We selected eight representative cities across mainland China for this study (Fig. 1). Two cities were selected from each region except northwestern and southwestern China (Table 1). The eight cities vary significantly with respect to their total population, footprint areas, and urbanization rate. In this study, the footprint of a city is composed of the grids that have an hourly number of location requests no less than the median of the daily NLR time series of that grid over the whole month, i.e., the grids with at least one NLR every hour on average.

Haikou and Zhuhai are located in southern China, which has mean annual precipitation between 1600 and 3000 mm. Among the eight cities, Zhuhai is the least-populated city, but it has the highest urbanization rate. In central China, we selected Hefei and Xiangyang, which have mean annual precipitation between 800 and 1600 mm. Two cities, Lanzhou and Hengshui, were selected from a semi-humid region in northern China with a mean annual precipitation between 400 and 800 mm. Hengshui has the largest footprint area but the lowest urbanization rate among the cities. Harbin and Jilin are located in northeastern China. The mean annual precipitation of Harbin and Jilin ranges from 400 to 800 mm and between 800 and 1600 mm, respectively. Harbin is the most populated among the eight cities.

The smartphone location data were obtained from the Tencent big data portal (https://heat.qq.com/, last access: 2 April 2019). The portal provides location request records of global smartphone users via the Tencent Maps application programming interface (API). A location request record is generated when a smartphone user requests any LBS, which includes but is not limited to navigation, car hailing, food and merchandise delivery, or social media check-ins. Table 2 lists the popular LBS applications that collect users' location requests. These apps are developed for various purposes, including social communication, entertainment video watching, mobile web browsing, e-commerce trading and shopping, mobile game playing, traveling and transportation, and so on. Every application has a large group of active users who request LBSs using a large number of monthly unique devices across China.

The Tencent big data portal releases the number of location requests per a 0.01∘×0.01∘ regular grid for every 4–5 min. Compared with other Chinese social media platforms, Tencent is the most popular one with the largest social community, which is reported to have nearly 1.1 billion monthly active users as of 2018 (https://www.tencent.com/en-us/company.html, last access: 26 August 2019). Ma (2019) compared the NLR dataset with visitor numbers in a few places and confirmed that the NLR data are a good proxy for investigating dynamic population changes. We collected the NLR data of the grids within the administrative boundaries of the eight cities from 1 to 31 August 2017.

This study used the Version 05B Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG) 30 min precipitation dataset (Huffman et al., 2019), which has a spatial resolution of 0.1∘×0.1∘. This dataset has been evaluated and widely used (Wang et al., 2017; Zhao et al., 2018; Su et al., 2018). The news reports about the flooding events in the eight cities were mainly collected from the Chinese mainstream online media, including Xinhuanet, Ecns.cn, Sohu, etc.

The smartphone location request record can be represented by a series of spatial points as follows: {(xi, yi, Tsi)}, i=1, 2, …, n. Each point contains its geographic coordinates (x, y) and a time (T) when the LBS is requested. The NLR was then aggregated to time series per grid or per city as illustrated below.

At the city level, a time series hourly NLR was established by adding up all location requests from the grids within the footprint area of that city. The magnitudes of the NLR in different cities vary significantly due to the different numbers of smartphone users. To make the NLR in different cities comparable, we normalized the NLR using the median-interquartile normalization method, which is more robust to anomalies than other common approaches using sample mean and standard deviation (Geller et al., 2003).

We employed the Seasonal Hybrid Extreme Studentized Deviate (S-H-ESD) method (Vallis et al., 2014) to detect anomalies from the time series NLR, which can be represented by the following additive model: 1Ts=T+S+R, where T, S, and R denote the trend, seasonality, and residual components in the time series data, respectively. The S-H-ESD method assumes that the trend and the seasonality would not be significantly disrupted by rapidly evolving events that last for only a few hours. Two major steps are involved in the method. First, it uses the piecewise median method to fit and remove the long-term trend and then the seasonal and trend decomposition using locally estimated scatterplot smoothing (STL) to remove seasonality (Cleveland et al., 1990). Using the STL to remove the long-term trend would introduce artificial anomalies (Vallis et al., 2014). In this study, the underlying trend in the time series NLR is approached using a piecewise combination of the biweekly medians, which show little changes over the whole time series.

