the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
An empirical model to calculate snow depth from daily snow water equivalent: SWE2HS 1.0
Johannes Aschauer
Adrien Michel
Tobias Jonas
Abstract. Many methods exist to model snow densification in order to calculate the depth of a single snow layer or the depth of the total snow cover from its mass. Most of these densification models need to be tightly integrated with an accumulation and melt model and need many forcing variables at high temporal resolution. However, when trying to model snow depth on climatological timescales, which is often needed for winter tourism related applications, these preconditions can cause barriers. Often, for these types of applications empirical snow models are used. These can estimate snow accumulation and melt based on daily precipitation and temperature data, only. To convert the resultant snow water equivalent time series into snow depth, we developed the empirical model SWE2HS. SWE2HS has been calibrated on a data set derived from a manual observer station network in Switzerland and validated against independent data from automatic weather stations in the European Alps. The model fits the calibration data with root mean squared error (RMSE) of 8.4 cm, coefficient of determination (R2) of 0.97 and BIAS of 0.2 cm and is able to reach RMSE of 20.5 cm, R2 of 0.92 and BIAS of 2.5 cm on the validation data. The temporal evolution of the bulk density can be reproduced reasonably well on both data sets. Due to its simplicity, the model can be used as post-processing tool for output of any other snow model that provides daily snow water equivalent output. SWE2HS is available as a Python package which can be easily installed and used.
Johannes Aschauer et al.
Status: closed
-
RC1: 'Comment on gmd-2022-258', Anonymous Referee #1, 12 Feb 2023
The manuscript ‘An empirical model to calculate snow depth from daily snow water equivalent: SWE2HS 1.0’ by Aschauer et al. provides a novel empirical model approach to convert daily snow water equivalent into snow depth in a simple way without having to rely on physically-based complexity or additional variables. The model uses a multi-layer densification approach based on exponential settling and takes changing maximum snow densities over time as a function of overburden and SWE losses into account. SWE2HS was calibrated on a dataset of the Swiss manual observer station network at 58 locations and was validated with 10 automatic weather stations in the European Alps. The chosen objective functions RMSE, R² and BIAS show good results for the calibration data set and quite good results for the validation data set, however, in the latter case, the RMSE is more than double as high (8.4 cm vs. 20.5 cm). I believe this model presentation is interesting to the readers of the journal as well as to the snow-hydro community. I see an advantage in using SWE2HS as a post-processing tool for HS conversions especially for SWE measurement devices and conceptual hydrological models, which simulate SWE instead of HS. In general, the manuscript is well written. However, it needs some clarifications before considering it for publication. The methods are valid, but need in some parts a better description. Please see my comments below.
General comments:
- Please give more information on your model SWE2HS in the abstract, which is currently fully missing in this version of the abstract. You only mention that you developed SWE2HS and that it has been calibrated and validated; but important information on the characteristics of the model are missing (e.g., multi-layer densification; solely based on SWE; exponential settling; changing of maximum snow density over time due to overburden and SWE losses).
- In the Introduction section, you distinguish between empirical and semi-empirical models (l. 42ff). In the manuscript, your SWE2HS model is sometimes described as empirical (e.g. in the title) and sometimes as semi-empirical (esp. in the Discussion and Conclusions sections). Please be consistent and define whether your model is empirical or semi-empirical. According to your definition in the introduction, it is rather empirical.
- In the current version, your model is for operation on a daily base. Would the model also work with hourly values and if not, what would you need to change in your model?
- In Section 3.1, you apply the ‘delta’-snow model by Winkler et al. (2021). Please introduce at least the main characteristics of this model.
- The manuscript would largely benefit from a figure illustrating the main steps of the density model / settling mechanism described in Section 2.2 in a schematic (see for example Figure 1 in Winkler et al. (2021) although you have less processes involved than the ‘delta’-snow model).
