Learning Urban Climate Dynamics via Physics-Guided Urban Surface–Atmosphere Interactions
Authors: Jiyang Xia
Fenghua Ling
Zhenhui Jessie Li
Junjie Yu
Hongliang Zhang
David Topping
LEI BAI
Zhonghua Zheng
Venue: NeurIPS 2025 poster ()
Keywords: urban climate; climate emulation; emulator; hybrid model; physics-AI
Primary area: machine_learning_for_sciences
TL;DR: We propose a hybrid physics-AI model incorporating urban surface energy processes and physical priors for improved local urban climate emulation.

Abstract: Urban warming differs markedly from regional background trends, highlighting the unique behavior of urban climates and the challenges they present. Accurately predicting local urban climate necessitates modeling the interactions between urban surfaces and atmospheric forcing. Although off-the-shelf machine learning (ML) algorithms offer considerable accuracy for climate prediction, they often function as black boxes, learning data mappings rather than capturing physical evolution. As a result, they struggle to capture key land-atmosphere interactions and may produce physically inconsistent predictions. To address these limitations, we propose UCformer, a novel multi-task, physics-guided Transformer architecture designed to emulate nonlinear urban climate processes. UCformer jointly estimates 2-m air temperature $\(T\)$, specific humidity $\(q\)$, and dew point temperature $\(t\)$ in urban areas, while embedding domain and physical priors into its learning structure. Experimental results demonstrate that incorporating domain and physical knowledge leads to significant improvements in emulation accuracy and generalizability under future urban climate scenarios. Further analysis reveals that learning shared correlations across cities enables the model to capture transferable urban surface–atmosphere interaction patterns, resulting in improved accuracy in urban climate emulation. Finally, UCformer shows strong potential to fit real-world data: when fine-tuned with limited observational data, it achieves competitive performance in estimating urban heat fluxes compared to a physics-based model.

Learning Urban Climate Dynamics via Physics-Guided Urban Surface-Atmosphere Interactions
Jiyang X,a Fenghua Ling²
Zhenhui Jessie Li Junjie Yu Lei Bai Zhonghua Zheng!
Hongliang Zhang*
David O. Topping'
The University Manchester' 2 Shanghai AI Laboratory
3 Yunqi Academy of Engineering 4 Fudan University
[jiyang. xia, junjie. yu, david. topping, zhonghua.zher 2heng)Gmanchester ac uk (lingfenghua, bailei] org.cn jessielzh@gmail. com zhanghl @fudan. edu.
Abstract
Urban warming differs markedly from regional background trends, highlighting the unique behavior of urban climates and the challenges they present. Accurately predicting local urban climate necessitates modeling the interactions between urban surfaces and atmospheric forcing. Although aff-the-shelf machine learning (ML) algorithms offer considerable accuracy for climate prediction, they often function as black boxes, learning data mappings rather than capturing physical evolution. a result, they struggle capture key aand-atmosphere interactions and may pro- duce physically inconsistent predictions. To address these limitations, we propose UCformer, novel multi-task, physics-guided Transformer architecture designed to emulate nonlinear urban climate processes. UCformer jointly estimates 2-m air temperature (7)) specific humidity (q), and dew point temperature (t) in urban areas, while embedding domain and physical priors into its learning structure. Experimen- results demonstrate that incorporating domain and physical knowledge leads to significant improvements in emulation accuracy and generalizability under future urban climate scenarios. Further analysis reveals that learning shared correlations across cities enables the model to capture transferable urban surface prrface-atmospherr interaction patterns, resulting in improved accuracy in urban climate emulation. Finally, UCformer shows strong potential to fit real-world data: when fine-tuned with limited observational data, it achieves competitive performance estimating urban heat fluxes compared physies-based model.
Introduction
Occupying only ~3% of the Earth's land surface 27 urban areas concentrate more than 50% of the global population [30]. emit -70% of total greenhouse gases [I], and represent the primary settings where humans experience the impacts of climate change [46]. This disproportion between the climatic importance of cities and their limited representation in global land cover highlights the pressing need to understand and predict urban climate. Nevertheless, urban climates remain largely underrepresented in machine learning (MI.)-based climate models 77 12 23 A primary reason is that urban areas constitute only -8% of grid cells in coarse-resolution global climate models (0.9² x 1.25"), leading their marginalization in most ML-based approaches. Moreover, urban climate modeling poses unique challenges that are not captured by these approaches.
"hii work was done during his internship at Shanghai Artificial Intelligence Laboratory. 'The code and datasets of this work are available at https://gilub..oo//nneeeeee UCformer.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Urban climate modeling is particularly challenging due to the heterogeneous nature of urban surfaces. Urban environments feature complex structures such street canyon morphology, varied surface ther- mal and radiative properties, and irregular land use configurations [[]]. Such diversity significantly affects local energy exchanges and atmospheric coupling (25). These complexities remain difficult to capture with existing ML--hased climate models. Despite advances in spatial resolution, most models rely on purely data-driven mappings and lack representation underlying physical processes
41 44 These limitations bring two key learning challenges for ML-based urban climate models: (1) learning is often inefficient due to the complexity and variability of urban environment, and (2) limited physical interpretability hinders their generalization to different urban climate scenarios.
physics- guided modeling approach, particularly one that learns physics- based models, appears to be a compelling solution to these challenges. The physics- physics-based models enable the physically interpretable representation of urban climate processes [9
32 5 38, which can guide the learning is crucial
process in MI. approaches. Encoding the interaction between urban to capture the challenge posed by the complexity of urban environment (Fig. []. Moreover, these interactions drive the evolution of surface energy fluxes, which are further modulated within the urban canyon and collectively underpin the surface energy balance, providing physical foundation for predicting urban climate variables.
Here, we propose UCformer, a physics-guided deep learning archi- tecture tailored for local urban cli- mate modeling. UCformer incorpo- rates physical and climatic knowledge through two carefully designed com- ponents: (1) a domain-specific en- coder that dynamically encodes urban surface-atmosphere processes, captur- ing the modulation of atmospheric forcing by surface features and em- bedding surface fluxes latent vari- ables; (2) a seyssics-guidee decoder that embeds inductive biases derived from physical laws, allowing the learn- ing process capture variable inter- dependence as an emergent property rather than as isolated prediction tar- gets. Extensive experiments show that UCformer achieves superior perfor- mance in multi-tast task urban climate es- timation, with 12.7% relative im- provement in urban temperature pre- diction accuracy and a 13.4% gain in generalization to future urban climate dynamics compared to the best baseline. Furthermore, learning a neural model based on simulated data cuts city-scale climate simulation (55 years) time from 12 hours to 17 seconds, making large-scale scenario analysis practical and efficient (discussed in Appendix [. pp. Additionally, despite being trained on phy aicssbbbaaeed simulations, UCformer shows strong potential to fit real-world data. While our solution is motivated by urban climate modeling, the underlying design principles are grounded in general surface- attocceemm interaction mechanisms, which can be shared across other Earth science domains.
X;: atmospheric forcing
atmosphere
urban surface features
F: surface fluxes
X,
T.
interacts Xg driving
X5
w
root
urban canyon
wall
road
X,
interaction among F
predicted urban climate variables
pervious road
impervious road
Urban surface-atmosphert interactions in urban climate system. Atmospheric forcing is modulated by urban surface characteristics, and urban climate states are diag- nosed through the surface energy balance. We encode X and X, as inputs, model fluxes F as latent representations, and estimate T, and f as outputs.
Figure 1:
We summarize our contributions and findings as follows:
We introduce a comprehensive ML-ready dataset tailored for urban climate modeling, filling critical gap in existing climate benchmarks. The dataset captures detailed urban surface characteristics, atmospheric forcing. and physics- based outputs, and is designed to facilitate MI. research the unique challenges posed by urban climate systems.
We propose physics-guided modeling approach that integrates domain and physical knowl- edge into the neural network to represent urban aurface-atmosphert processes, enabling excellent accuracy of local urban climate estimations.

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With its domain- specific encoder and physics physics-guided guided decoder, our model effectively gen- eralizes future urban climate dynamics. excels at multi-task estimations, and extends well to sparse real-world data. This physics- gusded design presents transferable concept for broader Earth system sciences, demonstrating strong potential for tackling complex multi-task learning and modeling sparse data.
2
Related work
ML for urban climate modeling. Urban climate modeling simulates interactions between atmo- spheric forcing and urban surfaces characterized by long-term averages and distributions. Multi- model ensemble climate projections that incorporate urban surface energy processes are crucial for dimmat-innformed urban development [22]. However, such projections are universally unavailable and challenging to implement [22]. Zhao et al. 46 first fills this gap by developing a reduced-order regression model to generate local urban climate projections under different scenarios, facilitating the comprehension of the impacts of climate change on local urban climates. Zheng et al. 47] expands the work of Zhao et al. [46] by introducing non-linear regression models to map the local response of urban climate to atmospheric forcing. Meyer et al. [22 develops an urban neural network to estimate radiation and fluxes reflected to the atmosphere following the effects of urban parameterization, en- abling it to be coupled to numerical models and thereby reducing computational demands. However, these models primarily focus on learning data mappings, while often overlooking the underlying physical evolution, such as the influence of urban surface characteristics surface energy processes (discussed in Appendix (A.)), as well as the physical relationships between urban climate variables. Moreover, the generalizability of these methods remains insufficiently explored, particularly in the context of urban climate dynamics over long time spans.
Physics-guided ML. Concerns regarding the generalizability and interpretability of ML have led to the development of new machine learning strategies in some scientific domains, known as physics- For instance, Read et al. 29 introduced a physics- guided loss (a simplified energy budget formulation) that penalizes MI predictions violating energy conservation, enabling their long short-term memory model to better generalize to unseen scenarios. Some studies, however, have shown that physical loss function does not consistently improve model generalization [44 6) In contrast, physics-guides architecture embeds physical meaning into neural network neurons or incorporates domain-speciff knowledge into model structures to achieve task- specific designs 9 3) Drawing the relationship between predictands, Zanetta et al. 44] changed the neural network architecture by adding an equation layer to derive two additional predictands which ensure the predictands obey the physical laws and thus enhance the model interpretability. Such strategies enhance model interpretability and generalizability, and hold the potential to advance modeling of the interactions between urban environments and atmospheric processes. Building on the inspiration provided by these methods, our work explores a physics-guide MI. model tailored to urban climates, refining the understanding of urban climate projection.
guided MI. or physics-infon -nnfore- MI. 18 41 39
3 Methods
3.1 Problem formulation
The urban climate modeling problem be summarized as mapping from set of atmospheric forcing Xy set of urban climate predictands i given the local urban surfaces characteristies (X,):
Fo (a) = P(X,XX.).
(1)
where represents the parameters of the model and the atmospheric forcing X, E TTXCNN consists C' variates modeled at N different cities. T denotes an interdependency time sequence, where the simulation of urban climate is influenced by previous timesteps. Currently, this interdependency is omitted at the daily scale (20 46). To fill the gap in fine-grained temporal urban climate projections, this work extends the timestep to every 3 hour, making essential to capture dependencies between timesteps. For more details, see Appendix A.3
3

