Introduction

By 2050, it is projected that nearly 70% of the global population will reside in urban areas, resulting in a multitude of challenges for urban sustainability1. Urbanization is marked by the transformation of natural landscapes into built environments, which affects the local hydroclimates2,3. Unlike the extensively studied urban heat island effect and its mechanistic controlling factors4,5, urban effects on clouds remain understudied6. It is well-known that land-atmosphere coupling affects the atmospheric boundary-layer (ABL) cloud formation7,8,9. Meanwhile, recent studies10 show that it is a widely occurring phenomenon that cities enhance the formation of local clouds. Yet, the effects of urban morphology, such as a city’s average building height and density of the built-up areas, on the boundary-layer cloud formation through modifying the urban surface-atmosphere exchanges still remains elusive.

Compared to rural surroundings, an urban area with its stronger momentum and thermal surface heterogeneities6,11 can potentially affect the formation of clouds. The sizes of urban surface heterogeneities range from momentum heterogeneity represented by urban morphology at the micro-scale (~100 m) to thermal heterogeneity related to urban-rural contrast of surface heating at the convective scale (~10 km). At the convective scale that is commensurate with the city scale, larger and more prolonged sensible heat flux compared to rural surroundings12 leads to a deeper and more unstable boundary-layer, transporting moisture to a higher atmospheric level and increasing cloud amount above the urban surface6,13. Such thermal heterogeneity also leads to the urban breeze circulations (UBCs),14,15,16, which transport moisture from rural surfaces to the urban atmosphere17. Studies pointed out that the structure of UBC depends on the difference in heating rates between urban and rural surfaces, the background stratification, urban morphology such as the dimension of the city, and urban canopy parameters such as building height and building density15,18. However, the role of urban morphology on UBCs and the subsequent impact on local cloud patterns is still not well understood.

Compared to the influence of surface heating on moisture transport and boundary-layer clouds in cities6,10, the impact of micro-scale momentum surface heterogeneity, i.e., roughness elements such as buildings and trees, on local clouds is even less studied19,20. However, at the scale of the roughness elements, their geometric structures and spatial arrangement can significantly affect the momentum and scalar transport in urban environments21,22,23,24,25,26,27. When background flow exists in addition to urban surface heating, the enhanced moisture convergence due to roughness at the urban center28,29,30,31 could increase vertical mixing and boundary-layer height32, facilitating the formation of clouds. On the other hand, lower scalar transfer efficiency compared to momentum over urban canopy has been noted by previous studies25. The ventilation efficiency, represented by the air exchange rate of a city decreases with increasing city size33 and increasing building height34. As a result, the presence of urban canopy may also suppress vertical mixing, decrease ABL height, and impede the vertical transport of moisture and formation of clouds over urban surface. Therefore, the contrasting effects of urban roughness on scalar transport could lead to distinct modifications of the local cloud formation process, especially considering a wide range of geometric characteristics of urban roughness. Yet, the underlying mechanisms remain unclear.

A recent study using observational data over 400 cities in the US revealed the urban signatures on local clouds10, but the mechanisms of city-scale surface heating and micro-scale urban morphology affecting the local cloud formation cannot be disentangled from the observations. As a city’s micro-scale surface heterogeneities can be characterized by different morphological parameters, it could be speculated that if micro-scale urban surface heterogeneities do affect cloud patterns, observational data will show the “signatures” of cities corresponding to different morphological types. Using the concept of local climate zones (LCZs)22 might provide one potential way to characterize urban morphological types within the urban morphology parameter space (Fig. 1a). At the city-scale, a simple geometric mean of the urban morphology parameters (Fig. 1b) characterizes the entire city as one type of morphology. Note that despite the known caveats of LCZs for land-cover, here we only apply it to systematically differentiate morphological types measured by some key geometric parameters, such that each individual city can be described by a “basic unit” of morphological type. Thus, this consideration motivates the current study to set up numerical simulations that explicitly resolve such “basic unit” of urban morphological types and micro-scale turbulence using large-eddy simulations (LES)35,36,37. An idealized setup of free convective condition, i.e., in absence of a background horizontal wind, is considered in LES. The idealized setup provides the first necessary step to understand the mechanisms of micro-scale surface heterogeneity impacting the formation of shallow cumuli, which will help to interpret satellite observations of cloud climatology10 across cities characterized by different morphological types. Two research questions will be examined in this study:

  1. 1.

    Under free-convective conditions, how do different aspects of urban morphology modify vertical velocity, and how do these changes influence the formation of boundary-layer clouds?

  2. 2.

    Can the mechanistic relationships identified in the LES be detected in satellite-based cloud climatology, and how can they provide a basis for improving the parameterization of cloud formation in larger-scale weather and climate models?

Fig. 1: The local climate zone (LCZ) map of an example city.
Fig. 1: The local climate zone (LCZ) map of an example city.
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a Color scale indicates the LCZ type with corresponding urban morphology parameters such as building height (h), street width (d), and building density (λp), defined as ratio of plan area to the total urban surface area. b The average of the parameters across all LCZ types represents the city-scale urban morphology type that differs across different cities. LCZ 1: compact highrise; LCZ 2: compact midrise; LCZ 3: compact lowrise; LCZ 4: open highrise; LCZ 5: open midrise; LCZ 6: open lowrise; LCZ 7: lightweight low-rise; LCZ 8: large lowrise; LCZ 9: sparsely built; LCZ 10: heavy industry; LCZ 11: dense trees; LCZ 12: scattered trees; LCZ 13: Bush, scrub; LCZ 14: low plants; LCZ 15: bare rock or paved; LCZ 16: bare soil or sand; LCZ 17: water.

