the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Mar 2021
Exploring the role of soil storage capacity for explaining deviations from the Budyko curve using a simple water balance model
Abstract. The Budyko curve is a widely used framework for predicting the steady-state water balance –solely based on the hydro-climatic setting of river basins. While this framework has been tested and verified across a wide range of climates and settings around the globe, numerous catchments have been reported to considerably deviate from the predicted behavior. Here, we hypothesize that storage capacity and field capacity of the root zone are important controls of the water limitation of evapotranspiration and thus deviations of the mean annual water balance from the Budyko curve. For testing our hypothesis, we selected 16 catchments of different climatic settings and varied the corresponding parameters of a simple water balance model that was previously calibrated against long-term data and investigated the corresponding variations of the simulated water balance in the Budyko space. We found that total soil storage capacity –by controlling water availability and limitation of evapotranspiration– explains deviations of the evaporation ratio (EVR) from the Budyko curve. Similarly, however to a lesser extent, the evaporation ratio showed sensitivity to alterations of the field capacity. In most cases, the parameter variations generated evaporation ratios enveloping the Budyko curve. The distinct soil storage volumes that matched the Budyko curve clustered at a normalized storage capacity equivalent to 5–15 % of mean annual precipitation. The second, capillarity-related soil parameter clustered at around 0.6–0.8, which is in line with its hydropedological interpretation. A simultaneous variation of both parameters provided additional insights into the interrelation of both parameters and their joint control on offsets from the Budyko curve. Here we found three different sensitivity patterns and we conclude the study with a reflection relating these offsets to the concept of catchment coevolution. The results of this study could also be useful to facilitate evaluation of the water balance in data-scarce regions, as they help constrain parameterizations for hydrological models a priori using the Budyko curve as a predictor.
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RC1: 'Comment on hess-2021-174', Anonymous Referee #1, 15 Apr 2021
Dear colleagues,
I was first very enthusiastic when starting to read your paper that I ultimately found too theoretical in its present form:
- The main critic that I would make is that in your analysis of Budyko’s empirical formulation of water balance you are using… model results. Testing a model with a model… As a starting point it’s perfectly OK, but you should at least in a second step try to validate this with actual data. I know it’s not easy, because it requires a large dataset with root-zone capacity estimates (but you should be able to get this at least for Germany of the USA ?). A second critic that I would make is that you decide that the soil characteristics are the first-order determinant of the deviations of the the Budyko curve. I don’t say you are wrong, but I say this requires to be proved. There are other hypotheses in the literature: for example one of our papers (de Lavenne and Andréassian, 2018), we suggest based on actual streamflow data that the phase synchronicity of precipitation and potential evaporation explains the deviation of the Budyko-type curves.
Minor remarks
- Please change your notations to follow the recommendations of HESS: only one letter for a variable (possibly a subscript)
- 77: please adapt your references : Turc and Mezentsev published their formula 40 years before Choudhury, and Tixeront published his formula almost 20 years before Fu…
- 83: you write that it is inappropriate to try to represent the deviations of the Budyko-type relationship with a single parameter… I do not agree. Again, in our 2018 paper, we showed that it was possible to parameterize the parameters of the Turc-Mezentsev and the Tixeront-Fu formulation with a climatic index.
- 176: rainfall seasonality is not enough, you need an index that tells you whether rainfall and potential evaporation are in phase or out of phase
- L 572: You write that your research “did not purely take place in the realm of simulations”… but I would object that you almost staid there!
References
de Lavenne, A. & V. Andréassian. 2018. Impact of climate seasonality on catchment yield: a parameterization for commonly-used water balance formulas. Journal of Hydrology, 558: 266-274, https://doi.org/10.1016/j.jhydrol.2018.01.009
Mezentsev, V., 1955. Back to the computation of total evaporation (ÐÑÑ Ñаз о ÑаÑÑеÑе ÑÑеднего ÑÑммаÑного иÑпаÑениÑ). Meteorologia i Gidrologia - ÐеÑеоÑÐ¾Ð»Ð¾Ð³Ð¸Ñ Ð¸ ÐидÑологиÑ, 5: 24-26.
Tixeront, J., 1964. Prévision des apports des cours d'eau (Prediction of streamflow), IAHS publication n°63: General Assembly of Berkeley. IAHS, Gentbrugge, pp. 118-126.
Turc, L., 1954. The water balance of soils: relationship between precipitations, evaporation and flow (Le bilan d'eau des sols: relation entre les précipitations, l'évaporation et l'écoulement). Annales Agronomiques, Série A(5): 491-595.
Citation: https://doi.org/10.5194/hess-2021-174-RC1 -
AC2: 'Reply on RC1', Jan Bondy, 26 Apr 2021
We thank the reviewer for his comments and suggestions.
We agree with the reviewer that we are ultimately testing a model with a model. However, these models are independent from each other, and the models used are so simple that they are surely not overfitted. The starting point for our virtual experiments were hydrological models calibrated on observations. As stated in the study, we aimed at exploring and targeting the role of one specific characteristic (soil storage) for explaining significant offsets from the Budyko curve. We tried to isolate this influence on the water balance, and understand a bit better its qualitative and quantitative behavior and relationship to the Budyko curve.
Validation datasets for catchments including root zone depths are indeed difficult to obtain. It would furthermore also be challenging, if not impossible, to disentangle the other second-order influences (confounding variables) on the mean water balance. Such an approach would again require the discussion about the deviations from the soil storage perspective in this hypothetical validation dataset – which would probably end up being a whole study on its own. This motivated us to look at it in a different manner. We decided to test the role of controls related to soil storage volume in the Budyko framework in virtual experiments that allow masking out other influences.
The fact that we are focusing on soil characteristics in this paper does not mean that we consider these other factors being minor or absent. We do not want to conclude that soil characteristics are “the” first-order determinant of the deviations, but rather one among several controls, which we also mention explicitly. We focused on soil storage because, from a physical point of view, this factor should determine the available storage volume required to buffer the slower evaporation process. Testing this hypothesis in our virtual experiments showed that varying the soil parameters within reasonable ranges was sufficient to make the systems reach the Budyko curve in most cases. In our opinion, these results are a strong indication that soil storage characteristics can indeed have an important role in explaining deviations from the Budyko curve, and should not be neglected when studying these effects. We will carefully revise discussion and conclusions in this direction.
Thanks for pointing out the importance of the synchronicity of P and ETp. The importance of the phase lag did not appear that striking to us in this study, since there is no phase lag in the Peruvian basin (one of the two seasonal ones). For the other seasonal catchment (in the US) it does occur though and might well play a role. We will complement the discussion in that regard. In general, we tried to discuss potential explanations for deviating behavior from our soil storage-based reasoning; however, this part can of course never be all-encompassing.
We are also grateful for the other, more technical comments, and will gladly incorporate them in a revised version.
Citation: https://doi.org/10.5194/hess-2021-174-AC2
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RC2: 'Comment on hess-2021-174', Anonymous Referee #2, 20 Apr 2021
Review Bondy et al. 2021 HESSD
Bondy et al. investigate the role of soil storage capacity and field capacity on the long-term water balance of several catchments within the Budyko framework. They use a simple lumped hydrological model to explore how two parameters representing soil storage capacity and field capacity, respectively, affect the partitioning of precipitation into evapotranspiration and streamflow. The authors find that storage capacity is a strong control on modelled evapotranspiration, and to a lesser extent field capacity. They then discuss how these findings might relate to hydro-pedological processes and catchment co-evolution.
The paper is well written and within the scope of HESS. Understanding second-order controls on the long-term water balance is an important topic and the general idea of the paper is very interesting. I think, however, that the study requires major revisions before it can be published. Generally, I think it lacks some depth and some of the arguments or not sufficiently backed up by either the results or references. I will outline my major and minor comments below.
Major comments:
As you discuss briefly in Sect. 4.1.2., there are (significant) interactions between the model parameters. As the model is fairly simple, but most (all?) conclusions are based on varying the model parameters, I think it would be good to spend some more time on exploring parameter interactions (e.g. by performing a more thorough sensitivity analysis), not just of the two main parameters, but of all four parameters. How important are the other two parameters for the water balance of the model? How realistic is it to fix three parameters and vary the fourth with respect to real systems (in which potentially only certain combinations of parameters occur)? This is particularly important for your discussion of co-evolution later in the manuscript: is a model with three fixed parameters and one varied parameter really representing a meaningful evolutionary trajectory?
