Rainstorm interpolation method considering mountain torrent drainage basin topographic factors

Abstract

The invention discloses a rainstorm interpolation method considering mountain torrent drainage basin topographic factors, and particularly relates to the technical field of hydrological space-time interpolation influenced by elevation. Data preparation comprises drainage basin basic data, thematic data and drainage basin rainfall data; the drainage basin rainfall data is detected and then divided to obtain three typical flood fields of the drainage basin, and the obtained three typical flood fields of the drainage basin are subjected to interpolation research by adopting an inverse distance weighting method, a Kriging method and a geographically weighted regression method which are added with topographic factors respectively; wherein the distance weight and the elevation weight are determined by the inverse distance weight method considering the terrain, firstly, the weight of the inverse distance weight method considering the terrain is determined, and the weight distribution in the horizontal distance and the weight distribution in the vertical distance are included; the method is subjected to cross validation to obtain an average relative error, an average absolute error and a root-mean-square error, and the characteristics and the watershed applicability of the rainstorm interpolation method are obtained.

Description

Technical Field

[0001] The invention relates to the technical field of hydrological spatiotemporal interpolation influenced by elevation, and in particular to a rainstorm interpolation method taking into account topographic factors of a mountain torrent area. Background Art

[0002] In recent decades, global extreme climate events such as El Niño and La Niña have tended to intensify. Countries in the world-famous monsoon climate zone, with complex weather systems and extreme sensitivity to extreme climate events, will be affected by flood disasters. Due to the influence of climate change, recurrent rainstorms and floods are becoming more frequent, posing a great challenge to flood prevention and disaster reduction. Carrying out a study of the topography of the mountain torrent area basin considering geographical factors can effectively target sudden situations such as mountain torrent disasters, as well as effective and timely early warning and response. When discussing the basin rainstorm interpolation method, we try to add terrain factors to improve the existing spatial interpolation method, and study the precipitation interpolation method considering the spatiotemporal process. The applicability of different spatial interpolation methods considering terrain factors in the spatial interpolation of basin rainstorms can provide a reference for the prevention and control of mountain torrent disasters. For this reason, a rainstorm interpolation method considering the terrain factors of the mountain torrent area basin is urgently needed. Summary of the invention

[0003] To this end, the present invention provides a rainstorm interpolation method that takes into account the terrain factors of the mountain torrent area basin to solve the problems raised in the background technology.

[0004] In order to achieve the above object, the present invention provides the following technical solution: a rainstorm interpolation method considering the terrain factors of the mountain torrent area, comprising:

[0005] Data preparation, including basin basic data, thematic data and basin precipitation data;

[0006] After detecting the precipitation data of the basin, the basin was divided into three typical floods, and the three typical floods in the basin were interpolated using the inverse distance weighted method with terrain factors, the kriging method, and the geographically weighted regression method.

[0007] Among them, the inverse distance weighted method considering the terrain is used to determine the distance and elevation weights. First, the weight determination of the inverse distance weighted method considering the terrain is considered, including the allocation of weights on horizontal distance and vertical distance;

[0008] The above methods were cross-validated to obtain the average relative error, mean absolute error and root mean square error, and the characteristics of the rainstorm interpolation method and its applicability in the watershed were obtained.

[0009] Preferably, the three typical floods in the basin include whether the rainfall in 1 hour is greater than 16 mm, whether the rainfall in 12 hours is greater than 30 mm, and whether the rainfall in 24 hours is greater than 16 mm;

[0010]

[0011] In formula (1): S i The ratio of the rainfall in the i-th period to the average rainfall in the rainstorm; n is the number of periods; V t The larger the value, the more uneven the distribution of rainstorm time is;

[0012] In formula (2): t m is the time of occurrence of the main rain peak; T is the rainfall duration; C p The larger the value, the later the rain peak appears.

[0013] In formula (3): α i is the Thiessen polygon area weight factor; α i is the rainfall at the ith rainfall station; P i is the basin surface rainfall; n has the same meaning as formula (1), V p The larger the value, the more uneven the spatial distribution of heavy rain is.