In the second step, the S-H-ESD method employs the Generalized Extreme Studentized Deviate (GESD) statistic (Rosner, 1975) to identify significant anomalies in the residuals. The GESD calculates the statistic (G) based on the mean (r‾) and the standard deviation (s) of the observations. 2G=maxrj-r‾s Given the upper bound of u suspected anomalies, the GESD performs u separate tests. In each test, the GESD re-computes the statistic G after removing the observation rj that maximizes |rj-r‾| and then compares G with the critical value λ as defined below. 3λ=(k-1)t1-a/(2k),k-2λkk-2+t1-a/(2k),k-22, where k denotes the number of the observations in the time series after eliminating a suspected anomaly in the last run, and tp,d represents the pth percentile of a t distribution with a d degree of freedom. In this study, we set the significance level a to 0.05 and the number of anomalies to no more than 25 % of the total observations. Each test identifies one anomaly in the residuals when G>λ. The identified anomaly is either a positive or negative, depending upon whether the residual is greater or smaller than 0, respectively.

In this study, an individual anomaly is represented with a vector, 4v=(x,y,t,obs,res), where x and y denote the coordinates of the grid centroid, t denotes the observation time, and “obs” and “res” denote the observation and the residual (R in Eq. 1) in the time series. This study uses an anomaly's absolute residual to describe its unusual deviation from its expectation.

A rainstorm disaster, once it significantly impacts the cities, usually can trigger an outbreak of NLR anomalies in multiple places across the city. To collectively characterize the abnormal human responses, this study defines three indices: the total number (Nt), the total residual (Rt), and the mean density (Dt) of the positive or negative anomalies. The mean density is defined as follows: 5Dt=∑i=1NtBiNt, where Bi denotes the number of neighborhood anomalies within a Manhattan distance of a five grid (∼5 km) radius of the ith anomaly. The radius is large enough to cover most urban facilities nearby the anomaly.

An anomaly score is then defined based on the aforementioned indices to evaluate the city residents' responses to a rainstorm event. First, we surveyed the hourly changes of the indices and calculated the quartiles (Q1–Q3) and interquartile range (IQR) of each index for every hour every day. The score of an index is defined by 6SV,t=Vt-Q1IQRifVt≤Q1,0ifQ1<Vt<Q3,Vt-Q3IQRifVt≥Q3, where Vt represents one of the three indices at time t. According to Tukey's fences (Tukey, 1977), the score is considered an outlier if its absolute value is greater than 1.5 or an extreme if it is greater than 3. The final anomaly score is the mean of the three index scores.

In this study, we examined city residents' responses to the rainfall events in August 2017. The national average precipitation of this month is 124.6 mm, which is the highest in 2017 and 21.3 % more than the average precipitation for August in previous years.

We defined a rainfall event as a precipitation process that lasts for at least 2 h and with no rain preceding it for at least 1 h. The severity of a rainfall event is described by its duration, accumulated precipitation, and peak rainfall intensity. The duration refers to how long a rainfall event lasts, and the accumulated precipitation is the total precipitation received during a rainfall event. The peak rainfall intensity (Id) is widely used to estimate the possible rainfall intensity threshold that triggers city flooding (Cannon et al., 2007; Diakakis, 2012) and is defined as below. 7Id=max∑i=jj+d-1Pid,j=1,2,…,N-d+1, where Pi denotes the precipitation during the ith time interval, N denotes the total number of the time intervals in a rainfall time series, and d denotes the width of the moving time window that was used to search for the maximum accumulated precipitation in a rainfall event. Based on the peak rainfall intensity, the August rainfall events in the eight cities can be categorized as a moderate rainstorm (0.5 mm h-1<I1≤4 mm h-1), a heavy rainstorm (4 mm h-1<I1≤8 mm h-1), or a violent rainstorm (I1≥8 mm h-1).

For the purpose of calculation, we downscaled the precipitation data to the same spatial resolution as that of the NLR using the nearest-neighbor interpolation method. At the city level, the rainfall of a city is defined as the total of the half-hour Tropical Rainfall Measuring Mission (TRMM) precipitation within the human footprint. At the grid level, the rainfall of each grid refers to the total precipitation received by that grid within a certain time period.