I would also be more cautious when it comes to interpreting the parameter values. You look at a simple lumped model, so I wonder if there’s a way to be more convincing about what these parameters actually mean. There is some discussion about their range being reasonable, but I think that’s all a bit too general, and does not relate explicitly to any of the catchments you studied here. You could use some catchment attributes (e.g. soil texture) to see whether the optimised parameters match what you would expect from independent data or expert knowledge (e.g. are the calibrated parameter values different for catchments with sandy/silty/clayey soils?).
You justify using a (nowadays) rather small sample by saying that you want to focus on 16 distinctly different catchments. But then there is very little discussion or information about the catchments you study, except for the climatic attributes shown in Fig. 1. I miss a more detailed description of the catchments studied, in particular as a way to back up the model results with some real world system characteristics. Because if the catchments are selected based primarily on (widely available) climatic attributes, then I wonder why you didn’t use a larger sample of catchments to obtain more robust conclusions.
I am not convinced by the idea of co-evolution, at least how it is presented here. I think this section needs much more supporting evidence than a relatively simple modelling experiment (which mostly focuses one variable parameter). I think a more in-depth discussion about the catchments you study would help in that respect (see also my comment above). You cite a few papers, but Hartmann et al. (2020), for instance, look at pro-glacial moraines, and you use it to back up the very general statement that “Both porosity and the fraction of silt and clay increase with time”.
I am also wondering over what time scales such a co-evolution might happen. This is something many discussions about co-evolution do not mention explicitly. Many of the catchments you study are in areas that are perhaps not directly impacted by water abstractions etc. right now, but they’ve been impacted by humans for a long time. For example, the catchments in the south east of BW are in an area with a lot of agriculture, and also the Black Forest has been heavily impacted/managed in many areas. How does such a long history of agriculture or forestry affect co-evolution?
Minor comments:
There are a few typos, which I won’t list individually, but I would suggest to reread the manuscript carefully
L.9: I would write “Budyko framework“ instead of “Budyko curve“
L.10: I suggest writing validated instead of verified (also in L.36)
L.10. “wide range of climates and settings“ – what kind of settings?
L.17: I suggest defining evaporation ratio (as ET/P) here instead of introducing the acronym
L.33: Perhaps a bit picky, but stating that Budyko “observed a considerable degree of clustering around the Budyko curve” sounds a bit odd, as he probably didn’t think of it as the “Budyko curve”.
L.37 and following: I like the idea of presenting how you came up with the project by looking at Peruvian catchments, but in the end you only use one catchment in Peru. Weren’t there more Peruvian catchments available?
Table A-1: It would be interesting to also know the names of the rivers/gauging stations.
Section 2.4: What exactly is the special similarity to HBV? The model just seems to be one (of many) bucket-type models.
L.223: Why did you not use daily values to calculate KGE?
Why did you not choose an independent evaluation period to ensure the model isn’t overfitted (e.g. a 15y-15y split)?
You consider a water balance error of < 15% to be small – that does not sound that small to me, especially given that you study the long-term water balance.
It seems like in the arid catchments, you systematically overestimate the water balance by approx. 10%. Is that just more pronounced because streamflow is lower here and hence a similar absolute error appears bigger? What if you used relative error in ET instead of Q, since you mostly focus on ET?
Table 2: The upper limit for Smax here is 800mm, but later you mention that you vary it from 1 to 2000mm
L.292: “a clear clustering at 5-15%” – to me this doesn’t look like a clear clustering as half of the points are above 20% (and two are not shown)
Figure 5 (right): I would suggest writing the definition of the normalised storage volume (e.g. Smax/P) on the y-axis. Also consider using (a), (b), etc. as labels for subplots
L.368 and 400: write “parameter values” instead of “parameterisation”
L.440: “The lower the number of rainy days…” That’s only true if the total rainfall depth is the same. If there are 50 rainy days with a total of 500mm, and 100 days with a total of 1000mm, the depth per event would be the same. It would be useful to perform a quick check, as it seems like total rainfall is correlated with the number of rainy days.
L.573: I am not sure what you mean here. What’s the alternative approach? A modelling experiment with artificial data?
L.576: “tangible catchment properties”… that’s an example of a statement I find too general, an issue I already raised in my major comments. Yes, you discuss the ranges of the parameter values, but you’re looking at calibrated parameter values from a lumped model without any in-depth catchment analysis. I don’t think that’s necessarily a problem, but I think you should discuss more clearly what your study can tell us and what not.
Lastly one general comment about the role of storage: what about storage in (deeper) layers and the role of groundwater? While some plants might have access to groundwater, catchments underlain by permeable aquifers might also “lose” water, which might limit evapotranspiration.
Citation: https://doi.org/10.5194/hess-2021-174-RC2 -
AC3: 'Reply on RC2', Jan Bondy, 27 Apr 2021
We thank you for the insights and comments which will help us to improve the manuscript. We will for now focus on the major points brought up in the review.
One issue raised in several parts of the review is related to the characteristics of the selected catchments, which we agree to have neglected slightly. We will provide more information on the catchments, also including soil type or texture, and relate this info to our results and the discussion accordingly. Data on soil properties, however, are not widely available, or are limited in accuracy and representativeness, especially at the catchment scale. We also want to emphasize that the point of our study was not to explain the as-is state of the catchments (or their calibrated parametric representations), but to use them in a virtual experiment approach with 16 catchments and realistic boundary conditions, in order to explore the role and sensitivity of soil storage characteristics in deviations from the Budyko curve. We found rather consistent sensitivity patterns - most of the systems reached the Budyko curve through variation of the soil characteristics in reasonable ranges. But we agree that it will be interesting to compare the individual deviations with actual soil data.
A second major point concerns the coevolution of catchments, which we adopted from Troch (2015) for the discussion part. We agree with the reviewer that human activities have altered catchments and their soils, this influence being however comparably recent (more extensive agriculture maybe over the past 200-300 years), whereas soils developed with the climate at least since the last ice age which ended around 10.000 years ago. Coevolution of catchments or landscape elements happens at a range of time scales (Troch 2015), from geological ones to climatic and ecosystem scales. The rate of “hydrologic aging”, however, is hard to assess and depends on the drivers as nicely described by Troch.
In our study, we only tried to limit direct water balance-impacting measures like abstractions, to be able to estimate at least the present hydrologic partitioning/water balance. We did not aim to assess the potential alteration of catchment elements due to anthropogenic activity. We are also not really capable of modeling coevolution of form and functioning in hydrological systems. However, the Budyko curve yields a widely accepted framework to discriminate which combinations of catchment properties might have co-evolved and which not (as done e.g. by Schaefli 2011).
With our interpretation and visualization of parameter spaces regarding soil storage and its relationship to the Budyko curve, we aimed at understanding potential trajectories, analyze patterns found for climate groups, and tried to discuss deviations in the pattern for seasonal catchments in terms of the hydrologic age concept. We want to point out again that the focus of our study is not on best explaining the current state of the catchment but to quantify how even small changes in total storage or in the field capacity of the root zone control and explain frequently observed offsets from the Budyko curve. As catchments and soil properties are not static but changing, this naturally involves a co-evolutionary aspect.
The study by Hartmann et al. 2020 shows such a soil development at scales of centuries and millennia, both in terms of soil storage and retention characteristics. It is an exemplary study, that is correct. However, it shows for two different parent materials (on proglacial moraines), a similar qualitative development at different rates. That was supposed to corroborate our assumed weathering processes to discuss our variation scheme, but this aspect can of course not be generalized to all pedogenetic environments. We will discuss that point more critically in a revised version of the paper, and also include that other mechanisms including human activity can influence soil storage characteristics.
The last major concern was on model parameters and parameter interaction. We agree that varying only certain model parameters, while others remain unaltered, is a simplification of how real-world systems would develop or change. Any parameter variation or sensitivity study needs to take into account if the underlying model is representative. We are confident that conceptual hydrological models such as the HBV approach can represent hydrologic systems sufficiently well for describing catchment dynamics at the long-term scale, especially as we are considering that the virtual catchments we are exploring are not changing their properties during the simulation. We will clarify these points in the discussion.
