulated water content in deeper unsaturated/saturated zones (0‒25 cm, 25‒50 cm, and 50‒100 cm SM and GW storage). This is not surprising since this reflects a downward heat transfer and migration of thawing front. During a thawing/warming period, the soils typically have a downward temperature gradient (i.e., soil temperature decreases with increased soil depth), which causes a downward heat transfer and migration of thawing front. The thaw onset difference between different depths is consistent with (not against) the time lag analysis and the response time differences between satellite SSM and the subsurface water.
  The characteristic time length T: how does this relate to the time lag shown in Section 4? I believe the time lag analysis should provide some useful information on this. Otherwise, what is the use of such analysis?
  
  Response: The time lag is derived from the time lagged cross-correlation in SM variations between the near surface and deeper soil layers, and determines how the subsurface SM variability could be approximated by delaying/shifting the temporal variations in Satellite/SMAP near surface SM (SSM), while the characteristic time length determines how the subsurface water content variability can be estimated by smoothing the satellite/SMAP SSM time series with the exponential filter SWI. Since the time lag and the characteristic time length are applicable to two different approaches, an explicit/mathematical relationship between them cannot be quantified and is also not needed, although both the time lag (e.g. Figure 7) and the characteristic time length (e.g. Figure 11) increase with the soil depths. The time lag analysis can provide a quick approach for predicting/estimating deeper subsurface water changes by shifting the satellite/SMAP SSM time sequences, which can alleviate the need for integrated hydrologic modeling in some types of investigations (Line 490-500).
  For the comparison between SWI and model simulations, why was the middle layer (i.e. 50cm) ignored?
  
  Response: In the study, given the scarcity of in situ soil moisture measurements, it is not practical to determine the characteristic time length T (model-independent) using in situ data. Therefore, the classic T values (15 days for 0-20/25 cm soil layer and 20 days for 0-100 cm soil layer, as proposed by Wagner et al., 1999) are selected. As such, the calculated SWI is entirely independent of the model simulations so that we can compare the SWI to the modeled subsurface soil moisture (in Section 5.1). Since the widely-used/classic T value for the 0-50 cm soil layer is not evident (to the best of our knowledge), the 0-50 cm SWI comparison was not provided in Section 5.1. However, this will not impact the assessment of SWI results. Since the SWI for the 0-25 cm and the 0 -100 cm layers show very good agreement with the model simulations, it is expected that the SWI for the 0-50 cm layer is also in very good agreement with the model simulations. In addition, the optimal T analysis for the 0-50 cm SWI is provided in Figure 11.
  Line 483-: how do these results compared to the point-scale analysis using in-situ SM data?
  
  Response: See our above reply to Q3
  
  Line 517-518: I did not see any specific analysis on the relations between Topt and soil texture.
  
  Response: As mentioned in the manuscript (Line 423-426), the spatial variability of Topt is related to the soil texture. We will provide a table to specify the impact of soil texture on the characteristic time length in the revision.
  
  Citation: https://doi.org/10.5194/hess-2023-309-AC1
RC2:
'Comment on hess-2023-309', Anonymous Referee #2, 26 Feb 2024

This study conducted a thorough analysis, comparing SMAP soil moisture and the Soil Water Index (SWI) with both in situ measurements and simulations from HydroGeoSphere. The paper is commendably well-written and organized. However, discerning novelty and originality proves challenging, as the primary focus seems to be on the comparison and testing of various T values. I would have expected the paper to explore novel methodologies, see references below, beyond the conventional exponential filter method already utilized for SMAP. A more convincing exploration of alternative approaches would enhance the overall contribution of the study.
Li, M.; Sun, H.; Zhao, R. A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing. Remote Sens. 2023, 15, 5361. https://doi.org/10.3390/rs15225361
Stefan, V.-G.; Indrio, G.; Escorihuela, M.-J.; Quintana-Seguí, P.; Villar, J.M. High-Resolution SMAP-Derived Root-Zone Soil Moisture Using an Exponential Filter Model Calibrated per Land Cover Type. Remote Sens. 2021, 13, 1112. https://doi.org/10.3390/rs13061112

Citation: https://doi.org/10.5194/hess-2023-309-RC2
- AC2: 'Reply on RC2', Xiaoyong Xu, 09 Apr 2024
  