- The separation into calibration and validation datasets seems to be a bit unequal. Why didn’t you chose to validate for example a quarter of the dataset of the Swiss manual observer station network in addition to the automatic weather stations? It would be interesting to see how the validation performs on the Swiss manual observer station network as well. This would maybe overcome a bit the issue that you rely on the ‘delta’-snow model solely in the calibration dataset and do not use it also for validation. I would suggest to have two validation data sets. The one you already have with the automatic weather stations and a second one with parts of the Swiss manual observer station network. For the latter you could also use additional years, which you cut off at some stations for the calibration.
- In addition to Figure 1, showing an example of the model performance for one year at the station Kühroint, it would be interesting to see also further examples, e.g. for other locations, higher laying stations with a deeper snowpack, your calibration data etc. (this could be shown also in a supplementary).
Specific comments:
- 19: Although it might be clear for most readers in the snow-hydrological community what you mean with temperature-index models, please shortly explain and insert a reference.
- 37f: The sentence sounds a bit strange. I would reformulate to: ‘Various parametrizations exist and are usually based on estimating new snow density as a function of wind speed, temperature and relative humidity (references).’
- Section 2 ‘Density model’: For a better orientation for the reader, it would make sense to insert a (short) sub-chapter to introduce the general concept of the density model and not only present the ‘Settling mechanism’ in a sub-chapter. As mentioned in the general comments, it would be helpful to insert a schematic figure of SEWE2HS.
- 78: ‘increases with an exponential decay function’ instead of ‘increases exponentially’
- 80: Why does the model just remove SWE from the top layer when SWE decreases (this is counter intuitive (compared to reality) and needs clarification)? Would it be an option that SWE is removed from each layer proportionally?
- 93: ‘the’ is written twice. Delete it one time.
- 102: ‘which’ is written twice. Delete it one time.
- 104ff: You state that you neglect sublimation and that the snowpack has become wet entirely when the snowpack is decreasing. Please add a short discussion on these two simplifications, which are / might be different in reality and potential sources of errors due to these two assumptions in your discussion section.
- 127: It is helpful to describe the computation time and it seems to be quite fast. Which dataset did you chose for this exercise; was it a SWE output of a snow-hydrological model? If you performed such a potential application of your model, it would be valuable to report on that in more depth (in a separate section).
- Section 3 ‘Model calibration and validation’: It would make sense to insert for better orientation for the reader a sub-chapter for lines 135-166, e.g., ‘Calibration and validation methods’ before introducing the data sets in separate sub-chapters.
- 139f: It is not yet clear how you set the upper and lower bounds of possible values for each parameter (especially the parameters settling resistance R and v_melt (by the way, what is the unit of v_melt as it is denoted as a speed?)). Are the bounds based on literature values, experience, etc.?
- 163: The amount of your parameter set is high and sufficient. However, how did you come up with exactly 114688 parameter sets? Please introduce shortly the method of Saltelli (2002).
- 197ff: How often did you have the issue of filling up the data with linear interpolation (<= 5 days) and how often did you have data gaps?
- Figure 2: Which additional information can we get with the insets – are they really necessary?
- 233f: Please insert a reference on the Akaike Information Criterion.
- Figure 3: Please mention in the text the low R^2 of <0.4 for the validation data set for the month October. What could be the reason for the low R^2?
- Section Conclusion: This part is rather short. As you give a short summery, please add also a sentence on the calibration part.
Citation: https://doi.org/10.5194/gmd-2022-258-RC1 -
RC2: 'Comment on gmd-2022-258', Anonymous Referee #2, 15 Feb 2023
Summary
The manuscript entitled ‘An empirical model to calculate snow depth from daily snow water equivalent: SWE2HS 1.0’ presents an empirical model to derive daily snow depth (HS) from daily snow water equivalent (SWE) only. Density of each layer is modelled via an exponential function. Additionally, changes to due to overburden stress and SWE losses from runoff are considered. The model is calibrated using data from Switzerland and validated using a different dataset from automated weather stations in the European Alps (Austria, France, Germany, Switzerland). RMSE, R2 and Bias of the modeled HS with the obtained optimized parameters against the validation dataset are 20.5cm, 0.92 and 2.5cm compared to only 8.4cm, 0.97 and 0.2cm against the calibration dataset. The manuscript is well prepared but is lacking some details which should be addressed prior to being considered for publication.
