Divergent Urban Signatures in Rainfall Anomalies Explained by Pre‐Storm Environment Contrast

Diverse urban‐induced rainfall anomalies across different cities highlight the need for additional insights into land‐atmosphere interactions over complex urban environments. Based on empirical analyses of 144 warm‐season storms and high‐resolution numerical simulations over Nanjing, China, we show divergent patterns of urban‐induced rainfall anomalies for storms with contrasting synoptic conditions, despite of rainfall enhancement over downtown from a climatological perspective. We propose two simple gage‐based metrics to characterize both the thermal and turbulent conditions in pre‐storm environment, and classify storms into different groups. Our results show that elevated rainfall magnitudes and heavy rainfall frequency are equally expected in either downtown or suburb regions (upwind or downwind). This is mainly dictated by the relative dominance of urban‐induced thermal perturbations and mechanical turbulence (i.e., related to surface roughness) under different synoptic conditions. We develop four paradigms of urban rainfall modification, and thus provide a predictive understanding of rainfall anomalies in urban environments.


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The divergent urban signatures are tied to interacting or contradicting factors in the processes of heat, moisture, and momentum exchange between urban canopies and the lower atmosphere. For instance, urban-rural thermal contrast (i.e., UHI) enhances local convection that favors moist convergence into cities, while increased surface roughness associated with urban buildings might lead to blocked or bifurcated flows over urban-rural boundaries (Bornstein & Lin, 2000;NRC, 2012;Oke et al., 2017). These thermal perturbations and mechanical turbulence further dictate when and where positive rainfall anomalies are expected. Dou et al. (2015) observe enhanced rainfall over downtown Beijing for a storm with strong UHI, while storms tend to propagate toward downwind region when the thermal contrast is weak. The divergent urban signatures are further revealed based on modeling analyses of two storms with contrasting synoptic flow intensities over Nanjing, China . Elevated rainfall is expected over upwind rather than downtown or downwind region when the synoptic flow is calm. This highlights the dominant role of urban canopy as barriers in modifying regional rainfall processes (see also Yang et al., 2019 for additional evidence). A previous attempt to synthesize the divergent urban signatures is to classify storms according to their flow regimes (in terms of wind speed and direction, e.g., McLeod et al., 2017). Unfortunately, the impacts of the urban-induced thermal perturbations and mechanical turbulence have not been considered in tandem so far. Lorenz et al. (2019) set the first example of its kind by carrying out a climatological analysis of 11 yr warm-season rainfall anomalies over Berlin, Germany. Their results show downwind storm intensification is not a typical feature. However, it remains elusive to what extent the thermal perturbations and mechanical turbulence are important in dictating divergent urban-induced rainfall anomalies. These knowledge gaps thus impede a predictive understanding of urban rainfall modification.
Here, we expect to fill the knowledge gaps by synthesizing the divergence in urban-induced rainfall anomalies as reported in worldwide cities. We explain the divergence by proposing simple gage-based metrics that characterize both thermal and turbulent conditions in pre-storm environment. We choose Nanjing, China as the study area. This is primarily because the city has simple physiographic characteristics, that is, with the absence of land-water boundaries and complex terrains, that excludes complex interactions between cities and regional topography (e.g., Ryu et al., 2016;Yang et al., , 2019. We also emphasize that our analyses are designed to inform the urban hydrology community keen on hydrometeorological designs with flood-control purposes. A key issue of design storms (i.e., extreme rainfall with large recurrence intervals) is to adequately represent the impacts of climate change and urbanization on the flood-producing storms (e.g., W. Zhang et al., 2018). While previous climatological analyses highlight enhanced rainfall over urban areas (e.g., Daniels et al., 2016;Niyogi et al., 2017;Shastri et al., 2015;Singh et al., 2016Singh et al., , 2020Trusilova et al., 2008;D. Wang et al., 2021;Wu et al., 2019), we hypothesize that the signatures become divergent for severe flood-producing storms. Existing knowledge may thus fail to benefit hydrometeorological designs in cities.