We have tried to visualize parameter interactions in the 2d parameter spaces (Fig. 8). We focused on the parameters S_max and FC_frac, which can be related to two forms of soil storage volumes. They are important in the two stages of the evaporation process: at first, when the atmospheric demand is met, and secondly, when the capillary soil transport/supply is impeded by retention. The other two parameters were not included in this analysis. The k_res parameter is insensitive for the long-term annual water balance, since it does not affect the hydrologic partitioning but the dynamics of stream flow. The beta parameter is lumping several catchment characteristics and affects water partitioning and runoff dynamics, and thus cannot be interpreted in a straightforward manner. It originally was a shape parameter that is supposed to describe the growth of contributing areas with increasing relative saturation, which can be related to steepness, to macropore structures, bedrock permeability etc. Including beta in the analysis and Fig. 8 would in our opinion not add to their interpretability and understanding of the points we try to explore.
Citation: https://doi.org/10.5194/hess-2021-174-AC3
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AC3: 'Reply on RC2', Jan Bondy, 27 Apr 2021
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CC1: 'On the lower limit of the linear recession constant', John Ding, 22 Apr 2021
The linear recession constant kres is one of four parameters in their Budyko framework. Lower and upper limits for parameter kres are set by authors in Table 2 to be 0.05/d and 0.9/d, respectively.
Among 16 study catchments in Table C-1, three of whom reach the lower limit of 0.05/d: B-5, B-7 and P-1, but none the upper limit. (In Table C-1, Kres to read kres .)
Since one or more of these three catchments may have a lower kres value than 0.05/d, I suggest the lower limit be lowered by one order of magnitude to 0.005/d.
Citation: https://doi.org/10.5194/hess-2021-174-CC1 -
AC1: 'Reply on CC1', Jan Bondy, 26 Apr 2021
We thank Dr. Ding for this observant comment. These three catchment indeed reach the lower boundary of the parameter range. We will take your advice and reset the lower boundary to 0.005/d.
Citation: https://doi.org/10.5194/hess-2021-174-AC1
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AC1: 'Reply on CC1', Jan Bondy, 26 Apr 2021
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EC1: 'Comment on hess-2021-174 - Start interacting', Nunzio Romano, 23 Apr 2021
Dear Authors:
Until now, your original submission received some interesting comments from reviewers and discussants. I invite you to post some preliminary responses from your side so as to feed the discussion step of the journal and keep the exchange of ideas alive.Citation: https://doi.org/10.5194/hess-2021-174-EC1 -
RC3: 'Comment on hess-2021-174', Anonymous Referee #3, 24 Apr 2021
The Authors present a study to assess the role that the soil water storage might have in determining the water balance of catchments. The work is in the context of the Budyko framework, which uses a formula to relate the dryness index, ETp/P, to the evaporative ratio, ETa/P, where ETp, ETa and P are long-term averages of annual potential evapotranspiration, actual evapotranspiration, and precipitation. The Authors use a lumped hydrological model, based on the HBV model, applied to 16 catchments across Europe, the USA and Peru, with the goal of using the root soil water storage parameters to explain the difference between ETa/P expected from the Budyko curve and the modelled ones.
Although addressing a problem of likely interest to the readers of HESS, I believe the study presents several weaknesses that require attention. I have listed below some specific comments that I hope will help improve the manuscript.
1. Context: there is already a lot of work done on the Budyko framework and the role of soil storage in determining the location of catchments in the Budyko space. The Authors refer to the work by Milly (1993; https://doi.org/10.1029/93WR01934) dismissing all the contributions following that study. The model by Milly (1993) was further developed by Porporato et al. (2004; https://doi.org/10.1086/424970), who improved the description of ETa as a function of soil moisture leading to a better representation of the Budyko curve. Donohue et al. (2012; https://doi.org/10.1016/j.jhydrol.2012.02.033) used the model by Porporato et al. (2004) and the formula by Choudhury (1999; https://doi.org/10.1016/S0022-1694(98)00293-5) to analyze the role of root zone soil properties on the water balance of catchments in Australia. The work by Donohue et al. (2012) was further extended by Yang et al. (2016; https://doi.org/10.1002/2016WR019392). These studies were reviewed and compared by Daly et al. (2019a; https://doi.org/10.1016/j.advwatres.2019.103435). Daly et al. (2019b; https://doi.org/10.1029/2019WR025952) proposed a different scaling of variables based on the soil storage and showed that the Budyko space might not be the best to look at the water balance of catchments that are not very large.
When looking at this existing body of work, it becomes difficult to see the novel contribution of the study presented here. Additionally, the HBV model is very similar to the models by Milly (1993) and Porporato et al. (2004), with the exception of a better routing for the calculation of Q. However, HBV requires numerical simulations that make its application difficult for a large number of catchments. For example, the Authors limited their study to 8 catchments within the MOPEX dataset, while Daly et al. (2019b) were able to use the full MOPEX dataset.
2. Approach: as I understand, the main goal is to see how different values of soil storage parameters in the model drive the difference between the model results and the Budyko curve. This, which I believe is similar to Gentine et al. (2012; https://doi.org/10.1029/2012GL053492), seems to imply that the Budyko curve defines the expected behaviour of a catchment. However, because the Budyko framework only applies to very large catchments (see the book by Budyko, 1974), it is not surprising that smaller catchments do not follow the Budyko curve. Looking at the large body of literature on the Budyko framework and the models (parametric and non-parametric) developed to locate catchments within the Budyko space, it is not very clear what the study presented here is adding to generate new knowledge.
Minor suggestions:
- Lines 124-125: not clear how this is achieved without data of storage. It would be good to explain how the 5% error is evaluated.
- Table 2: it would be good to explain the meaning of the parameters and what they do within the model.
- Fig. 5: the ration Smax/P seems similar to the non-dimensional parameter introduced by Milly et al. (1993). This should be acknowledged.
- Lines 366: not clear what second-order means here.
- Lines 435-436: the number of rainy days, or rainfall frequency, has been used often in water balance models in the context of the Budyko framework. See, for example, Milly (1993), Porporato et al. (2004) and Daly et al. (2019a, b). This should be acknowledged.
Citation: https://doi.org/10.5194/hess-2021-174-RC3 -
AC4: 'Reply on RC3', Jan Bondy, 10 May 2021
Thank you for your valuable comments and your suggestions for completing our literature digest. In the following, we want to address some of those works, describe our motivation and our view on how our study fits in.
Donohue (2012) and Yang (2016) both build on Choudhury’s parametric Budyko equation, even though Donohue’s approach to relate the parameter n with physically meaningful characteristics from Porporato 2004’s water balance model is very interesting to tackle the issue of lack of physical meaning. As stated in our introduction and as shown extensively by Reaver et al. 2020 (cited in the intro), we have doubts that the n- parameter can be linked to catchment in a clear and transparent manner, it is in fact a largely empirical exponent. We think that our straightforward approach is more transparent to explain deviations from the non-parametric Budyko curve.
We agree with the reviewer, that Daly et al. (2019b) indeed present a very interesting approach to introduce a new hydrological space and a storage limitation by combining the physical storage capacity with the temporal variability of ETp and P, and suggest that soil storage is a key parameter in terms of the Budyko offsets. In fact, our findings are similar, though we also characterize the influence “finer pores” exert on water limitation of ET. We will acknowledge their work in a revised version, which will also help to discuss the interaction of soil storage with climatic variability in more detail.
Gentine et al. (2012) also investigated the relationship between the Budyko curve and (amongst other) soil storage. Our findings fit into what they reported for the Budyko-optimal rooting depths, while their results are based on a more complex soil water balance model. Our analysis, in turn, also includes the sensitivity of the Budyko position to the development of soils or its corresponding parameters. Plus, we found that the water balance is also sensitive to capillarity-controlled transport limitation, within reasonable ranges of field capacities.
The Budyko curve provides estimates of the mean hydrological partitioning as a function of climatic dryness. The fact that so many catchments cluster around the Budyko curve shows that climate is the first-order control for this partitioning. At the same time, it is an important factor for the development of soils and vegetation, which are dependent and interdependent elements of the hydrological system (Troch 2014). A potential evolution towards the Budyko curve or towards the maximization of its resources like water (Berghuijs 2020), should then be related to the potential to store water from temporally varying climatic forcing.
