Probabilistic soil moisture dynamics of water- and energy-limited ecosystems

Muñoz, Estefanía; Ochoa, Andrés; Poveda, Germán

doi:https://doi.org/10.5194/egusphere-2022-119

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https://doi.org/10.5194/egusphere-2022-119

Preprints

04 May 2022

| 04 May 2022

Probabilistic soil moisture dynamics of water- and energy-limited ecosystems

Estefanía Muñoz, Andrés Ochoa, and Germán Poveda

Abstract. We present an extension of the stochastic ecohydrological model for soil moisture dynamics at a point of RodríguezIturbe et al. (1999) and Laio et al. (2001). In the original model, evapotranspiration is a function of soil moisture and vegetation parameters, which makes the model suitable for water–limited environments. Based on the Leuning’s stomatal conductance approach, the C₃ photosynthesis model of Farquhar et al. and the Penman–Monteith equation, we model daily transpiration as a negative exponential function of available photosynthetically active radiation. This function allowed us to broaden the Rodríguez-Iturbe et al. (1999) and Laio et al. (2001) model to encompass both water– and energy–limited ecosystems by introducing the dependence of maximum evapotranspiration on available photosynthetically active radiation. We illustrate the extended model with two study cases from the FLUXNET database, DE–Hai in Germany and GF–Guy in French Guiana, and analyze the sensibility of soil moisture dynamics and the long-term water balance to available radiation. Our results show that the analytical solution presented by Rodríguez-Iturbe et al. (1999) continues to be valid as the maximum evapotranspiration rate is calculated in terms of available energy and assuming stationary in the radiation regime.

Received: 29 Mar 2022 – Discussion started: 04 May 2022

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Estefanía Muñoz, Andrés Ochoa, and Germán Poveda

Status: closed

RC1:
'Comment on egusphere-2022-119', Anonymous Referee #1, 03 Jun 2022
Review of “Probabilistic soil moisture dynamics of water– and energy–limited

Ecosystems” by Muñoz et al.

Summary

The authors present an adaptation of the ecohydrological model for soil moisture dynamics at a point of Rodríguez-Iturbe et al. (1999) and Laio et al. (2001) that is currently restricted to water-limited conditions. The adaptation proposed is to limit Tmax in the Laio et al. model by available energy (PAR) using an empirical relationship between PAR en Tmax based on flux data and inspired by the Farquhar C3 assimilation and the Leuning model of stomatal conductance which both increase with PAR (the latter because it is an increasing function of assimilation).

Major comments

This is a relatively limited extension of an existing model, but interesting enough to warrant a publication in HESS. However, for such a limited innovation, the paper is much too long winding. It can be reduced considerably. Why are so many equations related to the Farquhar model (in the main text and the appendix) provided, while in the end no assimilation is calculated: only soil moisture and water balance components. These could be left out or only the equations presented that are needed to support the arguments.

By the way: do we really need Penman-Monteith? According to Penman Monteith, Figure 2 seems to show that Tmax increases linearly with radiation and does not saturate? This seems a contradiction. With the exponential function chosen.

While the paper is too long, it should also be heavily restructured, A much simpler setup would be the following:

Introduction

Short recap of the Laio et al model (only Eqs 7, 8, 9, 10, 12)

Short review of transpiration under both water and energy limited conditions.

Describe Figure 1. Also describe why the T-R or T-PAR relationship is a saturating curve? Is this based on Leunings stomatal conductance model and C3 Farquhar assimilation and Penman monteith? Please explain.

Support the chosen form of Tmax(PAR) with flux data (Figure 4). Here the fluxnet dataset can be introduced.

Leading to the adaptation of the Lai et al model replacing Tmax with Tmax(PAR)

Sensitivity study (Figures 5,6)

Validation: (see remark hereafter).

Appendices A and B can be removed.

To show the importance of the addition an additional validation step is needed. Since you are looking at fluxnet data, at least qualitatively you should be able to show that the pdfs of soil moisture (or at least evapotranspiration) obtained from your adaption are closer to the observed values at the flux sites than the original ones obtained from Laio et al (all other parameters being equal). I realize that the assumption of stationarity does not hold for the German site due to seasonality, but you could focus on one summer month (July) and one early spring month (April) separately to have a water limited and an energy limited example.

Minor comments

Abstract, line 8: sensibility -> sensitivity.