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3.2 UCformer overview
Drawing inspiration from the urban surface- attooshhrr interaction in some physics- models 21 [5], we strategically design this variant Transformer for urban climate emulation, named UCformer. As shown in Fig. 2 instead of stacking and embedding all features together. we embed atmospheric forcings X5 and urban surface parameters X, into two independent embedding blocks (each forming an independent sequence), respectively. This embedding strategy accounts for the inherent differences between the two types of data, while enabling seamless integration with the encoder component. The encoder of our model functions as urban climate process adaptive operators described in Sec. 3.3 which consists of two blocks. The first encoder block learns the modulation of atmospheric forcing by urban surfaces, reflecting their role in shaping urban climate dynamics. The subsequent blocks focus on learning and simulating the flux iterative calculation processes within the urban canyon. Urban 2-m air temperature (7), specific humidity (q), and dew point temperature (t) subsequently diagnosed via the physics-guided decoder, which embeds inductive biases derived from governing physical laws that characterize the intrinsic relationships among the target variables.
Embedding
Spmaln-Specific
Akrrssppii Fording Xy
Sudbnuu
Brrmiig peed
Ertbedaing Block
Kr
Morm
Vr
Urbon Surface Charockristes
V
X;
SelSattenion
Embedddnng
Uber Amooshhrr Interacion Blook
Surtace Planes
Blook
Inter actionn Block
Morro
Add
-er
Qy
K7
mrman oe polka
4
Worm
Q
V₂
Vector
Ieter medilé
Add Poon
K₁
Cress-attenion
Output
ww-yhhic--Guiiiee Guiiie Decoder
Figure 2: UCformer architecture. A: feature embedding strategy. Atmospheric foreing and urban surface features are separately embedded as query, key, and value matrices. B: The structure of the domain-specifts encoder, which contains the urban surfacc-atmosphere interaction block and flux iteration block. C: The structure of the thysics-guided decoder. This module enables the model to diagnose target variables by aggregating information from its physically coupled counterparts. D: Predictands are processed by three separate fully connected layers. A component-leve mapping bridging the physics-based model and machine learning modules is provided in Appendix A.4 A.4
3.3 Domain-specific encoder with urban surface-attooshhre interaction operators
The atmospheric forcing X, is modulated by the urban surface characteristics X, the sub-grid scale in physics-based models. Specifically, the interaction between X and X can be broadly categorized as follows: firstly, the individual urban surfaces absorb solar and longwave radiation, and there is radiatively interaction between these surfaces. Fluxes from each urban surface interact with each other in the urban canyon (Fig. D]. Then, the temperature (2), specific humidity (q), dew point temperature (t), and other variables output to the atmosphere are predicted. Consequently, characterize the above process by the following simplified equation:
i= EH,
(2)
sum ()
(3)
5= Σ [ WmoorSooff.. + ) Suc.A) wwhee Stoofue.A = o(X,,
(4)

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É= - not Looot yLy L) (1 (oo Wooor) f 4), where Lroofue 1- xx),
(5)
Eq. defines the prediction of set of urban climate variables (f), based on the sensible flux (H),
latent flux (F), and ground flux (G) in the urban canyon [25]. Eq. denotes that the sum of fluxes must be balanced by the net solar radiation (5) and net longwave radiation (L) absorbed by the urban canyon [25]. Eq. and Eq. 19 the numerical solutions of radiation in the urban canyon [2),
where the net solar radiation including visible (A) direct and diffusion radiation of roof (S A and
other surfaces (S
Features X and X, are important to derive the radiation and fluxes required in the urban canyon energy budget balance. We model the processes (Eq. [ and Eq. 5 through cross-attentin operator to represent the interaction between X including solar radiation (S, () and longwave radiation (Teg 4), and x,, which encompasses properties such as emissivity and albedo, formulated as:
O₁K7 V ddz
f = =ostmmar
(6)
where Q, is derived from Xy. while the key (K,) and value (V, matrices are obtained from X.. This assignment reflects the physical principle that atmospheric forcing, such radiation and wind fields, dynamically responds to heterogeneous urban surfaces, which modulate energy and fluxes. Then the output (F) of the cross-attention operator goes through serval self-attention operators representing the iterative fluxes interactions (Eq. [ and Eq 3)
QFKT VE.
i = sof toftmax
(7)
Vd
where & E T is regarded the latent representative of urban climate predictands with dimensionality D.
3.4 Physics-guided decoder incorporating soft physical constraints
The physics-guided decoder enables the model to infer each target variable not in isolation, but by leveraging the latent representations of its physically coupled counterparts, imposing soft form of physical constraint. The variables of interest in this work (7, q. I) are physically coupled through set of physical equations, including the empirical Magnus- Tetens formula:
b (T, RH)
T
RH
a (T, RH) where (T, b+ In
(8)
100
RH 100 = q QP 100, where e, = c exp
a
0.622e,
b T
where a, 6 and are empirical coefficients, and RH represents the relative humidity. Eq. 9 is derived from the ideal gas law for dry air and water vapor. The saturation water vapor pressure (c.) in Eq. follows the identical structure the August-Rocher Recee-Roooheeaaeee constraint among T, q and can be described by an implicit equation F(T, g. t, P) = 0. However, the absence of pressure (P) prevents explicit incorporation of the physical equation into the model architecture or loss function. We propose a more flexible, representation-leve approach to encode physical relationships. Rather than treating each variable as modeling i = W + b. Our approach encourages the model to learn physical dependencies as emergent properties. Specifically, we reformulate the prediction of as:
equation [44]. Thus, the physical
independent prediction target, such
W (Z Zg. 2T) +
(10)
where g(2,, Zg. 2r) denotes a latent functional mapping that captures the interaction among the variables through cross-atted cross-attention mechanism. This enables the model to adaptively aggregate information from the latent representations of T and when predicting I, formulated as:
g( 2r)
a( Keoncal(s, V Veoneat(z,
(11)
According to Eq. 10 and Eq. the thyyics-guided decoder can be described as: y1 W A, A,
(12)
where A, is the cross-attention score of variates j and & with respect to target variate i.
5

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4 Experiments
To evaluate our models, we conduct experiments both simulation and observational datasets and try to answer the following questions:
How does the model perform on the local urban climate emulation task and generalize beyond training data, particularly in emulating future climate dynamics and transferring the model to previous unseen cities?
As a dhysics-guides ML model, what are the respective roles of the domain-specific encoder and the prysscs-guided decoder in capturing urban climate processes?
Does learning shared representations of urban surface- aatfocheee interactions across cities lead to better performance than city-specific or locally focused models?
What is the potential of the chysics-guided ML model, developed using simulation data, to extend to real-world settings?
4.1 Dataset and setup
Simulation data. The simulation datasets derived from the physics- based Community Land Model Urban (CLMU) [25), offering city-scale urban climate simulations for six cities (see Ap- pendix B.I.. These datasets explicitly incorporate urban surface-atmosplin
processes and comprise comprehensive atmospheric forcings and detailed urban surface characteristics. The training set consists of data spanning from 2020 to 2044, with 8 time steps per day, totaling 1, 1,095,000 data points. The validation and test sets comprise data from 2045-2044 and 2050-2055, each containing 219,000 data points. We further use the data from 2070 2074 assess the generalizability of our model (The discrepancy in data distribution is detailed in Appendix A..5). Detailed descriptions of the dataset implementation and the variables used for model development are provided in Appendix B. and
B.2
Observational data. The observational data are sourced from Lipson et al. [9]] including observed atmospheric forcing and features surrounding the site. In this work, atmospheric forcing and heat flux data from the "UK-King's 's College" site in London its potential to transition from physics-based simulation estimates to real-world data emulations. Specifically, the dataset of UK-King's College contains observational data from 201 2012-04-04 00:00:00 to 2013-12-31 23:30:00 with a time step of 30 minutes. After the clean process (drop samples with "NaN" value for target labels), this dataset processes 19,725 data points.
used fine-tune UCformer, investigating
Training objectives. Deterministic urban climate emulation models can be trained by minimizing the MSE for rolled-out estimates. The model in this work is trained to minimize the aggregated MSE loss for multi-task estimates: L = Lr + Ly + L, The objective is to optimize the model parameters 8 by minimizing the total loss l" arg ming L. The model is optimized using the Adam optimizer: 9 + 0 - v,, and the learning rate (77) is adjusted dynamically using a scheduler: < 0.97.
Implementation details. We implemented the model using PyTorch and finalized its configuration via hyperparameter tuning with Optuna 2 35 GPU hours (NVIDIA 4090). The model was trained using the Adam optimizer and Gaussian Error Linear Unit (GELU) activation function, with a batch size 64, a learning rate set to le-5, a training epoch of 50, and a dropout rate of 0.1. Appendix B.3 lists the detailed configuration of models.
4.2 Baselines
Since there are no widely adopted models specifically designed for urban climate emulation, we select baselines based on prior work related to urban climate modeling [47] 46] and urban representation [2]. Although the task investigated in this work does not fall strictly under the category of time series forecasting problem where future values are predicted from labeled historical sequences [36 [7]. our task involves input variables with inherent temporal structures, particularly atmospheric forcing. In this context, time-series feature representation and modeling become shared concern between our task and standard forecasting problems 14
Consequently, representative time series forecasting models are included in the baseline comparisons to enable more comprehensive assess- ment of the model's 's ability to leverage temporal information embedded in the input. Furthermore, physics- guided ML models are excluded from the bascline set due to the absence of methods tailored
48 40

