Natural Hazards : 3 Title : Time-domain correlation quantitative analysis method of regional rainfall-landslide 4 displacement responses based on a time-domain correlation model 5 All

Landslide deformation is the most intuitive and effective characterization of the evolution of 43 landslides and reveals their inherent risk. Considering the inadequacy of existing deformation monitoring 44 data in the early warning of landslide hazards, resulting in insufficient disaster response times, this paper 45 proposes a time-domain correlation model. Based on a regional rainfall-landslide deformation response 46 analysis method, a time-domain correlation measure between regional rainfall and landslide deformation 47 and a calculation method based on impulse response functions are proposed for prevalent rainfall48 induced landslide areas, and the correlation with the rainfall-triggered landslide deformation mechanism 49 is quantitatively modeled. Furthermore, using rainfall monitoring data to optimize the indicator system 50 for landslide deformation monitoring and early warning significantly improves the preliminary warning 51 based on landslide deformation. The feasibility of the method proposed in this paper is verified by 52 analyzing the historical monitoring data of rainfall and landslide deformation at 15 typical locations in 5 53 landslide hidden hazard areas in Fengjie County, Chongqing city. (1) The correlation models for the XP 54 landslide and XSP landslide involve a 5-day lagged correlation under a 56-day cycle and a 18-21-day 55 lagged correlation under a 49-52-day cycle, which means that the deformation in the above areas can be 56 modeled cyclically according to monitoring data, and early landslide warnings can be provided in 57 advance with a lag time. (2) The correlation models for the TMS landslide and OT landslide show 58 consistent correlations under a 48-50-day cycle and a 58-day cycle, which means that the deformation in 59 the above areas can be predicted based on rainfall accumulation, and real-time warnings of future 60 landslide deformation and displacement can be obtained. (3) The HJWC landslide presents a disorderly 61 correlation pattern, which means that a preliminary landslide deformation warning cannot be provided 62 based on rainfall alone; other monitoring data need to be supplemented and analyzed. 63

rainfall) are consistent. The minimum cumulative rainfall for landslides is 200 mm. ②The geological 122 environment in the study area is relatively fragile. The terrain provides good conditions for surface water 123 infiltration, surface water migration, and the occurrence of landslides ③The regional landforms are 124 mainly moderately eroded mountain and middle-low mountain landforms and eroded hilly landforms 125 with high hills, large undulations, and steep slopes; developed landslides are also prominent. The 126 sensitive slope is 20°~30°, and landslides tend to occur at elevations of 400~1000 m. This paper selects 127 five rainfall-triggered landslides, including the OT landslide, XP landslide, and HJWC landslide, and a total of 15 representative monitoring points for experiments. Table 1 lists the various monitoring points, 129 which will verify that the method proposed in this paper is suitable with adaptable applicability for different landslide scenarios under diverse conditions. 131 132 Fig.1 The tests were conducted at rainfall-triggered landslides such as the Xinpu landslide in Fengjie County. Chongqing,

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China   The experimental data in this paper consist of landslide surface deformation data and regional 140 rainfall data obtained from 2017 to 2020 at the Fengjie regional monitoring point, provided by Chongqing

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Planning and natural resources Bureau. The deformation variable is the vertical surface displacement 142 monitored by geodetic GPS instruments. The time interval is an hour, and the rainfall is recorded in an 143 hourly increment by a tipping bucket, and the data are unified in time sequences with a unit of days during data preprocessing.

Methods 146
The properties of the soil and rock comprising the landslide body in different regional environments of the landslide body. Hence, it is difficult to obtain an accurate correlation between regional rainfall and 149 landslide deformation by conventional statistical analysis. Accordingly, this article proposes the concept  Time-domain correlation modeling of regional rainfall-landslide deformation monitoring data The product between the correlation period T and the sampling duration t_s, that is, the time shift td of 191 the lagged signal, can be correlated with the estimated future deformation of the landslide with the real-192 time rainfall ahead of a lag time.