[0014] Preferably, the interpolation calculation process of the inverse distance weighted method considering the terrain involves the allocation of weights on the horizontal distance and the vertical distance, specifically including:

[0015] First, calculate the distance from the unknown point to the sampling point, and determine each sampling point based on the neighborhood search range and the maximum and minimum number of sampling points; calculate the horizontal distance and vertical elevation difference from the interpolation point to each sampling point;

[0016] Secondly, according to the horizontal distance and relative elevation from the interpolation point to each sample point and the selected power function, the horizontal distance weight and vertical distance weight of each sampling point are calculated respectively;

[0017]

[0018]

[0019] Where λ di is the weight of the horizontal distance at sample point i, W D is the weight of horizontal distance relative to vertical distance. i is the horizontal distance from the interpolation point to the sampling point; λzi is the weight of the vertical distance at the sample point i, W Z is the weight of vertical distance relative to horizontal distance; z i is the vertical distance from the point to be interpolated to the sampling point, that is, the elevation difference; finally, the value of the point to be interpolated is calculated by weighted summation based on the values ​​of each sampling point and its corresponding weight;

[0020]

[0021] Where P(x0,y0) is the point to be interpolated, λ di and λ zi is the horizontal distance weight coefficient and the vertical distance weight coefficient, P(x i ,y i ) is the measured value of sample point i.

[0022] Preferably, the calculation formula of the inverse distance weighted method considering terrain is as follows:

[0023]

[0024] in,

[0025]

[0026] Where W D , W Z are the weights of the influence of distance and elevation on precipitation, their sum is 1, P i is the precipitation at observation station i, d i is the distance between the point to be estimated and observation station i, in km, z i is the elevation difference between the point to be estimated and the observation station i, in m, z i +10 is to avoid the situation where the interpolation point is very close to or the same as some measured points in elevation, thus making the elevation too large.

[0027] Preferably, the calculation formula of the ordinary Kriging method considering the terrain is as follows:

[0028] The prerequisite for using cokriging interpolation is that the N regionalized variables Zk(x) (k=1,2...N) satisfy the assumption of second-order stationarity, that is, the mathematical expectation of Zk(x) exists in the entire study area and is a constant, that is, for any x:

[0029] E[Z k (x)]=m k (8)

[0030] In the entire study area, the covariance of Zk(x) exists and is stable, that is, it only depends on the distance h between variables and has nothing to do with x:

[0031] Cov[Z k (x), Z k (x+h)]=C(h) (9)

[0032] When h=0, the above equation becomes Var[Z k (x)]=C(0), that is, the variance of Zk(x) exists and is constant. Then under the assumption of second-order stationarity, the expectation of the co-regionalization variable is:

[0033] E[Z k (x)]=m k E[Z k’ (x)]=m k’ (k' is a variable other than k among N variables)

[0034] Second-order stationarity is a special case of the eigenvalue hypothesis, that is, if the second-order stationarity hypothesis is satisfied, the eigenvalue hypothesis must be satisfied; conversely, if the eigenvalue hypothesis is satisfied, the second-order stationarity hypothesis may not be satisfied. In coordinating ordinary kriging with an auxiliary variable, the estimate of any position to be interpolated X0 can be obtained using the following formula:

[0035]

[0036] In the formula, Z1 is the main variable, Z2 is the auxiliary variable, n is the number of measured points of variable Z1 in the neighborhood of the interpolation point x0, m is the number of measured points of variable Z2 in the neighborhood of the interpolation point x0, a i is the weight coefficient, indicating that the spatial sample point x i The observed value Z1(x i ) for the estimated value The contribution of j is the weight coefficient, indicating that the spatial sample point x j The observed value Z2(x j ) for the estimated value degree of contribution.

[0037] Preferably, the calculation formula of the geographically weighted regression method with elevation factor added considering the influence of terrain is as follows:

[0038] P i =β 0i +β xi X i +β yi Y i +β zi Z i (11)

[0039] Medium X i , Y i , Z i are the X coordinate, Y coordinate and elevation of point i, respectively, 0i is the constant term in the local regression coefficient, β xi , β yi , β zi is the regression coefficient at point i; P i is the spatial coordinate of the point to be interpolated.

[0040] The coefficient of determination R was used for geographically weighted regression considering the influence of terrain. 2And root mean square error RMSE to evaluate model accuracy;

[0041]

[0042] Where: V oi is the measured value at sample point i; V pi is the predicted value at point i; n is the total number of sample points; R 2 Between 0 and 1, the closer it is to 1, the higher the stability of the model; the smaller the RMSE, the higher the accuracy of the model prediction.