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to urban climate and the highly data- and task-specific nature of existing approaches, which typically rely on embedding explicit physical or partial differential equations 22 44 applicable in our setting.
that are not readily
Overall, we compare UCformer against several representative baselines: Multi-layer Perceptron following the top-pert pep-erffrmmnng architecture in the ClimSim benchmark [43 (MLP_ CBBP_ an automated machine learning method (AutoML), vanilla Transformer, and two time-series forecasting models adapted to our Tramework-Ilforee -nformer_mmolffied estimators are constructed in a task-specific manner, requiring separate training for each prediction
modified [48] and LSTNet LSTNee_modified modified [4]. Notably, AutoML
target.
4.3 Metrics
Two metrics screened to evaluate the overall performance of models: the root mean squared error (RMSE) and the Mean Emulation Skill Score (MESS) [44. Here we defined MESS as:
MESS = 1 MAE
(13)
MAE,T
where MAE. represents the mean absolute error (MAE) of urban climate emulators, while MAE refers to the MAE between the simulated urban climate and its corresponding atmospheric forcing. The MESS presented here aims to denote the emulation skill different models as MAE can be regarded as lower-bound expectation of an emulator. We might expect that models will have value of MESS between and (higher values are better). It also allows an emulator to score a much lower value than 0 if its emulation is much worse than simply using its atmospheric counterpart. For multi-task evaluation, we report the aggregated MESS (MESS.gg) across urban air temperature (T), specific humidity (g) and dew point temperature (t). Statistical significance is assessed via the paired Wilcoxon signed-rank test, as detailed Appendix(A.6
4.4 Main results
Skillful urban climate multi-task emulations by UCformer. We report the performance of models on the dataset of 2050-2054 Tab. [ UCformer consistently outperforms other models in terms of RMSE and MESS for both single-variable and integrated multi-task emulations. In addition, MLP_ MLP_CSB ranks second overall, achieving a multi-task emulation score (MESS) 1. 1,9088, and outperforming both modified sequence forecasting models, LSTNNetmodifer and informer_modiffed. This result indicates that simply modifying the data interface of time-series forecasting models to fit our task may not resolve the underlying mismatch in problem formulation. Such adaptation may impose assumptions about temporal dependencies that are not aligned with the objectives of urban climate emulation, and risk mischaracterizing the nature of the task. The performance gap may also be exacerbated by the extent to which these models are tailored for sequence forecasting. For example, although Informer builds complexity and parameter count than LSTNet (which combines CNN and RNN modules), the lighter LSTNet_modified achieves better results in our task.
Transformer-basee architecture with higher model
Table 1: Performance metrics for multivariate estimation. Bold values indicate the best performance.
2050-2054
method
MESS f
RMSE(K)]
MESS
RMSE(g/kg)
MESS
RMSE(K)]
MESS
MLP CSC
1,9088
0.3846
0.8128
0,2078
0,5524
0.1945
0.5436
AutoMI.
1.8584
0.3928
0.8088
0,2183
0.5216
0.1993
0.5280
Transformer
1.7173
0.3737
0.8136
0,2444
0.4631
0.2454
0.4406
LSTNet_modified
1.9065
0.3528
0.8286
0.2238
0.5075
0.1910
0.5704
Informer modified
1.7700
0.3567
0.8268
0.2325
0.4775
0.2003
0.4657
UCformer 2.0468
0.3264
0.8405
0.1851
0.6157
0.1777
0.5906
Generalizing future urban climate dynamics. The generalizability of ML models a widely concerned issue, and physics-guide guided models have been demonstrated to have physically reliable prediction results while being expected to have better generalization
(39]. We explored the tem- poral generalizability of our model using the dataset of 2070-2074 (out-of-sample) and report the performance in Tab. [2] The evaluation results on the testing dataset (Tab. T and the generalization
dataset (Tab. 2 highlight the strong temporal generalization ability of the UCformer. UCformer
7

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consistently achieves the lowest RMSE and highest MESS across all three variables in both datasets, outperforming all other models. Notably, the generalization dataset (2070-2074), the RMSE values of UCformer for all three variables are lower than most of the other models on the testing dataset (2050-2054) for the corresponding variables. Moreover, the probability density function (PDF) comparison in 2070-2074 is presented in Appendix A.7
Overall, UCformer consistently demonstrates a strong skill to approximate all predictands distribu- tions across time scale. In contrast, other baselines deliver notable deviations, On this basis, our results highlight the exceptional ability of UCformer generalize across time scales, showcasing its robustness and adaptability to future scenarios.
Table 2: Temporal generalization performance for multi-variate estimations for future scenarios.
2070-2074
T
method
MESS
RMSE(K]]
MESS
RMSEgg/kg)
MESST
RMSE(K)
MESS
MLP CSB
1,8809
0,4070
0.8031
0.2251
0.5394
0.1994
0.5384
AutoML
1.7995
0.4275
0.7941
0.2517
0.4947
0.2118
0.5108
Transformer
1.6746
0.3910
0.8032
0,2765
0.4348
0.2414
0.4366
LSTNet modiifed
1.8944
0.3703
0.8211
0,2356
0.5450
0,2023
0.5283
Informer modified
1.6585
0.3877
0.7803
0,2194
0.4202
0,2007
0,4586
UCformer 1.9451
0,3385
0.8358
0,2121
0.5671
0.1960
0.5422
Transferability to unseen cities. Spatial generalization remains central concern in the climate science community, given its importance for real-world applicability but also its inherent difficulty for most machine learning models. In this context, we conduct additional "leave-one-city-on experiments to evaluate the spatial generalization capabilities of UCformer, with results summarized in Tab.
The results indicate that UCformer demonstrates a notable degree of spatial generalization, although its performance exhibits variation across cities, potentially driven by differences in urban morphology and local climate conditions. For example, the temperature (I") estimation error increases from approximately 0.02 K in Singapore to 0.07 K in Rome, while the RMSE for dew point temperature (t) rises from 0.01 in Rome to 0.03 K London. These findings suggest that model spatial generalization may be sensitive to specific urban contexts climatic conditions, highlighting the need for further investigation into the underlying factors affecting spatial generalization.
Table 3: Performance metries UCformer "leave-one-city-our" experiments (values eepeeiittmyuuu"xxxxiemememt denote results under the original setting).
parentheses
2050-2054 Held-out city
T
MESS
RMSH(K),
MESST
RMSH(g/kg)
MESST
RMSE(K)
MESS
1.6629
0,2990
0.8127
0.1344
0.4357
0.1977
0.4144
London
(1.9007)
(0.2419)
(0.8541)
(0.1117)
(0.5171)
(0.1655)
(0.5295)
1.6989
0.4167
0.7699
0.1904
0.5063
0.2507
0.4225
New York City
(1.8901)
(0.3515)
(0,8030)
(0.1645)
(0.5741)
(0.2212)
(0.5130)
1.9369
0.4806
0.8349
0.2886
0.5555
0,2529
0.5465
Shanghai
(2.0024)
(0.4437)
(0.8486)
(0.2611)
(0.5986)
(0,2426)
(0.5552)
2.2840
0,2668
0,8581
0.2798
0.7060
0.1279
0.7198
Singapore
(2.4586)
(0,2412)
(0.8727)
(0.2130)
(0.7975)
(0.1036)
(0.7884)
1.8953
0.3965
0.8179
0,2587
0.5326
0.1649
0.5448
Sao Paulo
(2.1241)
(0.3561)
(0.8363)
(0.2074)
(0.6618)
(0.1435)
(0.6260)
1.8163
0.3972
0.7843
0.1571
0.5197
0.1975
0,5123
Rome
(1.9088)
(0.3242)
(0.8282)
(0.1477)
(0.5450)
(0.1896)
(0.5316)
4.5
Ablation studies
Domain and physics-guided neural operators are crucial for urban climate estimations. To evaluate the contribution of the two proposed components in urban climate emulation, we conducted ablation by replacing the domain-specific encoder and the physics guided decoder with vanilla encoder and decoder, respectively. Tab, highhights the impact of these neural operators and illustrates how UCformer outperforms the vanilla Transformer in multi-task learning. Instead of merely learning a direct mapping from Xy and X, to target variables, the sppeifi encoder (DE) models the evolution of urban climate physical processes. This approach enhances the representation of
thysics-guided