Results

Simulated results of flows and formation of clouds over different LCZs

Numerical simulations using LES (FastEddy®) were performed35,36,37 for seven morphological types of roughness based on the concept of local climate zone, which is a widely adopted way to represent different urban land cover land use types in numerical modeling38. Applying the concept of LCZ in numerical simulation setup also ensures the consistency between numerical modeling and observational analysis shown in later section. The computational domain is shown in Fig. 2. The summary of study cases and corresponding parameters are presented in Table 1. Details of the LES model and simulation setup can be found in “Materials and Methods”. Due to the idealized condition, we expect the findings remain valid for the urban-rural flow regimes that can be categorized as “bubble” in ref. 29. Specifically, if the ratio between background wind and the convective velocity scale at rural area, i.e., the background w*, is smaller than 0.7, the results are expected to be applicable. The background w* is defined as:

$${w}_{*}={\left(\frac{g}{{\theta }_{0}}{H}_{r}{z}_{i}\right)}^{1/3},$$
(1)

where θ0 = 300 K is a referential temperature; Hr is the surface flux at rural area; and zi is the initial boundary-layer height.

Fig. 2: Schematics of large-eddy simulation (LES) computational domain.
Fig. 2: Schematics of large-eddy simulation (LES) computational domain.
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Lx and Ly are length and width of the computational domain, respectively; LC is the size of the urban area; L is the size of a repeating unit; D is width of the building. The width between the two dashed lines is LC/5. The 9 buildings are only shown for illustration purpose and each case contains different numbers of aligned buildings.

Table 1 Summary of study cases and corresponding parameters
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Two cases (LCZ1 and LCZ8) with the most contrasting spatial patterns of cloud formation are first analyzed in Fig. 3. LCZ1 refers to the case with compact high-rise urban canopy and LCZ8 refers to sparse low-rise urban canopy. The distinct cloud patterns in LCZ1 and LCZ8 (Fig. 3a, b) are quantified by the liquid water path (LWP), defined as

$$LWP={\int }_{\!\!\!0}^{{L}_{z}}{\rho }_{d}{q}_{l}dz,$$
(2)

where ρd is dry air density; ql is liquid water mixing ratio; and Lz is the height of the computational domain. The cloud patterns over rural area in both cases are similar, which is expected because of the same surface heat and moisture fluxes being imposed. However, cloud patterns differ over the urban area. For compact high-rise urban canopy (LCZ1), most of the clouds form close to the urban-rural interface; whereas in sparse low-rise urban canopy (LCZ8), clouds form over the entire urban area, especially over the street intersections. Other cases of different morphological types are shown in Supplementary information (Figs. S7–11). Noticeably, the most compact high-rise case (LCZ1_dense) shows enhanced cloud formation at the corners of the urban region. Cloud formation over urban core is enhanced for cases with wider canyon width (d), i.e., cases LCZ5 and LCZ6. These results imply that spatial patterns by the contrast in roughness height at the rural-urban interface, as well as the geometry of building arrangement within the urban core, which will be further explored in the next section by considering two velocity scales.

Fig. 3: Simulated results of cloud pattern and cloud amount.
Fig. 3: Simulated results of cloud pattern and cloud amount.
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a, b Distribution of liquid water path (LWP) for LCZ1 and LCZ8. LCZs represents local climate zones. Black dashed lines represent urban-rural interface. c Horizontally averaged LWP over urban area with respect to the integrated turbulent kinetic energy (TKE) contributed by vertical turbulent velocity from cloud base to domain top. \(TK{E}_{w,urban}={\langle \frac{1}{2}{\rho }_{d}{w}^{{\prime} }{w}^{{\prime} }\rangle }_{urban}\). Black solid line is the linear fit of the dataset, y = 0.418x−0.998, R2 = 0.94, p = 2.6 × 10−4. LCB is cloud base height, defined as the minimum height that ql > 0. LCB = 614 m for all simulated cases.

To explain the differences in the spatial distribution of LWP, we examine the x and z components of the velocity averaged in y direction (between the white dotted lines in Fig. 2) at the vertical plane (Fig. 4a–d). For both cases, two distinctive regimes of flow patterns can be identified over the urban area: the urban-rural interface, where UBC is present and the urban core (See schematic in Fig. 5a). For compact high-rise urban canopy, the distinctive structure of UBC appears in the urban-rural interface with large magnitude of updraft and downdraft (Fig. 4a, c). Within the urban core, w in compact high-rise urban canopy has a smaller magnitude than that in the interface, implying reduced turbulence mixing. In contrast, for sparse low-rise urban canopy (Fig. 4b, d), magnitudes of w in the rural-urban interface and urban core are similar. The coherent updrafts and downdrafts, especially below z = 250 m, are imposed by the length scales of the surface morphology (D and L). Throughout the urban core, updrafts of length scale L − D, i.e., the street width, can even extend beyond the boundary layer height, in contrast to the magnitude and spatial organization of w in compact high-rise urban canopy.

Fig. 4: Simulated results of velocity field, water vapor and liquid water fluxes.
Fig. 4: Simulated results of velocity field, water vapor and liquid water fluxes.
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a, b show the vertical profiles of x velocity u; c, d show the z velocity w; e, f show the vertical turbulent water vapor flux \({w}^{{\prime} }{q}_{v}^{{\prime} }\) averaged in y direction; and g, h show the vertical turbulent liquid water flux \({w}^{{\prime} }{q}_{l}^{{\prime} }\) averaged in y direction. Two extreme cases in terms of urban form are displayed: a, c, e, g correspond to compact high-rise urban canopy (LCZ1); b, d, f, h correspond to sparse low-rise urban canopy (LCZ8). LCZs represents local climate zones. Plots are averaged in y direction between the two white dashed lines in Fig. 2. Black dashed lines represent urban-rural interface. Black solid lines represent the top of boundary-layer over the urban area. The height of boundary-layer is defined as the height at which the variance of the vertical velocity fluctuation over urban area \({\sigma }_{w,urban}^{2}\) decreases to 10% of its near-surface maximum68.