[0043] The present invention has the following advantages:

[0044] The inverse distance weighted method that takes terrain into consideration in the present invention can reflect the correlation with terrain factors in the interpolation results of local areas. The inverse distance weighted method that takes terrain into consideration can improve the interpolation accuracy. The Kriging method that takes terrain into consideration can achieve the highest improvement in interpolation accuracy. The geographically weighted regression method that takes terrain into consideration adds the elevation factor as one of the parameters for precipitation estimation; therefore, the correlation coefficient of the geographically weighted regression method is improved, and the terrain factor makes the distribution of the interpolation results have a certain correlation with the terrain, so that the true value of rainfall can be obtained more accurately in areas with different altitudes. The rainstorm interpolation method that takes into consideration the terrain factors of the mountain torrent basin of the present invention can improve the interpolation accuracy and solve the influence of terrain problems such as elevation on interpolation. It can be used in hydrological station networks such as groundwater monitoring stations and rain gauges to support industry management. It can also accurately and effectively perform higher-precision interpolation calculations in response to terrain with significant elevation changes, especially for the spatiotemporal interpolation of rainfall in mountainous areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flow chart of a rainstorm interpolation method considering topographic factors of a mountain torrent area provided by the present invention;

[0046] Figure 2 The spatial distribution map of the GWR regression coefficients of the heavy rain on June 27, 2013 in the L basin provided in this embodiment;

[0047] Figure 3 The spatial distribution map of the GWR regression coefficients of the rainstorm on August 22, 2013 in the L basin provided in this embodiment;

[0048] Figure 4 The spatial distribution map of the GWR regression coefficient of the rainstorm on May 24, 2014 in the L basin provided in this embodiment;

[0049] Figure 5 The GWR spatial interpolation result map considering the elevation of the heavy rain on June 27, 2013 in the L basin provided in this embodiment;

[0050] Figure 6The GWR spatial interpolation result map considering the elevation of the heavy rain on August 22, 2013 in the L basin provided in this embodiment;

[0051] Figure 7 The GWR spatial interpolation result map considering elevation for the heavy rain on May 24, 2014 in the L basin provided in this embodiment. DETAILED DESCRIPTION

[0052] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] like Figure 1 As shown, this embodiment provides a rainstorm interpolation method taking into account the terrain factors of the mountain torrent area basin, including:

[0054] Data preparation, including basin basic data, thematic data and basin precipitation data;

[0055] The basic data of the watershed mainly describe the basic situation of the watershed, including remote sensing images of the watershed, river network of the watershed, administrative divisions and other data; the thematic data include digital elevation model of the watershed, data of rain gauge stations in the watershed, and land use data of the watershed; the precipitation data of the watershed include daily and hourly rainfall data of 18 stations from 2013 to 2014.

[0056] After detecting the precipitation data in the basin, three typical floods in the basin were obtained;

[0057] Preferably, the three typical floods in the basin include whether the rainfall in 1 hour is greater than 16 mm, whether the rainfall in 12 hours is greater than 30 mm, and whether the rainfall in 24 hours is greater than 16 mm;

[0058]

[0059] In formula (1): S i The ratio of the rainfall in the i-th period to the average rainfall in the rainstorm; n is the number of periods; V t The larger the value, the more uneven the distribution of rainstorm time is;

[0060] In formula (2): t m is the time of occurrence of the main rain peak; T is the rainfall duration; C p The larger the value, the later the rain peak appears;

[0061] In formula (3): α iis the Thiessen polygon area weight factor; α i is the rainfall at the ith rainfall station; P i is the basin surface rainfall; n has the same meaning as formula (1), V p The larger the value, the more uneven the spatial distribution of heavy rain is.

[0062] The three typical floods in the basin were interpolated using the inverse distance weighted method with terrain factors, the kriging method, and the geographically weighted regression method.

[0063] Among them, the inverse distance weighted method considering the terrain is used to determine the distance and elevation weights. First, the weight determination of the inverse distance weighted method considering the terrain is considered, including the distribution of weights on horizontal distance and vertical distance; this has a significant impact on the interpolation results, and the distribution of weights affects the relative size of the impact of distance and elevation on the interpolation results. Considering the selection of the power function of the inverse distance weighted method considering the terrain, the weight of the horizontal distance changes with the distance and is proportional to the power of the inverse of the distance. Similarly, the vertical distance weight changes with the elevation and is proportional to the power of the inverse of the relative elevation.