General comments
- The model relies on HS records that are converted to SWE following Winkler et al. 2021 but this model is not described in sufficient detail to understand its impact (or lack thereof) on the optimization of the SWE2HS model. Please add short description of key/pertinent elements of the ΔSNOW model.
- The paper converts daily HS records to SWE following Winkler et al. 2021 and uses these modeled SWE data, corrected using biweekly manual SWE measurements, to calibrate their SWE2HS model. RMSE and bias between modeled and measured SWE is 30.0mm and -1.09 mm. The model is well tuned to the calibration dataset but has larger errors compared to the validation data. Could some of this be due to the modeled SWE? The current text gives the impression that such differences are mainly due to the in situ SWE and not to the model which I find to be a bit simplistic especially given the relative magnitudes of the above errors relative to the SWE2HS calibration and validation statistics. The impact of the differences in modeled vs observed SWE in model calibration and thus accuracy should be discussed as a limitation in Sect 5.2.
- The model was trained on the Switzerland data and then validated using an entirely different dataset covering a different spatial domain which adds additional complexity when interpreting the results. It’s not clear whether (or to what extent) the validation results are due to regional variability, modeled SWE for calibration vs measured SWE for validation, etc. Figure 4 shows clear differences between the calibration and validation datasets. Did the authors consider dividing the Switzerland data into calibration and validation datasets (and also perhaps divide the validation dataset into calibration and validation) to untangle some of these issues.
- Results could be discussed in greater detail, perhaps with additional sites considered (see specific comment regarding figures). The authors point out in which months the model accurately does or does not describe HS but offers little explanation as to why. The 'why' would help users understand the strengths and limitations of the model.
Specific comments
Figures:
- Sect 3.1 and 3.2 -> it would be helpful to provide a map showing the locations of the calibration and validation sites that were used in the analysis.
- Figure 1: It might be instructive to present both a ‘typical’ site as well as an ‘excellent’ and ‘poor’ site. This might help illustrate a wider range of conditions where the model performs well and poorly. Could be added in the main text or as a supplementary figure.
Abstract:
- Please add some specifics about the SWE2HS model. i.e. that it relies only on SWE, uses exponential settling functions and considers changes due to overburden stress and SWE losses from runoff.
- Please note the regional applicability of the SWE2HS model.
- L10: please note the locations and type of validation data (i.e. AWS Austria, France, Germany, Switzerland)
Introduction
- The authors present the need for this model in terms of tourism applications [L25]. Please mention why SWE (and not HS) is often desired and is the focus of many of the models mentioned. i.e. climate, hydrology, HS easier to measure operationally, etc.
Section 3
- I found it a bit difficult going back and forth between calibration, calibration data and then validation data and methods. Perhaps group methods and data together? Or add a sentence or two to the first part of Sect 3 that touches on validation (in addition to calibration). See also comment about additional Figure for the cal/val data.
Specific editorial suggestions
L42: suggest ‘The first category is purely empirical whereby densification dynamics are described via exponential settling functions.’
L77: suggest ‘The maximum density starts with an…’
L78: suggest ‘The maximum density starts with an initial value at creation time of the layer and subsequently increases towards…’
L80: Implications of this simplification? i.e. removing the top layer instead of decreasing all layers.
L85: suggest ‘The density of a layer at day i asymptomatically converges…’
L90: suggest ‘The maximum density to which the density of a snow layer converges, ρmax in Eq. 1, also evolves over time.’
