the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Sep 2022
An analytical generalization of Budyko framework with physical accounts of climate seasonality and water storage capacity
Abstract. The Budyko framework is an effective and widely used method for describing long-term water balance in large catchments. However, it only considers the limits of water and energy in evaporation (E), and ignores the impacts of climate seasonality and water storage capacity (Sc), resulting in errors for Mediterranean climate and catchments with small Sc. Here we combined the Ponce-Shetty model with Budyko hypothesis, and analytically generalized Budyko framework with physical accounts of climate seasonality and Sc. Precipitation (P), potential evaporation (PE), and Sc are used to represent the limits of water, energy, and space for E, respectively. Our results show that previous Budyko-type equations can be treated as special cases of generalized Budyko-type equations with uniform P and PE and infinite Sc. The new generalized equations capture the observed decrease in E due to asynchronous P and PE and small Sc, and perform better than the Budyko-type equations with varying parameters in the contiguous United States with fewer parameters. Overall, our generalization of Budyko framework improves the robustness and accuracy for estimating mean annual E with the aid of physical interpretation, and will facilitate water balance assessment at regional to global scales.
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RC1: 'Comment on hess-2022-309', Anonymous Referee #1, 09 Nov 2022
This paper proposes to take into account climate seasonality and water storage capacity into the Budyko framework. Two Budyko-type equations are used to mimic the water partitioning of the Ponce-Shetty model at a 4-month time interval. In comparison to the original Budyko-type equations where one 'n' parameter is required, it's adding two parameters: a second 'n' parameter that is calibrated over all catchments, and the water storage capacity 'Sc' that is regionalised on each catchment using soil descriptors. Results highlight improved performances compared to the original Budyko-type equations. I only have a few suggestions for improvement.
Main remarks:
- Despite the convincing improvement of the new formulation, it is rather unsatisfactory to advise calculating the water balance on a 4-month time scale. In the proposed formulation, no water storage/release can span over more than 4 months, and since the periods are fixed, each period is assumed to be independent (e.g. precipitation at the end of January is not influencing the hydrology of February). As recognized by the authors, for many catchments, such as catchments influenced by snow or large groundwater reservoirs, such assumption cannot be accepted. The authors solve this problem by removing these problematic catchments from their database, which I think is a good first step. However, the expression "generalised budyko equation" might be confusing, as the proposed formulation is somehow restricting the genericity of the Budyko framework. In addition, it would also have been more acceptable to relax the assumption behind the fixed periods by introducing sliding periods instead. Total annual evaporation could then have been estimated by summing the differences between two successive periods.
- From this study, it is somewhat difficult to rank the shortcomings of the Budyko framework that this paper is addressing. Is it seasonality or water storage capacity that is the main weakness of the Budyko framework? It would be useful, I think, to disentangle the effect of these two factors with modeling that takes into account, or not, each one. Indeed, the uncertainty in the water storage capacity may suggest that the sensitivity of this parameter is lower. Since the authors say that the original Budyko framework is just a special case of their formulation, it would be useful to treat it in a stepwise fashion (also with the idea of keeping a parsimonious framework).
- The conclusion that the new formulation is a better model is based primarily on the catchments that are located on the west coast of the United States, while the eastern part appears to be a mix of improved and degraded performance. What characterizes these catchments? No physiographic or hydroclimatic descriptors are used to help us interpret under what conditions the new equations perform better or worse (or where the 4-months assumptions is more acceptable).
- The term "seasonality" may need to be better defined and compared to the literature on this topic. It is sometimes used to refer to the synchrony between P and PE regimes (when citing papers on this topic), and sometimes to describe the need to refine the time scale at which the water balance should be performed. I understand that both aspects are encompassed in the term "seasonality" but they are treated differently in the literature and in this paper (e.g. this work does not work well with asynchronous climate seasonality, which could be unexpected and confusing if we do not agree on what "incorporating seasonality" mean).
Minor remarks:
- l85-87: the fact that most of the hydrological response is observed within 4 months may not always mean that the travel time is less than 4 months (concept of celerity vs velocity)
- Table 1: why not using E, PE and P for Budyko-type equation instead of X, Xmax and Z?
- Table 1: Yang-Fu expression E -> Ea
- l264: include -> includes
- l336: descrese -> decreases
- l410 : it would be helpful to explain why does a 12-month water balance (and so without seasonality taken into account) do not tend to give similar performance to the original Budyko framework (in relation to my second main comment)Citation: https://doi.org/10.5194/hess-2022-309-RC1 -
AC1: 'Reply on RC1', Xu Zhang, 12 Jan 2023
Dear Reviewer,
Thank you very much for reviewing our manuscript and providing valuable comments that greatly improve our work. We have paid attention to all comments and made revisions accordingly. Our responses have been provided in the supplementary file, in which your comments are in black and our replies are in blue.
Best wishes
Xu Zhang on behalf of all authors.