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urban surface-atmospile atmosphere interaction and facilitates local urban climate emulations. Additionally, the poysscs--uided decoder (PD) further boosts emulation accuracy.
Table 4: Ablation study regarding the effectiveness of the domain encoder (DE) and physic- guided decoder (PD).
2050-2054
Module
4
method
DE
PD
gF
RMSF
MESST
RMSE (g/kgN)
MESST
RMSE (K).,
MESST
Transformer
X
1.7173
0.3737
0.8136
0.2444
0.4631
0.2454
0,4406
/
1.9673
0.3389
0,8366
0.2022
0.5713
0.1879
0,3594
UCformer
x
/
1.9013
0.3176
0.8417
0.2181
0.5441
0.1964
0.5156
/
2.0468
0.3264
0.8405
0.1851
0.6157
0.1777
0.5906
Learning shared representations of urban climate processes improves emulation performance. Urban climates exhibit distinct patterns tied to their geographic context, but may share learnable regularities across cities. UCformer, our proposed model, is by default trained using a multi-city strategy to capture shared surface crrfauce-atmospherr interaction patterns. To assess the contribution of this shared correlation learning, we introduced a single-city training setting (denoted UCformer_singlee where separate model is trained independently for each city using only its local data. This ablation isolates the effect of inter-city representation sharing on emulation performance.
As shown in Tab. [ training across multiple cities significantly improves overall urban climate modeling performance. Per-city results are provided in the Appendix AA.8] where five cities show notable gains. However, performance declines in Singapore suggest that city-specific training may be preferable for cities with highly uniform climatic conditions. In particular, Singapore exhibits significantly smaller temperature fluctuations throughout the year compared to the other cities, which may limit the benefits of shared representation learning. These results indicate that while shared modeling is generally effective, its utility may vary depending on the climatic distinctiveness of cities.
Table Ablation study on the impact of shared correlation learning in urban climate emulation. The results are first computed on each city individually and then averaged.
2050 2054
Number of Cities
/
method
MESS
RMSE (KX)
MESSI
RMSE (g/kg))
MESST
RMSE (K))
MESS1
UCformer single
=
1.6126
0,3941
0.8020
0.2294
0.4368
0.2391
0.1738
UCformer
N=
2.0468
0,3264
0,8405
0.1851
0.6157
0,1777
0.5906
4.6
The potential from simulation to real world
To address the challenge posed by the scarcity of climatic observations in urban areas, we ex- plored the potential of UCformer to fit real-world data. Since the flux tower observations do not include temperature, humidity, or dew point data, we fine-tuned UCformer on partial real- world data to enable prediction of new predictands (sensible heat flux Qn and latent heat flux Qie) (detailed in Appendix B.4]. In Tab. 6 we investigated the importance of data scarcity on UCformer fine-tuning by providing proportional data in chronological order (with the remain- ing data serving as the testing set). Note that we used the metrics MAE and correlation coeffi- cient (r) for evaluation in this section to align with the reference 19.. Overall, the performance of UCformer in emulating Qie and Qn improves as the amount of fine-tuning data increases.
We conducted a comparative experi- ment to evaluate how well UCformer can fit real-world data under limited observational conditions, comparing it against the physics-based model CLMU and baseline trained solely on observations. First, UCformer was fine-tuned using 20% of the avail- 50%
Table 6: The importance of data scarcity on model perfor- mance for Qie and Qn estimations.
Data percent
Qie
MAE (W/
rf
MAE (W/m?)
20%
15.2
0.4135
24.9
0.8726
30%
13.7
0.4268
30.2
0.8396
13.7
0.4776
27.1
0.8979
able observational data to estimate
Qie and Qn- Using the same subset, we trained UCformer_ob, baseline model with the same architecture and hyperparameters but without any simulation-based training. Additionally, CLMU was run over the test period, driven by real-world atmospheric forcing. to provide chysics-basee reference.

---

Fig. 3 presents the results of the three experiments. UCformer (Fig. (a), (d)) significantly outper- forms the physics-based model CLMU (Fig. (b). (e)) in estimating Qie and Qn. achieving higher and lower MAE. Furthermore, the observed-data-
model UCformer_ obb (Fig. ( (f)) performs
noticeably worse than UCformer. However, it is observed that neither physics-based nor data-driven models are capable of appropriately estimating negative values of urban heat flux. Despite these challenges, UCformer has demonstrated strong potential to extend to real-world data in addressing the challenge of observational data scarcity.
Simulation plus observed data
Simulation only
Observed data only
200 (a)
r=0.42
250 (b)
0=
36
200
(c)
[= 1..44
Observed [W/mm²
MAE-15.16
MAE-16.88
MAE - 7:95 17:95
150
150
150
100
50
50-
50-
0-
0-
-50
200
-50
150
250
0
100
200
UCformer estimated Qle
CLMU simulated Qle
UCformer, obb estimated Qle
(d)
D-0.7
(e)
[
0.80
(f)
r-0, r=0.79
Observed Qh [W/m²]
400
MAE
24.93
400
MAE=51.07
400
300
300
300
200
100
100
100
0
200
200
400
UCformer estimated Qh
CLMU simulated Qh
UCformer_oe _o estimated Qh
0.0002 0.0004
0.0006
0.0008 Kernel Density
0.0010
0.0012
0.0014
Figure 3: Comparison of latent Qie and sensible Qn heat flux estimations from UCformer (left column), CLMU (middle column), and UCformer obb (right column). UCformer fine-tuned with 20% observed data; CLMU driven by real-world forcing; UCformer_oo -oformer_obbbt trained only on limited observations. The rainbow color represents the kernel density.
5 Conclusion
We introduce UCformer, a novel approach that integrates urban climatic and physical knowledge to model the interaction between atmospheric forcing and urban surfaces in urban climate systems. Our model outperforms relevant baselines, achieving lower RMSE and demonstrating superior emulation skills, while also exhibiting enhanced generalization to future urban climate dynamics. For the scareity of real-world data problems, our model showcases strong potential for extension to real- world settings, outperforming a numerical model and a baseline model trained only on observational data in this regard. This work bridges ML techniques with the pressing needs urban climatology, but it is constrained by limited data availability. Long-term atmospheric forcing and simulated urban climate data are crucial yet scarce, hindering the evaluation of UCformer under diverse climate change scenarios. Additionally, although the models' temporal and spatial generalization has been evaluated, further work is needed to assess their performance across different spatial scales. This represents another limitation of the present study. While ML continues show promise in climate projections, local urban climate modeling remains critically understudied. We hope this work stimulates the MI. community to pursue novel MI. approaches tailored to the unique challenges of heterogeneous urban environments.
10

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Acknowledgements
Zhonghua Zheng appreciates the support provided by the academic start-up funds from the Department of Earth and Environmental Sciences at The University of Manchester.
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Appendix
A Addtional results and figures
A.1 Model efficiency
In addition to U'former, this work evaluated two representative sequence-to-sequence models, that is, LSTNet and Informer, which can be adapted urban climate estimation.
All models were tested with batch size of 128 on an NVIDIA 5090 GPU, The inference time for UCformer our test set (219,000 data points) is approximately 1.4 seconds, with 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 transformer- based model), our model has fewer parameters and shorter inference time. Relative smaller LSTNet, which utilizes CNN+RNN architecture, UCformer also demonstrates an advantage in inference efficiency.
A.2 Impact urban representation on local urban climate emulation
Based on the work of Zheng al. 477. Zhao al. [6), we exclude urban surface features from the mapping of atmospheric forcing to urban climate to show the impact of urban representation on local urban climate emulations. The results in Fig. -re based on the vanilla Transformer, the benchmark models used in this work. In this comparison experiment, we maintain consistent hyperparameters, training data, and test data, except for the excluded urban surface features.
of
0.60
0.34
RUSS 140
0.30
1.0
0.26
0.40
2045
2046
2047 (2)
2048
2049
2045
2046
2047
2048
2049
2045
2046
2047
2048
2049
(B)
0.7
0.6
1.0
RMSSE
0.5
0.8
0.3
2045
2046
2047
2048
2049
2045
2046
2047 (e)
2048
2049
2045 2046
2047
2048
2049
(d)
Figure 4: Ablation study regarding the urban representation in urban climate modeling. (a) to (f) denote the emulations of temperature for six citics. Orange dots indicate estimation results with the urban representation included, and blue dots indicate estimation results in the absence of the urban representation.
A.3 Impact of the interdependency of timesteps on fine-grained temporal scale
We use the same dataset as well as hyperparameters to reveal the impact of time series on urban climate emulations. The results based on our model are presented Fig. [ when interdependencies between time steps are ignored on fine-grained time scales, the emulated representation of the local urban climate is compromised.
21