L91: suggest ‘is that snow which has experienced a high load reaches a higher…’
L93: delete one of the ‘the’ in ‘The third assumption is that the…’
L96: ‘Afterwards, ρmax increases towards …’
L104: ‘Whenever SWE in the snowpack decreases we assume that the snowpack wet entirely and we attribute…’
L168: ‘To calibrate the SWE2HS…'
L192: ‘As a validation dataset’ or ‘For validation…’
Citation: https://doi.org/10.5194/gmd-2022-258-RC2 -
AC1: 'Reply to RC1 and RC2 on gmd-2022-258', Johannes Aschauer, 28 Apr 2023
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2022-258/gmd-2022-258-AC1-supplement.pdf
Status: closed
-
RC1: 'Comment on gmd-2022-258', Anonymous Referee #1, 12 Feb 2023
The manuscript ‘An empirical model to calculate snow depth from daily snow water equivalent: SWE2HS 1.0’ by Aschauer et al. provides a novel empirical model approach to convert daily snow water equivalent into snow depth in a simple way without having to rely on physically-based complexity or additional variables. The model uses a multi-layer densification approach based on exponential settling and takes changing maximum snow densities over time as a function of overburden and SWE losses into account. SWE2HS was calibrated on a dataset of the Swiss manual observer station network at 58 locations and was validated with 10 automatic weather stations in the European Alps. The chosen objective functions RMSE, R² and BIAS show good results for the calibration data set and quite good results for the validation data set, however, in the latter case, the RMSE is more than double as high (8.4 cm vs. 20.5 cm). I believe this model presentation is interesting to the readers of the journal as well as to the snow-hydro community. I see an advantage in using SWE2HS as a post-processing tool for HS conversions especially for SWE measurement devices and conceptual hydrological models, which simulate SWE instead of HS. In general, the manuscript is well written. However, it needs some clarifications before considering it for publication. The methods are valid, but need in some parts a better description. Please see my comments below.
General comments:
- Please give more information on your model SWE2HS in the abstract, which is currently fully missing in this version of the abstract. You only mention that you developed SWE2HS and that it has been calibrated and validated; but important information on the characteristics of the model are missing (e.g., multi-layer densification; solely based on SWE; exponential settling; changing of maximum snow density over time due to overburden and SWE losses).
- In the Introduction section, you distinguish between empirical and semi-empirical models (l. 42ff). In the manuscript, your SWE2HS model is sometimes described as empirical (e.g. in the title) and sometimes as semi-empirical (esp. in the Discussion and Conclusions sections). Please be consistent and define whether your model is empirical or semi-empirical. According to your definition in the introduction, it is rather empirical.
- In the current version, your model is for operation on a daily base. Would the model also work with hourly values and if not, what would you need to change in your model?
- In Section 3.1, you apply the ‘delta’-snow model by Winkler et al. (2021). Please introduce at least the main characteristics of this model.
- The manuscript would largely benefit from a figure illustrating the main steps of the density model / settling mechanism described in Section 2.2 in a schematic (see for example Figure 1 in Winkler et al. (2021) although you have less processes involved than the ‘delta’-snow model).
- The separation into calibration and validation datasets seems to be a bit unequal. Why didn’t you chose to validate for example a quarter of the dataset of the Swiss manual observer station network in addition to the automatic weather stations? It would be interesting to see how the validation performs on the Swiss manual observer station network as well. This would maybe overcome a bit the issue that you rely on the ‘delta’-snow model solely in the calibration dataset and do not use it also for validation. I would suggest to have two validation data sets. The one you already have with the automatic weather stations and a second one with parts of the Swiss manual observer station network. For the latter you could also use additional years, which you cut off at some stations for the calibration.
- In addition to Figure 1, showing an example of the model performance for one year at the station Kühroint, it would be interesting to see also further examples, e.g. for other locations, higher laying stations with a deeper snowpack, your calibration data etc. (this could be shown also in a supplementary).