Fig. 5: Schematic of urban morphology influences vertical motions and simulated results of two vertical velocity scales.
Fig. 5: Schematic of urban morphology influences vertical motions and simulated results of two vertical velocity scales.
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a Schematic of urban breeze circulation (UBC) model with urban canopy. uUBC and wUBC are the streamwise and vertical velocity scales of UBC and LUBC is the length scale of UBC. b Schematic of the model for vertical turbulence σw. The annular areas between the building wall and the dashed box indicate regions that vertical turbulence is influenced by the buildings with width δ. σw,0 and σw,b are the standard deviations of the vertical velocity fluctuations without urban canopy and influenced by urban canopy, respectively; D is building width and L is the distance between two building centers (size of the repeating unit). c Vertical velocity scale of UBC wUBC for all simulated cases. wUBC is defined as the average vertical velocity within the range of the horizontal length scale of LUBC. LUBC is defined as the lag that the auto-correlation function of 〈w〉y reaches the minimum value. d Vertical turbulence above urban core for all simulated cases. σw,core is defined as the maximum standard deviation of w over urban core. Urban core is urban area exclude a region with width LUBC surrounding urban-rural interface.

The difference in velocity fields between sparse low-rise urban canopy and compact high-rise urban canopy implies that the compact high-rise urban morphology (LCZ1) intensifies UBC while suppresses the vertical turbulent transport of momentum inside the urban core. The transport of heat in the two cases also differ, as a deeper boundary layer is seen in sparse low-rise urban canopy over the urban area (black solid lines in Fig. 4a–d). Given identically imposed surface sensible heat flux and initial profile of potential temperature in all simulation cases, the coherent thermals over the urban core in sparse low-rise urban canopy more efficiently transports heat than the turbulent eddies in compact high-rise urban canopy, resulting in a deeper boundary layer.

The turbulent water vapor flux and liquid water fluxes averaged in y direction for compact high-rise urban canopy and sparse low-rise urban canopy are shown in Fig. 4e–h. The vertical turbulent water vapor flux \({\langle {w}^{{\prime} }{q}_{v}^{{\prime} }\rangle }_{y}\) is positive near the surface (qv is water vapor mixing ratio). The vertical turbulent liquid water flux \({\langle {w}^{{\prime} }{q}_{l}^{{\prime} }\rangle }_{y}\) (ql is liquid water mixing ratio) is zero below cloud base (LCB = 614 m), where LCB is diagnosed from the simulated fields as the lowest level at which the horizontally averaged ql exceeds 10−4 g kg−1. The regions above cloud base with a large positive \({\langle {w}^{{\prime} }{q}_{l}^{{\prime} }\rangle }_{y}\) corresponds to a large positive \({\langle {w}^{{\prime} }{q}_{v}^{{\prime} }\rangle }_{y}\), which also corresponds to the updrafts extending from the cloud base to heights beyond the boundary layer, i.e., the penetrating thermals. Therefore, the cloud depth, which can be approximately determined by the height difference between the cloud base and boundary layer height9, is determined by the magnitude of updrafts above the cloud base. These observations imply that in addition to previously recognized effect of city-scale surface heating that leads to persistent low clouds6, different urban surface morphological types modulate the spatial patterns of shallow cumuli by modifying the spatial coherence and magnitude of updrafts under free convective condition. Therefore, in compact high-rise urban canopy, UBC dominantly contributes to the upward transport of moisture, leading to most of the shallow cumuli formation close to the urban-rural interface. While in sparse low-rise urban canopy, the transport of moisture is due to strong coherent updrafts over the urban core, unlike the UBC-dominated mechanism in compact high-rise urban canopy. Clouds form over the entire urban area, especially over the street intersections, where the vertical transport of water vapor by updraft is not impeded by buildings.

The effect of urban morphology on vertical velocity

The flows and turbulent moisture fluxes for compact high-rise urban canopy and sparse low-rise urban canopy highlight the close connection between urban morphology and the vertical motions. All of the simulated LCZ cases are further explored in this section to understand the importance of energetic thermals that transport surface moisture beyond the cloud base causing cloud formation. We consider the correlation between LWP and the mean kinetic energy of turbulence contributed by the vertical motions (TKEw,urban) per unit area, which is given by half of the variance of vertical velocity fluctuation for the air column over the urban area from z = LCB to Lz. Figure 3c shows that under free convective condition, these two quantities are linearly correlated for all LCZ cases. Therefore, we focus on the characteristics of the near-surface vertical motions, which are strongly modulated by surface morphological types. In addition, the bulk roughness length for each simulated roughness type is used as a diagnostic metric to examine its correlation with LWP (see Fig. S12). The value of LWP shows a general decreasing trend with increasing bulk roughness length, consistent with the idea that higher surface roughness may suppress vertical moisture transport due to increased drag. However, since both roughness-induced convergence and drag suppression are simultaneously at play, some intermediate roughness height and density cases show deviations from this trend. This also implies that we need to define new velocity scales to reflect the two mechanisms, rather than relying on the bulk roughness length.

Here we define two velocity scales, wUBC and σw,core, which characterize the vertical motions in the urban-rural interface and the urban core, respectively. The magnitude of vertical component of UBC, wUBC, is defined as the average of vertical velocity within the length scale of UBC, LUBC. LUBC represents the distance between the centers of updraft and downdraft of the UBC and is obtained by taking the lag distance that the auto-correlation function of 〈w〉y reaches the minimum value. \({({\langle {w}^{{\prime} }{w}^{{\prime} }\rangle }_{core})}^{1/2}\) varies with z and the maximum of \({({\langle {w}^{{\prime} }{w}^{{\prime} }\rangle }_{core})}^{1/2}\) above the building height is defined as σw,core. Analytical scaling analyses of wUBC and σw,core are considered to understand the effect of urban morphology on wUBC and σw,core. To further validate the physical relevance of these two velocity scales, we compare their values normalized by the convective velocity scale w* (see Fig. S13), which confirms that both wUBC/w* and σw,core/w* fall within typical convective boundary-layer ranges39.