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0.450
0.35
0.425
RMSE (K)
0.400
0.7
0.375
0.25
0.350
2045
2045
2047
2048
2049
2045
2046
2047 (0)
2048
2049
2045
2045
2047
2048
2049
(0)
0.55
0.375
RMSE (K)
0.50
0.350
0.325
0.30
0.45
0,300
0.25
0.275
7047
2047 (e)
2047
(d)
(1)
Figure 5: Ablation study regarding the interdependency of timesteps in urban climate modeling. (a) to (f) denote the emulations temperature for six cities. Orange points indicate interrelated time series explicitly characterized in the input feature matrix, while blue points represent time series that are not interrelated within the input feature matrix.
A.4 The correspondence between the physics-based model elements and the MI. modules
Table 7 clarifies the mapping between the model components and the elements of the inference scheme.
Table 7: Mapping between physics-based components and machine learning modules.
Model Component
Role
Inference
Input(s)
Output(s)
Scheme encodes atmospheric
forcing embedding
atmospheric forcing features
forcing tokens
layer
forcing characteristics encodes urban surface feature characteristies learns interactions be- tween urban surfaces atmosphere
urban surface embed-
urban surface features
urban surface to- kens
ding layer
surface- atmosphere interac- tion block
urban
forcing query tokens, urban surface key tokens, urban surface value to- kens updated interaction-enennee tokens
interaction- encoded tokens
surface fluxes interac- tion block
learns urhan surface- surface radiatively interaction T (lemperature) estima- tion
intermediate fea- tures tokens
decoder branch
intermediate T query tokens, catenated q and tokens (as keys and values)
esitmated T
decoder branch 2
q (specific humidity) esti- mation
intermediate query tokens, con- catenated T and tokens (as keys and values)
esitmated
decoder branch 3
(dew point temperature) estimation
intermediate query tokens, concate- nated T and q tokens (as keys and values)
esitmated
A.5 The discrepancy of data distribution
Fig. shows the climatic shift in urban atmospheric conditions over a long-term climate change (from 2044 to 2074) under the SSP3-7.0 scenario, resulting in distributional differences across datasets. The first column (from left) represents atmospheric temperature, the second column shows downwelling shortwave radiation, and the third column shows downwelling longwave radiation.
22

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IRIEUOSA 20044)
01-
0.00
1.004
0.00
200
300
310
0.000
9398
0010
0.15 8823 6025
1000
220
300
500
4033%
54,
50030, Pway, Jean
Gecaraite6200-22944
3.000
0.09
0.00
3.000
22231.30
30000 Jank
Figure 6: Differences in the data distribution of key atmospheric forcing variables (Xy) across datasets. The first column (from left) represents atmospheric temperature, the second column shows downwelling shortwave radiation, and the third column shows downwelling longwave radiation.
A.6 Statistical significance metric
The paired Wilcoxon signed-rank test is a non-parametric statistical method 35 and was conducted evaluate the significance of differences between model estimations. Tab. shows the details of Paired Wilcoxon signed-rank tests for model results.
Table 8: The Results of Paired Wilcoxon signed-rank tests. For all models, except for the ablation study (paired test with Transformer results), the results were paired and tested against those of UCformer.
T
q
In-distribution
AutoML
#*
84
Transformer
MLP_ MLP_CSB
#
*
8%
Generalization (Out of Sample)
AutoML Transformer
#*t #il
MLP_CSB
** W*l
Ablation studies
UCformer(DE)
#:
3:
3%
UCformer(PD)
UCformer single
**
8%
UCformer(RA)
#*
UCformer(TH)
#*
3%
UCformer(RA&TH)
Wile
** represents p <0.05 (95% confidence level), indicates <0.10 (90% confidence level), and non-marked values show no significant difference the 90% confidence level.
In the modeling of interactions between urban surfaces and the atmosphere, urban surface parameters often difficult to acquire and update. Therefore, in this section, quantified the impact of different urban surface parameters on UCformer emulation performance to explore the importance of these parameters data-driven urban climate emulation. For this purpose, three different feature datasets, each excluding specific urban surface parameters, were provided to re-train UCformer. In particular, urban surface parameters leveraged in CLMU can divided into three subsets, the morphological parameters (height-to- width ratio, the fraction of roof, impervious road, etc.), radiative parameters (albedo and emissivity of roof, wall and road) and thermal parameters (heat capacity and thermal conductivity of roof, wall and road) [.. As such, shown in Tab. three datascts and
23

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their corresponding models were developed to evaluate the impact of the radiative parameters (RA), the thermal parameters (TH), and the combination of the two parameters, respectively, on UCformer emulation skill.
An insight can be gained in Tab. that 7 estimation is less affected by the lack of urban radiative parameters but more affected by the absence of thermal parameters, which aligns with the sensitivity study based on physics-based simulations [24). Overall, the importance of urban surface parameters varies by variable, underscoring the need to tailor urban surface feature selection to improve the emulation accuracy of multiple climate variables.
Table Ablation study regarding the impact of different urban surface sets (X₂)) on urban climate emulations. RA and TH refer radiative and thermal parameters, respectively.
2050-2054
X
method
RA
TH
MESS
RMSE (K).
MESST
RMSE (kg/kg)
MESST
RMSE
MESSF
X
1.8668
0.3495
0.8252
0.0002
0.5428
0,2046
0.4988
UCformer
1,9473
0.3211
0.8462
0.0002
0.5505
0.1852
0.5507
X
1.9236
0.3463
0,8276
0.0002
0.5389
0.1891
0.5571
V
2,0468
0.3264
0,8405
0.0002
0.6157
0.1777
0.5906
A.7 Generalize performance
The PDF of the models for the three predictands in 2070-2074 are shown in Fig. 7 UCformer demonstrates strong generalization ability approximate all predictands distributions across time scale. However, AutoML, the Transformer model, and MLR consistently deliver notable deviations of three predictands.
0.06
R0F
0.04
0.02
0.00
260
270
260
290
300
310
320
urban air Temperature (K)
60
PDF
20
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
urban specific humidity (kg/kg)
0.10
AutoML MLR.
Transformer
0.06
UCformer
0.04
0.02
0.00
2i0
215
220
225
230
235
2á0
245
urban dew point temperature (K)
Figure 7: Probability distributions of urban 2-m air temperature (a), specific humidity (b), and dew point temperature (c) for the years 2070-2074, GroudTruth denotes the simulation results of CLMU,

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A.8 Per-city results of shared correlation learning in urban climate emulation
Tab. 10 presents the per-city results under two training settings: shared multi-city training and independent city-specific training. The results highlight consistent performance gains from shared modeling most cities, with the exception of Singapore.
Table 10: Per-city RMSE results. Values marked with (o) correspond to city-specific modeling.
2050-2054
T
method
RMSE(K)
RMSE(K)))
RMSF(g/g)
RMSF(g/ggX)
RMSE(K)
RMSE(KX*)
London
0.2419
0.2801
0.1117
0.1358
0.1655
0.2198
New York city
0.3515
0.4990
0.1645
0,2400
0.2212
0.3253
Shanghai
0.4437
0.5123
0.2611
0,3968
0,2426
0.3119
Singapore
0.2412
0.1733
0,2130
0.1860
0.1036
0.0872
Sao Paulo
0.3561
0.4427
0.2074
0.2670
0.1435
0.2018
Rome
0.3242
0.4573
0.1477
0.2211
0.1896
0,2888
B Implementation details
B.1 Simulation implementation and urban canyon scheme
Community Land Model (CLM) is important component of the Community Earth System Model of CLM (CLMU) was developed by Oleson et al. [26] to simulate the urban energy and flux calculation processes. CLMU is driven by the atmospheric forcing data provided by the atmosphere component of CESM or observational data and 33
(CESM) [10]. The urban sepresetation/paaanntttzaattl
34). CLMU adopts urban canyon scheme to achieve urban surfac--atmospheicc processes [26] The urban canyon scheme of CLMU comprises the roof, sunlit and shaded walls, impervious and pervious roads. The parameters of these urban surfaces include morphological characteristics (e.g.. height-to-widtth ratio, roof fraction, pervious road fraction, building height, and roof thickness), radiative properties (e.g., emissivity and albedo of roofs, roads, and walls), and thermal properties (e.g., thermal conductivity and heat capacity of roofs, roads, and walls) [T] The two-dimensional structure of an urban canyon is characterized by a road at the center, flanked by building walls and rooftops on both sides (with varying height-to toshht-t--widhh ratios across different cities). Specifically, the energy balance process in CLMU is subject to urban surface input parameters and is calculated by the flux interactions within simplified bulk urban air mass. Additionally, it should be noted that the urban energy balance in the current version of CLMU operates independently within a sub-grid [15], enabling focused investigation of the urban surface-atmon ctrrppe-atmmosperiicccc processes. We refer readers the CLMU technique document 25 for the detailed description of the urban canyon scheme. Combined with the exceptional performance of CLMU demonstrated in an urban land surface model comparison project [9), well-suited as a benchmark for developing urban climate emulators.
valuable tool for urban climate study (46. 45 16
42
We conducted CLMU simulations under the SSP3-7.0 scenario for six cities (London, New York City, Shanghai, Singapore, Sao Paulo, and Rome) with diverse background climates and urban surfaces obtain training, validation, and testing data for data-driven methods. To be specific, CLMU was conducted to output instantaneous urban climate simulation outcomes for 8 time steps per day (every 3 hours) for the period of 2020 to 2074 after a 5-y spin-up (2015-2019) The simulation data were divided into 4 subsets: data for the period 2020-204: were used as training data (1,095,000 data points), 2045-2049 data were used for validation (219,000 data points), and data from 2050-2054 (219,000 data points) were mainly used to evaluate model performance. Besides, we further used simulation data from 2070-2074 (219,000 data points) to test model generalization ability.
B.2 Atmospheric forcing and urban surfaces variables
This work screened the forcing data from the atmospheric component of the Community Earth System Model (CESM) at native resolution of 0.9º x 1.25%. Urban surface characteristies were extracted from CLMU's static surface input files at the same resolution. The CLMU output in single-poim mode shares this spatial resolution, which aligns with the default resolution used global urban climate projections. However, it is worth noting that the objective of this work is to capture the underlying physical mechanisms governing urban climate, rather than to perform estimations tied to specific spatial resolution. This design choice inherits the resolution-agnostii nature of the
25