Line 25: replace “there are seasonal environments .. fluctuates” with “There are areas where both regimes occur depending on the season.

Lines 28-32: I do not understand this part. Why are is situ and remote sensing data and numerical simulations presented as three categories. The type of data used and the way equations are solved are two separate issues.

Line 33: “from such complex processes”. What complex processes are meant here?

Line 62, start with: “The remaining part of this paper is organized as follows:”

Line 92: tappers -> tapers

Lines 260-262: groundwater can have a major impact on the pdf of soil moisture and evaporation. See e.g.: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005WR004696

https://www.sciencedirect.com/science/article/pii/S0304380010001079
Citation: https://doi.org/10.5194/egusphere-2022-119-RC1
- AC1: 'Reply on RC1', Estefanía Muñoz, 13 Aug 2022
  
  Dear Reviewer,
  We would like to thank you for taking the time to assess our manuscript and for your valuable comments and suggestions. We agree that the manuscript could be restructured to make it easier to follow and that some points should be better explained to avoid confusion. We have analyzed the comments carefully and the detailed responses are presented in the attached document.
  Sincerely,
  Estefanía Muñoz, Andrés Ochoa and Germán Poveda
  
  Citation: https://doi.org/10.5194/egusphere-2022-119-AC1
RC2:
'Comment on egusphere-2022-119', Anonymous Referee #2, 07 Jul 2022

The manuscript 2022-119 presents an extension of a minimalist probabilistic soil moisture model by Rodriguez-Iturbe, Laio, Porporato and co-workers (hereafter, Laio’s model). The point of departure is that Laio’s model considers only water limited ecosystems and, as such, needs extension for enhanced generality. The extension is achieved by altering one of the original model parameters, that representing the evapotranspiration rate under well-watered conditions, ET_{max}, (apparently-see below) in two ways: via implementing the Penman-Monteith equation, to determine the reference crop transpiration; and based on an empirical radiation-transpiration relationship, derived from sub-hourly data.

I have some substantial concerns regarding the motivation of this work and the approach(es) followed.

1) As recognized in some lines of the manuscript (L173) but not elsewhere (e.g., L122), Laio’s model does take into account the energy constraint, precisely via ET_{max}. With respect to other sensitivity analyses on ET_{max}, here a standard process-based model or an empirical relationship are used to explain variations in such parameter. But, in the end, in its current form, the manuscript appears a sensitivity analysis. Beyond the somewhat misleading framing of this work, all in all changes to the soil moisture balance due to different radiation levels are modest – something that was already concluded in Daly and Porporato (2006, Water Resources Research). Furthermore, neither Laio’s model nor the proposed extension take into account the effect of extremely high soil moisture values.

2) More importantly, Laio’s model is a stochastic soil moisture model, taking into account the randomness in precipitation timing and amount. Radiation fluctuates too, as also apparent from the data used for the empirical relationship. This work appears not to consider this aspect in any way, despite considering daily data (from the sub-hourly upscaling). I find this incorrect. Moreover, a solution to this problem is available in Daly and Porporato (2006, Water Resources Research). If, instead, the point is to consider the average seasonal radiation, then this should be made clear when applying Penman-Monteith and would mean dropping the empirical radiation-transpiration relationship.

3) The relative role of Penman Monteith and the empirical radiation-transpiration relationship remains unclear. From my reading, it seems that one of them would suffice in reaching the goal of linking ET_{max} to radiation (but see point 2 regarding a potential crucial difference).

I also found the manuscript difficult to follow. Aside from the role of Penman Monteith vs the empirical relation (see point 3 above), the structure of the text (and subdivision in sections and subsections) is not intuitive and there are many details reported that appear of low relevance to the questions at hand, or so well established not to require anything beyond a reference (e.g., Table 1 and 2; Appendix A and B). I also note that a large number of references are reported in support of rather general points (e.g., L120), where one or two well-chosen references would suffice and serve the reader better.

Finally, there are some misleading or incorrect statements. Examples are:

- L88: the definition of s

- L90: the fact that transpiration depends only on maximum stomatal conductance, where (as also apparent from Penman Monteith formula) transpiring biomass and leaf-atmosphere coupling play a role too

- L173 (see point 1 above)

- L239: the pdf of s is obtained under *stochastic* steady state, not steady state. This is an important difference

There are also few typos, e.g., lines 92, 137, 730 (and elsewhere).

