Learning Urban Climate Dynamics via Physics-Guided Urban Surface–Atmosphere Interactions

Q1: More emphasis on clarifying how the physical models connect to the machine-learning models.

Response:

We thank the reviewer for this valuable suggestion. Following your advice, we have added a table to clarify the mapping between the model components and the elements of the inference scheme. This table will be included in the appendix of the revised manuscript.

Q2: The code should include additional details to make it easier to use.

Response:

We appreciate the reviewer’s suggestion, which made us realize the importance of providing an easy-to-use example for model training and inference. Although we have aimed to ensure full transparency regarding our technical design, model structure, loss functions, and experimental setup, we acknowledge that we have not included the data loading or training scripts in the current code release during the review process. We will release additional code, including data loading and training routines, as well as a simple example for model training and inference, to facilitate reproducibility.

Q3: Evaluate with a held-out city to demonstrate spatial robustness.

Response:

Spatial generalization remains quite a challenging issue in global climate and urban climate prediction/estimation. While our work primarily focuses on improving temporal generalization, we agree that evaluating spatial generalization is crucial for real-world applications. To provide further insight, we conducted additional “leave-one-out” experiments. When selecting training cities, we intentionally chose cities with significantly different urban morphology or climate regimes. Therefore, to better assess spatial generalization, we performed supplementary experiments where one city was held out during training. The results are provided below for your reference (results in parentheses indicate performance under the original setting).

The results show that UCformer exhibits a certain degree of spatial generalization, but its performance varies notably across cities and is strongly influenced by both urban morphology and local climate conditions. For instance, the RMSE of temperature estimates ranges from approximately 0.02 K in Singapore to 0.07 K in Rome, while the RMSE of dew point temperature estimates ranges from about 0.01 K in Rome to 0.03 K in London.

Overall, these findings suggest that while UCformer is capable of spatial generalization, its performance is influenced by the uniqueness of the target city’s urban and climatic conditions. We acknowledge spatial generalization as an important direction for future research. In particular, we plan to further investigate the shared representations of urban climate processes proposed in Section 4.5, and aim to explore whether scaling laws emerge with respect to the number and diversity of cities included during training, and how these factors affect the model's spatial generalization capability across heterogeneous urban environments and climate regimes.

Q1: Explanation of the results comparing model simulations to Flux tower measurements.

Response:

1.Model performance on Flux tower measurements: As correctly noted by the reviewer, UCformer was pre-trained on CLMU simulation data and then fine-tuned using a subset of Flux tower measurements. In this work, the CLMU model was not calibrated using these observations. It is important to note that CLMU is a state-of-the-art land surface model and ranks among the top performers in simulating Flux tower data across more than 30 models (Urban-PLUMBER project, see reference [17] in the manuscript).

Given that UCformer was fine-tuned with only a small amount of observational data, we are encouraged to see that it outperforms CLMU in this setting. This result is particularly noteworthy because calibrating physical models like CLMU to site-specific observations is computationally intensive. These results suggest that UCformer has strong potential to support real-world urban climate applications, especially in data-scarce environments where traditional model calibration is not feasible

2.Model Performance on Latent Heat: Latent heat flux in urban areas is influenced by complex factors such as soil moisture, vegetation, and human activities like irrigation. Both physical and ML models struggle to simulate latent heat accurately, as also noted in the Urban-PLUMBER project (reference [17] in the manuscript), which benchmarks leading physical models. This difficulty arises because key variables such as vegetation and irrigation are often missing, uncertain, or represented in a highly simplified manner. In addition, unaccounted-for human influences further complicate the simulation.

Future research could address this limitation by integrating the aforementioned variables into the model, provided that high-quality and complete observational data are available. In addition, explicitly guiding the model learning process with surface energy balance constraints may further improve ML model performance in estimating latent heat flux in urban environments.

Q2: Spatial resolution and characteristics of the training dataset.

Response:

Our study focuses on learning the underlying physical processes governing urban climate, rather than making estimations at a fixed spatial resolution. This is because the training data were generated using the single-point mode of the physics-based CLMU model, which does not operate on a fixed resolution. Instead, its spatial footprint is determined by the resolution of the atmospheric forcing and surface input data. Specifically, during model development, we used forcing data from the atmospheric component of the Community Earth System Model at a native resolution of 0.9° × 1.25°. Urban surface characteristics were extracted from CLMU’s static surface input files at the same resolution. The CLMU output in single-point mode shares this spatial resolution, which aligns with the default resolution used in global urban climate projections.