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physics mrysics-based model. CLMU can operate in single-point mode and does not assume fixed spatial resolution. Instead, its spatial footprint is implicitly determined by the resolution of the atmospheric forcing and surface input data, As demonstrated in Section 4.6] both our model and CLMU are able to operate using flux tower data with finer spatial granularity (-500 m), further supporting the resolution-agnostic nature of the learned physical processes.
The variables used develop the data-driven models are listed in Table II To enhance training efficiency (except for the decision tree-based model), all data were first standardized using the mean and standard deviation of the training set. After standardization, the training data were scaled the range (-1, 1) based on the minimum and maximum values of the standardized training set [18 4
Table 11: List of features considered in this study. all fields are taken from the CLM simulation. features marked with were omitted in the model development due to they have constant or nearly identical values across the training area.
Type
Fields
Description
Unit
Embedding as atmospheric
a2x3h Faxa_ swndr
Direct near-infrared incident solar radiation
W
forcing
a2x3h Faxa swvdr
Direct visible incident solar radiation
W m
a2x3h Faxa swndf
Diffuse near-infrared incident solar radiation
W m
a2x3h Faxa swvdf
Diffuse visible incident solar radiation Convective precipitation rale Large-scale (stable) precipitation rate
W m
a2x3h Faxa raine
kg 2
a2x3h Faxa rainl
kg m m=
a2x3h Faxa snowe
Convective snow rate (water equivalent)
kg m 2s
a2x3h Faxa snowl
Large-scale (stable) Zonal wind the lowest model level
(water equivalent)
kg 2
a2x3h Sa_u
ms
a2x3h Sa
Meridional wind at the lowest model level
ms
a2x3h Sa thot
Temperature at the lowest model level
K
a2x3h Sa_shum
Specific humidity the lowest model level
kg kg
a2x3h Sa_ Sa_pbot
Pressure at the lowest model level
Pa
a2x3h Faxa_
Downward longwave heat flux Height at lowest model level
W 2
a2x3h Sa_z
m
doma lon
Longitude Latitude
deg
dom_lat
deg
Embedding as urban surface
CANYON_HY HWR
Canyon height to width ratio
features
WTLUNIT ROOF
Fraction of roof Fraction of pervious road Emissivity impervious road Emissivity of pervious road Emissivity of roof Emissivity of wall
unitless
WTROAD PERV
unitless
EM IMPROAD"
unitless
EM PERROAD*
unitless
EM ROOF
unitless
EM_WALL
unitless
ALB IMPROAD DIR
Direct albedo of impervious road
unitless
ALB B_OOROOFFOO DIR
Direct albedo of roof
unitless
ALB PERROAD DIR
Direct albedo of pervious road
unitless
ALB WALL DIR
Direct albedo of wall
unitless
TK_ ROOF
Thermal conductivity of roof
W m K
TK. WALL
Theral conductivity of wall
W 1mmik
K
TK. IMPROAD
Thermal conductivity of impervious road Volumetric heat capacity of roof
W m
-
CV CV_ROOF
Jm im-"k "K
CV CV_WAI WALL
Volumetric heat capacity of wall
KK-
CV IMPROAD
Volumetric heat capacity of impervious road
mm "K""
COSZEN
Cosine of solar zenith angle
deg
26