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The abovementioned critical value R_a of rainfall-triggered deformation is extracted by quantitatively 194 partitioning the regional rainfall history curve to extract the time-domain characteristics of the triggering 195 event at different stages. Formula (3) represents the rainfall interval curve partitioned by determining the 196 average rainfall of each rainfall event. Then, considering the objective environmental factors such as the 197 regional rock composition, surface shape, and soil quality, the effective rainfall coefficient k(Chen et al.    deformation response process can be discerned on the basis of whether the signal curve is initially steady 211 before experiencing a sudden increase, reaches its peak, and then becomes stable again. Combined with 212 this principle of signal mutation, the abnormal deformation response point D_s is calculated as the key 213 parameter of the signal time shift td, and the corresponding formula is expressed as follows: When the signal mutation rate mr is the maximum signal curvature of the overall performance of the deformation has ceased, a moment will come when the phased maximum of accumulated deformation will be generated, after which the landslide evolution process will enter a stable surface deformation

D D mr
(4) 220 To obtain a credible time-domain correlation measure, it is necessary to extract the signal waveform 221 characteristics of the landslide deformation response process, further calculate the constituent parameters 222 of the correlation measure to obtain the value interval, and introduce the impulse response function 223 during the signal processing phase to calculate the specific measured value, as depicted in Figure 3.

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(1) Impulse period function φ(T) . In the definition of the relevant time parameters of the response 246 function, the signals h(t) and δ(t) are assumed to start at the same time due to the obvious existence 247 of persistent precipitation. When the input rainfall signal shows a periodically repeating waveform, the amplitudes as the response function for measuring the rainfall-landslide deformation correlation period.

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(2) Delay response function φ(td). When the rainfall impulse signal pair and the deformation pulse 251 signal have a relative offset (lag) on the time axis, their related time parameters will also change. This 252 dependence is described by a shift function based on the signal with zero padding while considering the 253 pulse period, as shown in the following formula: Integrating the abovementioned regional rainfall with the landslide deformation correlation 256 measurement analysis and calculation method, the deformation mechanism and correlation properties of 257 rainfall-triggered landslides can be broadly classified based on the regional monitoring data, as shown in 258 Table 2.

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(1) Rainfall-landslide deformation consistency model (M 1 ): Under the action of rainfall and infiltration, 260 the regional surface balance is easily damaged, and sliding occurs. The effect is expressed as a slow and 261 long-term surface deformation process, as a rainfall process, and as a deformation process. There is good 262 temporal consistency between the correlation period T and the pulse period function φ(T), and the cross-

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Generally, the lag times of landslides that occur in accumulated soil, landfills, loess, clay, clastics and 271 bedrock range from short to long, and the thickness of the same type of landslide ranges from thin to 272 thickness.

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(3) Rainfall-landslide deformation turbulence model (M 3 ) : Because landslide deformation is a slope displacement caused by the coupling of multiple factors, some landslide areas may exhibit little rainfall 275 or weak deformation responses to rainfall; that is, there is a discrepancy in the correlation between the 276 landslide response and rainfall. Such situations cannot be accurately forecasted, and early warning 277 systems based on rainfall will fail to predict these landslides.

correlation model 281
This paper uses signal processing technology to quantitatively measure the correlation between 282 regional rainfall and landslide deformation. The flow chart of the method is illustrated in the figure below.

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The core steps are as follows: ①Considering the presence of noise in landslide deformation monitoring

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First, the regional rainfall data and landslide deformation monitoring data are processed in a unified time 306 series; that is, the time series quantity t norm , rainfall r norm , and deformation variable d norm (unit: days) the mutation point D_s described in formula (3). Finally, the interval is used to perform adaptive Kalman In the above formula, F_t and B_t are the state change matrices in the Kalman filter, ∆t is the sampling 314 time, v norm is the current estimate, v norm is the measured value, and v norm−1 is the previous estimate.

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Because of the seasonal cyclic characteristics of regional rainfall and the asynchronous time-domain 316 correlation between rainfall and deformation in landslide hazards, the combined time-domain waveforms 317 cannot be judged directly, and this paper uses the time-domain correlation measure as a dynamic 318 parameter to transform the monitoring signals into a characteristic structure for the quantitative analysis 319 of regional rainfall-landslide deformation response. Eq. (7) clusters the noise-reduced deformation

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To calculate the time-domain correlation measure of regional rainfall-landslide deformation, the

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Results 345 This paper selects all the GDA10068 monitoring points in the XP landslide area for a quantitative  (Table 1), and the results 354 are shown in Table 3. The gain parameter of the Kalman filter is further updated according to formula (6) 355 to realize adaptive hierarchical noise reduction for the landslide deformation signal. The experimental 356 effect of this filter is shown in Figure 5.

Conclusions 439
This paper proposes a method for the quantitative analysis of regional rainfall-landslide deformation