On the use of random graphs in analysing resource utilization in urban systems

Urban resource models increasingly rely on implicit network formulations. Resource consumption behaviours documented in the existing empirical studies are ultimately by-products of the network abstractions underlying these models. Here, we present an analytical formulation and examination of a generic demand-driven network model that accounts for the effectiveness of resource utilization and its implications for policy levers in addressing resource management in cities. We establish simple limiting boundaries to systems' resource effectiveness. These limits are found not to be a function of system size and to be simply determined by the system's average ability to maintain resource quality through its transformation processes. We also show that resource utilization in itself does not enjoy considerable size efficiencies with larger and more diverse systems only offering increased chances of finding matching demand and supply between existing sectors in the system.


RSOS-200087.R0
Review form: Reviewer 3 Is the manuscript scientifically sound in its present form? Yes

Are the interpretations and conclusions justified by the results? No
Is the language acceptable? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
In this paper, the authors try to provide an analytical assessment of generic network formulation of urban resource models. The paper presents and analytical formulation and examination of a demand-driven network model that accounts for the effectiveness of resource utilization which enables the authors to better frame the existing empirical efforts and provide a better understanding of available policy levers in addressing resource management in cities.
I think the subject is adequate and has enough to be published with some small changes. These changes are format and not content.
In my opinion, the abstract must be rewritten. It does not reflect well what is done and, it seems like an introduction that does not correspond in the abstract. Technically an abstract is a set of short and organized statements that describe, synthesize and comprehensively represent the main ideas of a scientific work. But in this case, it does not describe what is done comprehensively, nor does it represent the main ideas of the article.
More often than not, the sections of the papers must be: Introduction (to introduce the subject of study) Related works (study related papers and motivation) Methodology (how the objectives will be achieved, usually including a flow chart), 3 The reviewers and Subject Editor have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.
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I think the subject is adequate and has enough to be published with some small changes. These changes are format and not content.
In my opinion, the abstract must be rewritten. It does not reflect well what is done and, it seems like an introduction that does not correspond in the abstract. Technically an abstract is a set of short and organized statements that describe, synthesize and comprehensively represent the main ideas of a scientific work. But in this case, it does not describe what is done comprehensively, nor does it represent the main ideas of the article.
More often than not, the sections of the papers must be: Introduction (to introduce the subject of study) Related works (study related papers and motivation) Methodology (how the objectives will be achieved, usually including a flow chart), 3. You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org) and the production office (openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact --if you are going to be away, please nominate a co-author (if available) to manage the proofing process, and ensure they are copied into your email to the journal.
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General Comments
The paper uses a network approach to represent resource use in urban systems and finds that if you make some simplifying assumptions, the performance is not a function of system size, rather by average efficiency characteristics of the processes in the city.
Unfortunately, I find the assumptions are too simplifying and guide the conclusion rather more than any valid representation of urban systems. ie the model and the assumptions together do not represent urban systems well and the result is more about random graphs than cities.
Among the assumptions the authors ignore net additions, assume vertices (processes) are identical, in degree and out degree are the same (balanced), and any heterogeneity in flows is taken from a standard uniform distribution. On Page 10 at line 9 the authors themselves acknowledge that the choice of a uniform distribution is pivotal in the approximation of numerical results.
The oversimplification of urban systems fails to acknowledge the specialised, heterogeneous nature of economic and productive sectors that use different resources, and threshold effects that come with size and clustering of resourceuse activities.
There is some confusion between 'efficiency' and 'efficacy'. Efficacy is the ability to produce a desired or intended result. In complex systems, it may be interpreted to be about whether or not the system retains function or achieves some purpose. Efficiency is a measure of the extent to which input is well used for an intended task or function (e.g. to maintain efficacy) and I believe the author's have confounded the two topics in their definition of effectiveness (page 4 lines 24-27) Other than those lines abovementioned I cannot see the argument why Equation 3 is about effectiveness except that the authors define it as such. It looks much more like an efficiency measure.
In general I am unsure of the consistent use of efficiency and effectiveness terminology and e.g. the authors sometimes use "efficiency" to refer to parameters (λ, φ) that they also refer to as 'disutility factors' The introduction, analysis and discussion are not strongly connected to urban systems which is really only mentioned in the example of recycling of bricks. It is arguably false to say that urban systems can be represented with random

Appendix A
The methodology derives explicitly from a forthcoming article, reference [22] and it is uncertain whether that has been successfully peer-reviewed. Given that the results from the method are so strongly coupled with the validity of that research I would suggest rejection until the predecessor of this paper is accepted and published. Otherwise there is intransparency on the derivation of the method is or whether the present paper is an advance on the currently inaccessible reference [22].
The present paper does present a useful network formalism that connects to concepts of material flow analysis MFA and on page 10 (Line 38-52) the example of recycling/reclaiming bricks connects usefully to topics of circular economy ( more so than urban systems in general). I think that the method presented could be used with process data from MFA or life-cycle inventories to arrive at macroscopic network efficiency results on complex production processes.