Close to the surface, the direction of UBC is from rural to urban, i.e., from areas with lower sensible heat to high sensible heat as shown in Fig. 5a. The increased momentum roughness from rural to urban area enhances convergence at the urban rural interface and increases the magnitude of wUBC. This can be shown by considering the mass conservation equation31. Figure 5c indicates that cases with higher building height h tend to have higher values of wUBC, except cases LCZ6 and LCZ1_dense for reasons to be explained later. This means that more intense updrafts are found at the urban-rural interface for cases with taller buildings. In addition, in the urban core, the rate of work done against the drag force imposed by urban roughness reduces the production of vertical velocity variance. More densely packed buildings with a higher λp will lead to lower vertical velocity variance. Such a trend is well reflected by σw,core in Fig. 5d. In fact, in some cases, the magnitude of vertical velocity variance also affects the strength of UBC, as surface heating generated upward motions near the urban-rural interface are less obstructed by buildings with wider spacing. As a result, LCZ6 with lower λp has a higher wUBC than LCZ8; LCZ1_dense with a higher λp has a lower wUBC than LCZ1.

These observations can be used to derive a parameterization for σw,core. Considering a horizontal plane at some height z below the building top shown in Fig. 5b, σw,b is the standard deviation of vertical velocity fluctuation averaged over regions bounded by the dashed-lines and the lateral surfaces of the buildings. This bounded region has a dimension of δ, as indicated in Fig. 5b. Beyond δ, the standard deviation of vertical velocity fluctuation σw,0 is dominated by surface heating, as this region lies within the urban core but outside the building-influenced zone, where neither urban-rural interface circulations nor building-induced roughness effects are present. For regions within a certain distance, δ, to the lateral surfaces of the buildings, the standard deviation of vertical velocity fluctuation σw,b is smaller than σw,0 due to the flows doing work against the drag force. An area weighted average of the standard deviation of vertical velocity over this horizontal plane is

$${\sigma }_{w,core}=\frac{{(D+2\delta )}^{2}-{D}^{2}}{{L}^{2}-{D}^{2}}{\sigma }_{w,b}+\frac{{L}^{2}-{(D+2\delta )}^{2}}{{L}^{2}-{D}^{2}}{\sigma }_{w,0},$$
(3)

in which D is building width and L is distance between two building centers (L is also the repeating unit size as shown in Fig. 2).

The analysis of σw with respect to the distance to the lateral surfaces of the buildings confirms our assumption that for a certain height, σw further away from a certain distance to the buildings (δ = 15 m in this case) approaches a constant value at z = 15 m, which is half of the building height for the case with the lowest h (Fig. S1a). As shown by the LES results, σw increases logarithmically with distance from the building walls (Fig. S1a). Increasing σw with distance away from the building walls is also found in experimental results in natural convective flows over a vertical plane in wind tunnel and field studies around a high-rise building40,41,42. Thus, without loss of generality, near the wall:

$${\sigma }_{w,b}(x)=\frac{{\sigma }_{w,0}}{{{{\rm{ln}}}}\frac{\delta }{{z}_{0u}}}ln\frac{x}{{z}_{0u}},$$
(4)

in which x is the distance to the wall; z0u = 0.1 m is the roughness length of urban surface (including all walls of buildings); and δ ≪ L, the expression of σw,core can be written as

$${\sigma }_{w,core}={\sigma }_{w,0}\left(1-\frac{\delta }{L\,{{{\rm{ln}}}}(\frac{\delta }{{z}_{0u}})}\frac{4\sqrt{{\lambda }_{p}}}{1-{\lambda }_{p}}\right),$$
(5)

in which the relation λp = D2/L2 is used to replace D. In Equation (5), σw,core decreases with λp, which is consistent with our simulated results (Fig. 5d). To further validate our model, we compare the results obtained with the proposed parameterization (modeled results) against those from the LES (simulated results). From analysis of the LES results, we took δ = 15 m and σw,0 as the vertical turbulence averaged from δ to half of the canyon width d/2, the comparison between analytical and simulated results shows good agreements (Fig. S1b). Therefore, Equation (5) quantifies the modulating effect of urban morphology on σw,0, which can be seen as the turbulence vertical motion above the urban core due to surface heating only. In practice, σw,0 could be approximated from ground-based remote sensing (e.g., Doppler lidar) measurements of vertical velocity profiles in urban areas6 or diagnosed from planetary boundary layer schemes43. The geometry-related parameters such as building width D and size of repeating unit L can be extracted from urban morphology dataset. It might be tempting to extend the parameterization to predict LWP over urban regions. However, it should be approached with caution as cloud amount is influenced not only by morphology but also by many other factors, such as city size, the magnitude of surface heat flux and its contrast with rural surroundings, boundary-layer height, background temperature and humidity profiles, and background winds. Nevertheless, current study reveals that the vertically integrated TKE contributed by vertical motions over the urban core (i.e., Fig. 3) correlates with the LWP. Future work could consider factors modifying the profiles of σw to develop more realistic parameterization for cloud enhancement.

In summary, by examining across distinct urban morphological types, this section has demonstrated that the amount of shallow cumuli is closely connected to the vertical velocity, showing a linear relationship between the LWP and the depth integrated turbulence kinetic energy (TKE) above the cloud base. We also show that magnitude of the vertical velocity characterizing the UBC at the urban-rural interface increases with the building height h due to roughness-enhanced convergence, while its magnitude at the urban core decreases with the building density λp. A simple parameterization is proposed to quantify the effect of building block dimension and building density on σw.

Observational evidence of urban cloud cover varying with urban morphology parameters

The findings in the previous section based on idealized LES results are useful to understand the importance of vertical motions under free convective conditions for shallow cumuli formation, especially highlighting the distinct roles of the coherent vertical updrafts associated with the UBC at the urban-rural interface and the turbulent mixing above the urban core. It can also be hypothesized from the numerical simulation results that comparing across cities with distinct morphological types, cities with taller and less densely packed buildings tend to show increased amount of shallow cumuli. With this hypothesis in mind, we analyzed the relative cloud enhancement ΔCloud derived from MODIS cloud masks (MYD35_L2 C6.1) from 2002 to 2020 (See details in “Materials and Methods”) in 44 major US cities. The analysis focuses on nighttime observations during the warm season months (April-September).

