Gravity Change Caused by Heavy Rainfall Detected by A gPhone Gravimeter in Zhengzhou, China

0. INTRODUCTION

Since July 17, 2021, Henan Province in China has suffered extremely heavy rainfall, among which Zhengzhou City suffered a heavy rainstorm from 8–9 o'clock, with an hourly rainfall of 201.9 mm and heavy water accumulation in many sections on July 20, causing heavy casualties and property losses. According to the annual average rainfall data, the annual rainfall in Zhengzhou is about 640.8 mm, but the average monthly rainfall in July is only 146.2 mm. The rainfall is deemed a rare weather event in climate history in terms of both intensity and influence. Continuous intense rainfall process was exacerbated by severe surface flood. The water has a significant effect on gravity, and the effect is mainly through Newtonian attraction by the mass of water. Although gravity changes associated with rainfall are often observed because of changes in underground water table or soil moisture, the effects are strongly dependent on climate, weather, geology and the geometric setting of the gravity station (Peng et al., 2021; Wang et al., 2014; Li and Shen, 2011; Imanishi et al., 2006). Imanishi (2000) observed a strong correlation between residual gravity and local rainfall, it shows that a gravity decrease of 1.4 μGal (1 μGal = 1 × 10^-8 m·s^-2) induced by a total of 38.5 mm of rainfall in one hour was observed by a superconducting gravimeter. A gPhone gravimeter has been established in Zhengzhou Seismic Station (113.59°E, 34.65°N, 225 m) since 2008 based on the Crustal Movement Observation Network of China (CMONOC). The gravimeter was about 10 m below the ground surface, it can be seen as an underground station (Figure 1).

Figure  1.  Location of the Zhengzhou Seismic Station and topographic relief. (a) low-resolution (1'×1') topographic relief; (b) high-resolution (30 m × 30 m) topographic relief.

DownLoad: Full-Size Img PowerPoint

In this paper, we investigate the short-term of effect of heavy rainfall on gravity observed at the Zhengzhou Seismic Station using rainfall data as well as gravimeter data. Newtonian and loading attraction by the mass of flood water above the gravimeter will be shown.

1. DATA PROCESSING

The raw gravity data of gPhone gravimeter can be downloaded from the Gravity Network Center of China (GNCC) in Wuhan through Internet in real time. The raw data was in 1 Hz sample rate along with the observed barometric pressure variations and stored in daily files of the Tsoft format (Van Camp and Vauterin, 2005). Rainfall is also recorded every 1 min routinely. Flooding caused a power outage for several days, and the raw gravity records were interrupted in 00:00:01, July 21. Raw data are changed to minute sampling data using a low-pass filter with a cut-off frequency of 720 cpd (circle per day). It was shown in Figure 2.

Figure  2.  Gravity and atmospheric pressure at the Zhengzhou Seismic Station. (a) Gravity observation; (b) atmospheric pressure.

DownLoad: Full-Size Img PowerPoint

Before using the gravity data for the study of short-term rainfall effects, major instrumental perturbations such as spikes, earthquakes, steps and gaps should be corrected. The minute re-sampling data has no these perturbations described as above. To obtain the effect of short-term rainfall on gravity, the filtered gravity data need to be corrected for other geophysical contributions such as Earth tide, pressure and polar motion. We used DDW model (Dehant et al., 1999) for Earth tide correction, and -0.3 μGal·hPa^-1 of atmosphere pressure admittance value for atmospheric pressure correction. The pole tide, induced by polar motion and length-of-day variations, was modeled using daily Earth orientation parameters provided by the International Earth Rotation Service (ftp://hpiers.obspm.fr/iers/eop/eopc04/). The gravity sensor of the gPhone system consists of a low drift, and the instrument drift correction was neglected due to the length of the observation time is less than three days. Finally, the corrected gravity residual in 1 min sample rate was obtained using Tsoft (Van Camp and Vauterin, 2005) as shown in Figure 3.

Figure  3.  Residual gravity after correction for solid Earth tide, atmospheric effects and Earth's rotation.

DownLoad: Full-Size Img PowerPoint

2. RESULTS AND ANALYSIS

Gravity changed caused by heavy rainfall at Zhengzhou Seismic Station was shown in Figure 3. This is the heaviest rainfall events since 1951. After correction for tidal and atmospheric effects, it can be seen that the residual gravity stayed at a steady value but with a large amplitude, the amplitude was over 5 μGal, and gravity change caused by heavy rainfall was clearly detected since 7 o'clock on July 20. There is no noticeable time lag in the response of gravity to rainfall. The decrease in gravity continued with the accumulation of rainfall. A significant gravity change (near 10 μGal) was observed, which has a significant correlation with the rainfall in Zhengzhou Seismic Station in time, and the change amplitude is far greater than the observation error of the gPhone gravimeter. Unfortunately, we can not estimate the gravity recovery response due to the interrupted of the gPhone gravimeter. The total magnitude of the gravity change is about 10 μGal, the cumulative rainfall is 408.5 mm in Zhengzhou Seismic Station (7:00–8:00 on July 20), and the ratio of the rainfall amount (in mm) and the gravity change (in μGal) is -0.025 μGal·mm^-1.