In light of these thoughts, we consider it insightful to explore the relationship of soil storage and the non-parametric Budyko curve in a virtual experiment approach. We wanted to test with realistic boundary conditions (meteorological forcing), and different parametrizations (catchments), how systems position themselves in the Budyko space with evolving soil volume and retention characteristics. The computational burden of this simplified HBV model is not so significant that we could not add more catchments to the study. However, we do not see that it will yield different results. This would be the case if we analyzed calibrated root zone storage parameters of the model in relation to the Budyko curve offsets. Here, we use the beta store of the HBV model as a learning tool to explore Budyko curve offsets by first-order sensitivities to soil parameters, after the model was calibrated. The sensitivity pattern will of course gradually change, when using a different catchment at the same dryness index, but we do not expect anything fundamentally new or different. The asset of using a model is to learn exemplarily, and we do assume that sensitivities to total storage and field capacity are meaningful and interpretable (see also work of Gharari and Hrachowitz using the FLEX Topo).
Our study was motivated by the various attempts of using the Budyko framework for deriving expected values for constraining hydrological models or estimating the water balance in data-scarce and data-uncertain catchments for practical applications, and the question what will cause the considerable offsets from Budyko that are observed in various cases. Several ideas are discussed the literature. We wanted to focus on the soil in detail, and tried to analyze the sensitivities and offsets that can be expected through the storage volume and capillary transport limitations of the evaporation flux in a straightforward modeling approach. We investigated parameter spaces spanned by both the soil storage characteristics, which neither are independent of each other, nor are not static characteristics of a catchment. We therefore also analyzed 2D parameter spaces and tried to look at them from the perspective of soil evolution. We are not aware of a similar study into these issues. Most Budyko offset studies focus on explaining current catchment water balances and most of them use parametric Budyko frameworks. We will clarify this point in the revised version.
An extensive debate about the spatial scale and “applicability” issues of the Budyko framework is probably beyond the scope of this discussion. On the one hand, also larger catchments ≥ 10.000 km2 (Budyko 1974) show clear offsets from the Budyko curve that must be related to second-order controls such as for instance soil storage or climate variability, even though the influence of specific catchment idiosyncrasies certainly increases at smaller scales – however, some of the mesoscale catchments we analyzed didn’t show a larger offset than other larger catchments. On the other hand, mesoscale catchments often present the scale of interest, and in our opinion, this corresponds exactly to the spatial scale where such second-order controls like storage can play a crucial role in the mean water partitioning (e.g., Daly 2019b). Our study explicitly investigates soil-related deviations at this mesoscale. The MOPEX dataset, which is used for many of the Budyko studies, shows a distribution where most catchment areas are below 3000 km2, thus technically not in the range of “applicability” of Budyko. The data, however, still show clustering of the catchments around the Budyko curve – with smaller or greater deviations. We will try to add a comment that acknowledges the discussion about spatial scales and the Budyko curve in the revised version.
We would also consider your minor suggestions in a revised version of the manuscript. Thank you again for your helpful input!
Citation: https://doi.org/10.5194/hess-2021-174-AC4
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AC4: 'Reply on RC3', Jan Bondy, 10 May 2021
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RC4: 'Comment on hess-2021-174', Anonymous Referee #4, 27 Apr 2021
The authors have investigated the role of catchment-scale soil properties on long-term water balance. In particular, they have allowed soil storage capacity and field capacity parameters of the HBV model to vary and plotted the evaporation ratio values in the Budyko space. The authors argue that the two parameters can explain any deviation from the Budyko. The manuscript is written well. However, I find it hard to appreciate the usefulness of the paper. Below are my comments that the authors may find useful.
- The entire analysis is based on the premise that the HBV model provides a perfect picture of hydrological processes. Ideally, the values of soil storage and capillary storage fraction should come from field observations. I understand it is practically impossible to conduct large scale field measurements, but then the whole reasoning presented by the authors is pretty circular.
- What the authors are saying are not unknowns. Is it surprising to hear that the soil parameters affect long-term water balance?
- It is not very clear how the Budyko curve is helping in improving our understanding here. In my opinion the Budyko curve is an unnecessary entity in the analysis. The same conclusion (that the soil parameters influence long-term water balance) can be drawn without including the Budyko curve in the analysis.
Additional comments:
- The impact of observational errors have not been taken into account. It possible that, at least for some of the study basins, the deviation of the observed EVR value from the Budyko curve is due to observational errors.
- Line 125: The reasoning is not clear. Why do you need to select only the catchments with a closed water balance?
- Figure 9: Is it possible that number of rainy days is working as a proxy for something else, say mean precipitation? Otherwise, please provide a solid reasoning of why number of rainy days should matter.
Overall, in my understanding the article provides very little novel insight on catchment-scale hydrological processes. The authors may consider including some observed data to strengthen their analysis. Alternatively, they can re-orient their focus to answer some really interesting questions related to hydrological processes. I am sorry, I could not be more encouraging.
Citation: https://doi.org/10.5194/hess-2021-174-RC4 -
AC5: 'Reply on RC4', Jan Bondy, 12 May 2021
We thank you for reviewing and commenting our paper. We would like to clarify some of the irritations expressed in the review.
The focus of the study is to understand how soil storage characteristics relate to offsets from the Budyko curve. The Budyko curve is therefore an inherent part of the study, and could not simply be left out.
The HBV model evidently does not provide a “perfect picture” of hydrological processes, but it is a well-known and widely accepted conceptual hydrological model. The modeling concept appears suited for our approach, especially to distinguish between free and capillary-bound water storage. The soil parameters are, to a certain degree, interpretable and relatable to physical characteristics of catchments. We agree with you that observation data on this kind of catchment properties is lacking, and we therefore chose virtual experiments as a way of investigation. We cannot see, however, how this approach would suffer from a circular reasoning.
We want to stress that we do not claim that the soil storage parameters can explain any deviation from the Budyko curve, or that it is surprising that soils affect the long-term water balance. There is a practical motivation to use the Budyko curve to constrain hydrological modelling, or estimate water balances in data-scarce or ungauged catchments. This matter was brought forward in several other studies. It was, however, vastly unclear what abundant or deficient soil storage could mean in terms of offsets from this expected behavior, and if a variation of soil parameters alone within plausible ranges would lead to matching the Budyko curve, or not. We found these to be interesting questions.
Our results show that soil storage, but also capillarity characteristics, can lead to considerable deviations from Budyko, and thus should be included in any interpretation of Budyko offsets. We have also discussed how this could be interpreted in terms of soil development.
The focus of the study on soil properties does not mean that other influences are not important. Other studies have already shown other factors can be responsible for deviations as well. Some of our catchments also did not reach the curve through variation of the soil parameters, while others did. While this is important to discuss, it is beyond the scope of the paper to analyze and compare all possible influences.
We encourage the reviewer to take a second look at our study along the viewpoints sketched above. We will check if our objectives could be stated more clearly in a revised manuscript to avoid possible misunderstanding.
The additional comments are also gratefully acknowledged. Please find specific answers to these below.
Additional comments:
- The impact of observational errors have not been taken into account. It possible that, at least for some of the study basins, the deviation of the observed EVR value from the Budyko curve is due to observational errors.
You are right, observational errors have not been part of the discussion, and can of course be the reason for deviations from the Budyko curve. We would include your point in the discussion in a revised manuscript. However, our study does not aim at judging or explaining the measured catchment water balances, but to explore the sensitivity of Budyko deviations to storage parameters. In that sense, measurement errors in the study catchments’ water balances could affect the parametrization of the remaining model parameters that are fixed during the variation process. However, typical observational errors would not change the overall picture we got in terms of sensitivity patterns and the relationship to Budyko. In addition, at least the MOPEX dataset and the one from Germany are supposed to ensure a certain data quality.
- Line 125: The reasoning is not clear. Why do you need to select only the catchments with a closed water balance?
The Budyko framework predicts the mean hydrologic partitioning of rainfall into evapotranspiration and runoff – while storage changes average out at the long-term scale. If the water balance is not closed, for example because water passes a gauge underground and the evaporation ratio is estimated by ET_a = P – Q, runoff is mistaken for evapotranspiration, and the evaporation ratio is thus overestimated. Several catchments in the German dataset thus plotted outside the Budyko space. We compared evaporation ratios computed by P-Q with actual evaporation estimates from an agrometeorological model and selected catchments where the two estimates were more or less (5% error) in accordance.
- Figure 9: Is it possible that number of rainy days is working as a proxy for something else, say mean precipitation? Otherwise, please provide a solid reasoning of why number of rainy days should matter.