Rather than using simple citywide averages of building height and plan area fraction, which may not accurately represent the morphological structures responsible for turbulent generation and cloud modulation, we define an effective morphology for each city. In this study, the simulations are designed as idealized experiments to theoretically understand the underlying physical processes by which urban morphology influences vertical motions and cloud formation. Given the complex and highly heterogeneous morphological distributions in real cities, using the most representative morphological characteristics is essential. Specifically, we utilize LCZ classifications to identify the dominant urban types within each city, assigning representative values of building height (h) and plan area fraction (λp) to each LCZ. These LCZ-weighted values reflect the spatially coherent and thermodynamically meaningful morphology, enabling more realistic and physically interpretable cross-city comparisons. The magnitude of ΔCloud is analyzed with respect to the street-canyon aspect ratio h/d, building density λp, and city size. Given that there are many compounding factors other than urban form parameters, such as the effect of urban aerosols across different cities44,45 and different nocturnal local climatology10,46, which jointly impact the variation of relative cloud enhancement, the variation of morphological parameters cannot be regarded as the only factor impacting urban cloud formation. Instead, mechanisms revealed by idealized LES will be used to help us interpret the observations.

The Pearson correlation coefficient matrix of analyzed parameters is shown in Fig. 6a. ΔCloud is positively (negatively) correlated with h/d (λp) with p values smaller than 0.001 as indicated in Fig. 6b. Although h/d and λp have statistically significant (p < 0.05) positive correlations with city size, city size is insignificantly correlated with ΔCloud. Other statistical tests, such as Spearman correlation coefficient and partial correlation coefficient computed between h/d, λp, and ΔCloud, also show similar results (Table S1). Overall, the mean, median, and standard deviation of ΔCloud for the quartiles of h/d and λp suggest that ΔCloud increases with h/d and decreases with λp (Fig. 6c, d). Linear regressions of ΔCloud against h/d and λp are performed (Fig. S2). Data show that ΔCloud is always positive (in the range of 0–15%). The differences between inland, coastal, and mountain cities do not account for the scatter. The values of h/d and λp in majority of the large US cities cluster around 0.5 and 0.3, perhaps due to similarity in urban planning. This could also be an inherent limitation of the LCZ map dataset, where only categorical values of h/d and λp are available. High-resolution data products47 of building heights and street dimensions could be applied in future studies to improve the accuracy of h/d and λp. To address this limitation, we performed bootstrap sampling of half the cities without replacement, repeated ten thousand times. Distributions of p values and R-square values are shown in Fig. S2, indicating over 75% and 80% of the linear regression results for h/d and λp show statistically significant positive and negative correlations, thus confirming the robustness of the results.

Fig. 6: Observational evidance of urban cloud cover varying with urban morphology parameters.
Fig. 6: Observational evidance of urban cloud cover varying with urban morphology parameters.
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a Heatmap of the Pearson correlation coefficient matrix; b Heatmap of p values associated with each correlation coefficient; c Relative cloud enhancement ΔCloud averaged over quartiles of street-canyon aspect ratio h/d, where standard deviation and median for each quartile are also indicated; d ΔCloud averaged over quartiles of building plan area fraction λp, where standard deviation and median for each quartile are also indicated. Q1 to Q4 represents 0–25%, 25–50%, 50–75%, and 75–100% percentiles of h/d and λp in (c) and (d), respectively. Error bars represent the range between the minimum and maximum values.

Relating the previously discussed mechanisms to the observed trends here: it can be concluded that the increasing urban cloud enhancement for cities with higher h/d might be related to roughness-enhanced convergence; whereas the decreasing trend with λp could be a manifestation of the reduced vertical turbulent transport over a denser urban canopy. We do not directly compare the simulated cloud amount quantified by LWP with the observed results because a city consists of different LCZ types (Fig. 1a) and many confounding factors could influence ΔCloud. The LES results over highly idealized LCZ types under simplified boundary conditions are useful for isolating the effect of urban morphology and reveal mechanistic processes, which highlight the importance of the vertical motions generating coherent updrafts favorable for the formation of shallow cumuli.

Discussion

In this study, the effect of different urban morphology on boundary-layer cloud formation is investigated by means of a combination of numerical simulation using LES modeling (FastEddy®) and observations. In the numerical simulations, urban and rural surfaces retain their respective differences in surface heat fluxes, while the moisture sources and background atmospheric water vapor are prescribed to be identical, so that the influence of morphological dynamics on moist convection can be isolated from moisture heterogeneity. Despite the idealized set-up in the numerical simulation and the simplified assumptions in the parameterization of σw, useful insights on the effect of urban morphology on local cloud formation are obtained. The key findings are summarized below.

  1. 1.

    Both urban surface heating6,10 and roughness contribute to the local cloud enhancement. LES results show that under conditions of no background wind, surface heating and roughness-induced convergence modulate the vertical motions in the atmospheric boundary layer. Heat and moisture transport by organized updrafts play a dominant role in the cloud amount and their spatial patterns. For example, higher variance of the vertical velocity fluctuation is positively correlated with the cloud amount as shown in Fig. 5a. Organized updrafts either at the urban-rural interface ((Fig. 4g) or the urban core (Fig. 4h) lead to substantial cloud formation.

  2. 2.

    Results from building-resolving LES in this study provide insight into the plausible mechanisms by which urban morphological types influence the boundary-layer cloud formation. These results also corroborate cloud climatology observations based on satellite data. Given no background flow and the boundary-layer development solely via sensible heating, taller urban canopy could intensify UBC by convergence. When the building density, λp of an urban area increases, the variance of vertical velocity fluctuation over the urban core is reduced because of increased drag. Turbulent vertical transport of heat and moisture in such case is reduced compared to the transport by organized updrafts.