However, as shown in Section 4.6, we further evaluated both UCformer and the physical model using flux tower data with a much finer spatial footprint (~500 m), demonstrating the model’s ability to generalize across scales. Overall, our framework is flexible and can incorporate higher-resolution forcing and surface data as they become available. With the growing availability of urban-scale reanalysis and detailed surface datasets, UCformer can be extended to simulate urban climate at finer spatial scales, supporting localized planning and adaptation analysis.

Q3: Data distribution and why not include weather station data for evaluation.

Response:

1.Data distribution and model spatial generalization: Thank you for this insightful question. Our preliminary analysis shows that spatial generalization is highly challenging when training on a limited number of cities. Model performance depends on both urban surface features and regional climate. For instance, a model trained on London generalizes well to Edinburgh, likely due to their similar climates, despite differences in urban morphology. In contrast, performance drops in Shanghai, where both climate and surface characteristics differ markedly.

Regarding whether model predictions are particularly erroneous in certain contexts, we recognize that standard metrics such as RMSE do not fully capture the model’s effectiveness in urban climate estimation. For example, in our original settings experiment, the temperature RMSE of Shanghai was 0.4437, while the MESS score was above 0.84. These high values indicate a substantial difference between urban and background temperatures in Shanghai. As a result, although RMSE reflects the overall prediction error, the MESS metric provides important context for assessing the model’s relative ability to distinguish urban climate from its background environment.

Additionally, your concern is also of interest to other reviewers regarding the model’s performance on held-out cities. In response, we conducted additional "leave-one-out" experiments, as we intentionally chose these training cities with significantly different urban morphology or climate regimes. The latest results are provided below for your reference (original-setting results shown in parentheses).

2.Why not include weather station data for evaluation: We did not include weather station data in our main evaluation for several reasons. First, weather stations are typically sited in non-urban environments (e.g., hilltops or airports) following World Meteorological Organization (WMO) guidelines, which aim to measure background weather conditions. As a result, their observations may not accurately reflect true urban climate characteristics. Second, while some low-cost sensors capture urban air temperature, it is often difficult to obtain detailed information on the surrounding urban surface characteristics. This limitation also motivated our use of physics-based simulations, which provide urban climate variables conditioned on specific atmospheric forcing and surface features.

We fully acknowledge the importance of real-world evaluation. In this study, we used Flux tower observations as an alternative. Unlike typical weather stations, this Flux tower is fully embedded in an urban environment and provides both detailed atmospheric data and rich information on surrounding surface conditions. This aligns closely with the inputs to our model, making it a meaningful and appropriate benchmark. Therefore, we chose the Flux tower dataset rather than weather station data to evaluate real-world performance.

Weakness: The primary aim of the model and how UCformer could be applied to guide management and planning of urban environments.

Response:

Our primary goal is to emulate a physical model simulation and learn urban climate processes. We agree that the manuscript would benefit from more discussion on computational efficiency and its practical relevance. Specifically, our model reduces the simulation time for a 55-year city-scale run from ~12 hours to ~17 seconds. This substantial speed-up enables applications previously constrained by computational cost. For example, with scenario-adaptive modules, UCformer could be fine-tuned to quickly assess urban climate responses to strategies such as green roofs, added vegetation, reflective surfaces, or altered building density. In optimization tasks requiring large-scale scenario testing, this efficiency offers clear advantages over conventional models, supporting planners and policymakers in adaptive urban management. We appreciate the reviewer’s suggestion and will include these points in the revised manuscript.

Although our primary goal is to emulate physical model simulations, we also care about UCformer’s performance against real-world data. Therefore, in Section 4.6, we evaluated UCformer using ground truth measurements from Flux tower observations (please refer to our response to Q3 for the rationale behind not using weather station data). We chose CLMU as the comparison baseline in this part because it is a widely used and well-regarded physical model in urban climate research. In the Urban-PLUMBER project (reference [17] in the manuscript), which benchmarks leading physical models against Flux tower measurements, CLMU ranked among the top performers. Given its credibility and relevance, it serves as a robust baseline for evaluating UCformer’s performance against observational data.

Q1: Problem definition.

Response:

We have to clarify that time-series forecasting is fundamentally different from the problem we address in this work. In forecasting, the model typically receives a sequence of past target labels (e.g., temperature at previous time steps) as part of the input in order to predict future values. In contrast, our task does not include any past target labels in the input. Instead, we aim to estimate a sequence of urban climate variables (e.g., temperature, humidity) based solely on external predictors, namely, atmospheric forcing and urban surface characteristics within the same time window, rather than predicting future values based on past observations.