Data and Methodology
Our empirical analyses are primarily based on 73 rain gages over and surrounding Nanjing (Figure 1a). These rain gages provide continuous hourly rainfall observations during the warm-season months (i.e., April-September) of 2014-2017. The rainfall records have been through strict quality control procedures (see Yang, Li, et al., 2021 for details). There are 33 meteorological stations (co-located with rain gages) that provide observations of 2 m temperature and 10 m wind (both speed and direction) during 2014-2016. We develop a storm catalog based on the hourly rainfall time series from rain gages within the city domain (see Figure 1 for location). This ensures the existence of interactions between each storm and the city. An individual storm is automatically selected based on the thresholds of hourly rain rate as well as the length and accumulated rainfall during the dry-down period between any two individual storms (see Text S1 in Supporting Information S1 for details). We discard storm events with durations less than 4 hr. These short-duration storms are mostly localized thunderstorms, and are not frequently responsible for severe flood hazards over Nanjing. Our storm catalog consists of 144 warm-season storm events in total. The average storm duration is 12.7 hr, with 43% events exceeding 12 hr. These storms are frequently associated with the propagation of extratropical cyclones from the upper Yangtze River or landfalling tropical cyclones from the western Pacific (Ding & Sikka, 2006;Ding et al., 2001;Jiang et al., 2020;Tao & Ding, 1981;J. Wang et al., 2020).
We characterize the pre-storm environments for each storm in the catalog (i.e., 32 storms are not characterized due to absent meteorological observations in 2017). For thermal conditions, we calculate the difference of 2 m temperature between two urban sites and two rural sites (i.e., ∆T, see Figure 1a for locations, and Text S2 in  Figure S1 in Supporting Information S1 for more information). Black thick lines represent the boundary of downtown Nanjing.
Supporting Information S1 for details). For turbulent conditions, we calculate the mean urban canopy wind by averaging the 10 m wind from all meteorological stations within downtown Nanjing (i.e., ). Both metrics are calculated over the three-hour period prior to storm. The urban-rural temperature difference ranges from −2.9°C to 4.0°C. There are 80 storms with positive temperature anomalies (i.e., urban minus rural). The average thermal contrast for these storms is 0.80°C. The mean urban canopy wind speed ranges from 0.2 to 5.1 m/s, with east as the dominant wind direction. The average urban canopy wind speed is 1.9 m/s. By using 0.80°C and 1.9 m/s as the two independent criteria, we obtain four storm groups that represent different combinations of thermal (i.e., Hot for ∆T ≥ 0.80°C and Warm for 0°C ≤ ∆T < 0.80°C) and turbulent conditions (i.e., Windy for ≥ 1.9 m/s and Calm for 0.2 m/s ≤ < 1.9 m/s). The four groups are referred to as: Hot-Windy, Hot-Calm, Warm-Windy, Warm-Calm. The number of storms within each group is 14, 20, 26, and 20, respectively (see Figure S4 in Supporting Information S1 for statistics). Additionally, there are 32 storms with negative ∆T. These storms (referred to as Cool storm group) will be discussed separately, as they are relatively less frequent than their counterparts (i.e., storms with positive ∆T). Our results are not sensitive to the choice of threshold values used for storm grouping (see Text S3 in Supporting Information S1 and Section 3.1 for details).  Table S2 in Supporting Information S1 for details). The Advanced Research version of the Weather Research and Forecasting model (WRF, V3.8.1) is used in this study. We configure three one-way nested domains, with the grid spacing of 9, 3, and 1 km, respectively (Figure S1a in Supporting Information S1). The outer domain covers eastern China, while the innermost domain centers over the city of Nanjing (Figure S1b in Supporting Information S1). The WRF physics options are mostly adapted from Yang, Li, et al. (2021). The Japanese 55 yr Reanalysis (with a spatial resolution of 1.25° and a temporal resolution of 6 hr) are chosen as initial/boundary forcings. We carry out ensemble simulations for each storm using different microphysics schemes (including Thompson, WSM6, and Morrison) and initial conditions by varying the model's initialization time (see Tables S3 and S4 in Supporting Information S1 for details). We present the ensemble mean in the following analyses (similarly also see Doan et al., 2022). We focus on the innermost domain, due to its highest spatial resolution and its ability to resolve fine-scale convective processes (Kain et al., 2008).