Climatic variability such as frequency of rainfall events (expressed here by rainy days/year) has already been identified by Milly (1994) to be a sensitive parameter for the mean water balance. In the annex pdf we attached additional correlation plots for the EVR range / the sensitivity of EVR to soil storage volume:
- Figure 1 shows again the plot from the manuscript (Figure 9)
- Figure 2-4 correlates the EVR range to mean rainfall depth of a rainy day, to mean annual precipitation and to the dryness index
Figure 2 and 3 show that no. of rainy days is not working as a proxy for mean precipitation. Dryness explains 65% of the variance, while no. of rainy days explains 93%.
With a given amount of total annual rainfall, the number of rainfall days relates to the mean depth of rainfall events as well as to the average interstorm period. The time between rainfall events influences the soil depletion (ETa resulting from ETp and rel. soil saturation) and thus the mean antecedent soil moisture state before rainfall events. More storage capacity leads to less saturated soils on average which in turn enhances infiltration and the amount of water available for evapotranspiration. We will include these explanations in the discussion of this point.
Status: closed
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RC1: 'Comment on hess-2021-174', Anonymous Referee #1, 15 Apr 2021
Dear colleagues,
I was first very enthusiastic when starting to read your paper that I ultimately found too theoretical in its present form:
- The main critic that I would make is that in your analysis of Budyko’s empirical formulation of water balance you are using… model results. Testing a model with a model… As a starting point it’s perfectly OK, but you should at least in a second step try to validate this with actual data. I know it’s not easy, because it requires a large dataset with root-zone capacity estimates (but you should be able to get this at least for Germany of the USA ?). A second critic that I would make is that you decide that the soil characteristics are the first-order determinant of the deviations of the the Budyko curve. I don’t say you are wrong, but I say this requires to be proved. There are other hypotheses in the literature: for example one of our papers (de Lavenne and Andréassian, 2018), we suggest based on actual streamflow data that the phase synchronicity of precipitation and potential evaporation explains the deviation of the Budyko-type curves.
Minor remarks
- Please change your notations to follow the recommendations of HESS: only one letter for a variable (possibly a subscript)
- 77: please adapt your references : Turc and Mezentsev published their formula 40 years before Choudhury, and Tixeront published his formula almost 20 years before Fu…
- 83: you write that it is inappropriate to try to represent the deviations of the Budyko-type relationship with a single parameter… I do not agree. Again, in our 2018 paper, we showed that it was possible to parameterize the parameters of the Turc-Mezentsev and the Tixeront-Fu formulation with a climatic index.
- 176: rainfall seasonality is not enough, you need an index that tells you whether rainfall and potential evaporation are in phase or out of phase
- L 572: You write that your research “did not purely take place in the realm of simulations”… but I would object that you almost staid there!
References
de Lavenne, A. & V. Andréassian. 2018. Impact of climate seasonality on catchment yield: a parameterization for commonly-used water balance formulas. Journal of Hydrology, 558: 266-274, https://doi.org/10.1016/j.jhydrol.2018.01.009
Mezentsev, V., 1955. Back to the computation of total evaporation (ÐÑÑ Ñаз о ÑаÑÑеÑе ÑÑеднего ÑÑммаÑного иÑпаÑениÑ). Meteorologia i Gidrologia - ÐеÑеоÑÐ¾Ð»Ð¾Ð³Ð¸Ñ Ð¸ ÐидÑологиÑ, 5: 24-26.
Tixeront, J., 1964. Prévision des apports des cours d'eau (Prediction of streamflow), IAHS publication n°63: General Assembly of Berkeley. IAHS, Gentbrugge, pp. 118-126.
Turc, L., 1954. The water balance of soils: relationship between precipitations, evaporation and flow (Le bilan d'eau des sols: relation entre les précipitations, l'évaporation et l'écoulement). Annales Agronomiques, Série A(5): 491-595.
Citation: https://doi.org/10.5194/hess-2021-174-RC1 -
AC2: 'Reply on RC1', Jan Bondy, 26 Apr 2021
We thank the reviewer for his comments and suggestions.
We agree with the reviewer that we are ultimately testing a model with a model. However, these models are independent from each other, and the models used are so simple that they are surely not overfitted. The starting point for our virtual experiments were hydrological models calibrated on observations. As stated in the study, we aimed at exploring and targeting the role of one specific characteristic (soil storage) for explaining significant offsets from the Budyko curve. We tried to isolate this influence on the water balance, and understand a bit better its qualitative and quantitative behavior and relationship to the Budyko curve.
Validation datasets for catchments including root zone depths are indeed difficult to obtain. It would furthermore also be challenging, if not impossible, to disentangle the other second-order influences (confounding variables) on the mean water balance. Such an approach would again require the discussion about the deviations from the soil storage perspective in this hypothetical validation dataset – which would probably end up being a whole study on its own. This motivated us to look at it in a different manner. We decided to test the role of controls related to soil storage volume in the Budyko framework in virtual experiments that allow masking out other influences.
The fact that we are focusing on soil characteristics in this paper does not mean that we consider these other factors being minor or absent. We do not want to conclude that soil characteristics are “the” first-order determinant of the deviations, but rather one among several controls, which we also mention explicitly. We focused on soil storage because, from a physical point of view, this factor should determine the available storage volume required to buffer the slower evaporation process. Testing this hypothesis in our virtual experiments showed that varying the soil parameters within reasonable ranges was sufficient to make the systems reach the Budyko curve in most cases. In our opinion, these results are a strong indication that soil storage characteristics can indeed have an important role in explaining deviations from the Budyko curve, and should not be neglected when studying these effects. We will carefully revise discussion and conclusions in this direction.
Thanks for pointing out the importance of the synchronicity of P and ETp. The importance of the phase lag did not appear that striking to us in this study, since there is no phase lag in the Peruvian basin (one of the two seasonal ones). For the other seasonal catchment (in the US) it does occur though and might well play a role. We will complement the discussion in that regard. In general, we tried to discuss potential explanations for deviating behavior from our soil storage-based reasoning; however, this part can of course never be all-encompassing.
We are also grateful for the other, more technical comments, and will gladly incorporate them in a revised version.
Citation: https://doi.org/10.5194/hess-2021-174-AC2
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RC2: 'Comment on hess-2021-174', Anonymous Referee #2, 20 Apr 2021
Review Bondy et al. 2021 HESSD
Bondy et al. investigate the role of soil storage capacity and field capacity on the long-term water balance of several catchments within the Budyko framework. They use a simple lumped hydrological model to explore how two parameters representing soil storage capacity and field capacity, respectively, affect the partitioning of precipitation into evapotranspiration and streamflow. The authors find that storage capacity is a strong control on modelled evapotranspiration, and to a lesser extent field capacity. They then discuss how these findings might relate to hydro-pedological processes and catchment co-evolution.
The paper is well written and within the scope of HESS. Understanding second-order controls on the long-term water balance is an important topic and the general idea of the paper is very interesting. I think, however, that the study requires major revisions before it can be published. Generally, I think it lacks some depth and some of the arguments or not sufficiently backed up by either the results or references. I will outline my major and minor comments below.
Major comments:
As you discuss briefly in Sect. 4.1.2., there are (significant) interactions between the model parameters. As the model is fairly simple, but most (all?) conclusions are based on varying the model parameters, I think it would be good to spend some more time on exploring parameter interactions (e.g. by performing a more thorough sensitivity analysis), not just of the two main parameters, but of all four parameters. How important are the other two parameters for the water balance of the model? How realistic is it to fix three parameters and vary the fourth with respect to real systems (in which potentially only certain combinations of parameters occur)? This is particularly important for your discussion of co-evolution later in the manuscript: is a model with three fixed parameters and one varied parameter really representing a meaningful evolutionary trajectory?
I would also be more cautious when it comes to interpreting the parameter values. You look at a simple lumped model, so I wonder if there’s a way to be more convincing about what these parameters actually mean. There is some discussion about their range being reasonable, but I think that’s all a bit too general, and does not relate explicitly to any of the catchments you studied here. You could use some catchment attributes (e.g. soil texture) to see whether the optimised parameters match what you would expect from independent data or expert knowledge (e.g. are the calibrated parameter values different for catchments with sandy/silty/clayey soils?).
You justify using a (nowadays) rather small sample by saying that you want to focus on 16 distinctly different catchments. But then there is very little discussion or information about the catchments you study, except for the climatic attributes shown in Fig. 1. I miss a more detailed description of the catchments studied, in particular as a way to back up the model results with some real world system characteristics. Because if the catchments are selected based primarily on (widely available) climatic attributes, then I wonder why you didn’t use a larger sample of catchments to obtain more robust conclusions.