[0064] The selection of neighborhood sample points for the inverse distance weighted method considering terrain is consistent with that for the inverse distance weighted method not considering terrain in order to simplify the calculation. Both methods use a fixed or variable search radius with the point to be interpolated as the center to select neighborhood sample points.

[0065] Specifically, the interpolation calculation process of the inverse distance weighted method considering the terrain involves the allocation of weights on horizontal distance and vertical distance, including:

[0066] First, calculate the distance from the unknown point to the sampling point, and determine each sampling point based on the neighborhood search range and the maximum and minimum number of sampling points; calculate the horizontal distance and vertical elevation difference from the interpolation point to each sampling point;

[0067] Secondly, according to the horizontal distance and relative elevation from the interpolation point to each sample point and the selected power function, the horizontal distance weight and vertical distance weight of each sampling point are calculated respectively;

[0068]

[0069] Where λ di is the weight of the horizontal distance at sample point i, W D is the weight of horizontal distance relative to vertical distance. i is the horizontal distance from the interpolation point to the sampling point; λzi is the weight of the vertical distance at the sample point i, W Z is the weight of vertical distance relative to horizontal distance; z iis the vertical distance from the point to be interpolated to the sampling point, that is, the elevation difference; finally, the value of the point to be interpolated is calculated by weighted summation based on the values ​​of each sampling point and its corresponding weight;

[0070]

[0071] Where P(x0,y0) is the point to be interpolated, λ di and λ zi is the horizontal distance weight coefficient and the vertical distance weight coefficient, P(x i ,y i ) is the measured value of sample point i.

[0072] The inverse distance weighted method considering terrain factors is based on the fact that the distance of elements in geographic space has a greater impact on its closer elements than on things that are farther away, that is, things that are close in space have greater similarity. This premise adds the elevation factor when considering the spatial position. When predicting the value of a geographic element at a certain position in space, the inverse distance weighted method considering terrain also uses the values ​​of the measured sample points adjacent to this geographic element to predict the value of the geographic element at that location. The closer the distance to the predicted position and the smaller the elevation difference with the predicted position, the greater the contribution of the measured value of the sample point to the predicted value. And the speed at which the weight of the inverse distance weighted method considering terrain changes with distance also depends on the power of the inverse distance function. Finally, the weighted average of each sample point is used as the value of the point to be interpolated.

[0073] Taking into account the influence of various factors, the calculation formula of the inverse distance weighted method considering terrain is as follows:

[0074]

[0075] in,

[0076]

[0077] Where W D , W Z are the weights of the influence of distance and elevation on precipitation, their sum is 1, P i is the precipitation at observation station i, d i is the distance between the point to be estimated and observation station i, in km, z i is the elevation difference between the point to be estimated and the observation station i, in m, z i +10 is to avoid the situation where the interpolation point is very close to or the same as some measured points in elevation, thus making the elevation too large.

[0078] Ordinary Kriging considering terrain is the co-ordinary Kriging method with terrain factors added. Co-ordinary Kriging is a development of ordinary Kriging interpolation. It introduces other auxiliary variables on the basis of the main variables of ordinary Kriging interpolation, and uses the autocorrelation of the main variables combined with the cross-correlation between the main variables and the auxiliary variables to make better predictions. Co-ordinary Kriging is based on the theory of co-regionalized variables and the cross-variogram as a basic tool. The co-regionalization theory develops the optimal valuation method of regionalized variables from a single attribute to more than two co-regionalized attributes. The cross-variogram is a basic means to quantify the randomness and structure of regionalized variables. The calculation formula of the ordinary Kriging method considering terrain is as follows:

[0079] The prerequisite for using cokriging interpolation is that the N regionalized variables Zk(x) (k=1,2...N) satisfy the assumption of second-order stationarity, that is, the mathematical expectation of Zk(x) exists in the entire study area and is a constant, that is, for any x:

[0080] E[Z k (x)]=m k (8)

[0081] In the entire study area, the covariance of Zk(x) exists and is stable, that is, it only depends on the distance h between variables and has nothing to do with x:

[0082] Cov[Z k (x),Z k (x+h)]=C(h) (9)

