I could not agree more with Luca Brocca’s observations, both regarding the open questions on scaling and the need for a more in-depth discussion of them.

How to exploit these similarities across scales, e.g. regarding preferential flow, in modelling? Truly a challenging topic which, I am afraid, I will not be able to do full justice in this paper. There exists a plethora of upscaling and downscaling methods (see, e.g., Blöschl, 2005), some of which account for connectivity, such as connectivity functions at the local and catchment scales (Western et al., 2001) and top-kriging at the catchment and regional scales (Skøien and Blöschl, 2007). The more general point in this paper is that the use of observed process patterns seems to me a key element in coming up with the structure and the parameters of such scaling methods. This means, rather than conjecturing the scaling relationships (which we do when, e.g., assuming that Richards equation applies to the catchment scale), the idea is to learn from observed patterns. From the patterns it is also possible to establish cause-effect relationships directly at the scale of interest, without resorting to scaling methods, when viewing hydrology through the prism of scale. In this case no upscaling methods are needed.

Reviewer RC1 has asked how applied hydrology could benefit from looking at flood generation patterns at different scales, and in the response I have provided a number of examples from my own work in the response, which could also help shed light on the scaling question posed here. I believe that flood design has benefitted from process patterns such as those in Fig. 6 (runoff generation) and Fig. 7 (flood types) through the flood frequency hydrology approach (Merz and Blöschl, 2008). Flood forecasting has benefitted from using observed snow and soil moisture patterns as well as preferential flow representations in the soil (Blöschl, 2008). And risk assessment of spring contamination has benefited from observed patterns of evidence on surface runoff (Reszler et al., 2018).

I will add these practical examples to the conclusions sections, but feel that an in-depth discussion of the topic – notwithstanding its importance – goes beyond what this paper tries to achieve. It would be worthwhile thinking about a follow up discussion or paper focusing more specifically on upscaling that builds on patterns.

References

Blöschl, G. (2005) On the fundamentals of hydrological sciences. Article 1 in: Encyclopedia of Hydrological Sciences, M. G. Anderson (Managing Editor), J. Wiley & Sons, Chichester, pp. 3-12.

Blöschl, G. (2008) Flood warning - on the value of local information. International Journal of River Basin Management, 6 (1), pp. 41-50.

Merz R. and G. Blöschl (2008) Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information. Water Resources Research, 44 (8), article number W08432.

Reszler, C., J. Komma, H. Stadler, E. Strobl and G. Blöschl (2018) A propensity index for surface runoff on a karst plateau. Hydrology and Earth System Sciences, 22, pp. 6147-6161, https://doi.org/10.5194/hess-22-6147-2018, 2018.

Skøien, J. O. and G. Blöschl (2007) Spatiotemporal topological kriging of runoff time series. Water Resources Research, 43, article number W09419.

Western, A.W., G. Blöschl and R. B. Grayson (2001) Towards capturing hydrologically significant connectivity in spatial patterns. Water Resources Research, 37 (1), pp. 83-97.

I would like to thank RC1 for the thought provoking questions and the opportunity to expand on them. Below I will share some of my thoughts, noting that the topic deserves fuller discussion, perhaps in the format of a future workshop.

The Digital twin concept (Rigon et al., 2022) is very relevant to the context of this paper. I would think that one can speak of “Weak Digital Twins” and “Strong Digital Twins”. In the weaker sense they are really hyperresolution models with the appropriate data assimilation and user interfaces, e.g. following the definition of Bauer et al. (2021, p. 80): “A digital twin of Earth is an information system that exposes users to a digital replication of the state and temporal evolution of the Earth system constrained by available observations and the laws of physics.” In the strongest sense, the connections between the physical and digital systems are fully implemented which goes beyond a user interface and, following the original idea from manufacturing, fully integrates water management processes, ideally with water-human feedbacks (Sivapalan et al., 2012). The perspective of Rigon et al. (2022), I think, is slightly more oriented toward science than to management and emphasises the potential of forging a more coherent science community, something I consider extremely important (Blöschl et al., 2019). So, in response to the question posed by RC1, a digital twin will perhaps not in itself resolve the scale issue, but it may help hydrologists do more coordinated research and thus also address the scale issue. I will add a comment in section 2 of the paper to refer to digital twins.

The question of how this journey through scales has helped improve flood design, flood forecasting and flood risk assessment is, again, a very good one. I feel very strongly about the synergies of theory and practice. Good science will lead to more accurate practical methods, and practice may provide data and direction for promoting science progress (Sivapalan and Blöschl, 2017). I believe that the scales perspective can indeed help practice. For example, flood design has benefitted from process patterns such as those in Fig. 6 (runoff generation) and Fig. 7 (flood types) through the flood frequency hydrology approach (Merz and Blöschl, 2008), which is also recommended in the German and Austrian flood estimation standards (DWA, 2012; ÖWAV, 2019). Flood forecasting has benefitted from using observed snow and soil moisture patterns as well as preferential flow representations in the soil (Blöschl et al., 2008; Blöschl, 2008). And risk assessment of spring contamination has benefited from observed patterns of evidence on surface runoff (Reszler et al., 2018). Again I will add a comment on my perspective on this in the conclusions section.