  3. 3.

    Two velocity scales wUBC and σw,core associated with UBC at the urban-rural interface and the strength of upward motions at the urban core can be defined and calculated based on LES results. wUBC increases with h and σw,core decreases with λp. These two velocity scales provide a mechanistic basis for parameterizing the effect of urban morphological types on shallow cumulus convection. Capturing such morphology-driven modulation of vertical velocity fluctuations is essential for representing the dynamical effects of different cities under convective conditions in coarser-scale weather and climate models. Due to the limitations of free convective conditions considered in this study, future studies could expand the simulations to mixed convective conditions. Despite limitations in this work, the insights into these two velocity scales could guide future improvements to σw parameterizations in models that do not explicitly resolve buildings, ultimately leading to improved PBL schemes and more realistic cloud formation simulations.

The study is restricted in the following aspects. Firstly, due to the assumption of quasi-steady state forcing, the numerical model neglected the diurnal cycle of cloud formation, when the effect of time-varying surface flux is important, potentially leading to intermittent updrafts and more complex interactions with urban morphological effects. Secondly, idealistic boundary conditions, such as a square-shape city, buildings with the same height and width, and urban surface with uniform surface heating are imposed. The moisture source heterogeneities are ignored, which are known to be prevalent in an urban setting6,48. Thirdly, the urban morphology data are limited by simplifying assumptions in the parameters for LCZ categories. Higher fidelity data might be helpful to adequately distinguish cities of different urban forms. Last but not least, all simulations are conducted under free-convective conditions without background wind. In real urban environments, background wind is often present and can play a critical role in modulating the relative importance of buoyancy- and shear-driven turbulence, thereby influencing UBCs and local cloud formation. Future studies should investigate how varying background wind speeds affect the transition from free to mixed convection, and how this transition interacts with urban morphological parameters.

Methods

Description of the numerical model

The FastEddy® model, which is a graphics processing unit (GPU)-resident LES model, is used to conduct numerical experiments. The model solves the fully compressible Navier-Stokes equations cast in flux-conservative form on a non-uniform mesh. The full set of non-hydrostatic governing equations are given by:

$$\frac{\partial {\rho }_{d}}{\partial t}=-\frac{\partial {\rho }_{d}{\widetilde{u}}_{i}}{\partial {x}_{i}}+{F}_{\rho },$$
(6)
$$\frac{\partial {\rho }_{d}{\widetilde{u}}_{i}}{\partial t}+\frac{\partial {\rho }_{d}{\widetilde{u}}_{i}{\widetilde{u}}_{j}}{\partial {x}_{j}}=-\frac{{\rho }_{d}}{{\rho }_{m}}\left(\frac{\partial {\widetilde{p}}^{{\prime} }}{\partial {x}_{i}}+g{\rho }_{m}^{{\prime} }{\delta }_{i3}\right)-\frac{\partial {\tau }_{ij}}{\partial {x}_{j}}+{F}_{{u}_{i}},$$
(7)
$$\frac{\partial {\rho }_{d}{\widetilde{{\theta }}_{d}}}{\partial t}+\frac{\partial {\rho }_{d}\widetilde{{u}_{j}}{\widetilde{{\theta }}_{d}}}{\partial {x}_{j}}=-\frac{\partial {\tau }_{\theta j}}{\partial {x}_{j}}+\frac{{\widetilde{{\theta }}_{d}}{L}_{v}}{{T}_{d}{c}_{p}}{f}_{cond}+{F}_{\theta },$$
(8)
$$\frac{\partial {\rho }_{d}\widetilde{{q}_{v}}}{\partial t}+\frac{\partial {\rho }_{d}\widetilde{{u}_{j}}\widetilde{{q}_{v}}}{\partial {x}_{j}}=-\frac{\partial {\tau }_{{q}_{v}j}}{\partial {x}_{j}}-{f}_{cond}+{F}_{{q}_{v}},$$
(9)
$$\frac{\partial {\rho }_{d}\widetilde{{q}_{l}}}{\partial t}+\frac{\partial {\rho }_{d}\widetilde{{u}_{j}}\widetilde{{q}_{l}}}{\partial {x}_{j}}=-\frac{\partial {\tau }_{{q}_{l}j}}{\partial {x}_{j}}+{f}_{cond}+{F}_{{q}_{l}},$$
(10)

where ~ indicates the filtered quantity (omitted in main text); the subscripts “d” and “m” denote dry and moist, respectively; ui (m s−1) is the velocity vector in Cartesian coordinate (i = 1, 2, or 3); t (s) is time; ρd (kg m−3) is dry air density; Td (K) is air temperature; qv and ql (kg kg−1) are water vapor and liquid water content as a ratio to the mass of dry air; g = 9.8 m s−2 is gravitational acceleration; Lv = 2.5 × 106 J kg−1 is the latent heat of vaporization; cp = 1005 J K−1 kg−1 is the specific heat of dry air at constant pressure; τij (m2 s−2) is the sub-grid scale (SGS) stress tensor; τθj (K m s−1), \({\tau }_{{q}_{v}j}\) (kg kg−1 m s−1) and \({\tau }_{{q}_{l}j}\) (kg kg−1 m s−1) are the SGS temperature, water vapor and liquid water fluxes, respectively. ρm (kg m−3) is the moist air density given by

$${\rho }_{m}={\rho }_{d}(1+{q}_{v}+{q}_{l}).$$
(11)

The moist perturbation of density \({\rho }_{m}^{{\prime} }\) (kg m−3) is calculated as the departure from the dry hydrostatic component ρdh (Pa) as

$${\rho }_{m}^{{\prime} }={\rho }_{m}-{\rho }_{dh}.$$
(12)

θd (K) is dry potential temperature, and is related to temperature and pressure by

$${\theta }_{d}={T}_{d}{({p}_{0}/p)}^{{R}_{d}/{c}_{p}},$$
(13)

where p (Pa) is air pressure; p0 = 105 Pa is a reference pressure; Rd = 287.053 J K−1 kg−1 is dry air ideal gas constant. \({p}^{{\prime} }\) (Pa) is the pressure perturbation given by

$${p}^{{\prime} }={\left[\frac{{R}_{d}{\rho }_{d}{\theta }_{m}}{{p}_{0}^{{R}_{d}/{c}_{p}}}\right]}^{\gamma }-{p}_{dh},$$
(14)

where γ = cp/cv = 1.4 is the ratio of specific heat of dry air at constant pressure to constant volume; and θm (K) is the modified potential temperature given by

$${\theta }_{m}={\theta }_{d}[1+({R}_{v}/{R}_{d}){q}_{v}],$$
(15)

where Rv = 461.5 J K−1 kg−1 is water vapor ideal gas constant.