Citation: https://doi.org/10.5194/egusphere-2022-119-RC2
- AC2: 'Reply on RC2', Estefanía Muñoz, 13 Aug 2022
  
  Dear Reviewer,
  We would like to thank you for taking the time to review our manuscript and for your valuable comments and suggestions. After reading your comments and those of the other reviewers, we decided to restructure the manuscript as described in the response to comment 4 in the attached file. This is to make it clearer and more concise. Please see the mentioned document for responses to your comments point by point.
  Sincerely,
  Estefanía Muñoz, Andrés Ochoa and Germán Poveda
  
  Citation: https://doi.org/10.5194/egusphere-2022-119-AC2

Status: closed

RC1:
'Comment on egusphere-2022-119', Anonymous Referee #1, 03 Jun 2022
Review of “Probabilistic soil moisture dynamics of water– and energy–limited

Ecosystems” by Muñoz et al.

Summary

The authors present an adaptation of the ecohydrological model for soil moisture dynamics at a point of Rodríguez-Iturbe et al. (1999) and Laio et al. (2001) that is currently restricted to water-limited conditions. The adaptation proposed is to limit Tmax in the Laio et al. model by available energy (PAR) using an empirical relationship between PAR en Tmax based on flux data and inspired by the Farquhar C3 assimilation and the Leuning model of stomatal conductance which both increase with PAR (the latter because it is an increasing function of assimilation).

Major comments

This is a relatively limited extension of an existing model, but interesting enough to warrant a publication in HESS. However, for such a limited innovation, the paper is much too long winding. It can be reduced considerably. Why are so many equations related to the Farquhar model (in the main text and the appendix) provided, while in the end no assimilation is calculated: only soil moisture and water balance components. These could be left out or only the equations presented that are needed to support the arguments.

By the way: do we really need Penman-Monteith? According to Penman Monteith, Figure 2 seems to show that Tmax increases linearly with radiation and does not saturate? This seems a contradiction. With the exponential function chosen.

While the paper is too long, it should also be heavily restructured, A much simpler setup would be the following:

Introduction

Short recap of the Laio et al model (only Eqs 7, 8, 9, 10, 12)

Short review of transpiration under both water and energy limited conditions.

Describe Figure 1. Also describe why the T-R or T-PAR relationship is a saturating curve? Is this based on Leunings stomatal conductance model and C3 Farquhar assimilation and Penman monteith? Please explain.

Support the chosen form of Tmax(PAR) with flux data (Figure 4). Here the fluxnet dataset can be introduced.

Leading to the adaptation of the Lai et al model replacing Tmax with Tmax(PAR)

Sensitivity study (Figures 5,6)

Validation: (see remark hereafter).

Appendices A and B can be removed.

To show the importance of the addition an additional validation step is needed. Since you are looking at fluxnet data, at least qualitatively you should be able to show that the pdfs of soil moisture (or at least evapotranspiration) obtained from your adaption are closer to the observed values at the flux sites than the original ones obtained from Laio et al (all other parameters being equal). I realize that the assumption of stationarity does not hold for the German site due to seasonality, but you could focus on one summer month (July) and one early spring month (April) separately to have a water limited and an energy limited example.

Minor comments

Abstract, line 8: sensibility -> sensitivity.

Line 25: replace “there are seasonal environments .. fluctuates” with “There are areas where both regimes occur depending on the season.

Lines 28-32: I do not understand this part. Why are is situ and remote sensing data and numerical simulations presented as three categories. The type of data used and the way equations are solved are two separate issues.

Line 33: “from such complex processes”. What complex processes are meant here?

Line 62, start with: “The remaining part of this paper is organized as follows:”

Line 92: tappers -> tapers

Lines 260-262: groundwater can have a major impact on the pdf of soil moisture and evaporation. See e.g.: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005WR004696

https://www.sciencedirect.com/science/article/pii/S0304380010001079
Citation: https://doi.org/10.5194/egusphere-2022-119-RC1
- AC1: 'Reply on RC1', Estefanía Muñoz, 13 Aug 2022
  
  Dear Reviewer,
  We would like to thank you for taking the time to assess our manuscript and for your valuable comments and suggestions. We agree that the manuscript could be restructured to make it easier to follow and that some points should be better explained to avoid confusion. We have analyzed the comments carefully and the detailed responses are presented in the attached document.
  Sincerely,
  Estefanía Muñoz, Andrés Ochoa and Germán Poveda
  