I am not convinced by the idea of co-evolution, at least how it is presented here. I think this section needs much more supporting evidence than a relatively simple modelling experiment (which mostly focuses one variable parameter). I think a more in-depth discussion about the catchments you study would help in that respect (see also my comment above). You cite a few papers, but Hartmann et al. (2020), for instance, look at pro-glacial moraines, and you use it to back up the very general statement that “Both porosity and the fraction of silt and clay increase with time”.
I am also wondering over what time scales such a co-evolution might happen. This is something many discussions about co-evolution do not mention explicitly. Many of the catchments you study are in areas that are perhaps not directly impacted by water abstractions etc. right now, but they’ve been impacted by humans for a long time. For example, the catchments in the south east of BW are in an area with a lot of agriculture, and also the Black Forest has been heavily impacted/managed in many areas. How does such a long history of agriculture or forestry affect co-evolution?
Minor comments:
There are a few typos, which I won’t list individually, but I would suggest to reread the manuscript carefully
L.9: I would write “Budyko framework“ instead of “Budyko curve“
L.10: I suggest writing validated instead of verified (also in L.36)
L.10. “wide range of climates and settings“ – what kind of settings?
L.17: I suggest defining evaporation ratio (as ET/P) here instead of introducing the acronym
L.33: Perhaps a bit picky, but stating that Budyko “observed a considerable degree of clustering around the Budyko curve” sounds a bit odd, as he probably didn’t think of it as the “Budyko curve”.
L.37 and following: I like the idea of presenting how you came up with the project by looking at Peruvian catchments, but in the end you only use one catchment in Peru. Weren’t there more Peruvian catchments available?
Table A-1: It would be interesting to also know the names of the rivers/gauging stations.
Section 2.4: What exactly is the special similarity to HBV? The model just seems to be one (of many) bucket-type models.
L.223: Why did you not use daily values to calculate KGE?
Why did you not choose an independent evaluation period to ensure the model isn’t overfitted (e.g. a 15y-15y split)?
You consider a water balance error of < 15% to be small – that does not sound that small to me, especially given that you study the long-term water balance.
It seems like in the arid catchments, you systematically overestimate the water balance by approx. 10%. Is that just more pronounced because streamflow is lower here and hence a similar absolute error appears bigger? What if you used relative error in ET instead of Q, since you mostly focus on ET?
Table 2: The upper limit for Smax here is 800mm, but later you mention that you vary it from 1 to 2000mm
L.292: “a clear clustering at 5-15%” – to me this doesn’t look like a clear clustering as half of the points are above 20% (and two are not shown)
Figure 5 (right): I would suggest writing the definition of the normalised storage volume (e.g. Smax/P) on the y-axis. Also consider using (a), (b), etc. as labels for subplots
L.368 and 400: write “parameter values” instead of “parameterisation”
L.440: “The lower the number of rainy days…” That’s only true if the total rainfall depth is the same. If there are 50 rainy days with a total of 500mm, and 100 days with a total of 1000mm, the depth per event would be the same. It would be useful to perform a quick check, as it seems like total rainfall is correlated with the number of rainy days.
L.573: I am not sure what you mean here. What’s the alternative approach? A modelling experiment with artificial data?
L.576: “tangible catchment properties”… that’s an example of a statement I find too general, an issue I already raised in my major comments. Yes, you discuss the ranges of the parameter values, but you’re looking at calibrated parameter values from a lumped model without any in-depth catchment analysis. I don’t think that’s necessarily a problem, but I think you should discuss more clearly what your study can tell us and what not.
Lastly one general comment about the role of storage: what about storage in (deeper) layers and the role of groundwater? While some plants might have access to groundwater, catchments underlain by permeable aquifers might also “lose” water, which might limit evapotranspiration.
Citation: https://doi.org/10.5194/hess-2021-174-RC2 -
AC3: 'Reply on RC2', Jan Bondy, 27 Apr 2021
We thank you for the insights and comments which will help us to improve the manuscript. We will for now focus on the major points brought up in the review.
One issue raised in several parts of the review is related to the characteristics of the selected catchments, which we agree to have neglected slightly. We will provide more information on the catchments, also including soil type or texture, and relate this info to our results and the discussion accordingly. Data on soil properties, however, are not widely available, or are limited in accuracy and representativeness, especially at the catchment scale. We also want to emphasize that the point of our study was not to explain the as-is state of the catchments (or their calibrated parametric representations), but to use them in a virtual experiment approach with 16 catchments and realistic boundary conditions, in order to explore the role and sensitivity of soil storage characteristics in deviations from the Budyko curve. We found rather consistent sensitivity patterns - most of the systems reached the Budyko curve through variation of the soil characteristics in reasonable ranges. But we agree that it will be interesting to compare the individual deviations with actual soil data.
A second major point concerns the coevolution of catchments, which we adopted from Troch (2015) for the discussion part. We agree with the reviewer that human activities have altered catchments and their soils, this influence being however comparably recent (more extensive agriculture maybe over the past 200-300 years), whereas soils developed with the climate at least since the last ice age which ended around 10.000 years ago. Coevolution of catchments or landscape elements happens at a range of time scales (Troch 2015), from geological ones to climatic and ecosystem scales. The rate of “hydrologic aging”, however, is hard to assess and depends on the drivers as nicely described by Troch.
In our study, we only tried to limit direct water balance-impacting measures like abstractions, to be able to estimate at least the present hydrologic partitioning/water balance. We did not aim to assess the potential alteration of catchment elements due to anthropogenic activity. We are also not really capable of modeling coevolution of form and functioning in hydrological systems. However, the Budyko curve yields a widely accepted framework to discriminate which combinations of catchment properties might have co-evolved and which not (as done e.g. by Schaefli 2011).
With our interpretation and visualization of parameter spaces regarding soil storage and its relationship to the Budyko curve, we aimed at understanding potential trajectories, analyze patterns found for climate groups, and tried to discuss deviations in the pattern for seasonal catchments in terms of the hydrologic age concept. We want to point out again that the focus of our study is not on best explaining the current state of the catchment but to quantify how even small changes in total storage or in the field capacity of the root zone control and explain frequently observed offsets from the Budyko curve. As catchments and soil properties are not static but changing, this naturally involves a co-evolutionary aspect.
The study by Hartmann et al. 2020 shows such a soil development at scales of centuries and millennia, both in terms of soil storage and retention characteristics. It is an exemplary study, that is correct. However, it shows for two different parent materials (on proglacial moraines), a similar qualitative development at different rates. That was supposed to corroborate our assumed weathering processes to discuss our variation scheme, but this aspect can of course not be generalized to all pedogenetic environments. We will discuss that point more critically in a revised version of the paper, and also include that other mechanisms including human activity can influence soil storage characteristics.
The last major concern was on model parameters and parameter interaction. We agree that varying only certain model parameters, while others remain unaltered, is a simplification of how real-world systems would develop or change. Any parameter variation or sensitivity study needs to take into account if the underlying model is representative. We are confident that conceptual hydrological models such as the HBV approach can represent hydrologic systems sufficiently well for describing catchment dynamics at the long-term scale, especially as we are considering that the virtual catchments we are exploring are not changing their properties during the simulation. We will clarify these points in the discussion.
We have tried to visualize parameter interactions in the 2d parameter spaces (Fig. 8). We focused on the parameters S_max and FC_frac, which can be related to two forms of soil storage volumes. They are important in the two stages of the evaporation process: at first, when the atmospheric demand is met, and secondly, when the capillary soil transport/supply is impeded by retention. The other two parameters were not included in this analysis. The k_res parameter is insensitive for the long-term annual water balance, since it does not affect the hydrologic partitioning but the dynamics of stream flow. The beta parameter is lumping several catchment characteristics and affects water partitioning and runoff dynamics, and thus cannot be interpreted in a straightforward manner. It originally was a shape parameter that is supposed to describe the growth of contributing areas with increasing relative saturation, which can be related to steepness, to macropore structures, bedrock permeability etc. Including beta in the analysis and Fig. 8 would in our opinion not add to their interpretability and understanding of the points we try to explore.
Citation: https://doi.org/10.5194/hess-2021-174-AC3
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AC3: 'Reply on RC2', Jan Bondy, 27 Apr 2021
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CC1: 'On the lower limit of the linear recession constant', John Ding, 22 Apr 2021
The linear recession constant kres is one of four parameters in their Budyko framework. Lower and upper limits for parameter kres are set by authors in Table 2 to be 0.05/d and 0.9/d, respectively.