Specific comments:
- 19: Although it might be clear for most readers in the snow-hydrological community what you mean with temperature-index models, please shortly explain and insert a reference.
- 37f: The sentence sounds a bit strange. I would reformulate to: ‘Various parametrizations exist and are usually based on estimating new snow density as a function of wind speed, temperature and relative humidity (references).’
- Section 2 ‘Density model’: For a better orientation for the reader, it would make sense to insert a (short) sub-chapter to introduce the general concept of the density model and not only present the ‘Settling mechanism’ in a sub-chapter. As mentioned in the general comments, it would be helpful to insert a schematic figure of SEWE2HS.
- 78: ‘increases with an exponential decay function’ instead of ‘increases exponentially’
- 80: Why does the model just remove SWE from the top layer when SWE decreases (this is counter intuitive (compared to reality) and needs clarification)? Would it be an option that SWE is removed from each layer proportionally?
- 93: ‘the’ is written twice. Delete it one time.
- 102: ‘which’ is written twice. Delete it one time.
- 104ff: You state that you neglect sublimation and that the snowpack has become wet entirely when the snowpack is decreasing. Please add a short discussion on these two simplifications, which are / might be different in reality and potential sources of errors due to these two assumptions in your discussion section.
- 127: It is helpful to describe the computation time and it seems to be quite fast. Which dataset did you chose for this exercise; was it a SWE output of a snow-hydrological model? If you performed such a potential application of your model, it would be valuable to report on that in more depth (in a separate section).
- Section 3 ‘Model calibration and validation’: It would make sense to insert for better orientation for the reader a sub-chapter for lines 135-166, e.g., ‘Calibration and validation methods’ before introducing the data sets in separate sub-chapters.
- 139f: It is not yet clear how you set the upper and lower bounds of possible values for each parameter (especially the parameters settling resistance R and v_melt (by the way, what is the unit of v_melt as it is denoted as a speed?)). Are the bounds based on literature values, experience, etc.?
- 163: The amount of your parameter set is high and sufficient. However, how did you come up with exactly 114688 parameter sets? Please introduce shortly the method of Saltelli (2002).
- 197ff: How often did you have the issue of filling up the data with linear interpolation (<= 5 days) and how often did you have data gaps?
- Figure 2: Which additional information can we get with the insets – are they really necessary?
- 233f: Please insert a reference on the Akaike Information Criterion.
- Figure 3: Please mention in the text the low R^2 of <0.4 for the validation data set for the month October. What could be the reason for the low R^2?
- Section Conclusion: This part is rather short. As you give a short summery, please add also a sentence on the calibration part.
Citation: https://doi.org/10.5194/gmd-2022-258-RC1 -
RC2: 'Comment on gmd-2022-258', Anonymous Referee #2, 15 Feb 2023
Summary
The manuscript entitled ‘An empirical model to calculate snow depth from daily snow water equivalent: SWE2HS 1.0’ presents an empirical model to derive daily snow depth (HS) from daily snow water equivalent (SWE) only. Density of each layer is modelled via an exponential function. Additionally, changes to due to overburden stress and SWE losses from runoff are considered. The model is calibrated using data from Switzerland and validated using a different dataset from automated weather stations in the European Alps (Austria, France, Germany, Switzerland). RMSE, R2 and Bias of the modeled HS with the obtained optimized parameters against the validation dataset are 20.5cm, 0.92 and 2.5cm compared to only 8.4cm, 0.97 and 0.2cm against the calibration dataset. The manuscript is well prepared but is lacking some details which should be addressed prior to being considered for publication.
General comments
- The model relies on HS records that are converted to SWE following Winkler et al. 2021 but this model is not described in sufficient detail to understand its impact (or lack thereof) on the optimization of the SWE2HS model. Please add short description of key/pertinent elements of the ΔSNOW model.