-
AC1: 'Reply on RC1', Xu Zhang, 12 Jan 2023
-
RC2: 'Comment on hess-2022-309', Anonymous Referee #2, 18 Nov 2022
This study proposes a generalization of the Budyko framework beyond the use of a single average aridity index. The key idea is to better account for seasonality and the related phase lags between precipitation and radiation and also for storage characteristics. While, I like the scope of the study and agree that the proposed generalizations are really important, I think the study suffers from several short comings.
May major concern is the obvious inconsistency between the “discretization” of the hydrological year into 4 months long periods, with the conceptualization of the first partitioning stage of the Ponce-Shetty model.
The idea that precipitation equals recharge/infiltration dW of/in the subsurface store and fast “flow” Q is only correct during rainfall events, because evaporation and transpiration can be neglected then.
P= Q + dW.
This equation is not correct during a 4 months period, consisting of rain and fair weather periods, it simply violates the mass balance, because parts of P are released as evaporation and transpiration during this period.
This implies that a one parameter Budyko (Eq 17.) cannot be used to model this partitioning for increments of 4 months, because in this time precipitation is simply not equal to fast runoff and storage change, but parts are released as ET. This does simply violate mass conservation at the soils surface, and the problem arises from the fact that the entire model is formulated for steady state partitioning, which essentially implies that storage changes are zero. This can be easily inferred from the water balance equation for any compartment (e.g. the soil), which should be the based for any kind of model concept (which is not the case here). So I think that the entire model analysis is based on a physically inconsistent reasoning. Either you have changes in storage or have steady states, you cannot have both.
Technical points:
- The manuscript would benefit from proof reading, at least I miss “definite articles” in front of many nouns.
- I would avoid abbreviations like “E” in headers, there are better ways to keep thinks short.
- Fluxes are generally equal to storages changes in time (not to storage itselft), would be nice to have proper equations, with proper variable definitions.
- I miss units/dimensions for most of the variables.
- Equation 8 proposes that the entire stock is “active” and released as base flow or ET. This is not consistent with soil physics and soil water retention curve, which corroborate that water stored at tension larger than pF =4.2 (permanent wilting point) is not available for transpiration (and also not for base flow generation).
- Eq. 9 is not correct, see comment above, expect that the authors refer to the active storage.
- With boundary conditions you mean upper and lower bounds of the terms?
- P going to infinity doesn’t make sense to me, at least not physically.
- Soil water storage is also limited by infiltration capacity, not only by storage volume. Both factors are not necessarily correlated, think about clay soils.
Citation: https://doi.org/10.5194/hess-2022-309-RC2 -
AC2: 'Reply on RC2', Xu Zhang, 12 Jan 2023
Dear Reviewer,
Thank you very much for reviewing our manuscript and providing valuable comments that greatly improve our work. We have paid attention to all comments and made revisions accordingly. Our responses have been provided in the supplementary file, in which your comments are in black and our replies are in blue.
Best wishes
Xu Zhang on behalf of all authors.
Status: closed
-
RC1: 'Comment on hess-2022-309', Anonymous Referee #1, 09 Nov 2022
This paper proposes to take into account climate seasonality and water storage capacity into the Budyko framework. Two Budyko-type equations are used to mimic the water partitioning of the Ponce-Shetty model at a 4-month time interval. In comparison to the original Budyko-type equations where one 'n' parameter is required, it's adding two parameters: a second 'n' parameter that is calibrated over all catchments, and the water storage capacity 'Sc' that is regionalised on each catchment using soil descriptors. Results highlight improved performances compared to the original Budyko-type equations. I only have a few suggestions for improvement.
Main remarks:
- Despite the convincing improvement of the new formulation, it is rather unsatisfactory to advise calculating the water balance on a 4-month time scale. In the proposed formulation, no water storage/release can span over more than 4 months, and since the periods are fixed, each period is assumed to be independent (e.g. precipitation at the end of January is not influencing the hydrology of February). As recognized by the authors, for many catchments, such as catchments influenced by snow or large groundwater reservoirs, such assumption cannot be accepted. The authors solve this problem by removing these problematic catchments from their database, which I think is a good first step. However, the expression "generalised budyko equation" might be confusing, as the proposed formulation is somehow restricting the genericity of the Budyko framework. In addition, it would also have been more acceptable to relax the assumption behind the fixed periods by introducing sliding periods instead. Total annual evaporation could then have been estimated by summing the differences between two successive periods.
- From this study, it is somewhat difficult to rank the shortcomings of the Budyko framework that this paper is addressing. Is it seasonality or water storage capacity that is the main weakness of the Budyko framework? It would be useful, I think, to disentangle the effect of these two factors with modeling that takes into account, or not, each one. Indeed, the uncertainty in the water storage capacity may suggest that the sensitivity of this parameter is lower. Since the authors say that the original Budyko framework is just a special case of their formulation, it would be useful to treat it in a stepwise fashion (also with the idea of keeping a parsimonious framework).
