Climate-sensitive Urban Planning through Optimization of Tree Placements

We thank the reviewer for taking the time to review our paper and raising interesting points. We are glad that the reviewer acknowledges that our work “considers a novel spatial optimization problem with a very relevant application”. Below, we address the concerns and questions of the reviewer.

W1,W4: ML contribution & missing evaluation

We kindly refer the reviewer to Section 4.1 that thoroughly compares our method to SOLWEIG. Next, we provide further details about the computational speed-ups of our method: we report speed-ups of factors of 30, 17, 44000, and 400000 for the time periods: day, week, year, or decade, respectively, when comparing using our model that directly outputs the aggregated mean radiant temperature to first predicting the mean radiant temperature for each time step and then aggregating over all time steps. Note that using deep learning methods compared to physical modeling with SOLWEIG achieves another factor of ca. 22x [1]. Note that prior works exclusively used physical simulation models. To contextualize the amount of speed-up we gain, let us consider an example: consider that the optimization takes 1 minute with our method and optimizes the tree positions for the time period decade. Consequently, the estimated runtime for SOLWEIG would be 1 min*400000*22=ca. 16.73 years.

As mentioned by the reviewer, the main contribution of our work is the introduction of a “novel spatial optimization problem with a very relevant application”. Prior work mostly focused just on computational efficiency or improved modeling, i.e., improving the forward direction. In contrast, we consider the backward direction, i.e., making interventions in the input to optimize some physical quantity, i.e., in our case reducing the mean radiant temperature. Besides that we do not use it as a surrogate model but learn to directly predict aggregated results which goes beyond a simple replacement.

W2, Q1: Sequential or joint optimization

After greedily placing trees subsequently, the iterative search jointly optimizes all tree positions. We note that sequential placements would incur significantly more computational costs and, thus, we did not run such.

Thanks for pointing out the missing evaluation in the algorithm. We indeed need to evaluate the new candidate. We fixed the algorithm in the revised manuscript.

W3, Q3: Simplifying assumptions

We note that many limitations could be overcome in future work. The main issue for most limitations is the data bottleneck, i.e., the data often is not available, or limitations of physical modeling (refer to Appendix C for more details in the revised manuscript). Both could be overcome by future advances in easier access, e.g., by means of estimating them through satellite imagery, as well as advances in physical modeling.

Q2: Model architecture choice

Our approach is not specific to the model architecture. The goal of our work is not just to show good numbers but to outline a novel optimization problem that uses deep learning approaches for the optimization of physical quantities. Consequently, the model architecture is a non-important implementation detail in our opinion and future work could improve upon it.

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[1] Briegel, Ferdinand, et al. "Modelling long-term thermal comfort conditions in urban environments using a deep convolutional encoder-decoder as a computational shortcut." Urban Climate 2023.

Thank you for the follow-up and updated score! We appreciated the discussion and your constructive feedback.

Concerning the venue, we believe that ICLR is a good platform for our work. Our aim is to prompt ML experts leveraging their skills across various scientific domains to reconsider the prevailing emphasis mostly exclusively on computational efficiency or general forward modeling. Instead, we would be happy if the takeaway of our paper for them would be to consider alternative ML applications in the scientific domain more often, such as optimization of some physical quantity.

We thank the reviewer for taking the time to review our work. We are glad that the reviewer acknowledges that our manuscript is “sound” and that the “results of the experiments support the claims”.

Originality; new insights

We would like to kindly remind the reviewer that this work was submitted to an applications track, where the primary goal is to showcase the application of recent deep learning methods to innovative problem setups. Unlike the majority of previous works which focus on computational efficiency gains or refining forward modeling, our paper targets a distinctive direction. Our emphasis lies in the use of deep learning to actively optimize an important physical parameter of the real-world, i.e., in our example the improvement of outdoor human thermal comfort. Note that our problem formulation extends beyond this example, i.e., essentially it boils down to making physically meaningful interventions to achieve some goal.

Besides the aforementioned, we would briefly like to note that our work is the first to optimize tree locations to reduce the mean radiant temperature over time spans of weeks or even entire decades. This also allows us to investigate the effect of optimized tree locations over longer time periods (Section 4.3). Overall, we believe that our work may provide an interesting example of how to utilize advancements in deep learning to actively support in solving challenging real-world optimization problems.

Focus on one city

We openly acknowledge this as a limitation (also refer to our limitations section). However, note that SOLWEIG has been successfully applied to various cities across the world with distinct local climatic regions. Consequently, we are confident that our approach will also work for other climatic regions. However, we hope that the reviewer understands that getting the respective data is unfortunately challenging. Future advancements in estimating the needed data from, e.g., satellite imagery, may overcome this data bottleneck. Lastly, we chose five areas with distinct characteristics and found that our approach works across all of them.

W1: Where does the data come from?