Among 16 study catchments in Table C-1, three of whom reach the lower limit of 0.05/d: B-5, B-7 and P-1, but none the upper limit. (In Table C-1, Kres to read kres .)
Since one or more of these three catchments may have a lower kres value than 0.05/d, I suggest the lower limit be lowered by one order of magnitude to 0.005/d.
Citation: https://doi.org/10.5194/hess-2021-174-CC1 -
AC1: 'Reply on CC1', Jan Bondy, 26 Apr 2021
We thank Dr. Ding for this observant comment. These three catchment indeed reach the lower boundary of the parameter range. We will take your advice and reset the lower boundary to 0.005/d.
Citation: https://doi.org/10.5194/hess-2021-174-AC1
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AC1: 'Reply on CC1', Jan Bondy, 26 Apr 2021
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EC1: 'Comment on hess-2021-174 - Start interacting', Nunzio Romano, 23 Apr 2021
Dear Authors:
Until now, your original submission received some interesting comments from reviewers and discussants. I invite you to post some preliminary responses from your side so as to feed the discussion step of the journal and keep the exchange of ideas alive.Citation: https://doi.org/10.5194/hess-2021-174-EC1 -
RC3: 'Comment on hess-2021-174', Anonymous Referee #3, 24 Apr 2021
The Authors present a study to assess the role that the soil water storage might have in determining the water balance of catchments. The work is in the context of the Budyko framework, which uses a formula to relate the dryness index, ETp/P, to the evaporative ratio, ETa/P, where ETp, ETa and P are long-term averages of annual potential evapotranspiration, actual evapotranspiration, and precipitation. The Authors use a lumped hydrological model, based on the HBV model, applied to 16 catchments across Europe, the USA and Peru, with the goal of using the root soil water storage parameters to explain the difference between ETa/P expected from the Budyko curve and the modelled ones.
Although addressing a problem of likely interest to the readers of HESS, I believe the study presents several weaknesses that require attention. I have listed below some specific comments that I hope will help improve the manuscript.
1. Context: there is already a lot of work done on the Budyko framework and the role of soil storage in determining the location of catchments in the Budyko space. The Authors refer to the work by Milly (1993; https://doi.org/10.1029/93WR01934) dismissing all the contributions following that study. The model by Milly (1993) was further developed by Porporato et al. (2004; https://doi.org/10.1086/424970), who improved the description of ETa as a function of soil moisture leading to a better representation of the Budyko curve. Donohue et al. (2012; https://doi.org/10.1016/j.jhydrol.2012.02.033) used the model by Porporato et al. (2004) and the formula by Choudhury (1999; https://doi.org/10.1016/S0022-1694(98)00293-5) to analyze the role of root zone soil properties on the water balance of catchments in Australia. The work by Donohue et al. (2012) was further extended by Yang et al. (2016; https://doi.org/10.1002/2016WR019392). These studies were reviewed and compared by Daly et al. (2019a; https://doi.org/10.1016/j.advwatres.2019.103435). Daly et al. (2019b; https://doi.org/10.1029/2019WR025952) proposed a different scaling of variables based on the soil storage and showed that the Budyko space might not be the best to look at the water balance of catchments that are not very large.
When looking at this existing body of work, it becomes difficult to see the novel contribution of the study presented here. Additionally, the HBV model is very similar to the models by Milly (1993) and Porporato et al. (2004), with the exception of a better routing for the calculation of Q. However, HBV requires numerical simulations that make its application difficult for a large number of catchments. For example, the Authors limited their study to 8 catchments within the MOPEX dataset, while Daly et al. (2019b) were able to use the full MOPEX dataset.
2. Approach: as I understand, the main goal is to see how different values of soil storage parameters in the model drive the difference between the model results and the Budyko curve. This, which I believe is similar to Gentine et al. (2012; https://doi.org/10.1029/2012GL053492), seems to imply that the Budyko curve defines the expected behaviour of a catchment. However, because the Budyko framework only applies to very large catchments (see the book by Budyko, 1974), it is not surprising that smaller catchments do not follow the Budyko curve. Looking at the large body of literature on the Budyko framework and the models (parametric and non-parametric) developed to locate catchments within the Budyko space, it is not very clear what the study presented here is adding to generate new knowledge.
Minor suggestions:
- Lines 124-125: not clear how this is achieved without data of storage. It would be good to explain how the 5% error is evaluated.
- Table 2: it would be good to explain the meaning of the parameters and what they do within the model.
- Fig. 5: the ration Smax/P seems similar to the non-dimensional parameter introduced by Milly et al. (1993). This should be acknowledged.
- Lines 366: not clear what second-order means here.
- Lines 435-436: the number of rainy days, or rainfall frequency, has been used often in water balance models in the context of the Budyko framework. See, for example, Milly (1993), Porporato et al. (2004) and Daly et al. (2019a, b). This should be acknowledged.
Citation: https://doi.org/10.5194/hess-2021-174-RC3 -
AC4: 'Reply on RC3', Jan Bondy, 10 May 2021
Thank you for your valuable comments and your suggestions for completing our literature digest. In the following, we want to address some of those works, describe our motivation and our view on how our study fits in.
Donohue (2012) and Yang (2016) both build on Choudhury’s parametric Budyko equation, even though Donohue’s approach to relate the parameter n with physically meaningful characteristics from Porporato 2004’s water balance model is very interesting to tackle the issue of lack of physical meaning. As stated in our introduction and as shown extensively by Reaver et al. 2020 (cited in the intro), we have doubts that the n- parameter can be linked to catchment in a clear and transparent manner, it is in fact a largely empirical exponent. We think that our straightforward approach is more transparent to explain deviations from the non-parametric Budyko curve.
We agree with the reviewer, that Daly et al. (2019b) indeed present a very interesting approach to introduce a new hydrological space and a storage limitation by combining the physical storage capacity with the temporal variability of ETp and P, and suggest that soil storage is a key parameter in terms of the Budyko offsets. In fact, our findings are similar, though we also characterize the influence “finer pores” exert on water limitation of ET. We will acknowledge their work in a revised version, which will also help to discuss the interaction of soil storage with climatic variability in more detail.
Gentine et al. (2012) also investigated the relationship between the Budyko curve and (amongst other) soil storage. Our findings fit into what they reported for the Budyko-optimal rooting depths, while their results are based on a more complex soil water balance model. Our analysis, in turn, also includes the sensitivity of the Budyko position to the development of soils or its corresponding parameters. Plus, we found that the water balance is also sensitive to capillarity-controlled transport limitation, within reasonable ranges of field capacities.
The Budyko curve provides estimates of the mean hydrological partitioning as a function of climatic dryness. The fact that so many catchments cluster around the Budyko curve shows that climate is the first-order control for this partitioning. At the same time, it is an important factor for the development of soils and vegetation, which are dependent and interdependent elements of the hydrological system (Troch 2014). A potential evolution towards the Budyko curve or towards the maximization of its resources like water (Berghuijs 2020), should then be related to the potential to store water from temporally varying climatic forcing.
In light of these thoughts, we consider it insightful to explore the relationship of soil storage and the non-parametric Budyko curve in a virtual experiment approach. We wanted to test with realistic boundary conditions (meteorological forcing), and different parametrizations (catchments), how systems position themselves in the Budyko space with evolving soil volume and retention characteristics. The computational burden of this simplified HBV model is not so significant that we could not add more catchments to the study. However, we do not see that it will yield different results. This would be the case if we analyzed calibrated root zone storage parameters of the model in relation to the Budyko curve offsets. Here, we use the beta store of the HBV model as a learning tool to explore Budyko curve offsets by first-order sensitivities to soil parameters, after the model was calibrated. The sensitivity pattern will of course gradually change, when using a different catchment at the same dryness index, but we do not expect anything fundamentally new or different. The asset of using a model is to learn exemplarily, and we do assume that sensitivities to total storage and field capacity are meaningful and interpretable (see also work of Gharari and Hrachowitz using the FLEX Topo).
