General comments:

This study constructed a simple theoretical thermodynamic model that explains the key mechanisms of the urban heat island (UHI) by integrating the surface energy balance (SEB) theory with a simplified day-night model. Using this approach, the authors demonstrated that the UHI primarily results from two factors: the reduced diurnal temperature range (DTR) due to the larger heat capacity of urban materials, and the increased mean temperature associated with lower urban albedo. The study further compared the model’s theoretical predictions with observed UHI characteristics and long-term changes in a megacity (Seoul) and a major city (Suwon) in South Korea. The results showed that long-term changes in the UHI in both cities are significantly correlated with the urban-rural difference in DTR, highlighting the role of urban heat storage in UHI intensity.

Even today, when sophisticated urban models incorporating complex processes are widely used, I agree that simple models can still be effective, depending on the objective. By omitting minor factors and focusing on dominant processes, such models can distill the essence of the phenomenon and provide important insights. At the same time, however, it is crucial to clearly demonstrate the novelty of the presented results and conclusions to meet the standards of a scholarly article, regardless of the methods employed.

I have carefully read the paper several times and re-examined the related literature to evaluate the novelty of this study and to identify its potential contributions to urban climate and land surface process research. However, the novelty of the study is not clearly demonstrated and could not be identified. The following points, in particular, require improvement.

Specific comments:

[1]

A key issue in evaluating this paper is whether the novelty of introducing a new model to explain already well-known mechanism should be acknowledged. The manuscript proposed a theoretical model based on SEB theory, proceeding from the view that the key factors of the UHI mechanism are the large heat capacity of urban materials and urban albedo (specifically, the lower albedo typically found in cities), and then evaluated the sensitivity of surface air temperature to these two factors. The model produces the following result:

l.369–372

“The results confirm that the primary drivers of the UHI are the reduction in DTR due to the increased heat capacity of urban surface materials and the increase in average temperature due to lower albedo in urban areas. The combination of these factors results in a UHI characterized by higher nighttime temperatures in cities compared to rural areas, while also leading to the occurrence of a temporary UCI during the day.”

However, this description reflects knowledge that is already widely recognized in the field. The importance of heat capacity as a primary driver of the UHI was first emphasized by Mitchell (1961), and then many studies have conducted quantitative assessments of the contribution of heat capacity to the UHI using mathematical models (e.g., Myrup, 1969; Oke, 1982; Oke, 1987; and Grimmond and Oke, 1999). While the simple model of Myrup (1969) failed to reproduce the larger nighttime UHI, Oke (1982) provided a mathematical explanation for this phenomenon. Similarly, the effects of albedo have been quantitatively evaluated in numerous studies (e.g., Sailor, 1995). Atkinson (2003) compared the effects of several factors, including heat capacity and albedo, on the UHI, though his conclusions differ from those presented in this study. The studies introduced here are limited to pioneering studies; numerous investigations have subsequently been carried out employing different models and focusing on various cities (e.g., Adachi et al., 2016). As a result, previous studies have already established the following points reiterated here: (i) heat capacity is a principal driver of the UHI, (ii) nighttime UHI typically exceeds daytime UHI, and (iii) the fundamental effects of heat capacity and albedo on surface air temperature.

The manuscript states that the proposed model aims to provide a qualitative rather than a quantitative understanding. However, as noted above, qualitative aspects are already well understood, while current research largely seeks quantitative insights based on detailed observations and sophisticated models. Against this backdrop, the authors should clearly articulate what advantages this model offers.

• Mitchell, J. M. (1961): The Temperature of Cities. Weatherwise, 14(6), 224–258. https://doi.org/10.1080/00431672.1961.9930028
• Myrup, L. O. (1969): A Numerical Model of the Urban Heat Island. J. Appl. Meteor. Climatol., 8, 908–918, https://doi.org/10.1175/1520-0450(1969)008<0908:ANMOTU>2.0.CO;2.
• Oke, T.R. (1982): The energetic basis of the urban heat island. Q.J.R. Meteorol. Soc., 108: 1-24. https://doi.org/10.1002/qj.49710845502
• Oke, T.R. (1987): Boundary Layer Climates. Routledge. pp464. https://doi.org/10.4324/9780203407219
• Grimmond, C. S. B., and T. R. Oke, (1999): Heat Storage in Urban Areas: Local-Scale Observations and Evaluation of a Simple Model. J. Appl. Meteor. Climatol., 38, 922–940, https://doi.org/10.1175/1520-0450(1999)038<0922:HSIUAL>2.0.CO;2.
• Sailor, D. J. (1995): Simulated Urban Climate Response to Modifications in Surface Albedo and Vegetative Cover. J. Appl. Meteor. Climatol., 34, 1694–1704, https://doi.org/10.1175/1520-0450-34.7.1694.
• Atkinson, B. (2003): Numerical Modelling of Urban Heat-Island Intensity. Boundary-Layer Meteorology, 109 (3), pp 285‐310.
• Adachi, S. A., F. Kimura, H. G. Takahashi, M. Hara, X. Ma, H. Tomita, (2016): Impact of high-resolution sea surface temperature and urban data on estimations of surface air temperature in a regional climate. J. Geophys. Res., 121(18), 10486-10504, doi:10.1002/2016JD024961.