We carry out two sets of WRF simulations, that is, CTRL and "No-Urban." Both simulations use the same model configurations (i.e., five ensemble members for each storm), including the single-layer Urban Canopy Model and the updated three-category urban land use/land cover over eastern China (Figure 1a). The exception is for "No-Urban" simulations, the urban land use within domain 3 is replaced by cropland (i.e., the dominant land use type, Figure 1b). The difference between CTRL and "No-Urban" simulations shows urban-induced rainfall anomalies over Nanjing. Figure 1 shows the composite of heavy rainfall magnitudes (represented by the 95th percentile of storm total rainfall) and frequency (represented by the number of hours with hourly rain rate exceeding 25 mm/hr) of the entire storm catalog (144 in total). A notable feature is that the high values of both rainfall magnitudes and frequency are observed over downtown Nanjing, with strong gradients from the center toward surrounding rural regions. For instance, the number of heavy rainfall hours is approximately 20 hr for three urban rain gages, while most rural rain gages witness less than 10 hr of heavy rainfall (i.e., 0.07 hr per storm on average, Figure 1d). The spatial patterns of heavy rainfall magnitudes and frequency derived from the storm catalog resemble that of the warm-season rainfall climatology over Nanjing (see Figure 3 in Yang, Li, et al., 2021). This highlights a climatological tendency of intense and frequent rainfall over downtown Nanjing, demonstrating a strong urban signature in warm-season rainfall anomalies. The signature can be represented by a limited number of storms. The spatial patterns of the composite metrics remain unchanged by only analyzing storms during 2014-2016 (112 in total, Figure S2 in Supporting Information S1).

Empirical Analyses
The spatial patterns of the composite rainfall magnitudes and frequency become remarkably divergent when classifying the storms into different groups according to their pre-storm environments (i.e., thermal and turbulent conditions, Figure 2). Since synoptic flows are variant in directions across storms, we rotate the geographic positions of rain gages relative to the city center according to the direction of mean urban canopy wind , by making the due north as the downwind. We implement the rotation procedures for every storm within the catalog. For the two "Windy storm" groups (i.e., Hot-Windy and Warm-Windy, Figures 2a and 2e), storms are more likely to produce heavy rainfall (in terms of both magnitude and frequency) than their counterparts for the two "Calm storm" groups (i.e., Hot-Calm and Warm-Calm, Figures 2c and 2g). This is expected as extreme rainfall over eastern China is mainly associated with strong synoptic forcings, for example, extratropical cyclones, tropical cyclones, and monsoonal fronts (e.g., Ding, 1992;Ding & Chan, 2005;Ding et al., 2001;Lai et al., 2020;Lau et al., 1988;Luo et al., 2016).
There are sharp contrasts in the spatial patterns between the two "Hot storm" groups (i.e., Hot-Windy and Hot-Calm) and two "Warm storm" groups (i.e., Warm-Windy and Warm-Calm). Larger storm total rainfall and more frequent heavy rainfall tend to be observed over downtown Nanjing when the urban-rural thermal contrast is large (Figures 2a-2d). We observe a second cluster of larger magnitude and frequency of heavy rainfall over the upper left quadrant (i.e., downwind left, approximately 40-60 km away from the city) for the Hot-Windy storm group (Figures 2a and 2b, see Figure S5 in Supporting Information S1 for statistics). The rainfall anomalies over this quadrant are statistically different from the other three quadrants (based on the Student's t test, P = 0.05, Figure S5a in Supporting Information S1). The positive rainfall anomalies over the city (79.2% above the domain-average, Figure S5a in Supporting Information S1) might be partially associated with the enhanced convection driven by the elevated surface temperature within the urban canopy (e.g., Harnack & Landsberg, 1975;Shepherd, 2006;Simón-Moral et al., 2021;Yuan et al., 2020). The second cluster of positive rainfall anomalies is associated with the mechanic perturbations of urban canopy through enhanced surface roughness (i.e., buildings) that leads to decelerated flows. This contributes to enhanced convergence over the downwind region when the flows bypass the city (e.g., Debbage & Shepherd, 2019;Kim et al., 2021;Shem & Shepherd, 2009;Yue et al., 2021;D.-L. Zhang et al., 2019). By contrast, we observe a large spread of heavy rainfall over the four quadrants for the Hot-Calm storm group, with storm centers frequently over downtown (44.9% above the domain-average, Figures 2c and 2d). This is driven by the surface pressure gradient induced by urban-rural thermal contrast that induces city-inward wind anomalies and enhanced moist convergence over the city (e.g., Oke et al., 2017).