As noted in Strength S1, the reviewer acknowledges that our work proposes a novel and important downstream task, which centers on the significant divergence between urban and background climates. Specifically, our goal is to explore how urban climates are shaped by atmospheric forcing and urban surface characteristics at a given time. For this reason, the models mentioned by the reviewer, such as VAR, ARIMA, PatchTST, and Autoformer, are fundamentally incompatible with our task formulation. These models rely heavily on past target labels and their temporal trends to forecast future values. In contrast, our model does not receive any historical target labels as input. Including such information would provide additional signals that could artificially enhance model performance by revealing patterns not accessible in our intended setting. This would compromise the goal of estimating urban climate conditions strictly from external drivers such as atmospheric forcing and surface characteristics. Therefore, these forecasting methods are not directly applicable or comparable in our case.

Q2: Why not include time-series forecasting baselines.

Response:

As clarified in our Response to Q1, our task is not a conventional time-series forecasting problem. Therefore, when selecting baseline models, we focused on approaches relevant to urban climate estimation or sequence-to-sequence mapping, rather than forecasting. The scarcity of research specifically on urban climate mapping has limited the available choices for suitable baselines, which may also have contributed to the reviewer's misunderstanding of our task as traditional sequence prediction.

Nonetheless, following the reviewer’s suggestions, we additionally evaluated two sequence models that can be reasonably adapted to our framework. We modified their data interfaces accordingly to accept atmospheric forcing and urban surface features as inputs, enabling them to estimate urban climate variables within our task setting. Specifically, we compared UCformer with Informer_modified and LSTNet_modified, as well as with a multivariate linear regression (MLR) model. It is important to note that, since our task is not time-series forecasting, classical forecasting models such as VAR/ARIMA are not appropriate baselines. Instead, MLR is a more suitable and basic baseline for mapping tasks such as ours. The supplementary results are provided below:

As shown in Table, UCformer achieves the best overall performance across all evaluation metrics compared to MLR, LSTNet_modified, and Informer_modified. These results demonstrate the advantage of our approach for urban climate estimation. We appreciate the reviewer’s suggestion, which allowed us to revisit the suitability of sequence forecasting models as baselines for our sequence regression task.

Q3: Model implementation and the designed physical components' codes.

Response:

1. Model implementation and reproducibility:

We respectfully disagree with the reviewer’s statement regarding reproducibility. We have fully released the code necessary to reproduce the results presented in the paper. In the manuscript, we clearly describe the data preprocessing steps (Appendix A.2), model training settings (Appendix A.3 and also in the GitHub repository), loss function (Section 4.1 "Training Objective"), and model checkpoint (GitHub repository). We have also made the datasets used in this work available for review. We have aimed for full transparency regarding our technical design, model structure, loss functions, and experimental setup. We believe these materials are sufficient for reproducing our results.

2. Technical part codes:

We thank the reviewer for examining our code and for these detailed comments. However, our architectural design deviates meaningfully from vanilla Transformers. Our contribution lies in adapting the architecture to encode physical process-specific inductive biases, rather than proposing entirely new operations. This is in line with contemporary scientific machine learning practices, which favor physically meaningful design over novelty for novelty’s sake.

(1) Regarding the Decoder components described in Section 3.4:

Section 3.4 and Equations (8)–(12) of our manuscript provide the theoretical basis for the soft physics-inspired constraints in our decoder design, as well as the rationale for using cross-attention to incorporate information from other variables when estimating each target variable. We have consistently stated that we do not embed explicit physical equations as hard constraints in the model. Instead, we aim to represent physically plausible dependencies between target variables through learnable, flexible mechanisms. In addition, Figure 2 (Section 3.2) clearly illustrates the use of cross-attention in the decoding process, which aligns with the reviewer's observation of "splitting the decoder into three branches.". As shown in the code (lines 214–224 of the forward function), our implementation of target variable decoding is consistent with both the manuscript and Figure 2: when estimating any given variable, information from the other two variables is also utilized.

(2) Regarding the Encoder components:

As shown in Figure 2 and Section 3.2 of the manuscript, our encoder is not a vanilla stack of Transformer blocks, but a multi-stage architecture designed to reflect the layered physical processes in urban climate systems:

The first encoder block uses cross-attention to model interactions between atmospheric forcing and static urban surface features. This is implemented in the climate_attention class (code line 46), where forcing_data attends to surface_data to simulate the modulation of dynamic inputs by static land characteristics.