We obtained the pre-processed data from Briegel et al [1]; refer for details to them. They were provided with spatial data and obtained past meteorological measurements from the internet. The input data is real data (from the point in time it was recorded) but mean radiant temperatures were simulated with SOLWEIG, as recording real measurements of mean radiant temperature is challenging (see below for a brief discussion on why).

Regarding ERA5 data: ERA5 Land data has a spatial resolution of ca. 9km x 9km, nor does it contain mean radiant temperatures. Please refer to [2] for further details. Note that all study areas are within the same ERA5 Land grid cell. This means, all study areas have the same global meteorological forcing data. Thus, we consider it as constant within our 500m x 500m areas.

W2: Comparisons to traditional physical models

We compare our modeling with SOLWEIG in Section 4.1. We find that the U-Net to SOLWEIG error (i.e., 1.93K) is smaller than the previously found errors of SOLWEIG to real sparse measurements (i.e., 4.4K; refer to Table 5 in [1]). Consequently, it indicates that U-Net is a well-suited computational shortcut and does not (or perhaps a negligible) trade-off between modeling performance and efficiency. Note that this is not typically the case when replacing a physical model with some data-driven approach.

W3: Questions about SOLWEIG and evaluation

Yes, SOLWEIG is a popular physical simulation model for estimation of mean radiant temperature. We provide details on SOLWEIG in Appendix C.

Regarding the L1 error: it is computed between the U-Net’s and SOLWEIG’s estimation. Note that obtaining real measurements of mean radiant temperatures is difficult and monetarily expensive, as both short- and longwave radiation from six directions need to be measured. In addition, such measurements can only be made for single points, which in turn makes comprehensive evaluation over an entire spatial area challenging.

W4: Comparison of #trees vs. positioning (optimization)

We added a comparison of the effect of planting more trees vs. optimizing or not optimizing their position in Appendix F.3. The results highlight the importance of our optimization, i.e., not optimizing would only harness ca. 50% of their potential in reducing mean radiant temperatures.

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[1] Briegel, Ferdinand, et al. "Modelling long-term thermal comfort conditions in urban environments using a deep convolutional encoder-decoder as a computational shortcut." Urban Climate 2023.

[2] https://confluence.ecmwf.int/pages/viewpage.action?pageId=74764925

Q1: Figure 1 legend

It is the difference between the status quo to the status after planting an additional 50 trees. We added green crosses in the figures to indicate the tree positions.

Q2: Gradient-based optimization

Yes, but it yielded very poor results. We mainly attribute this to the fact the discretization step was causing issues. We believe modeling mean radiant temperature with a GNN may be fruitful for future work and would allow for such an optimization.

Q3: Type of tree

We note that current physical simulation models, such as SOLWEIG, are not capable of distinguishing types of tree. We added a list of limitations of the physical model SOLWEIG in Appendix C to make ML experts aware of such limitations that our approach consequently inherits. Our approach would benefit from advances in incorporating such in physical modeling with SOLWEIG.

Q4: Discussion of experimental results

Our study focuses on mean radiant temperature and, thus, does not consider other effects, such as wind, air temperature or humidity. Thus, we outlined this limitation in Section 5 and proposed it as a next step to integrate them. For example, one could extend our approach to UTCI, a popular thermal comfort index that also includes such factors.

We optimized tree positions for winter and summer months and provided the additional results in Appendix F.2. We find that trees are predominantly positioned in larger, open areas and clustered together during the summer, whereas they are more broadly spread over the neighborhood during the winter.

We thank the reviewer for taking the time and raising constructive criticisms. We are glad that the reviewer appreciates our presentation and acknowledges that our “claims are backed by theoretical analysis and detailed experiments.” Below, we address the reviewer’s concerns and questions.

Additional technical description

We revised the manuscript and, e.g., added missing explanations of the hill-climbing algorithm. We would provide further feedback if the reviewer sees other parts that may require improvement.

Novelty in narrow application area

We would like to note that the majority of previous work on physical modeling focused on improving computational efficiency or improved modeling in the forward modeling. Our work instead focuses on finding interventions in the input, i.e., locations of trees, to optimize a physical quantity (backward direction). Our case study extends beyond the scope of the presented application area and may provide an interesting direction for future work in using deep learning approaches to support humans in challenging optimization problems.

500m x 500m is not a large neighborhood; what area is covered by previous work, and missing state-of-the-art

We kindly disagree. Note that prior work only used areas of sizes of ca. 50m x 80m [1] or 30m x 80m [2], i.e., our study areas are roughly two orders of magnitude larger. Further, they optimized for a maximum number of 8 [1] or 14 [2] trees, whereas we optimized for up to 200 trees. This makes our approach hardly comparable to prior work.

Missing dataset details and HP tuning

Thanks for pointing this out! We added the missing dataset details in Appendix B. Note that we did not perform hyperparameter tuning. We believe future work could already improve performance by optimizing the hyperparameters.