- The conclusion that the new formulation is a better model is based primarily on the catchments that are located on the west coast of the United States, while the eastern part appears to be a mix of improved and degraded performance. What characterizes these catchments? No physiographic or hydroclimatic descriptors are used to help us interpret under what conditions the new equations perform better or worse (or where the 4-months assumptions is more acceptable).
- The term "seasonality" may need to be better defined and compared to the literature on this topic. It is sometimes used to refer to the synchrony between P and PE regimes (when citing papers on this topic), and sometimes to describe the need to refine the time scale at which the water balance should be performed. I understand that both aspects are encompassed in the term "seasonality" but they are treated differently in the literature and in this paper (e.g. this work does not work well with asynchronous climate seasonality, which could be unexpected and confusing if we do not agree on what "incorporating seasonality" mean).
Minor remarks:
- l85-87: the fact that most of the hydrological response is observed within 4 months may not always mean that the travel time is less than 4 months (concept of celerity vs velocity)
- Table 1: why not using E, PE and P for Budyko-type equation instead of X, Xmax and Z?
- Table 1: Yang-Fu expression E -> Ea
- l264: include -> includes
- l336: descrese -> decreases
- l410 : it would be helpful to explain why does a 12-month water balance (and so without seasonality taken into account) do not tend to give similar performance to the original Budyko framework (in relation to my second main comment)Citation: https://doi.org/10.5194/hess-2022-309-RC1 -
AC1: 'Reply on RC1', Xu Zhang, 12 Jan 2023
Dear Reviewer,
Thank you very much for reviewing our manuscript and providing valuable comments that greatly improve our work. We have paid attention to all comments and made revisions accordingly. Our responses have been provided in the supplementary file, in which your comments are in black and our replies are in blue.
Best wishes
Xu Zhang on behalf of all authors.
-
AC1: 'Reply on RC1', Xu Zhang, 12 Jan 2023
-
RC2: 'Comment on hess-2022-309', Anonymous Referee #2, 18 Nov 2022
This study proposes a generalization of the Budyko framework beyond the use of a single average aridity index. The key idea is to better account for seasonality and the related phase lags between precipitation and radiation and also for storage characteristics. While, I like the scope of the study and agree that the proposed generalizations are really important, I think the study suffers from several short comings.
May major concern is the obvious inconsistency between the “discretization” of the hydrological year into 4 months long periods, with the conceptualization of the first partitioning stage of the Ponce-Shetty model.
The idea that precipitation equals recharge/infiltration dW of/in the subsurface store and fast “flow” Q is only correct during rainfall events, because evaporation and transpiration can be neglected then.
P= Q + dW.
This equation is not correct during a 4 months period, consisting of rain and fair weather periods, it simply violates the mass balance, because parts of P are released as evaporation and transpiration during this period.
This implies that a one parameter Budyko (Eq 17.) cannot be used to model this partitioning for increments of 4 months, because in this time precipitation is simply not equal to fast runoff and storage change, but parts are released as ET. This does simply violate mass conservation at the soils surface, and the problem arises from the fact that the entire model is formulated for steady state partitioning, which essentially implies that storage changes are zero. This can be easily inferred from the water balance equation for any compartment (e.g. the soil), which should be the based for any kind of model concept (which is not the case here). So I think that the entire model analysis is based on a physically inconsistent reasoning. Either you have changes in storage or have steady states, you cannot have both.
Technical points:
- The manuscript would benefit from proof reading, at least I miss “definite articles” in front of many nouns.
- I would avoid abbreviations like “E” in headers, there are better ways to keep thinks short.
- Fluxes are generally equal to storages changes in time (not to storage itselft), would be nice to have proper equations, with proper variable definitions.
- I miss units/dimensions for most of the variables.
- Equation 8 proposes that the entire stock is “active” and released as base flow or ET. This is not consistent with soil physics and soil water retention curve, which corroborate that water stored at tension larger than pF =4.2 (permanent wilting point) is not available for transpiration (and also not for base flow generation).
- Eq. 9 is not correct, see comment above, expect that the authors refer to the active storage.
- With boundary conditions you mean upper and lower bounds of the terms?
- P going to infinity doesn’t make sense to me, at least not physically.
- Soil water storage is also limited by infiltration capacity, not only by storage volume. Both factors are not necessarily correlated, think about clay soils.
Citation: https://doi.org/10.5194/hess-2022-309-RC2 -
AC2: 'Reply on RC2', Xu Zhang, 12 Jan 2023
Dear Reviewer,
Thank you very much for reviewing our manuscript and providing valuable comments that greatly improve our work. We have paid attention to all comments and made revisions accordingly. Our responses have been provided in the supplementary file, in which your comments are in black and our replies are in blue.
Best wishes
Xu Zhang on behalf of all authors.
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