The second block in the encoder is intended to learn radiative interactions among urban surfaces after atmospheric forcing, as represented by self-attention in Figure 2. These are implemented in the TransformerEncode class (code line 131), where the first encoder layer handles atmospheric-surface interactions and subsequent layers capture the updated properties and refine the representation, following the interaction logic described in the paper (code lines 139–140).

(3) Data loading, loss function, and training code:

The manuscript clearly presents the data input (Appendix A.1) and preprocessing steps (Appendix A.2), model training settings (Appendix A.3 and in the GitHub repository), and loss function (Section 4.1 "Training Objective"). The datasets used in this study have also been made available for review.

While the current code release does not include the dataloader and training loop, these components follow standard PyTorch implementations without any task-specific customization. Their omission does not hinder the understanding or verification of the framework’s core technical contributions, which are fully described and reproducible based on the provided materials.

To further support reproducibility, we will include the complete training pipeline—covering data loading and a training/inference example script—in the final code release.

In summary, although we adopt Transformer primitives for transparency and compatibility, our architectural choices are explicitly designed to reflect domain and physical knowledge—specifically, the hierarchical modeling of physical processes such as large-scale forcing interactions and localized radiative responses. This design goes beyond the standard use of self-attention and presents a structured inductive bias rooted in urban climate system behavior. Therefore, we respectfully argue that the UCformer encoder embodies architectural novelty that is both principled and practically motivated.

Thanks for the reply. While W2 has been addressed, my concerns on the other points remain. I still feel that the response seems more to dismiss my concerns rather than providing solid evidence from the implementation or mathematics.

W1: While you insist on the conceptual difference in your paper, in your implementation, it's not the case. It is evident that all models accept simple sequences with a shape of [batch_size, seq_length, feature_dim]. From your own code, the vanilla transformer is applied to your data without changing the model structure or applying any attention mask or constraints. Hence, it is unconvincing to claim "your task is fundamentally different". Your idea may be different, but your baseline implementation is very simple and has no difference from a common processing procedure.

**W3_1: ** Given the particularly few lines of code in the repository and the two very simple baselines you provided, I can't tell the real strength of your method.

For the convenience of other reviewers and the AC, I would like to ground my concern by pasting the second-best baseline code here.

Python

class MLPModel(nn.Module):
    def __init__(self, input_dim=30, negative_slope=0.01):
        super(MLPModel, self).__init__()
        self.activation = nn.LeakyReLU(negative_slope=negative_slope)

        # hidden layers
        self.hidden_layers = nn.Sequential(
            nn.Linear(input_dim, 192),
            self.activation,
            nn.Linear(192, 160),
            self.activation,
            nn.Linear(160, 128),
            self.activation,
            nn.Linear(128, 160),
            self.activation,
            nn.Linear(160, 160),
            self.activation,
            nn.Linear(160, 32),
            self.activation
        )

        # output layers
        self.out1 = nn.Linear(32, 1)
        self.out2 = nn.Linear(32, 1)
        self.out3 = nn.Linear(32, 1)

    def forward(self, x):
        x = self.hidden_layers(x)
        y1 = self.out1(x)
        y2 = self.out2(x)
        y3 = self.out3(x)
        out = torch.cat((y1, y2, y3), dim=1)
        return out

It is so simple, yet its performance is so strong—stronger than the more sophisticated Transformer and AutoML baselines. This raises a severe doubt in my mind: How difficult is the task itself? Are the improvements achievable from simple engineering tricks, for example, slightly altering the structure by using nn.LayerNorm, changing activation functions, or adding residual connections to this MLP?

Unfortunately, the authors refrain from replying some code, so I will not have an opportunity to verify this during the rebuttal process.

W3: I agree that it is not necessary to embed strict physics constraints. However, the problem is the cross-attention module in equations 10-12 is so strong in its expressive power that it can learn any dependency and is not biased toward a more "physics correct" one. Mathematically, the gradients with respect to the model's core parameters are generally non-zero, meaning the model can always update its weights to fit any function. We all know "Attention is All You Need."

But if you insist on this point, I'm open to it. I just think it is an overclaim. In this way, in geographic information science, tons of data can be splitted into multiple part, (e.g. population, economics, traffic dynamics), applying cross-attention, and we can claim it is guided by some physics or spatial-temporal dynamics, without really injecting the domain knowledge. You do similar things by using cross-attention and throwing the physics equations away. Is this reasonable or convincing?

Summary

To summarize, all of my concerns remain with your implementation, particularly:

• The very little code in the repository.
• The simple design of your model.
• And the strong but very simple baselines.