The urban canopy effect is more clearly revealed by focusing on the Warm-Windy storm group, but is different from that demonstrated in the Hot-Windy storm group (Figures 2e and 2f). The elevated magnitude and frequency of heavy rainfall are observed in the lower right quadrant (i.e., upwind right, within 25 km away from the urban-rural interface). The mean anomaly of the median storm total is 9.3 mm (53.4% above the domain-average, Figure S5e in Supporting Information S1). This is about two times on average as large as that over downtown Nanjing (27.7% above the domain-average, Figure S5e in Supporting Information S1). The increased surface roughness leads to reduced momentum and thus enhanced convergence when the airflows initially approach the city. When both the thermal and turbulent conditions are moderate, that is the Warm-Calm storm group, the spatial pattern of heavy rainfall is determined by the relative dominance of thermal perturbations and mechanical turbulence. We notice a cluster of relatively heavy storm magnitude (about 46 mm) over the due eastern boundary of downtown Nanjing (Figures 2g and 2h). The flows over downtown induced by enhanced convergence are deflected to the right relative to flow direction by the Coriolis force (Collier, 2006;Fan et al., 2019;Lu & Li, 2022;Ohashi & Kida, 2002;Oke, 2002;Oke et al., 2017;Yang, Ni, et al., 2021). Our results pertaining to the divergent rainfall patterns remain unchanged by specifically focusing on those extreme events, that is, the 90th percentile of storm rainfall total and the maximum number of heavy rainfall hours ( Figures S6 and S7 in Supporting Information S1). For the Cool storm group (32 storms, ∆T < 0°C), the inversed pressure gradient leads to divergence over the city (i.e., clockwise airflows in the northern hemisphere), which together with the urban canopy effect contributes to enhanced rainfall (around 50%) over the upwind left quadrant ( Figure S8 in Supporting Information S1). Similar contrasts across storm groups exist using different thresholds for storm classification (Figures S9-S11 in Supporting Information S1). . The left column shows the median value of storm total rainfall (in mm), while the second column shows the average number of heavy rainfall hours (i.e., with hourly rain rate exceeding 5 mm/hr) for storms within each corresponding group. The numbers shown in the plots represent the radial distance away from the center of downtown Nanjing (in km, positive is toward east). The 25 km circle can roughly represent the extent of downtown Nanjing. The due north represents the downwind direction. The spatial pattern is interpolated from the observations of geographically rotated rain gages (according to the city-averaged urban canopy wind direction 3 hr before each storm). The interpolation is smoothed using a two-dimensional convolutional filtering approach (e.g., Neyshabur, 2020;Shanks et al., 1972). The grid spacing is 5 km.

Modeling Analyses
We further provide insights into the contrasting rainfall anomalies by examining the difference between the CTRL and "No-Urban" simulations (i.e., the ensemble mean), to verify our empirical interpretations mentioned above. The CTRL simulations could capture the spatial and temporal rainfall variability of the storms (Figures S12 and S13 in Supporting Information S1). The mean bias of hourly rain rate between rain gage observations and the corresponding model grids ranges from −0.7 to 1.0 mm/hr. We compute the Heidke Skill Score (HSS) for the simulated rainfall to get a quantitative evaluation of the model's performance. The domain averaged HSS ranges from 0.26 to 0.70, indicating good model performance (Enenkel et al., 2006;Šaur, 2015). The spatial patterns of simulated rainfall total agree with the satellite-based rainfall estimates ( Figure S12 in Supporting Information S1), even though the magnitudes show a bit overestimation. The evaluation statistics for the 2 m temperature and 10 m wind speed are within comparable ranges to previous analyses (see Table S5 in Supporting Information S1 for details, e.g., Chen et al., 2022Chen et al., , 2021He et al., 2019;Miglietta et al., 2010;Misaki et al., 2019;Nilo et al., 2020). Model biases can be further reduced with additional efforts, for example, improving parameterizations of sub-grid processes (e.g., Q. Li et al., 2021;Shen et al., 2019;Yu et al., 2021;X. Zhang, Yang, et al., 2021), but this is beyond the scope of the present study.