- The paper converts daily HS records to SWE following Winkler et al. 2021 and uses these modeled SWE data, corrected using biweekly manual SWE measurements, to calibrate their SWE2HS model. RMSE and bias between modeled and measured SWE is 30.0mm and -1.09 mm. The model is well tuned to the calibration dataset but has larger errors compared to the validation data. Could some of this be due to the modeled SWE? The current text gives the impression that such differences are mainly due to the in situ SWE and not to the model which I find to be a bit simplistic especially given the relative magnitudes of the above errors relative to the SWE2HS calibration and validation statistics. The impact of the differences in modeled vs observed SWE in model calibration and thus accuracy should be discussed as a limitation in Sect 5.2.
- The model was trained on the Switzerland data and then validated using an entirely different dataset covering a different spatial domain which adds additional complexity when interpreting the results. It’s not clear whether (or to what extent) the validation results are due to regional variability, modeled SWE for calibration vs measured SWE for validation, etc. Figure 4 shows clear differences between the calibration and validation datasets. Did the authors consider dividing the Switzerland data into calibration and validation datasets (and also perhaps divide the validation dataset into calibration and validation) to untangle some of these issues.
- Results could be discussed in greater detail, perhaps with additional sites considered (see specific comment regarding figures). The authors point out in which months the model accurately does or does not describe HS but offers little explanation as to why. The 'why' would help users understand the strengths and limitations of the model.
Specific comments
Figures:
- Sect 3.1 and 3.2 -> it would be helpful to provide a map showing the locations of the calibration and validation sites that were used in the analysis.
- Figure 1: It might be instructive to present both a ‘typical’ site as well as an ‘excellent’ and ‘poor’ site. This might help illustrate a wider range of conditions where the model performs well and poorly. Could be added in the main text or as a supplementary figure.
Abstract:
- Please add some specifics about the SWE2HS model. i.e. that it relies only on SWE, uses exponential settling functions and considers changes due to overburden stress and SWE losses from runoff.
- Please note the regional applicability of the SWE2HS model.
- L10: please note the locations and type of validation data (i.e. AWS Austria, France, Germany, Switzerland)
Introduction
- The authors present the need for this model in terms of tourism applications [L25]. Please mention why SWE (and not HS) is often desired and is the focus of many of the models mentioned. i.e. climate, hydrology, HS easier to measure operationally, etc.
Section 3
- I found it a bit difficult going back and forth between calibration, calibration data and then validation data and methods. Perhaps group methods and data together? Or add a sentence or two to the first part of Sect 3 that touches on validation (in addition to calibration). See also comment about additional Figure for the cal/val data.
Specific editorial suggestions
L42: suggest ‘The first category is purely empirical whereby densification dynamics are described via exponential settling functions.’
L77: suggest ‘The maximum density starts with an…’
L78: suggest ‘The maximum density starts with an initial value at creation time of the layer and subsequently increases towards…’
L80: Implications of this simplification? i.e. removing the top layer instead of decreasing all layers.
L85: suggest ‘The density of a layer at day i asymptomatically converges…’
L90: suggest ‘The maximum density to which the density of a snow layer converges, ρmax in Eq. 1, also evolves over time.’
L91: suggest ‘is that snow which has experienced a high load reaches a higher…’
L93: delete one of the ‘the’ in ‘The third assumption is that the…’
L96: ‘Afterwards, ρmax increases towards …’
L104: ‘Whenever SWE in the snowpack decreases we assume that the snowpack wet entirely and we attribute…’
L168: ‘To calibrate the SWE2HS…'
L192: ‘As a validation dataset’ or ‘For validation…’
Citation: https://doi.org/10.5194/gmd-2022-258-RC2 -
AC1: 'Reply to RC1 and RC2 on gmd-2022-258', Johannes Aschauer, 28 Apr 2023
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2022-258/gmd-2022-258-AC1-supplement.pdf
Johannes Aschauer et al.
Model code and software
swe2hs Python package Johannes Aschauer https://doi.org/10.5281/zenodo.7228066
Johannes Aschauer et al.
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