I confirm that there are no particulars in processing the 1-D sequential data, so I doubt that your task is not fundamentally different, your baselines are not extensively tuned, and the improvements can be achieved with engineering tricks to better fit the datasets. While your paper's story looks pretty good, I retain my doubts as aforementioned.

Q1: Lack of comparison to other physics-informed ML models.

Response:

We thank the reviewer for raising this important point. As discussed in the Related Work section, prior physics-guided ML models often incorporate explicit physical equations into the loss function or model architecture to enhance generalization and interpretability. For example, Read et al. (reference [27] in the paper ) employ a simplified energy budget formulation in which each flux term can be derived either directly from the ML inputs or from a combination of inputs and ML-predicted surface water temperatures. When the predicted terms fail to satisfy energy balance, the model is penalized accordingly during training. Similarly, in the physics-informed model proposed by Zanetta et al. (reference [41] in the paper ), a hard physical constraints layer is introduced. This layer takes a subset of predicted target variables, such as temperature and air pressure, to derive other physically related quantities, such as humidity. The model then computes a composite loss over all variables, encouraging physically consistent predictions. In other words, these physics-informed models are typically highly data- and task-specific. However, as noted in our manuscript (line 182), our study focuses on estimating three key variables in urban climate—2-m air temperature, dew point temperature, and specific humidity. Due to the lack of critical variables such as urban canyon air pressure, it is not feasible to directly embed relevant physical equations into the loss function or network structure for our tasks.

As a result, it is not feasible to apply such physics-informed constraints in our setting, making these previous models unsuitable as baselines. Notably, our “softy” design, which does not depend on explicit physical constraints, enables broader applicability to diverse datasets, as shown in Section 4.6.

Q2: How UCformer generalize to cities not included in training.

Response:

Spatial generalization remains quite a challenging issue in global climate and urban climate prediction/estimation. While our work primarily focuses on improving temporal generalization, we agree that evaluating spatial generalization is crucial for real-world applications. To provide further insight, we conducted additional “leave-one-out” experiments. When selecting training cities, we intentionally chose cities with significantly different urban morphology or climate regimes. Therefore, to better assess spatial generalization, we performed supplementary experiments where one city was held out during training. The results are provided below for your reference (results in parentheses indicate performance under the original setting).

The results show that UCformer exhibits a certain degree of spatial generalization, but its performance varies notably across cities and is strongly influenced by both urban morphology and local climate conditions. For instance, the RMSE of temperature estimates ranges from approximately 0.02 K in Singapore to 0.07 K in Rome, while the RMSE of dew point temperature estimates ranges from about 0.01 K in Rome to 0.03 K in London.

Overall, these findings suggest that while UCformer is capable of spatial generalization, its performance is influenced by the uniqueness of the target city’s urban and climatic conditions. We acknowledge spatial generalization as an important direction for future research. In particular, we plan to further investigate the shared representations of urban climate processes proposed in Section 4.5, and aim to explore whether scaling laws emerge with respect to the number and diversity of cities included during training, and how these factors affect the model's spatial generalization capability across heterogeneous urban environments and climate regimes.

Q3: Model Efficiency.

Response:

In addition to UCformer, we evaluated two representative sequence-to-sequence models, that is, LSTNet and Informer, which can be adapted to urban climate estimation.

All models were tested with a batch size of 128 on an NVIDIA 5090 GPU. The inference time for UCformer on our test set (219,000 data points) is approximately 1.4 seconds, with a model size of about 9.35 million parameters. In comparison, Informer requires about 3.1 seconds for inference and has 11.38 million parameters, while LSTNet is more lightweight with 111.13 thousand parameters and an inference time of about 2.3 seconds. The inference efficiency (covering 5-year simulations for 6 cities) of the current model meets the requirements for operational urban climate applications.

These results indicate that, compared to Informer (a transformer-based model), our model has fewer parameters and a shorter inference time. Relative to a smaller LSTNet, which utilizes a CNN+RNN architecture, UCformer also demonstrates an advantage in inference efficiency.

Dear Reviewer PhTs,

Thank you once again for your thorough review and insightful suggestions. Your feedback has been invaluable in guiding the refinement and improvement of our work.

In response to your comments, we have provided a detailed explanation of why previous physics-informed ML models are not suitable for inclusion as baselines in this work. Additionally, we have conducted a significant new experiment using the “leave-one-out” strategy to evaluate the generalization capability of UCformer, particularly in cities with markedly different urban morphology or climate regimes. We have also added a discussion comparing the efficiency of our model with other ML-based climate models.

We are actively participating in the Author-Reviewer Discussion phase and are happy to provide any further clarification as needed.

Best regards,

The Authors of Submission 2584