The fcond (kg m−3 s−1) term in Equation (8), (9), and (10) represents the transfer between water vapor and liquid water (cloud) from condensation (fcond > 0) and evaporation (fcond < 0) processes. A saturation adjustment assumption is adopted assuming a homogeneous distribution of thermodynamical properties within a grid volume, and condensation only occurs when the grid solution becomes supersaturated with respect to liquid. The condensation forcing term is taken from Rutledge and Hobbs (1983)49, and has the following form:

$${f}_{cond}^{*}=\frac{{\rho }_{v}-{\rho }_{vs}}{1+\frac{{L}_{v}^{2}{q}_{vs}}{{c}_{p}{R}_{v}{T}_{d}^{2}}},$$
(16)

where ρv = ρdqv, ρvs = pvs/(RdTd) = ρdqvs. qvs is the saturation water vapor mixing ratio. pvs is the saturation vapor pressure computed using the 8th-order polynomial fitting from Flatau et al.50. The amount of evaporated liquid is bounded by the available cloud water:

$${f}_{lim}={\rho }_{d}{q}_{l},$$
(17)

and the final forcing becomes

$${f}_{cond}=\frac{max[{f}_{cond}^{*},-{f}_{lim}]}{{\tau }_{cond}},$$
(18)

where τcond is the relaxation time scale which is an adjustable parameter that provides a time scale for the condensation forcing that is consistent with the resolvable scales. Here τcond = 1.0 s is adopted and the sensitivity of the resulting liquid water distribution and turbulence quantities to the choice of τcond was tested by Muñoz-Esparza et al.37. Despite idealized numerical setup, the equations and parameters were tested in Muñoz-Esparza et al.37, such that local cloud formation under free convective conditions can be achieved.

\({F}_{{u}_{i}}\) (kg m−2 s−2) represents the force imposed by the buildings. \({F}_{{u}_{i}}\) is modeled using the immersed body force method (IBFM) from Chan and Leach (2007)51:

$${F}_{{u}_{i}}=-{C}_{d}{\rho }_{d}| {\widetilde{u}}_{i}| {\widetilde{u}}_{i},$$
(19)

where Cd is the drag coefficient modeled as

$${C}_{d}={\alpha }_{m}{\beta }_{r}{\Delta }^{-1},$$
(20)

where \(\Delta=\root{{3}}\of{\Delta x\Delta y\Delta z}\) is the nominal grid size; αm = 1000 is a constant coefficient; and βr represents the ratio of volume in a cell occupied by the immersed body. To rectify the small error due to the leakage of air flow into the immersed body, which tends to homogenizes the scalar fields across the building interface, similar forcing terms (Fρ (kg m−3 s−1), Fθ (kg K m−3 s−1), \({F}_{{q}_{v}}\) (kg m−3 s−1), and \({F}_{{q}_{l}}\) (kg m−3 s−1)) are added to the mass and energy conservation equations:

$${F}_{\rho }=-{C}_{t}| {U}_{s}| ({\rho }_{d}-{\rho }_{ref}),$$
(21)
$${F}_{\theta }=-{C}_{t}| {U}_{s}| ({\rho }_{d}{\widetilde{\theta }}_{d}-{({\rho }_{d}{\theta }_{d})}_{ref}),$$
(22)
$${F}_{{q}_{v}}=-{C}_{t}| {U}_{s}| ({\rho }_{d}{\widetilde{q}}_{v}-{({\rho }_{d}{q}_{v})}_{ref}),$$
(23)
$${F}_{{q}_{l}}=-{C}_{t}| {U}_{s}| ({\rho }_{d}{\widetilde{q}}_{l}-{({\rho }_{d}{q}_{l})}_{ref}),$$
(24)

where Us = 1 m s−1 is the velocity scale, Ct = αtβrΔ−1 for αt = 10, and the subscript ‘ref’ refers to the reference conditions. Details and validation of the IBFM are provided in Muñoz-Esparza et al.35.

The SGS stress tensor and scalar fluxes are modeled using a prognostic TKE equation52,53. All prognostic quantities are discretized at the grid cell center. The fifth-order weighted essentially non-oscillatory scheme54 is implemented as advection scheme. The third-order Runge-Kutta scheme55 is used for time advancement. Heat and moisture sources are imposed at the ground surface (not including the walls of the buildings), detailed set-up is given in Domain configuration and simulation set-up.

Domain configuration and simulation set-up

A total of seven simulations are performed. The details of the simulation setup are presented in Table 1. The configuration of rural and urban areas are depicted in Fig. 2. The length, width, and height of the computational domain are Lx = 11.28 km, Ly = 7.455 km, and Lz = 3 km, respectively. The number of grids in horizontal x and y, and vertical z directions are nx = 1504, ny = 994, and nz = 122, respectively. The grid size in the horizontal direction is dx = dy = 7.5 m; and the grid sizes in the vertical direction stretch from dz = 7.5 m close to the ground to dz = 58 m at the model top. Time step, dt, for all simulations is 0.02 s. The initial boundary-layer height, zi, for all simulations is 520 m. The urban area has a horizontal width of Lc = 3750 m and is located at the center of the domain. The rows of buildings align with each other. Free convective condition is assumed for all simulations, i.e., no mean background horizontal wind.