Specific Comments
Page 2 the elaboration on "Overshoot Day", Figure 1 and the first reference are unnecessary and Page 8 line 56 I assume densities refers to probability density?
Page 3 line 29 the terminology on "resource use" can be put in a footnote, moving the words …"moving forward and unless otherwise specified we will use the term resource use to refer to the exergetic content and quality of both energetic and material flows." We thank the reviewer for their time and careful examination of our manuscript. We have broken down and rearranged their comments in order to better address the reviewer's concerns thematically and implement their suggestions as appropriate. The colour coding is used to highlight substantial changes made in the manuscript corresponding to each point raised below. The remaining alterations are visible through tracked changes in red typeface.
1. "The methodology derives explicitly from a forthcoming article, reference [22] and it is uncertain whether that has been successfully peer-reviewed. Given that the results from the method are so strongly coupled with the validity of that research I would suggest rejection until the predecessor of this paper is accepted and published. Otherwise there is intransparency on the derivation of the method is or whether the present paper is an advance on the currently inaccessible reference [22]." ____ As mentioned in the opening cover letter, we confirm that the referenced manuscript, 'An Ecological-Thermodynamic Approach to Urban Metabolism: Measuring Resource Utilization with Open System Network Effectiveness Analysis', 1 was accepted for publication in Applied Energy prior to the submission of the current manuscript but not assigned a doi or an issue. Since early August, it has been available in press and its reference within the current manuscript has now been updated to reflect full citation information. We apologise for the unclear nature of the language used in the references making it difficult to discern whether the article had indeed undergone peer-review successfully.
2. "The introduction, analysis and discussion are not strongly connected to urban systems which is really only mentioned in the example of recycling of bricks. It is arguably false to say that urban systems can be represented with random graphs. It has been shown empirically that there are macroscopic returns to scale (sub-linear power law relations) in energy consumption {Bettencourt, 2007 #155} and, from a microscopic analysis, in economic productivity (Lobo et al.