  This study conducted a thorough analysis, comparing SMAP soil moisture and the Soil Water Index (SWI) with both in situ measurements and simulations from HydroGeoSphere. The paper is commendably well-written and organized. However, discerning novelty and originality proves challenging, as the primary focus seems to be on the comparison and testing of various T values. I would have expected the paper to explore novel methodologies, see references below, beyond the conventional exponential filter method already utilized for SMAP. A more convincing exploration of alternative approaches would enhance the overall contribution of the study.
  Li, M.; Sun, H.; Zhao, R. A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing. Remote Sens. 2023, 15, 5361. https://doi.org/10.3390/rs15225361
  Stefan, V.-G.; Indrio, G.; Escorihuela, M.-J.; Quintana-Seguí, P.; Villar, J.M. High-Resolution SMAP-Derived Root-Zone Soil Moisture Using an Exponential Filter Model Calibrated per Land Cover Type. Remote Sens. 2021, 13, 1112. https://doi.org/10.3390/rs13061112
  Response: Thanks for the comments. Although the authors agree that exploring other approaches (e.g., data assimilation and machine learning) would be also very useful for quantifying the potential of using SMAP soil moisture (SM) variability to predict subsurface water dynamics, the authors feel that the novelty of using a fully-integrated groundwater (GW)-surface water (SW) model for this type of study should be acknowledged and appreciated. Although the analysis methods used for quantifying the connections between satellite/SMAP soi moisture measurements and modelling results in this study have been widely used previously, fully-integrated groundwater (GW)-surface water (SW) models have not yet been used for this type of study. How a fully-integrated GW-SW model deals with soil moisture, GW, and runoff/streamflow is different from land surface models which are widely used previously. As stated in the manuscript (~Line 80-85), fully-integrated GW-SW model present better ability to reproduce realistic root zone SM and GW dynamics than surface-water models used in previous studies. Hence, these models are well suited to help expand our understanding of connections between satellite/SMAP SM and the variably-saturated subsurface flow regime. Therefore, the use of a fully-integrated groundwater (GW)-surface water (SW) model HydroGeoSphere (HGS) and the examination of the connections between SMAP soil moisture and the HGS simulations in this study has provided a novel exploration for this field. The specific novelty points and advances are discussed in Section 6.1 (Line 465-525). The authors have also been exploring other approaches (e.g., data assimilation and machine learning) for this type of study. Some preliminary results were presented on conferences (e.g., X Xu, SK Frey, AK Nayak, Assimilation of SMAP Soil Moisture for Advancing Integrated Groundwater-Surface Water Modeling, AGU Fall Meeting 2022; AK Nayak, X Xu, SK Frey, Improving Physically-Based Hydrologic Predictions With Deep Learning, AGU Fall Meeting 2023). The detailed analysis results will be presented in separate manuscripts that are in preparation.
  
  Citation: https://doi.org/10.5194/hess-2023-309-AC2

Aruna Kumar Nayak, Xiaoyong Xu, Steven K. Frey, Omar Khader, Andre R. Erler, David R. Lapen, Hazen A. J. Russell, and Edward A. Sudicky

Data sets

Quantifying the linkage between SMAP soil moisture and fully-integrated hydrologic simulations A. K. Nayak et al. https://doi.org/10.5281/zenodo.8145252

Aruna Kumar Nayak, Xiaoyong Xu, Steven K. Frey, Omar Khader, Andre R. Erler, David R. Lapen, Hazen A. J. Russell, and Edward A. Sudicky

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Jan 2024	149	53	6	208
Feb 2024	71	17	8	96
Mar 2024	40	12	5	57
Apr 2024	58	15	10	83
May 2024	31	14	2	47
Jun 2024	30	5	2	37
Jul 2024	25	9	5	39
Aug 2024	16	5	2	23
Sep 2024	9	11	0	20
Oct 2024	5	5	0	10
Nov 2024	14	5	0	19
Dec 2024	4	6	0	10

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Short summary

Satellite remote sensing measures only the near-surface soil water content. This study demonstrates that satellite-based near-surface soil water variability is a strong reflection of deeper subsurface water fluctuation and quantifies the response time differences between dynamics of satellite near-surface soil water and water in deeper subsurface. Result support the use of satellite near-surface soil water measurements as indicators and/or predictors of water resources in deeper subsurface.


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