Dear Authors,

I read your work and particularly the discussion of your paper with great pleasure. I guess there is consensus among the reviewers and myself that your manuscript addresses a highly sensitive issue – which became almost an evergreen. The reviewers came up quite a few important points that need more in depth reflection to assure that the presented work moves beyond similar attempts, which have already published in the literature and beyond a pure defense of conceptual models. Given the quality of your responses to these points I am rather confident that the revised version of your work will hold what the readers might expect to find, after reading such promising title.

Allow me to stress a few key points that might need special care during the revision process and I hope you forgive that I couldn’t resist to combine those with a few of my thoughts on this issue.

Let me first express that, though I am a physically based modeler, I found this terminology more misleading and offending than helpful as it essentially suggests that models outside of this category are unphysical. This is or course not true as they rely on the mass conservation etc. On the other hand physically based models are often called reductionist – which suggest they are clumsy and rely on brute computational power. I guess such categories take us nowhere and maybe it is much more precise to talk about spatially explicit and spatially integrated models.

That said let me come to the main points.
1) A key for making to approach the issue is maybe to reflect about the complementary merits of these model categories depending on their purpose? As highlighted by Marc Bierkens the merits depend on what we want to model, catchment scale integral response or space time dynamics of state variables. On top of that we might distinguish models for predictions from models for explaining (multi) causal relations in terrestrial system functioning. The sets of useful models for these to paradigms are not necessarily identical and the model paradigm in hydrology is strongly biased towards the prediction issue. This is of course due to the operational origin of hydrological models stream flow predictions.

2) In line with reviewer Thorsten Wagener I think that any meaning full model effort combines top down and bottom up thinking, this is not so much a quest of using PDE or ODE. So it might be helpful to better distinguish the models and the approaches to the model problem.

3) In line with Marc Bierkens I think that a section on modelling myths with “physically” based terms would yield a more balanced story line. Alternatively you could also approach the story by working out the key assumptions underlying both model philosophies (which are pretty different) and to reflect when they become invalid, because this shows the way to progress.

3.1) For instance with respect to “spatially explicit models”: In addition to what has been said by the authors, you might consider to add that spatially explicit models treat fluxes as the product of a driver (potential gradient) and a loss term (conductance). The definition of a potential requires local equilibrium or/ well-mixed conditions in the grid cell. Applications a grid scales larger than 1 m become therefore questionable (even if the land surface model community will not like this point).
The second big assumption in Darcy law is a) a purely diffusive flux which implies no kinetic energy in the flux and b) that gravity driven flux and capillarity driven flux are controlled by the same conductance – also during rainfall driven conditions. Both assumptions might be not appropriate when dealing with fast subsurface flows during rainfall driven conditions.

3.2) A key assumption for conceptual models is that catchments as a closed control volume do really exist and that surface water shed provides their boundaries . This assumption can in fact not be rejected within this paradigm, it is almost an axiom. Without relying on that one cannot compile a mass balance by separating of the input (assumed as the total rainfall) and total liquid loss (streamflow) and the residual (equal to storage and evaporation and transpiration). This has the nice implication that runoff generation in conceptual models is a continuous function of storage on a compact interval (between 0 and 1). This implies we can fit a polynomial to this function, due to the Weierstrass theorem. Spatially explicit models do not depend on the validity of the catchment idea.

I very much like characterization of catchment as low pass filters and the issue of dispersion. Yet this implies that event convolution (the classical integral model for linear systems) or even peace wise linearization is difficult, as this implies the transfer functions depend or conditional to the input and the state (which implies one can only integrate a short time) and then has to update the kernel. This is why modern conceptual models use time stepping and conceptual representation of the kernel/transfer functions for state updating.

4) As proposed by Mark Bierkens I would also encourage the authors re-think about their macro-microscale argumentation in their response to reviewer Ralf Loritz. I think the key point is that we cannot infer backwards on the microstate of the terrestrial system (e.g. the pattern of root depths) by knowing the macro state of the system – which implies that many subscale system configurations with purely stochastic and highly structure variability might be represented by the same macro state. This might not bother if we are interested in stream flow predictions, but if matters if we are interested in eco hydrology or distributed state dynamics. Whether the macroscale representation might be favorable or not, depends on our interest – so does the choice of the model, do we want to predict or to explain.

5) I agree with Ralf Loritz that neither physical nor conceptual models close the energy balance (which involves more that the land surface energy balance and soil heat flux, but also the interplay of potential and capillary binding energy of soil water as well as export of kinetic energy in stream flow) . I think the this section issue needs to be formulated in a less ambiguous manner

6) I would encourage the authors to better define how to measure process and spatial complexity, it is the a) the same as predictability (complex processes are more difficult to predict) or b) the amount of information in a time series, c) the number hidden dimensions, d) or is it the degree of non-linearity of the PDE, possible chaotic nature, and state dependent error propagation, c) the number of independent parameters (dimensionality) … I know this is not easy, but I feel that these terms might have many different meanings in the community.


A few details:
- Page 1: Intro Beyond the errors arising from uncertain data there might be much from measurement errors, which would become clear if we added error bars at least to our observation data.
- Page 5: I am not sure what spatial organization of connectivity means?
- Page 5: Top down models are not based on observed input – output relations ship but on their estimates based on input output data. (Otherwise we had no uncertainty if those were observable)
- Page 9: What is actually meant with process complexity – the order of the differential equation and its degree of non-linearity, what is meant with spatial complexity. The degree of spatial detail, isn’t this rather information than complexity?

Best regards,

Erwin Zehe