3. DISCUSSION

Because the gravity change depends on the relative height of the observation point, if the height of the gPhone's sensor is higher than the attraction point mass, then the gravity will increase due to the flood water mass is below the observation point (Zhou et al., 2014). For the local area, the gravity will decrease because the flood water mass is on the above of the station due to the terrain is flat (Figure 1). Therefore, short-term rainfall affects gravity, but the change trend depends on the height of observation point and its surrounding topography. The average elevation of Zhengzhou is about 108 m, the overall terrain is high in the southwest and low in the northeast with a ladder decline, and the Zhengzhou Seismic Station is located in the southwest of Zhengzhou (Figure 1), so the gravity change due to topographic effect should be considered. To estimate topography effect on gravity change, precipitation and the surrounding topography should be considered. Due to lack of precipitation data in the other stations of Henan Province, we can not estimate the topography effect on gravity change accurately. However, there is no doubt that flood at the lower height has an increasing effect on gravity, next we will compute the topography effect on gravity. Although rainfall is not the same concept as the water storage depth near the observation station, the water storage depth is affected by rainfall directly.

The gravity variations due to hydrology can be separated into two major scales: local ($\varPsi \le 0.1^ \circ$) and non-local ($0.1^ \circ < \varPsi < 1^ \circ$) (Llubes et al., 2004). The gravitational effect per unit mass with $\varPsi \le 0.1^ \circ$ is based on Newton's and cosines laws (Wang et al., 2016)

where G is the gravitational constant, d is the direct distance to the point mass of one kg, ${h}_{S}$ and ${h}_{P}$ are the heights of the gravimeter and the point mass respectively.

The loading effect per unit mass is computed using Green's function formalism as given by Farrell (1972).

where the ${h}_{n}$ and ${k}_{n}$ symbols represent the load Love number, M is the Earth's mass, g is the mean surface gravity and ${P}_{n}$ are the Legendre polynomials. To accelerate the computation, the loading effect is interpolated from tabulated values given by Wang et al. (2012).

The local effect within 0.1° was estimated with NASA Shuttle Radar Topography Mission Global 1 arc second elevation data from the SRTMGL1v003 product (https://lpdaac.usgs.gov/products/srtmgl1v003/), and the non-local effect was estimated with ETOPO1(https://www.ngdc.noaa.gov/mgg/global/global.html) data, which is a 1 arc-minute global relief model of Earth's surface that integrates land topography and ocean bathymetry. Here, we used SRTM and ETOPO1 data to compute the topography effect according to the different water storage height: 150, 200, 250, 300, 350, 400, and 450 mm. The estimated water storage height effect on gravity is depicted in Table 1.

Table  1.  Water storage height and its effect on gravity

Water storage height (mm)	Non-local (μGal)	Local (μGal)	Total (μGal)
150	0.21	-5.48	-5.27
200	0.28	-7.30	-7.02
250	0.36	-9.13	-8.77
300	0.43	-10.95	-10.52
350	0.50	-12.78	-12.28
400	0.57	-14.61	-14.04
450	0.63	-16.44	-15.81

 | Show Table

DownLoad: CSV

According to the Henan Meteorological Service, heavy rain occurred in Zhengzhou, Xinxiang, Jiaozuo, Luoyang and other cities, there were 1 163 rainfall stations with precipitation of over than 50 mm, of which 816 were over than 100 mm and 176 were over than 250 mm on July 20. The maximum precipitation is 672.0 mm occurred in Houzhai Town, Zhengzhou. The maximum hourly rainfall intensity appeared in Zhengzhou, which is about 201.9 mm. As we know, this event is very extremely rare, the rain formed a flood spread all over Zhengzhou, several other cities were paralyzed by flood waters, with cars submerged and tunnels flooded (about 300 mm water depth). The average precipitation is 458.2 mm in Zhengzhou City and 150 mm in Henan Province.

The estimated gravity change considering the load effect and the gravitational force of water at the same time is ranged from -5.27 to 18.81 μGal. The simulations show that non-local effect on gravity is positive, which means gravity increase, and the local effect on gravity is negative, which means gravity decrease, the local effect is larger than the non-local effect, and the total effect on gravity is negative. Because of the gravitational property that gravitation is proportional to the square of distance, the contribution of water mass in the near field dominates that from a far filed, and also considering that the rainfall is not uniform within the calculated area, we can use the observed gravity change to deduce the depth of water storage near the observation station. So we can get a conclusion that the average depth is about 300 mm, which is less than the accumulation of rainfall (408.5 mm).

4. CONCLUSION

Research has shown that the short-term of heavy rainfall on gravity observed at the Zhengzhou Seismic Station can be observed by using the gPhone gravimeter. The gravity series measured by gPhone gravimeter contains several geophysical contributions, after re-sampling and correcting the solid Earth tide, polar motion, atmospheric loading effects, the residual gravity stayed at a steady value but with a large amplitude, the amplitude was over 5 μGal, and gravity response caused by rainfall was clearly detected as gravity decrease since 7 o'clock on July 20, which has a significant correlation with the rainfall in time, and the change amplitude is far greater than the observation error of the instrument. The decrease in gravity continued with the accumulation of rainfall. The deduced water depth of surface ponding near the observation station is about 300 mm.