  Citation: https://doi.org/10.5194/egusphere-2022-119-AC1
RC2:
'Comment on egusphere-2022-119', Anonymous Referee #2, 07 Jul 2022

The manuscript 2022-119 presents an extension of a minimalist probabilistic soil moisture model by Rodriguez-Iturbe, Laio, Porporato and co-workers (hereafter, Laio’s model). The point of departure is that Laio’s model considers only water limited ecosystems and, as such, needs extension for enhanced generality. The extension is achieved by altering one of the original model parameters, that representing the evapotranspiration rate under well-watered conditions, ET_{max}, (apparently-see below) in two ways: via implementing the Penman-Monteith equation, to determine the reference crop transpiration; and based on an empirical radiation-transpiration relationship, derived from sub-hourly data.

I have some substantial concerns regarding the motivation of this work and the approach(es) followed.

1) As recognized in some lines of the manuscript (L173) but not elsewhere (e.g., L122), Laio’s model does take into account the energy constraint, precisely via ET_{max}. With respect to other sensitivity analyses on ET_{max}, here a standard process-based model or an empirical relationship are used to explain variations in such parameter. But, in the end, in its current form, the manuscript appears a sensitivity analysis. Beyond the somewhat misleading framing of this work, all in all changes to the soil moisture balance due to different radiation levels are modest – something that was already concluded in Daly and Porporato (2006, Water Resources Research). Furthermore, neither Laio’s model nor the proposed extension take into account the effect of extremely high soil moisture values.

2) More importantly, Laio’s model is a stochastic soil moisture model, taking into account the randomness in precipitation timing and amount. Radiation fluctuates too, as also apparent from the data used for the empirical relationship. This work appears not to consider this aspect in any way, despite considering daily data (from the sub-hourly upscaling). I find this incorrect. Moreover, a solution to this problem is available in Daly and Porporato (2006, Water Resources Research). If, instead, the point is to consider the average seasonal radiation, then this should be made clear when applying Penman-Monteith and would mean dropping the empirical radiation-transpiration relationship.

3) The relative role of Penman Monteith and the empirical radiation-transpiration relationship remains unclear. From my reading, it seems that one of them would suffice in reaching the goal of linking ET_{max} to radiation (but see point 2 regarding a potential crucial difference).

I also found the manuscript difficult to follow. Aside from the role of Penman Monteith vs the empirical relation (see point 3 above), the structure of the text (and subdivision in sections and subsections) is not intuitive and there are many details reported that appear of low relevance to the questions at hand, or so well established not to require anything beyond a reference (e.g., Table 1 and 2; Appendix A and B). I also note that a large number of references are reported in support of rather general points (e.g., L120), where one or two well-chosen references would suffice and serve the reader better.

Finally, there are some misleading or incorrect statements. Examples are:

- L88: the definition of s

- L90: the fact that transpiration depends only on maximum stomatal conductance, where (as also apparent from Penman Monteith formula) transpiring biomass and leaf-atmosphere coupling play a role too

- L173 (see point 1 above)

- L239: the pdf of s is obtained under *stochastic* steady state, not steady state. This is an important difference

There are also few typos, e.g., lines 92, 137, 730 (and elsewhere).

Citation: https://doi.org/10.5194/egusphere-2022-119-RC2
- AC2: 'Reply on RC2', Estefanía Muñoz, 13 Aug 2022
  
  Dear Reviewer,
  We would like to thank you for taking the time to review our manuscript and for your valuable comments and suggestions. After reading your comments and those of the other reviewers, we decided to restructure the manuscript as described in the response to comment 4 in the attached file. This is to make it clearer and more concise. Please see the mentioned document for responses to your comments point by point.
  Sincerely,
  Estefanía Muñoz, Andrés Ochoa and Germán Poveda
  
  Citation: https://doi.org/10.5194/egusphere-2022-119-AC2

Estefanía Muñoz, Andrés Ochoa, and Germán Poveda

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Short summary

Rodriguez-Iturbe et al. in 1999 presented a model to analytically describe soil moisture dynamics for water-limited ecosystems. In this paper, we extend the model to energy-limited ecosystems by introducing the dependence of maximum evapotranspiration on radiation, and we model this relationship through a negative exponential equation. We illustrate the extended model with two study cases and evaluate the sensibility of soil moisture and the long-term water balance to available energy.


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