PLoS ONE 2013)." ____
The reviewer is correct in arguing that it would be highly inaccurate to represent systems of cities as random graphs, especially with reference to the urban scaling body of literature. The use of the phrase 'urban systems' in this work, however, is in reference to systems and processes of material and energetic flows within an urban context and should not be confused with the usage referring to 'systems of cities' within the body of work on urban scaling, agglomeration advantage, and complexity. The first mention of urban systems within the text is now accompanied by an endnote highlighting the above semantic usage. Overall references to 'urban systems' throughout the text have also been modified and we hope that these are now less open to misunderstanding.
3. "The present paper does present a useful network formalism that connects to concepts of material flow analysis MFA and on page 10 (Line 38-52) the example of recycling/reclaiming bricks connects usefully to topics of circular economy (more so than urban systems in general). I think that the method presented could be used with process data from MFA or life-cycle inventories to arrive at macroscopic network efficiency results on complex production processes." ____ We appreciate the reviewer's acknowledgment of the utility of the work to the material flow analysis, circulareconomic analysis, and urban metabolism literature and the connection demonstrated with the brick reclamation example. As mentioned above, the manuscript's main preoccupation has in fact been with such system-level characterisation of flow processes in an intra-urban context, i.e. material flow, circular economy, etc. We have now attempted to convey this more explicitly by signposting this both within the introduction and also towards the end of the manuscript.
4. "Unfortunately, I find the assumptions are too simplifying and guide the conclusion rather more than any valid representation of urban systems. ie the model and the assumptions together do not represent urban systems well and the result is more about random graphs than cities.
The oversimplification of urban systems fails to acknowledge the specialised, heterogeneous nature of economic and productive sectors that use different resources, and threshold effects that come with size and clustering of resource use activities." We understand that the main objections of Reviewer 2 to (i) the use of random networks and (ii) the failure to acknowledge the efficiencies and agglomeration effects associated with clustering and specialisation are rooted in the assumption that the method has been used for modelling and simulation in a 'system of cities' context given the reviewer's references to the body of work by Bettencourt and colleagues. We agree with the reviewer that random graphs as used in the present work are not representative models of systems of cities. However, as already noted, the application and formulation at the core of this work seek to address resource flow systems within urban environments. The random network formulation and the simplifying assumptions made explicit in this work are, in practice, consistent with the existing literature within the material flow analysis, ecological network analysis, and energy systems domains which implicitly rely on similar formulation in their work. [2][3][4][5] 5. "Among the assumptions the authors ignore net additions, assume vertices (processes) are identical, in degree and out degree are the same (balanced), and any heterogeneity in flows is taken from a standard uniform distribution. On Page 10 at line 9 the authors themselves acknowledge that the choice of a uniform distribution is pivotal in the approximation of numerical results." ____ In addressing the reviewer's concern regarding the exclusion of stocks, we note that, from a resource utilisation perspective, the addition of dynamic stocks only serves to displace system effectiveness estimations in time. This is because stocks that are used by vertices as incoming resources are exergetically indistinguishable from extraboundary imports and would have required extraction or extra-boundary imports in a previous time step in any case. We have now made this clear in an endnote following the introduction of Equation 2.
As for the criticism regarding the compounding simplifying assumptions, we need to be clear that the assumptions enumerated by the reviewer are considered in a more discretised matter and implemented separately to establish specific system behaviours. The assumptions relating to balanced networks in Proposition 1 and sink/source only networks in Proposition 2 have been made to specifically establish the limiting envelop for the system-wide performance and are not meant as generic behavioural assumptions. We understand that this may not been immediately clear in Section 4 which seeks to establish such upper-and lower-limit limits for the system resource utilisation. We have attempted to clarify this by putting each proposition under a relevant sub-heading making clear references to the nature of the boundary being formulated.
See page 5 sub-section 'Upper limits to average system-wide resource utilisation' and page 6 sub-section 'Lower limits to average system-wide resource utilisation'. See also page 6 lines 3-7.
While acknowledging that we have in fact established the analytical upper-and lower-limits using independent but system-wide constant values of and which ignores process-level heterogeneities for convenience, the propositions still hold valid against Monte Carlo experiments that do incorporate process heterogeneities as the reviewer has noted. We have made this clear in the paragraph immediately preceding Figure 2  The reviewer is additionally concerned that the choice of the uniform distribution as the sole means of accounting for the process heterogeneities guides the model conclusion and is even acknowledged as such by the authors. This is not in fact the case. We acknowledge that better language could have been used to clear any doubts. The portion of manuscript in discussion has been meant as a clarification that although the choice might appear pivotal, it will not significantly affect the average expected value of the utilisation and would only serve to determine the variance of its distribution. We have edited the language in that section so better clarify this.
6. "There is some confusion between 'efficiency' and 'efficacy'. Efficacy is the ability to produce a desired or intended result. In complex systems, it may be interpreted to be about whether or not the system retains function or achieves some purpose. Efficiency is a measure of the extent to which input is well used for an intended task or function (e.g. to maintain efficacy) and I believe the author's have confounded the two topics in their definition of effectiveness (page 4 lines 24-27) Other than those lines abovementioned I cannot see the argument why Equation 3 is about effectiveness except that the authors define it as such. It looks much more like an efficiency measure." ____ We are inclined to agree with the reviewer's observation that the metric presented is in essence one of efficiency. However, our work builds on the work by Tan et al., and we follow that language for consistency. This work differentiates the metric from the commonly used system-wide efficiency measures within the exergy-based literature that are calculated based on the ratio of outgoing to incoming extra-boundary resource flows rather than those concerned with the efficiency of the resource utilisation within the system. 6,7 This is a subtle but distinct difference, and we thus follow this language set Tan et al. by referring to the metric as one of effectiveness.
In order to make this clear and avoid confusion, we have added a similar explanation to that above before the introduction of the model framework.
7. "In general I am unsure of the consistent use of efficiency and effectiveness terminology and e.g. the authors sometimes use 'efficiency' to refer to parameters ( , ) that they also refer to as 'disutility factors'" We apologise for the occasional inconsistency in the language used regarding process coefficients and . These have now been corrected within the manuscript such that they are consistently referred to as 'disutility factors'. The mentions of 'efficiency' with regard to process/flow factors have thus been wholly eliminated. 9. "Page 8 line 56 I assume densities refers to probability density?" The two instances of 'densities' have now been edited to refer to density functions and probability density as suited.
See page 8 line 2.
10. "Page 3 line 29 the terminology on 'resource use' can be put in a footnote, moving the words … 'moving forward and unless otherwise specified we will use the term resource use to refer to the exergetic content and quality of both energetic and material flows.'" While we are unaware of the editorial policy at Open Science regarding the use of footnotes and endnotes, the phrase has currently been incorporated as an endnote as suggested by the reviewer along with a few others. We would incorporate these notes as parenthetical statements within the text should the editorial guidelines require an elimination of endnote material.