[0083] When h=0, the above equation becomes Var[Z k (x)]=C(0), that is, the variance of Zk(x) exists and is constant. Then under the assumption of second-order stationarity, the expectation of the co-regionalization variable is:

[0084] E[Z k (x)]=m k E[Z k’ (x)]=m k’ (k' is a variable other than k among N variables)

[0085] Second-order stationarity is a special case of the eigenvalue hypothesis, that is, if the second-order stationarity hypothesis is satisfied, the eigenvalue hypothesis must be satisfied; conversely, if the eigenvalue hypothesis is satisfied, the second-order stationarity hypothesis may not be satisfied. In coordinating ordinary kriging with an auxiliary variable, the estimate of any position to be interpolated X0 can be obtained using the following formula:

[0086]

[0087] In the formula, Z1 is the main variable, Z2 is the auxiliary variable, n is the number of measured points of variable Z1 in the neighborhood of the interpolation point x0, m is the number of measured points of variable Z2 in the neighborhood of the interpolation point x0, a i is the weight coefficient, indicating that the spatial sample point x i The observed value Z1(x i ) for the estimated value The contribution of j is the weight coefficient, indicating that the spatial sample point x j The observed value Z2(x j ) for the estimated value Therefore, the co-ordinary kriging equations can also be expressed in the form of average covariance function and average variogram. It can be seen that the key to solving the problem of ordinary kriging interpolation is to solve the variogram and covariance function.

[0088] Geographically weighted regression considering topography, the geographically weighted regression considering topography adds elevation as one of the parameters for precipitation estimation. Since there is a certain spatial correlation between precipitation and elevation, adding elevation will improve the accuracy of the interpolation result. Geographically weighted regression considering topography takes into account that the variation characteristics of precipitation with elevation are very complex and not a simple linear relationship. However, when the basin elevation is not very prominent, simplifying the relationship between the two into a linear trend has been adopted by many studies.

[0089] The calculation formula of the geographically weighted regression method with elevation factor considering the influence of terrain is as follows:

[0090] P i =β 0i +β xi X i +β yi Y i +β zi Z i (11)

[0091] Medium X i , Y i , Z i are the X coordinate, Y coordinate and elevation of point i, respectively, 0i is the constant term in the local regression coefficient, β xi , β yi , β zi is the regression coefficient at point i; P i is the spatial coordinate of the point to be interpolated

[0092] The coefficient of determination R was used for geographically weighted regression considering the influence of terrain. 2 And root mean square error RMSE to evaluate model accuracy;

[0093]

[0094] Where: V oi is the measured value at sample point i; V pi is the predicted value at point i; n is the total number of sample points; R 2 Between 0 and 1, the closer it is to 1, the higher the stability of the model; the smaller the RMSE, the higher the accuracy of the model prediction.

[0095] The above method is then cross-validated to obtain the average relative error, mean absolute error and root mean square error, and the characteristics of the rainstorm interpolation method and its applicability in the watershed are obtained.

[0096] As the distance and relative elevation increase, the speed at which the weight decreases depends on the power function order. To determine the optimal power function order, this embodiment uses the inverse distance weight method of the optimal weight combination of distance 0.5 and elevation 0.5 to determine the power function order. Taking the rainstorm on June 27, 2013 as an example, the power function orders are positioned at 1 and 2 respectively, and finally the predicted value is obtained by the cross-validation method, and the interpolation accuracy is evaluated by three indicators.

[0097] Table 12013.06.27 rainstorm accuracy evaluation

[0098]

[0099]

[0100] From the analysis in Table 1, we can see that the interpolation results of the three indicators using the first power function are better than those of the second power function. This is because the second power function tends to add too much influence from points with small elevation differences with the interpolation points. This is not conducive to the interpolation effect. Therefore, for the rainstorm in this basin, the first power function is used in the vertical direction.

[0101] In order to reasonably set parameters and select the theoretical cross-variogram model when performing spatial valuation, the ordinary cokriging method needs to perform data analysis before interpolation prediction to find the inherent laws of the data. Since the ordinary cokriging method assumes that the data obeys the normal distribution, if it does not obey the normal distribution, appropriate data transformation is required to make it obey the normal distribution. In addition, ordinary cokriging also requires that the sampled data set does not have a global trend. If there is a certain degree of trend in the north-south direction or the east-west direction, it is necessary to remove the trend in the subsequent interpolation work. Therefore, before using ordinary cokriging for interpolation, it is very important to analyze the sample data and understand the distribution and trend of the data.