[2]

Related to comment [1], the manuscript requires a stronger review and citation of relevant prior work. Urban climate research has a long history and an extensive body of literature. There are multiple review papers (e.g., Kanda, 2007 and the list in Table 1 of that paper) that could serve as useful starting points. At a minimum, a more thorough survey of key prior studies directly relevant to the objectives of this work is needed. Such a review would help clarify the paper’s originality, position its contribution within existing knowledge, and highlight its significance to urban climate research.

• Kanda, M. (2007): Progress in Urban Meteorology :A Review. Journal of the Meteorological Society of Japan, 85B, 363-383. https://doi.org/10.2151/jmsj.85B.363

[3]

In the latter part of the paper, the authors compare the qualitative insights from their model with observations. However, the interpretations rely mainly on fundamental, well-known ideas, such as the reduction in DTR due to the large heat capacity of urban areas and the rough correlation between UHI intensity and population density. Sections 4.1 and 4.2 lack sufficient detail about the experimental setup and justification for parameter values. As a result, there is not enough information to interpret the results or replicate the analysis, which makes it difficult to assess the validity of the findings. Moreover, Section 4.3 is based on a largely speculative discussion of the observational results, without adequate evidence to support its claims.

Minor Concerns:

[1] What is the reason for the sudden change in the UHI of Suwon shown in Fig. 9(a) around 1998? It is worth considering whether the continuity of the observational data may have been affected by factors such as relocation of the observation sites or environmental changes in their immediate vicinity.

[2] L.294-296: The vulnerability of urban areas to climate change involves a broader and more complex set of factors beyond this single physical characteristic (e.g., Dodman et al., 2022).

• Dodman, D., and coauthors, (2022): Cities, Settlements and Key Infrastructure. In: Climate Change 2022: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK and New York, NY, USA, pp. 907–1040, doi:10.1017/9781009325844.008.

This study proposed a simplified mathematical model to explain the generation mechanism of urban heat islands (UHIs). This is a new attempt to understand the UHI phenomenon, however several limitations should be addressed.

The main conclusion of this study is that the UHIs occur due to the large heat capacity of urban areas. This can be misleading. It is true that the urban surface materials usually have large heat capacity values. However, besides the material properties, the large thermal inertia in urban areas can be attributed to the inefficient longwave cooling and also the increase in surface area. Due to the presence of high-rise buildings, the reduced sky view factors in cities greatly reduce the longwave cooling at night. The incease in surface areas (envelops) due to buildings also contribute to storing more heat in urban areas compared to a flat surface.  It would be great if the authors can quantify the individual contributions that result in large thermal inertia. If this is not possible, I strongly suggest that the authors clarify these points; otherwise, readers would simply think the UHIs are due to the large heat capacity of urban surface materials. 

I wonder if the dR/dT used in the defination of lambda (eq. 10) shows a clear diurnal variation or not in urban and rural areas. In the paper, constant values (11.8 or 30.9 W m-2 K-1) are used, but the use of a time-invariance value shoud be justified. If the dR/dT does vary with time, how can this temporal variation be considered in the theoretical model?  

The authors argue that the stronger UHI intensity at night than at day is due to the larger heat capacity. This may be partially true. However, the authours seem not to consider the difference in boundary layer height in the daytime and in the nighttime. The much shallower boundary layer at night both in urban and rural areas amplifies the effects of differential heat fluxes. For example, the difference in sensible heat flux between urban and rural areas is larger in the daytime (let's say 200 W m-2) than in the nighttime (e.g., 20 W m-2). However, the much deeper daytime boundary layer in the daytime (e.g., 1.5 km) than in the nighttime (e.g., 150 m) dilutes the differential heat flux effect. The authors are recommended considering this effect. 

I am not sure if section 4.3 is necesseary for this study. I see a weak connection between section 4.3 and the previous sections. The authors would need to provide strong rationales or links of this section.