The differences of the simulated storm total rainfall between CTRL and "No-Urban" simulations are shown in Figure S14 in Supporting Information S1. We implement a similar rotation procedure for the simulated rainfall fields with that for rain gage observations, to facilitate inter-comparisons across different storm events. The rotation procedure is repeated for the simulated hourly rainfall and wind fields (both u and v components), by referring to the mean steering-level wind direction (i.e., 700 hPa) over Nanjing to make the due north as the downwind. The rotation procedure is equally implemented for both the CTRL and "No-Urban" simulations, with their differences of the composite rotated rainfall fields shown in Figure 3.
The urban-induced rainfall anomalies largely resemble the rainfall composites as shown in empirical analyses. There are notable positive rainfall anomalies, that is, 30-60 mm, over the city (i.e., the 25 km circle in Figure 3) and its downwind region (i.e., 40-70 km away from the city) for the 14 September 2016 storm (i.e., a Hot-Windy case, Figure 3a). The anomalous wind vectors point upwind in the lower atmosphere (i.e., at 900 hPa), highlighting the role of urban canopy in decelerating the synoptic flows over the city (see Figure S15 in Supporting Information S1 for increased frictional velocity over the city). The transitional vectors of wind anomalies in the downwind region indicate the presence of convergence after the flows bypassing the city. A cyclonic structure of wind anomalies is observed for both the 11 July 2014 storm (i.e., a Hot-Calm case, Figure 3b) and the 28 June 2015 storm (i.e., a Warm-Calm case, Figure 3d), favoring convergence of moist flows toward the city, since there is increased surface temperature within the downtown region under weak synoptic flows (see Figure  S15 in Supporting Information S1 for temperature and water vapor mixing ratio contrasts). The cyclonic wind anomalies for the two storms are accompanied by anti-cyclonic circulations in the middle-level atmospheres (i.e., at 700 hPa, Figures S16b and S16d in Supporting Information S1). The cyclonic structure is more obvious for the 11 July 2014 storm, indicating the enhanced convection driven by strong urban-rural thermal contrast. A relatively strong urban canopy wind (i.e., = 1.8 m/s) for the 28 June 2015 storm leads to an imbalance of wind anomalies between the left and right quadrants (Figure 3d). A weak urban-rural temperature contrast less likely promotes airflows into the city, but can lead to convergence outside the city (i.e., on the right side perpendicular to the wind direction) due to the deflected flows over downtown. This is responsible for approximately 20 mm rainfall anomalies over the urban-rural interface east of the city. For the 4 July 2014 storm (i.e., a Warm-Windy case, Figure 3c), positive rainfall anomalies are mainly observed over the wing-sides of the city. We note that the wind vectors show a feature of bifurcated flows upwind of the city (Figure 3c, similarly see Dou et al., 2015;Miao et al., 2011;D.-L. Zhang et al., 2019). The perturbed flows converge after bypassing the city (see the wind vectors in Figure 3c). This leads to more rainfall over the downwind region for the Warm-Windy storm.