Our study was motivated by the various attempts of using the Budyko framework for deriving expected values for constraining hydrological models or estimating the water balance in data-scarce and data-uncertain catchments for practical applications, and the question what will cause the considerable offsets from Budyko that are observed in various cases. Several ideas are discussed the literature. We wanted to focus on the soil in detail, and tried to analyze the sensitivities and offsets that can be expected through the storage volume and capillary transport limitations of the evaporation flux in a straightforward modeling approach. We investigated parameter spaces spanned by both the soil storage characteristics, which neither are independent of each other, nor are not static characteristics of a catchment. We therefore also analyzed 2D parameter spaces and tried to look at them from the perspective of soil evolution. We are not aware of a similar study into these issues. Most Budyko offset studies focus on explaining current catchment water balances and most of them use parametric Budyko frameworks. We will clarify this point in the revised version.
An extensive debate about the spatial scale and “applicability” issues of the Budyko framework is probably beyond the scope of this discussion. On the one hand, also larger catchments ≥ 10.000 km2 (Budyko 1974) show clear offsets from the Budyko curve that must be related to second-order controls such as for instance soil storage or climate variability, even though the influence of specific catchment idiosyncrasies certainly increases at smaller scales – however, some of the mesoscale catchments we analyzed didn’t show a larger offset than other larger catchments. On the other hand, mesoscale catchments often present the scale of interest, and in our opinion, this corresponds exactly to the spatial scale where such second-order controls like storage can play a crucial role in the mean water partitioning (e.g., Daly 2019b). Our study explicitly investigates soil-related deviations at this mesoscale. The MOPEX dataset, which is used for many of the Budyko studies, shows a distribution where most catchment areas are below 3000 km2, thus technically not in the range of “applicability” of Budyko. The data, however, still show clustering of the catchments around the Budyko curve – with smaller or greater deviations. We will try to add a comment that acknowledges the discussion about spatial scales and the Budyko curve in the revised version.
We would also consider your minor suggestions in a revised version of the manuscript. Thank you again for your helpful input!
Citation: https://doi.org/10.5194/hess-2021-174-AC4
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AC4: 'Reply on RC3', Jan Bondy, 10 May 2021
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RC4: 'Comment on hess-2021-174', Anonymous Referee #4, 27 Apr 2021
The authors have investigated the role of catchment-scale soil properties on long-term water balance. In particular, they have allowed soil storage capacity and field capacity parameters of the HBV model to vary and plotted the evaporation ratio values in the Budyko space. The authors argue that the two parameters can explain any deviation from the Budyko. The manuscript is written well. However, I find it hard to appreciate the usefulness of the paper. Below are my comments that the authors may find useful.
- The entire analysis is based on the premise that the HBV model provides a perfect picture of hydrological processes. Ideally, the values of soil storage and capillary storage fraction should come from field observations. I understand it is practically impossible to conduct large scale field measurements, but then the whole reasoning presented by the authors is pretty circular.
- What the authors are saying are not unknowns. Is it surprising to hear that the soil parameters affect long-term water balance?
- It is not very clear how the Budyko curve is helping in improving our understanding here. In my opinion the Budyko curve is an unnecessary entity in the analysis. The same conclusion (that the soil parameters influence long-term water balance) can be drawn without including the Budyko curve in the analysis.
Additional comments:
- The impact of observational errors have not been taken into account. It possible that, at least for some of the study basins, the deviation of the observed EVR value from the Budyko curve is due to observational errors.
- Line 125: The reasoning is not clear. Why do you need to select only the catchments with a closed water balance?
- Figure 9: Is it possible that number of rainy days is working as a proxy for something else, say mean precipitation? Otherwise, please provide a solid reasoning of why number of rainy days should matter.
Overall, in my understanding the article provides very little novel insight on catchment-scale hydrological processes. The authors may consider including some observed data to strengthen their analysis. Alternatively, they can re-orient their focus to answer some really interesting questions related to hydrological processes. I am sorry, I could not be more encouraging.
Citation: https://doi.org/10.5194/hess-2021-174-RC4 -
AC5: 'Reply on RC4', Jan Bondy, 12 May 2021
We thank you for reviewing and commenting our paper. We would like to clarify some of the irritations expressed in the review.
The focus of the study is to understand how soil storage characteristics relate to offsets from the Budyko curve. The Budyko curve is therefore an inherent part of the study, and could not simply be left out.
The HBV model evidently does not provide a “perfect picture” of hydrological processes, but it is a well-known and widely accepted conceptual hydrological model. The modeling concept appears suited for our approach, especially to distinguish between free and capillary-bound water storage. The soil parameters are, to a certain degree, interpretable and relatable to physical characteristics of catchments. We agree with you that observation data on this kind of catchment properties is lacking, and we therefore chose virtual experiments as a way of investigation. We cannot see, however, how this approach would suffer from a circular reasoning.
We want to stress that we do not claim that the soil storage parameters can explain any deviation from the Budyko curve, or that it is surprising that soils affect the long-term water balance. There is a practical motivation to use the Budyko curve to constrain hydrological modelling, or estimate water balances in data-scarce or ungauged catchments. This matter was brought forward in several other studies. It was, however, vastly unclear what abundant or deficient soil storage could mean in terms of offsets from this expected behavior, and if a variation of soil parameters alone within plausible ranges would lead to matching the Budyko curve, or not. We found these to be interesting questions.
Our results show that soil storage, but also capillarity characteristics, can lead to considerable deviations from Budyko, and thus should be included in any interpretation of Budyko offsets. We have also discussed how this could be interpreted in terms of soil development.
The focus of the study on soil properties does not mean that other influences are not important. Other studies have already shown other factors can be responsible for deviations as well. Some of our catchments also did not reach the curve through variation of the soil parameters, while others did. While this is important to discuss, it is beyond the scope of the paper to analyze and compare all possible influences.
We encourage the reviewer to take a second look at our study along the viewpoints sketched above. We will check if our objectives could be stated more clearly in a revised manuscript to avoid possible misunderstanding.
The additional comments are also gratefully acknowledged. Please find specific answers to these below.
Additional comments:
- The impact of observational errors have not been taken into account. It possible that, at least for some of the study basins, the deviation of the observed EVR value from the Budyko curve is due to observational errors.
You are right, observational errors have not been part of the discussion, and can of course be the reason for deviations from the Budyko curve. We would include your point in the discussion in a revised manuscript. However, our study does not aim at judging or explaining the measured catchment water balances, but to explore the sensitivity of Budyko deviations to storage parameters. In that sense, measurement errors in the study catchments’ water balances could affect the parametrization of the remaining model parameters that are fixed during the variation process. However, typical observational errors would not change the overall picture we got in terms of sensitivity patterns and the relationship to Budyko. In addition, at least the MOPEX dataset and the one from Germany are supposed to ensure a certain data quality.
- Line 125: The reasoning is not clear. Why do you need to select only the catchments with a closed water balance?
The Budyko framework predicts the mean hydrologic partitioning of rainfall into evapotranspiration and runoff – while storage changes average out at the long-term scale. If the water balance is not closed, for example because water passes a gauge underground and the evaporation ratio is estimated by ET_a = P – Q, runoff is mistaken for evapotranspiration, and the evaporation ratio is thus overestimated. Several catchments in the German dataset thus plotted outside the Budyko space. We compared evaporation ratios computed by P-Q with actual evaporation estimates from an agrometeorological model and selected catchments where the two estimates were more or less (5% error) in accordance.
- Figure 9: Is it possible that number of rainy days is working as a proxy for something else, say mean precipitation? Otherwise, please provide a solid reasoning of why number of rainy days should matter.
Climatic variability such as frequency of rainfall events (expressed here by rainy days/year) has already been identified by Milly (1994) to be a sensitive parameter for the mean water balance. In the annex pdf we attached additional correlation plots for the EVR range / the sensitivity of EVR to soil storage volume:
- Figure 1 shows again the plot from the manuscript (Figure 9)
- Figure 2-4 correlates the EVR range to mean rainfall depth of a rainy day, to mean annual precipitation and to the dryness index
Figure 2 and 3 show that no. of rainy days is not working as a proxy for mean precipitation. Dryness explains 65% of the variance, while no. of rainy days explains 93%.
With a given amount of total annual rainfall, the number of rainfall days relates to the mean depth of rainfall events as well as to the average interstorm period. The time between rainfall events influences the soil depletion (ETa resulting from ETp and rel. soil saturation) and thus the mean antecedent soil moisture state before rainfall events. More storage capacity leads to less saturated soils on average which in turn enhances infiltration and the amount of water available for evapotranspiration. We will include these explanations in the discussion of this point.
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