Regarding the concept of "trading space for time", I believe we can learn a lot about the time evolution in one catchment from comparisons with other catchments. Hydrology is not a unique case in the spectrum of science disciplines to use comparative methods. For example ethnologists learn about the cultural evolution of music by comparing different ethnicities at the same time (Schneider, 2006), and chronosequences are the classical case in Earth science (Walker et al, 2010). However, such a space-time similarity does not necessarily imply that the cases compared are exact carbon copies shifted by a fixed time of e.g. 50 years. The learning is more about the underlying cause-effect relationships. In the case of flood generation processes, for example, Perdigão and Blöschl (2014) have suggested, that trading space for time is possible provided coevolution is taken into account through characteristic celerities that reflect the spatiotemporal symmetry. In practical terms their study has shown that “the spatial sensitivity of floods to precipitation exceeds that over time, in such a way that, given a 10% spatial increase in precipitation, there is a corresponding 23% increase in flood peaks, whereas given a similar 10% increase in precipitation over time, the flood peaks increase only about 6%.” They conclude further that “the interchangeability is found to be legitimate in regions with hydrogeological stability that have had the time to span the whole state space (thus enabling the ergodic hypothesis) or systems that, even not in equilibrium, are evolving at a similar pace (enabling the Taylor hypothesis). On the other hand, regions with transient hydrogeological activity do not comply with such hypothesis, therefore measures of coevolution or relative characteristic celerities have to be taken into account in the space-time trading.“ I should add that this is only one case study and an evaluation of whether these findings are more widely applicable is still needed.

The statement on the potential of scale research as a unifying framework was not specifically intended to relate to uncertainty but more generally to hydrology. The idea is to explore phenomena at commensurate scales (e.g. explaining regional scale flood patterns by regional scale climate and soil patterns, rather than soil preferential flow) and to establish cross scale links that may be similar, e.g., for floods and droughts (Blöschl, 2001, 2006). I will add an explanation to better bring out the idea of the quote. In fact, I believe that the entire paper is an example of how a scale perspective can help organise one’s thinking and thus contribute to progress.

Scale issues in time have been the subject of Sivapalan and Blöschl (2015). There are plans for a paper on flood changes in HESS (Blöschl, 2022). A paper on how one could learn from the temporal scales of floods is still to be written and could revolve around the propagation of information between time scales. An example of how the seasonal and event scales interact is discussed in Sivapalan et al. (2005).

References

Bauer, P., Stevens, B., and Hazeleger, W. (2021). A digital twin of Earth for the green transition. Nature Climate Change, 11(2), 80-83.

Blöschl, G. (2001) Scaling in hydrology. Hydrological Processes, 15, pp. 709-711. 

Blöschl, G. (2006) Hydrologic synthesis - across processes, places and scales. Special section on the vision of the CUAHSI National Center for Hydrologic Synthesis (NCHS). Water Resources Research, 42, article number W03S02. 

Blöschl, G. (2008) Flood warning - on the value of local information. International Journal of River Basin Management, 6 (1), pp. 41-50.

Blöschl, G. (2022) Understanding changing river flood hazards, Alfred Wegener Medal lecture. In EGU General Assembly Conference Abstracts (EGU22).

Blöschl, G. et al. (2019) Twenty-three Unsolved Problems in Hydrology (UPH) – a community perspective, Hydrological Sciences Journal, 64, pp. 1141-1158, doi: 10.1080/02626667.2019.1620507

Blöschl, G., C. Reszler and J. Komma (2008) A spatially distributed flash flood forecasting model. Environmental Modelling & Software, 23 (4), pp. 464-478.

DWA (2012) Estimation of flood probabilities. Guideline DWA-M 552, in German (Ermittlung von Hochwasserwahrscheinlichkeiten), German Association for Water, Wastewater and Waste (DWA) Hennef, Germany.

Merz R. and G. Blöschl (2008) Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information. Water Resources Research, 44 (8), article number W08432.

ÖWAV (2019) Rainfall-runoff modelling. Guideline 220, in German (Niederschlag-Abfluss-Modellierung), Austrian Water and Waste Management Association (ÖWAV), Vienna, Austria.

Perdigão, R. A. P., and G. Blöschl (2014) Spatiotemporal flood sensitivity to annual precipitation: Evidence for landscape-climate coevolution, Water Resour. Res., 50, 5492­5509, doi:10.1002/ 2014WR015365.

Reszler, C., J. Komma, H. Stadler, E. Strobl and G. Blöschl (2018) A propensity index for surface runoff on a karst plateau. Hydrology and Earth System Sciences, 22, pp. 6147-6161, https://doi.org/10.5194/hess-22-6147-2018, 2018.