All four lateral boundaries are periodic. Given the domain dimensions defined above, the urban footprint and its induced circulations remain well separated from the lateral boundaries. As a result, the influence of the urban area on the boundaries is negligible. A zero gradient top boundary condition is imposed for momentum and all scalars. Monin-Obukhov similarity theory is adopted to impose the momentum wall model for the bottom surface. In all simulations, the momentum roughness lengths of the rural and urban surfaces (excluding all walls of the buildings) are set as z0r = 0.02 m and z0u = 0.1 m, respectively35. The effect of the buildings on the flows are modeled using the IBFM, as described in the previous section. The scalar roughness length z0s is set to be 1/10 as large as the momentum roughness lengths in corresponding regions. A heat flux bottom boundary condition is applied in the simulation. Specifically, the spatially-averaged surface heat fluxes for rural and urban areas are Hr = 0.05 Km s−1 and Hu = 0.056 Km s−1, respectively, following the report of 56,57. For urban area, the heat flux for all the walls of the buildings is zero, and the heat flux for the ground surface varies with building density, λp, in order to keep the same total heating rate for all cases. The sources of water vapor are introduced into the simulation through a constant surface water vapor mixing ratio (in both space and time) of qv,0 = 0.017 kg kg−1 for both rural and urban surfaces in all simulated cases, in order to control variables and isolate the effects of urban morphology on cloud formation. Zero flux liquid water boundary conditions are applied at the rural, urban, and all walls of the buildings.

The flow is initialized with random noise added to a zero velocity profile. A four-layer atmospheric boundary layer (ABL) structure for initial temperature and water vapor profiles is imposed, as shown in Fig. S3. Below the initial boundary layer height zi = 520 m, a constant initial temperature of θi = 298.7 K is imposed; the water vapor concentration at z = zi is 0.0163 kg kg−1. This ABL structure is identical to that in ref. 37, which was directly compared with the LES results of58, and those LES results were validated against field measurements from the BOMEX campaign59. The initial liquid water concentration is set to zero across the entire domain. After the simulations reach quasi-steady state, instantaneous outputs of velocity, temperature, water vapor, and liquid water are analyzed.

The simulated results are the instantaneous outputs at t = 1950 s for all simulated cases. The pseudo-color plots in Fig. 4a–h are averaged in y direction within the two dashed lines shown in Fig. 2. The width between the two dashed lines is 1/5LC. The horizontal averaged quantities are denoted with 〈〉. Subscript x (y) indicates averaging in x (y) direction; subscript urban (core) indicates horizontal average over urban area (urban core). The turbulent fluctuation of a variable is calculated by subtracting its horizontal mean from that variable (e.g., \({w}^{{\prime} }=w-{\langle w\rangle }_{x,y}\)). Additional analyses at earlier times (e.g., 1650 s and 1800 s) show lower cloud amounts and a shallower boundary layer, but no qualitative differences in the results or conclusions.

Observational dataset

According to findings in ref. 10, the urban-rural land surface temperature difference and urban size are the most relevant controlling factors for the nighttime cloud enhancement during warm seasons. Therefore, we expect that the effect of urban morphological types of each city manifest the most in this subset of observational data. Nighttime cloud cover during warm seasons (April to September) over 44 cities with sizes greater than 1000 km2 are analyzed. This sampling also aligns our observations with the free-convective LES setup, because nocturnal winds are typically weaker than daytime winds, making calm-wind conditions more likely60. The selected cities are listed in Table S2, which contain 23 inland, 13 coastal cities, and 8 mountainous cities. Coastal cities, which are potentially subjected to land-sea breeze influences, are defined as those located within 70 km from the sea61,62. Mountainous cities are identified with a greater than 1000-m elevation difference with the highest point within 70-km buffered surrounding areas. Global Multi resolution Terrain Elevation Data 2010 (GMTED2010) is used to identify the elevation difference. The rest of the cities are identified as inland cities. The cloud cover is obtained from MODIS cloud masks (MYD35_L2 C6.1) from 2002 to 2020. The cloud enhancement, ΔCloud, is defined as the relative difference between cloud cover over an urban area, cloudurban, and that over the surrounding rural area, cloudrural, i.e., ΔCloud = (cloudurban − cloudrural)/cloudrural. According to10, the urban areas are defined using US Census urban areas product, and the background is each urban domain’s surrounding region but excludes a transition buffered area to avoid urban-influenced clouds in upwind and downwind directions in the atmosphere. The transition and background areas are buffered proportional to the urban size. Waterbodies are removed across the urban-background domains to avoid nonurban influences. A t test is conducted to identify the significance of ΔCloud for individual cities in each given month over 18 years at p = 0.05 level10. The uncertainties and potential bias of the cloud cover from MODIS are reported by refs. 63,64,65.

Two urban form parameters are selected for analysis: (1) street-canyon aspect ratio h/d, and (2) building density λp. Here h and d are building height and canyon width, respectively. Other urban form parameters such as sky view factor and impervious area fraction are correlated with the selected parameters, and are therefore not selected for analysis. The selected urban form parameters are calculated based on the LCZ map of the continental United States at a 100 m spatial resolution, derived from multiple Earth Observation datasets and expert and crowd-sourced LCZ class labels66,67. The LCZ map for each city is derived from the continental United States LCZ map, as shown in Fig. S4. Since the urban morphology near the center of the city (referred to as urban center hereafter) has the most variations among different cities, the spatially averaged h/d and λp over urban center are calculated to represent the urban morphology. The urban center of each city is defined as a circular area of 400 km2, centered at the city’s geographic center. A sensitivity test is conducted to show that the results are not sensitive to the selected urban center size (Figs. S5 and S6). The spatially averaged h/d and λp are derived from the distribution of h/d and λp over the urban center of each city, converted from the city scale LCZ map according to the typical values of each LCZ type (Table 3 in ref. 22).