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B.3 Model configuration
Table 12:
Hyperparameters used to train UCformer are listed along with their optimal values and the search space for tuning the unconstrained model, shown as the range or set of possible values and the sampling method. Note that attention heads and hidden size were not included in the optimization process due to the structural requirements of UCformer.
Hyperparameter
Valuc
Scarch
layers
4
[3-8] ~ choice
food-forward dimension
2048
512, 1024, 2048 choice
batch size learning rate dropout rate
128
64, 128 choice
le-5
[1c-5, 1e-2] ~ log uniform
0.1
[0.1-0.4] ~ choice
epochs
50
[50-200] choice
attention heads hidden size
3
384
Table 13: Hyperparameters used to train Transformer are listed along with their optimal values and the search space for tuning the unconstrained model, shown as the range or set of possible values and the sampling method.
Hyperparameter
Value
Search
layers
8
[3-8] ~> choice
food-forward dimension
2048
512, 1024, 2048 choice
batch size learning rate
32
32, 64, 128 choice
le-5
[le-5, le-2] ~ log uniform
dropout rate
0.14
[0.1-0.4] ~ choice
epochs
100
[50-200] choice
attention heads
4
2,4.8 choice
hidden size
128
128, 256, 512 ~ choice
The configuration of UCformer and Transformer is listed in Tabel 12 and Tabel 13
For AutoML,, used Python package named "FLAML" 37 achieve automated model selection and hyperparameter tuning (Automated Machine Learning, AutoML) for decision tree- rreebased models. Specifically,, FLAML enables automated optimal machine learning model selection and optimizes the search processes based on the evaluation metric and computational efficiency, that is, the "time budget" hyperparameter. The package then allows iterative selection of learners, hyperparameters. sample sizes, and resampling strategies. In this work, we configured AutoML for regression task with an "auto" estimator list, optimizing the RMSE metric, and time budget of 3,600 seconds (I hour) per trial. The "auto" estimator list includes tree-based models such as LightGBM [13] XGBoost 8) and Random Forest.
B.4 Fine-tuning model with real-world data
To align with the observational dataset, modified the input features of UCformer (from 30 to 23) and the output features (from 2), while keeping all parameters of UCformer updated during the fine-tuning process. The new predictions of sensible and latent heat fluxes constrained by the surface energy balance. This makes the physics-guided decoder in UCformer naturally adaptable to predicting these variables.
C Code of Ethics and Broader Impacts
Our research is ethical. The physics-guice model proposed in this paper enables local urban climate emulation, offering valuable applications in fields such as dlimate-informed urban planning and providing significant benefits to society.
The dataset used this study derived from a public numerical model, ensuring no issues related to infringement privacy leakage. The experiments conducted are fair, reproducible, and designed
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with minimal resource consumption, posing no environmental or societal impact. Furthermore, the proposed model free from bias and discrimination concerns. To promote transparency and accessibility, we open-source the model code and checkpoints on GitHub.
D Safeguard of Model
This paper introduces Sihyiccs-guider model for local urban climate emulation. It is essential to recognize that all models inherently contain some level of emulation error. Therefore, the proposed model should not be used as the sole basis for predicting major events or policymaking. Instead, its findings should be combined with other models and expert knowledge to ensure comprehensive and well-informed conclusions.
E
Assets
Our study complies with the licensing requirements for existing assets, as the data used in this paper are generated from an open-source model that is publicly accessible and authorized for academic research. The model proposed in this study constitutes novel contribution and is regarded as new asset.
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Reviews:
[{"review_id": "7h8ai3Dc5y", "reviewer": "Reviewer_PhTs", "summary": "This paper introduces UCformer, a multi-task, physics-guided Transformer architecture tailored for modeling urban climate dynamics. The model jointly predicts 2-m air temperature, specific humidity, and dew point temperature, embedding domain-specific urban surface-atmosphere interactions and physical priors into its architecture. The authors argue that conventional ML approaches inadequately capture complex urban processes due to a lack of physical grounding. UCformer addresses this gap via a domain-specific encoder and a physics-guided decoder, aiming to enhance generalizability and interpretability. Extensive experiments on both simulated and real-world datasets show that UCformer outperforms baseline models in predictive accuracy and generalization capacity, and can adapt to data-scarce real-world environments with minimal fine-tuning.", "questions": "Comparison to physics-guided ML: As the authors suggested, there are several physics-guided ML models, in particular in climate modeling. How does UCformer compares to these previous models? Are there some obvious reasons that these previous models are not applicable to urban climate modeling?\n\nReal-World Evaluation: How well does UCformer generalize to cities not included in training (e.g., cities with significantly different urban morphology or climate regimes)?\n\nModel Efficiency: Can the authors comment on inference time or model size relative to other ML-based climate models?", "limitations": "Yes", "rating": 4, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nIn terms of quality, the architecture is well-motivated, addressing an underexplored niche (urban climate modeling). Also, the experimental design is solid with diverse evaluation: emulation, generalization (future years), and transfer to real-world observations. There are clear performance gains over relevant baselines (Transformer, AutoML, MLP). Ablation studies reinforce the contribution of each module (encoder/decoder).\n\nIn terms of clarity, the paper is overall well-written.\n\nIn terms of significance, the paper addresses a critically understudied problem—urban climate prediction—with clear real-world implications (urban heat islands, planning). The paper could be highly impactful in climate-aware urban planning, if extended and validated further.\n\nIn terms of originality, embedding physics-informed priors directly into Transformer architectures in urban climate modeling is novel. The paper introduces a shared latent representation approach that exploits cross-city correlations, which is rare in ML climate literature.\n\n\nWeaknesses:\n\nI think the biggest weakness is that the paper lacks of detailed comparison to other physics-informed ML models, particularly in domains with overlapping temporal and spatial modeling needs. In Related work the authors have suggested several work on physics-guided ML, and hence the authors should have compared UCformer with previous work, or expain explain in the related work why previous work is not adequate for urban climate modeling.", "was_revised": true, "final_justification": "The rebuttal resolves the core issue for the above weakness, so I raised my score.", "rebuttal": "**Q1: Lack of comparison to other physics-informed ML models**.\n\n**Response:**\n\nWe 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.\n\nAs 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.\n\n\n\n**Q2: How UCformer generalize to cities not included in training.**\n\n**Response:**\n\nSpatial 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).\n\n| 2050-2054     |                 | T               |                 | q               |                 | t               |                 |\n| ------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- |\n| Held-out city | MESSagg         | RMSE(K)         | MESS            | RMSE(g/kg)      | MESS            | RMSE(K)         | MESS            |\n| London        | 1.6629 (1.9007) | 0.2990 (0.2419) | 0.8127 (0.8541) | 0.1344 (0.1117) | 0.4357 (0.5171) | 0.1977 (0.1655) | 0.4144 (0.5295) |\n| New York City | 1.6989 (1.8901) | 0.4167 (0.3515) | 0.7699 (0.8030) | 0.1904 (0.1645) | 0.5063 (0.5741) | 0.2507 (0.2212) | 0.4225 (0.5130) |\n| Shanghai      | 1.9369 (2.0024) | 0.4806 (0.4437) | 0.8349 (0.8486) | 0.2886 (0.2611) | 0.5555 (0.5986) | 0.2529 (0.2426) | 0.5465 (0.5552) |\n| Singapore     | 2.2840 (2.4586) | 0.2668 (0.2412) | 0.8581 (0.8727) | 0.2798 (0.2130) | 0.7060 (0.7975) | 0.1279 (0.1036) | 0.7198 (0.7884) |\n| Sao Paulo     | 1.8953 (2.1241) | 0.3965 (0.3561) | 0.8179 (0.8363) | 0.2587 (0.2074) | 0.5326 (0.6618) | 0.1649 (0.1435) | 0.5448 (0.6260) |\n| Rome          | 1.8163 (1.9048) | 0.3972 (0.3242) | 0.7843 (0.8282) | 0.1571 (0.1477) | 0.5197 (0.5450) | 0.1975 (0.1896) | 0.5123 (0.5316) |\n\nThe 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. \n\nOverall, 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.\n\n\n\n**Q3: Model Efficiency.**\n\n**Response:**\n\nIn addition to UCformer, we evaluated two representative sequence-to-sequence models, that is, LSTNet and Informer, which can be adapted to urban climate estimation.\n\nAll 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.\n\nThese 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."}, {"review_id": "undL22gdid", "reviewer": "Reviewer_8XNb", "summary": "This paper presents UCFormer, a physics guided deep learning model based on transformer architectures designed to capture urban climate processes and predict air temperature, dew point temperature, and specific humidity. The model includes an encoder that aims to capture how the urban surface modulates incoming shortwave and longwave radiation and surface fluxes within the urban canyon. This encoder returns a latent representation of the outcome variables: air temperature, dew point temperature, and specific humidity. A decoder then converts the latent representations of the outcome variables to their target values. The structure of these transformer-based encoders and decoders is designed to encourage the model to learn and use physical rules and relationships when modelling atmospheric forcing-urban surface interactions and  decoding latent representations of urban climate properties to target variables. The model is trained on simulated data generated by the Community Land Model Urban from six cities and evaluated on a test set of data from 2050-2055, a generalisability experiment with simulated data from 2070-2074, and a comparison with Flux tower measurements. Compared to a range of deep learning architectures, which were not designed to emulate urban climate processes, UCFormer generated more accurate predictions of the target variables on the test set and future generalisation set. The UCFormer was also fine-tuned to predict latent and sensible heat fluxes that are measured at Flux towers and compared to CMLU simulated fluxes. The UCFormer model was better correlated with Flux tower measurements than CMLU.", "questions": "There was also scope for more explanation of the results comparing model simulations to Flux tower measurements. As I understood what was presented, UCFormer was pre-trained using CMLU simulations and then calibrated (fine-tuned) with a subset of Flux tower measurements. Was the CMLU model also calibrated to Flux tower measurements? If not, are these results to be expected that UCFormer outperformed CMLU? Also, the model predictions of latent heat seem quite poor? Is there an explanation for this? And, how does this impact usability of the model or guide further research? \n\nA suggestion is to provide more details of the training dataset’s characteristics. Specifically, what was the spatial resolution / detail of the input data and where they were sourced from (e.g. parameters and variables characterising the urban surface). Also, it was not clear what the spatial resolution of the output predictions was? Providing such information would be useful to gauge what use cases the presented model is relevant for. \n\nI was interested in the distribution of predictions of target variables presented in the appendix. Have the author’s explored these in more detail and spatially and noted if there are certain geographic contexts / urban environments where model predictions are particularly erroneous? Relatedly, I would be interested in seeing results of the UCFormer predictions against observations from weather stations, and was there a reason the authors did not include such analysis as part of their evaluation?", "limitations": "Yes (in the appendix)", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "The authors present a well thought through and described approach to integrate physical rules and understanding of urban climate systems into a machine learning framework. The description of the model was comprehensive and there was a thorough set of evaluations and ablations studies. However, there was scope for more discussion of how the model could be applied to guide management and planning of urban environments. For example, if the primary aim of the model presented here was to emulate a physical model simulations, more detail could have been provided on computational efficiency gains (beyond a single line in the introduction) and why such gains are necessary (e.g. what kinds of analyses that have relevance for mitigating urban heat could be undertaken with more computationally efficient models?). However, if the primary aim was to more accurately simulate key urban climate variables, was there a reason why the authors did not evaluate the model against ground truth measurements (e.g. from weather stations) and compare physical models to the presented ML model? The comparison of UCFormer against other, more general, ML models was interesting. However, the improved performance of UCFormer is to be expected given the architecture is tailored for this task. It would have been interesting to see how UCFormer compared against other urban climate models.", "was_revised": true, "final_justification": "I thank the authors for their discussion during the review. Overall, I have not changed my rating of the paper primarily due to the above concerns regarding the validation.", "rebuttal": "**Q1: Explanation of the results comparing model simulations to Flux tower measurements.**\n\n**Response**:\n\n**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).\n\nGiven 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\n\n**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.\n\nFuture 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.\n\n**Q2: Spatial resolution and characteristics of the training dataset.**\n\n**Response:**\n\nOur 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.\n\nHowever, 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.\n\n**Q3: Data distribution and why not include weather station data for evaluation.**\n\n**Response:**\n\n**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.\n\nRegarding 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.\n\nAdditionally, 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).\n\n| 2050-2054     |                 | T               |                 | q               |                 | t               |                 |\n| ------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- |\n| Held-out city | MESSagg         | RMSE(K)         | MESS            | RMSE(g/kg)      | MESS            | RMSE(K)         | MESS            |\n| London        | 1.6629 (1.9007) | 0.2990 (0.2419) | 0.8127 (0.8541) | 0.1344 (0.1117) | 0.4357 (0.5171) | 0.1977 (0.1655) | 0.4144 (0.5295) |\n| New York City | 1.6989 (1.8901) | 0.4167 (0.3515) | 0.7699 (0.8030) | 0.1904 (0.1645) | 0.5063 (0.5741) | 0.2507 (0.2212) | 0.4225 (0.5130) |\n| Shanghai      | 1.9369 (2.0024) | 0.4806 (0.4437) | 0.8349 (0.8486) | 0.2886 (0.2611) | 0.5555 (0.5986) | 0.2529 (0.2426) | 0.5465 (0.5552) |\n| Singapore     | 2.2840 (2.4586) | 0.2668 (0.2412) | 0.8581 (0.8727) | 0.2798 (0.2130) | 0.7060 (0.7975) | 0.1279 (0.1036) | 0.7198 (0.7884) |\n| Sao Paulo     | 1.8953 (2.1241) | 0.3965 (0.3561) | 0.8179 (0.8363) | 0.2587 (0.2074) | 0.5326 (0.6618) | 0.1649 (0.1435) | 0.5448 (0.6260) |\n| Rome          | 1.8163 (1.9048) | 0.3972 (0.3242) | 0.7843 (0.8282) | 0.1571 (0.1477) | 0.5197 (0.5450) | 0.1975 (0.1896) | 0.5123 (0.5316) |\n\n**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.\n\nWe 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.\n\n\n\n**Weakness: The primary aim of the model and how UCformer could be applied to guide management and planning of urban environments.**\n\n**Response:**\n\nOur 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.\n\nAlthough 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."}, {"review_id": "Bzk1ysISRf", "reviewer": "Reviewer_CyZa", "summary": "This paper proposes UCformer, a Transformer-based architecture that integrates surface–atmosphere cross-attention and soft physics constraints for urban climate variables. It also introduces a new dataset built from multi-city, multi-decadal CLMU simulations. UCformer demonstrates improved RMSE and emulation skill over simple MLP, AutoML tree ensembles, and a vanilla Transformer.", "questions": "See weakness.", "limitations": "N/A", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\nS1. Novel and important downstream tasks. Predicting urban climate variables at 3-hour resolution—2 m air temperature, specific humidity, and dew point—is both timely and practically valuable.\nS2. Physics-guided design. The cross-attention encoder and decoder inject domain knowledge softly, offering interpretability without hard constraints.\nS3. A new dataset. The CLMU simulation corpus (2020–2074) across six cities with chronological train/val/test/generalization splits enables robust evaluation.\n\nWeakness\nWhile the paper’s motivation and contributions are clear, it overlooks a vast body of multivariate time-series forecasting research, leading to two critical issues:\n\nW1. Problem definition ignored.\nThe authors’ own formulation (Sec. 3.1) makes it explicit:\n– Inputs: $X_f\\in\\mathbb{R}^{T\\times C\\times N}$, a sequence of $C$ forcing variables over $T$ timesteps across $N$ cities\n– Outputs: multi-step predictions of temperature, humidity, dew point over the same window\nThis is precisely a multivariate sequence-to-sequence forecasting task. Yet the manuscript fails to cite or discuss decades of work on RNN/LSTM forecasters, TCNs/CNNs for sequences, advanced Transformers for time series (Informer, Temporal Fusion Transformer, Autoformer, PatchTST), or even classical VAR/ARIMA methods.\n\nW2. Inadequate baselines.\nThe experimental section only benchmarks UCformer against:\n\n1. An MLP “ClimSim-style” regression\n2. An AutoML-selected tree ensemble\n3. A vanilla Transformer with no temporal forecasting enhancements\n   \nIt omits specialized forecasting models such as LSTNet and DeepAR, TCN-based architectures, Informer/PatchTST, and VAR/ARIMA. Without these comparisons, we cannot determine whether UCformer’s gains derive from its physics guidance or simply from its choice of baselines unsuitable for time series.\n\nW3. Implementation.\nBeyond the aforementioned problems, the core technical part of the paper is essentially not reproducible. Until the review time (6.30 AOE), the authors haven't fully released the code in their provided anonymous GitHub link. More importantly, 1) none of the novel physics components discussed in Section 3.4 appears in the provided code, 2) in the main implementation, no non-standard architecture appears other than naming things “climate_attention” and splitting the decoder into three branches. Everything is built on vanilla PyTorch Transformer primitives, significantly different from the paper's description, and 3) No data loading, loss functions, or training code is provided. Hence, it is impossible to verify the true technical designs of the proposed framework.", "was_revised": true, "final_justification": "The authors have addressed the first two points of my concerns. But there are still lingering problems as suggested in my response.", "rebuttal": "**Q1: Problem definition.**\n\n**Response:**\n\nWe 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.\n\nAs 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.\n\n**Q2: Why not include time-series forecasting baselines.**\n\n**Response:**\n\nAs 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.\n\nNonetheless, 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:\n\n| 2050-2054         |            | T          |            | q          |            | t          |            |\n| ----------------- | ---------- | ---------- | ---------- | ---------- | ---------- | ---------- | ---------- |\n| Model             | MESSagg    | RMSE(K)    | MESS       | RMSE(g/kg) | MESS       | RMSE(K)    | MESS       |\n| MLR               | 0.2069     | 0.7774     | 0.6112     | 0.3562     | 0.2516     | 0.6551     | -0.6559    |\n| LSTNet_modified   | 1.9065     | 0.3528     | 0.8286     | 0.2238     | 0.5075     | 0.1910     | 0.5704     |\n| Informer_modified | 1.7700     | 0.3567     | 0.8268     | 0.2325     | 0.4775     | 0.2003     | 0.4657     |\n| UCformer          | **2.0468** | **0.3264** | **0.8405** | **0.1851** | **0.6157** | **0.1777** | **0.5906** |\n\nAs 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. \n\n**Q3: Model implementation  and the designed physical components' codes.**\n\n**Response:**\n\n**1. Model implementation and reproducibility:**\n\nWe 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.\n\n**2. Technical part codes:** \n\nWe 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.\n\n**(1) Regarding the Decoder components described in Section 3.4:**\n\nSection 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. \n\n**(2) Regarding the Encoder components:** \n\nAs 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:\n\nThe 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.\n\nThe 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).\n\n**(3) Data loading, loss function, and training code:**\n\nThe 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. \n\nWhile 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.\n\nTo further support reproducibility, we will include the complete training pipeline—covering data loading and a training/inference example script—in the final code release.\n\nIn 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."}, {"review_id": "GxxbV71zPI", "reviewer": "Reviewer_whR3", "summary": "The authors propose an attention-based approach that integrates urban climate knowledge and physical models to capture interactions between atmospheric phenomena and urban surfaces. Their method utilizes an encoder to model atmospheric–surface interactions and a decoder to guide the physical models. The experiments cover dataset descriptions, baseline comparisons, and ablation studies aiming to assess the robustness of the approach.", "questions": "1. I suggest adding a table that clarifies the mapping between the model and the elements of the inference scheme.\n2- I suggest providing a minimal code example that loads the data and runs the test exercises.\n3. Evaluate with a held-out city to demonstrate spatial robustness.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "The authors present an approach that combines data with physical models to study climatological phenomena in urban environments. Their results are outstanding, and ablation studies confirm that the correct components were integrated. They also provide code to reproduce the findings.\n\nHowever, there should be more emphasis on clarifying how the physical models connect to the machine-learning models, and the code should include additional details to make it easier to use.", "was_revised": true, "final_justification": "Thanks for the opportunity of reviewing this article. I appreciate the thoughtful insights provided by the reviewers and the arguments presented by the authors. After careful consideration, I decided to keep my score. Thanks", "rebuttal": "**Q1: More emphasis on clarifying how the physical models connect to the machine-learning models**.\n\n**Response:**\n\nWe 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.\n\n| Model Component                            | Role in Inference Scheme                                  | Input(s)                                                     | Output(s)                    |\n| ------------------------------------------ | --------------------------------------------------------- | ------------------------------------------------------------ | ---------------------------- |\n| forcing embedding layer                    | encodes atmospheric forcing characteristics               | atmospheric forcing features                                 | forcing tokens               |\n| urban surface embedding layer              | encodes urban surface feature characteristics             | urban surface features                                       | urban surface tokens         |\n| urban surface-atmosphere interaction block | learns interactions between urban surfaces and atmosphere | forcing query tokens, urban surface key tokens, urban surface value tokens | interaction-encoded tokens   |\n| surface fluxes interaction block           | learns urban surface-surface radiatively interaction      | updated interaction-encoded tokens                           | intermediate features tokens |\n| decoder branch 1                           | *T* (temperature) estimation                              | intermediate *T* query tokens, concatenated *q* and *t* tokens (as keys and values) | esitmated *T*                |\n| decoder branch 2                           | *q* (specific humidity) estimation                        | intermediate *q* query tokens, concatenated *T* and *t* tokens (as keys and values) | esitmated *q*                |\n| decoder branch 3                           | *t* (dew point temperature) estimation                    | intermediate *t* query tokens, concatenated *T* and *q* tokens (as keys and values) | esitmated *t*                |\n\n\n\n**Q2: The code should include additional details to make it easier to use.**\n\n**Response:**\n\nWe 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.\n\n\n\n**Q3: Evaluate with a held-out city to demonstrate spatial robustness.**\n\n**Response:**\n\nSpatial 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).\n\n| 2050-2054     |                 | T               |                 | q               |                 | t               |                 |\n| ------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- | --------------- |\n| Held-out city | MESSagg         | RMSE(K)         | MESS            | RMSE(g/kg)      | MESS            | RMSE(K)         | MESS            |\n| London        | 1.6629 (1.9007) | 0.2990 (0.2419) | 0.8127 (0.8541) | 0.1344 (0.1117) | 0.4357 (0.5171) | 0.1977 (0.1655) | 0.4144 (0.5295) |\n| New York City | 1.6989 (1.8901) | 0.4167 (0.3515) | 0.7699 (0.8030) | 0.1904 (0.1645) | 0.5063 (0.5741) | 0.2507 (0.2212) | 0.4225 (0.5130) |\n| Shanghai      | 1.9369 (2.0024) | 0.4806 (0.4437) | 0.8349 (0.8486) | 0.2886 (0.2611) | 0.5555 (0.5986) | 0.2529 (0.2426) | 0.5465 (0.5552) |\n| Singapore     | 2.2840 (2.4586) | 0.2668 (0.2412) | 0.8581 (0.8727) | 0.2798 (0.2130) | 0.7060 (0.7975) | 0.1279 (0.1036) | 0.7198 (0.7884) |\n| Sao Paulo     | 1.8953 (2.1241) | 0.3965 (0.3561) | 0.8179 (0.8363) | 0.2587 (0.2074) | 0.5326 (0.6618) | 0.1649 (0.1435) | 0.5448 (0.6260) |\n| Rome          | 1.8163 (1.9048) | 0.3972 (0.3242) | 0.7843 (0.8282) | 0.1571 (0.1477) | 0.5197 (0.5450) | 0.1975 (0.1896) | 0.5123 (0.5316) |\n\nThe 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. \n\nOverall, 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."}]