Rigon, R., Formetta, G., Bancheri, M., Tubini, N., D'Amato, C., David, O., and Massari, C.: HESS Opinions: Participatory Digital Earth Twin Hydrology systems (DARTHs) for everyone: a blueprint for hydrologists, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2021-644, in review, 2022.

Schneider, A. (2006). Comparative and systematic musicology in relation to ethnomusicology: a historical and methodological survey. Ethnomusicology, 50(2), 236-258.

Sivapalan, M. and G. Blöschl (2015) Time scale interactions and the coevolution of humans and water. Water Resour. Res., 51, 6988–7022, doi:10.1002/2015WR017896.

Sivapalan, M. and G. Blöschl (2017) The growth of hydrological understanding: Technologies, ideas, and societal needs shape the field. Water Resources Research, 53, 8137–8146, doi: 10.1002/2017WR021396

Sivapalan, M., G. Blöschl, R. Merz and D. Gutknecht (2005) Linking flood frequency to long-term water balance: incorporating effects of seasonality. Water Resources Research, 41, article number W06012.

Sivapalan, M., H. H. G. Savenije, G. Blöschl (2012) Socio-hydrology: A new science of people and water. Hydrological Processes. 26, 1270–1276 DOI: 10.1002/hyp.8426

Walker, L. R., Wardle, D. A., Bardgett, R. D., and Clarkson, B. D. (2010). The use of chronosequences in studies of ecological succession and soil development. Journal of Ecology, 98(4), 725-736.

I would like to thank RC2 for the kind assessment and the comments.

The July 2021 in Henan Province will be included in the introduction.

The connectivity at the continental scale would indeed profit from further clarification. The superposition of the polar and the subtropical jet stream over the Western Mediterranean, which often Vb cyclones, I would interpret as a „connection“ of atmospheric process (Hofstätter et al., 2019). Another example are precipitation characteristics related to atmospheric rivers (Kim et al, 2021). I will add an explanation of the argument to the paper as follows: “It appears that connectivity is also important at the continental scale, e.g. through preferential pathways of flood-generating cyclones; in the particular case of Vb events through the connection of the eddy-driven polar jet stream and the subtropical jet stream over the Western Mediterranean; and through the role of teleconnections (e.g. as quantified by the Northern Atlantic Oscillation (NAO) and Arctic Oscillation (AO) indices in affecting flood-relevant cyclones (Hofstätter et al., 2019). Another example of connectivity in the atmosphere are atmospheric rivers (Kim et al, 2021).“

References

Hofstätter, M. and Blöschl G.: Vb cyclones synchronized with the Arctic-/North Atlantic Oscillation. Journal of Geophysical Research: Atmospheres, 124, pp. 3259-3278, 2019. https://doi.org/10.1029/2018JD029420

Kim, J., Moon, H., Guan, B., Waliser, D. E., Choi, J., Gu, T. Y., and Byun, Y. H. (2021). Precipitation characteristics related to atmospheric rivers in East Asia. International Journal of Climatology, 41, E2244-E2257.

Many thanks for the thoughtful assessment of this paper.  

A discussion of a formalization of the scale and scaling ideas in the form of frameworks and analysis approaches is of course important, perhaps building on Blöschl and Sivapalan (1995) and the present paper but, given its focus, a formalization would go beyond what this paper tries to achieve. It would, however, be worthwhile thinking about a follow up discussion or paper focusing more specifically on upscaling that builds on patterns.

Yes, a focus on timescales was missing in Blöschl and Sivapalan (1995), and it is missing in this paper too. As pointed out in my response to reviewer RC1, scale issues in time have been the subject of Sivapalan and Blöschl (2015). Traditionally, hydrologists were more concerned with scale issues in space because of the lack of spatial information, while time series of hydrologic fluxes have been available for a long time. More recently, the situation has changed a bit, both because of the availability of spatial satellite data and the increased importance of hydrological change, so scale issues in time are definitely becoming very relevant, in particular when the interactions with human activities are involved.

A joint consideration of space scales and timescales is important and there has been some work on it (see, e.g., Skøien et al., 2003; Blöschl et al., 2015) but I fully agree that, given the important science questions and the data availability, there is now an opportunity for deepening our understanding of space scales and timescales considered together. 

References

Blöschl, G. and M. Sivapalan (1995) Scale issues in hydrological modelling - a review. Hydrological Processes, 9, pp. 251-290.

Blöschl, G., H. Thybo and H. Savenije (2015) A Voyage Through Scales - The Earth System in Space and Time. Edition Lammerhuber, Vienna, 123 pp.

Sivapalan, M. and G. Blöschl (2015) Time scale interactions and the coevolution of humans and water. Water Resour. Res., 51, 6988–7022, doi:10.1002/2015WR017896.

Skøien, J. O., G. Blöschl and A. W. Western (2003) Characteristic space scales and timescales in hydrology. Water Resources Research, 39, (10), article number 1304.