Synthesis
To further verify the insights obtained from our empirical and modeling analyses, we carry out a meta-analysis of the existing literature on urban rainfall modification (similarly see Liu & Niyogi, 2019). Our pool of literature integrates the reference list in Liu and Niyogi (2019) and additional google searches with the key words "urban rainfall anomalies" and "case study" (see Text S4 in Supporting Information S1 for details). We select 39 papers from the literature pool for further analysis. The 39 papers provide 48 case studies across worldwide cities. We classify those storm cases into four groups according to their thermal and turbulent conditions in the pre-storm environments. We evaluate whether the locations of positive urban-induced rainfall anomalies are consistent with our findings presented above. Our meta-analysis shows that about 90% of cases (ranging from 69% to 100%) are consistent with the urban-induced rainfall anomalies as found over Nanjing (Table S6 in Supporting Information S1). This confirms the dependence of divergent urban-induced rainfall anomalies on pre-storm environment. Those inconsistent cases might be partially related to interactions between regional topography and cities that contaminate the urban signatures. We provide a schematic summary of our findings in Figure 4. The schematic summary can potentially serve as the paradigms of urban rainfall modification, and thus provide a predictive understanding of rainfall anomalies in urban environments.

Conclusions and Discussions
Our analyses show divergent patterns of warm-season rainfall anomalies over Nanjing. The divergence is dictated by the relative importance of urban-induced thermal perturbations and mechanical turbulence under . A schematic summary of urban signatures (in terms of thermal perturbations and mechanical turbulence) in rainfall anomalies under different pre-storm environments. In (a) a notable urban heat island (UHI) and strong synoptic flows prior to the storm (i.e., Hot-Windy), (b) a notable UHI and relatively weak synoptic flows prior to the storm (i.e., Hot-Calm), (c) a moderate UHI and strong synoptic flows prior to the storm (i.e., Warm-Windy), and (d) a moderate UHI and relatively weak synoptic flows prior to the storm (i.e., Warm-Calm). Red and orange shades indicate the intensity of urban-rural thermal contrast. The blue plus signs show the location of positive rainfall anomalies, with the size indicating the magnitudes. The wind speed contrast is reflected by the length of the arrows. The schematic summary is partially inspired by Oke et al. (2017) (see Figure 4.35 in Chapter 4), but is comprehensively extended to establish explicit connections between cities and external weather phenomenon (i.e., warm-season rainfall) with different synoptic conditions. It is applicable to cities with simple geographic settings in the northern hemisphere.
contrasting pre-storm environments. Our results highlight the importance of considering pre-storm environments in land-atmosphere interactions, and thus provide a predictive understanding of urban rainfall modification. Although climatological analyses point to the dominance of urban-rural thermal contrast in dictating rainfall anomalies over Nanjing (e.g., the positive rainfall anomalies over downtown, Figure 1), they are unfortunately not readily able to benefit hydrometeorological designs with flood-control purposes. This is because elevated extreme rainfall and flood hazards over suburbs rather than downtown can be expected when there are favorable pre-storm environments, for instance, strong synoptic flows together with weak urban-rural thermal contrast (like the Warm-Windy storm group). A "poster-child" example is the deadly 14 July 2021 storm over Rotterdam-Brussels-Cologne region that caused unprecedented hazards over western Europe (Yang, Ni, et al., 2021). The mitigation strategies and flood hazard awareness over suburbs are always inadequate compared to those over downtown regions, which are thus responsible for elevated flood risks in complex urban environments. Our predictive understanding of urban rainfall modification may potentially contribute to storm now-casting algorithms for fine-scale flood prediction and adaptation in advance. The simple physiographic setting of Nanjing makes our knowledge potentially transferrable to worldwide cities. A caveat of our study is that we do not address the impacts of urban aerosols on top of thermal and turbulent perturbations. This can be remedied based on either empirical analysis with additional characterization of atmospheric environment or numerical simulations that explicitly represent the role of urban pollutants in microphysical processes (e.g., WRF-Chem).

Data Availability Statement
The data sets of this research are available at https://doi.org/10.6084/m9.figshare.21441678.v1. The Japanese 55 yr Reanalysis is available at https://doi.org/10.5065/D6HH6H41. The Integrated Merged MultisatellitE Retrievals for GPM products are available at https://gpm.nasa.gov/data/imerg. 14380804) and the Frontiers Science Center for Critical Earth Material Cycling Fund. The numerical simulations in this paper have been done on the computing facilities in the High-Performance Computing Center (HPCC) of Nanjing University. The authors thank the anonymous reviewer for providing valuable comments that substantially improve the manuscript.