Author rebuttal:

Meta-review: This paper introduces UCformer, a physics-guided transformer model for urban climate emulation, jointly predicting air temperature, dew point, and specific humidity. The authors release a valuable new simulation-based dataset spanning multiple cities and decades. Experiments demonstrate improved performance compared to some baseline ML methods and show UCformer can be fine-tuned to real-world data (from urban Flux tower) with competitive results against leading physical models.

The paper tackles an important, underexplored problem and presents a solid AI approach with good theoretical motivations. The released dataset is likely to be highly useful for future research. Reviewers noted the interdisciplinary value of the work.

Likely due to the modern transformer focused context, the authors failed to recognize reviewer CyZa's key point about under-engagement with the rich literature on time-series "forecasting". Might have been useful to instead frame it as time-series representations/feature-engineering and lack of such comparison can make it unclear whether this will have real world impact. Many of the "transformer" time-series models have the same problem as well, there is very little underlying data to really not just be overfitting with transformer style methods (which are very good at it without proper regularization under limited data constraints) which often do well on benchmark time-series tasks, but not in the real world. Given the main results are on simulated data with only limited observation-based evaluation (as highlighted by several reviewers), this raises even more concerns about generalization and impact as it's much easier to have train/test distribution easily match up, compared to the real world. I strongly encourage the authors, in the final version of this paper, to engage more deeply with the substantive criticisms raised by reviewer CyZa.

The rebuttal phase was constructive. Authors provided detailed responses on spatial generalization, model efficiency, and tried to clarify the rationale behind their choices. I appreciate the authors' commitment to code and data release making it easier for the community to run more experiments in this domain.
Decision: Accept (poster)