The eight cities could be categorized into two groups in terms of the total precipitation amount in August 2017 (Fig. 2a). The first group includes Haikou, Zhuhai, and Hefei, with total precipitation more than 400 mm. The summer monsoon brings plenty of water to the two coastal cities (i.e., Haikou and Zhuhai). Typhoon Hato, when it made landfall on 23 August, dumped an additional 68 and 108 mm of water on Haikou and Zhuhai, respectively. By contrast, the inland city Hefei, received 47.6 % more precipitation in 2017 than the average mainly due to a few unusual rainstorms in August 2017 (Hydrology and Water Resource Bureau of Hefei, 2018).

The second group includes all the other cities, which had less than 400 mm of precipitation in August 2017. The city Lanzhou is located in the northwestern China and had the least precipitation at 250 mm. The two inland cities, Xiangyang and Hengshui, both had slightly more precipitation at 300 mm. The precipitation of the two northeastern cities, Harbin and Jilin, ranged between 320 and 350 mm and was mainly brought in by the northwestern vortexes.

There were at least 15 rainstorms and 2 flooding events in each city. The cities of Haikou, Lanzhou, and Harbin witnessed more than 20 rainstorms and about a quarter of them caused serious flooding problems. The number of rainstorms in the other cities ranged from 15 to 20, and about 2 to 4 of them caused flooding problems in the cities.

We identified the peak rainfall intensity threshold value that likely triggers city flooding using the method developed by Cannon et al. (2007) and Diakakis (2012). The method plots peak the rainfall intensity of different time windows against the corresponding rainfall duration. The flood-triggering threshold is defined as the upper limit of the peak rainfall intensity that tends to lead to urban flooding but actually does not. As shown in Fig. 2b, for the rainfall thresholds calculated based on 0.5, 1, 2, and 3 h time windows, the city ranking shows no change with an order of Haikou, Jilin, Hengshui, Zhuhai, Hefei, Lanzhou, Harbin, and Xiangyang. The ranking shows some fluctuations when the flooding-triggering rainfall threshold values were calculated with a time window of more than 3 h. However, Haikou and Harbin are always the top two cities, whereas Xiangyang is the last one on the ranking list. It is worthy to note that a rainstorm with a peak rainfall intensity over the threshold of 5 mm h-1 would definitely trigger floods in Xiangyang. However, in Haikou, such a threshold value is 30 mm h-1. In other words, city flooding would occur in Haikou when it is hit by a rainstorm with a peak rainfall intensity over 30 mm h-1. In general, the difference between the threshold values among these cities reduces with a longer time window, indicating that the rainfall in a shorter time window is more critical to evaluate whether a city is prone to flooding.

The NLR records can serve as a proxy of the city residents' normal daily routine. The normalized NLR shows that the eight cities have a similar diurnal rhythm (Fig. 3a). The normalized NLR median climbs from a minimum at around 04:00 LT to a peak right at 12:00 LT. It starts to drop slightly and then peaks again at around 20:00 LT. This general pattern reflects the smartphone usage patterns of the city residents. Phone usage starts to drop after midnight when most residents start to rest. It reaches its first peak during lunchtime as residents may request more LBS to find a place to eat. After lunchtime, phone usage remains at a high plateau, probably due to more LBS requests for business purposes. Phone usage reaches the highest peak of the whole day right after normal work hours, indicating a significantly increased need for LBSs such as hailing nearby taxis to socialize with friends or go back home or sending geotagged posts for socializing.

The general diurnal pattern was superposed with subtle short-term NLR variations. The NLR in the southern cities peaks later at night and hits the bottom before dawn, which is different than in northern cities. This is very likely due to the different lifestyles between the northern and southern residents in response to economic activities and day length. It is well-known that southern China is more active in economic and social activities, and the southerners enjoy night activities more (Ma et al., 2019). By contrast, the northerners tend to end their nightlife earlier and also become active earlier, as the day breaks earlier in the north.

The total NLR is moderately correlated with the population of these cities (Fig. 3b). The 0.63 Pearson correlation coefficient (with a p value of 0.046) indicates a statistically significant positive relationship between the normalized NLR and the population. As a result, we believe the NLR data could reflect the collective geotagged behaviors of the city residents as a whole, and consequently it could serve as a proxy for human responses to different environmental and social events.