Cost comparison of planting new trees vs. transferring existing trees

We hope the reviewer understands that a cost comparison is out-of-scope for this work and may depend on many parts that are hard to control for. Nonetheless, we would like to point the reviewer to Section 4.4 that showcases that we could significantly better utilize the potential of urban trees by moving them to “better-suited” locations in terms of reduction in mean radiant temperature. This may be of interest in the consideration whether planting new trees or transferring existing ones is the most cost-efficient solution for a given city.

Correlation value between mean radiant temperature and mortality

We kindly refer the reviewer to Table 1 and Figure 3 of Thorsson et al. [3] for details.

I did not understand how the aggregated performance is worse than point prediction, the absolute number is lower

We compared the direct prediction of aggregated mean radiant temperature against making predictions for every time step and then aggregating the results. We did not compare with SOLWEIG’s results, as it is prohibitively expensive for our larger time periods (year & decade), and wanted to stay consistent within our comparisons. Below, we provide comparisons of the results of aggregated performance compared to SOLWEIG for both smaller time periods (day & week) that make clear why making point prediction and then aggregating is slightly better, though computationally significantly more expensive.

Isn't it a good thing that the temperature increases during nights and winters when the environment is colder?

Yes, this is indeed the case and it is beneficial. The effect can be seen in Figure 3. We did not delve into this deeper, as we chose to focus on mean radiant temperature reduction for combating heat stress.

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[1] Wallenberg, Nils, Fredrik Lindberg, and David Rayner. "Locating trees to mitigate outdoor radiant load of humans in urban areas using a metaheuristic hill-climbing algorithm–introducing TreePlanter v1. 0." Geoscientific Model Development 2022.

[2] Stojakovic, Vesna, et al. "The influence of changing location of trees in urban green spaces on insolation mitigation." Urban Forestry & Urban Greening 2020.

[3] Thorsson, Sofia, et al. "Mean radiant temperature–A predictor of heat related mortality." Urban Climate 2014.

We thank the reviewer for the thorough review and raising constructive criticisms. We are happy that the reviewer finds that our work “addresses a relevant, practical problem of potential societal impact” and some of our analyses “insightful”. Below, we address the concerns and questions of the reviewer.

W1: Methodological contribution

Our work aims to formulate a problem that can be solved by deep learning techniques. Compared to previous works in physical modeling with deep learning that (passively) typically just aimed at computational efficiency or improved modeling in the forward direction, we instead take an active position by optimizing the input s.t. it optimizes a physical measure to achieve a certain goal (backward direction).

W2: Error bars

As suggested by the reviewer, we have added error bars for the optimization of trees in our comparison of optimization strategies (Table 1). It clearly shows the superiority of our optimization method above common baselines for black-box optimization.

W3: Missing factors, such as population density, etc.

We also agree this is a limitation (as discussed in the limitations section). However, this is not a limitation of our method. Indeed, we can integrate such factors into the objective function if such data (e.g., the population density) is available. Consequently, it can be ensured that trees are planted in areas, in which they effectively improve the thermal comfort of individuals where they reside.

C1: Comparisons to prior works; contextualization of the speed-ups

Note that prior work only used areas of sizes of ca. 50m x 80m [1] or 30m x 80m [2], i.e., our study areas are roughly two orders of magnitude larger. Further, they optimized for a maximum number of 8 [1] or 14 [2] trees, whereas we optimized for up to 200 trees. This makes our approach hardly comparable to prior work.

Regarding the computational speed-ups of our method: we further report speed-ups of factors of 30, 17, 44000, and 400000 for the time periods: day, week, year, or decade, respectively, when comparing using our model that directly outputs the aggregated mean radiant temperature to first predicting the mean radiant temperature for each time step and then aggregating over all time steps. Note that using deep learning methods compared to physical modeling with SOLWEIG achieves another factor of ca. 22x [1]. Note that prior works exclusively used physical simulation models. To contextualize the amount of speed-up we gain, let us consider an example: consider that the optimization takes 1 minute with our method and optimizes the tree positions for the time period decade. Consequently, the estimated runtime for SOLWEIG would be 1 min*400000*22=ca. 16.73 years.

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[1] Wallenberg, Nils, Fredrik Lindberg, and David Rayner. "Locating trees to mitigate outdoor radiant load of humans in urban areas using a metaheuristic hill-climbing algorithm–introducing TreePlanter v1. 0." Geoscientific Model Development 2022.

[2] Stojakovic, Vesna, et al. "The influence of changing location of trees in urban green spaces on insolation mitigation." Urban Forestry & Urban Greening 2020.

[3] Briegel, Ferdinand, et al. "Modelling long-term thermal comfort conditions in urban environments using a deep convolutional encoder-decoder as a computational shortcut." Urban Climate 2023.