[0102] The elevation-based Geographically Weighted Regression (GWR) method adds elevation factors to the general GWR method to improve the GWR method. The model principle is exactly the same as the general GWR method. Therefore, the selection of the spatial weight method is also the same as the general GWR method. The Gaussian function method is also used for the spatial weight function. After determining the weight function in the terrain-based GWR model, it is also necessary to determine and optimize the bandwidth of the specific weight function.

[0103] Because the principle is the same as that of the ordinary geographical weighted regression method, the AIC criterion method is also used to determine and optimize the bandwidth. Consider the interpolation process of the geographical weighted regression method with elevation. First, the spatial weight of the rainstorm interpolation is calculated using the Gauss function. Secondly, the bandwidth of the spatial weight function is determined and optimized using the AIC criterion. Finally, the GWR model (geographically weighted regression) for spatial estimation of precipitation in the Liuyang River Basin based on terrain elevation is established. Finally, the characteristics of the rainstorm interpolation method and its applicability in the basin can be obtained through analysis of the results.

[0104] This example gives the spatial distribution of the regression coefficients corresponding to X, Y, and Z in the GWR model of heavy rain precipitation in a certain basin on June 27, 2013, as shown in Figure 2 shown.

[0105] The equations for constructing each station of the 2013.08.22 rainstorm are shown in Table 2, where P represents rainfall, X, Y, and Z are the X coordinate and Y coordinate of the point, and Z represents the elevation of the point.

[0106] Table 2 GWR models of each construction point considering terrain in Liuyang River Basin on August 22, 2013

[0107]

[0108] Figure 3 The spatial distribution of the regression coefficients corresponding to X, Y, and Z in the GWR model of heavy rain precipitation on August 22, 2013 is given.

[0109] The equations for constructing each station of the 2014.05.24 rainstorm are shown in Table 3, where P represents the rainfall, X, Y, and Z are the X coordinate and Y coordinate of the point, and Z represents the elevation of the point.

[0110] Table 3 GWR models of each construction point considering terrain in Liuyang River Basin on May 24, 2013

[0111]

[0112] Figure 4 The spatial distribution of the regression coefficients corresponding to X, Y, and Z in the GWR model of heavy rain precipitation on May 24, 2014 is given.

[0113] By considering both spatial location and elevation factors, the GWR model of each rainstorm is constructed. The calculation results are as follows: Figure 5-7 shown.

[0114] In general, the results of the GWR interpolation method considering terrain and the GWR interpolation method not considering terrain are quite different, and after adding the elevation factor, the GWR correlation coefficient has increased. Compared with the GWR interpolation results not considering terrain, the range and spatial distribution have changed. The terrain factor makes the distribution of the interpolation results have a certain correlation with the terrain. Precipitation tends to increase in places with high altitudes, and precipitation tends to decrease in places with low altitudes.

[0115] In order to test the interpolation accuracy, the cross-validation method is uniformly used to obtain the predicted value, and the mean absolute error (MAE), mean relative error (MRE), and root mean square error (RMSIE) are used to test the accuracy. The results are shown in Table 4.

[0116] Table 4 Evaluation of GWR heavy rain interpolation accuracy considering terrain

[0117]

[0118] Through cross-validation, according to the three accuracy verification formulas, it can be seen that the average absolute error of the GWR of the three rainstorms considering the terrain is less than 20, the average relative error is less than 0.1 in two of them, and the other one is about 0.2, the root mean square error of the first and second rainstorms is less than 20, and the third one is relatively large at about 25. Compared with the GWR that does not consider the terrain, the accuracy is improved. Compared with the inverse distance weighted method that considers elevation and the Kriging method that considers elevation, except for the third rainstorm, the accuracy of the other two rainstorms has been improved. In general, in terms of the rainstorm interpolation in this study, the GWR method considering elevation has better interpolation accuracy.

[0119] The principles of three interpolation methods under the influence of terrain factors are introduced, and three typical rainstorms in the basin are interpolated. From the interpolation results, it can be seen that after adding the terrain factors, the interpolation results do change to a certain extent. Among them, the spatial distribution of the interpolation results of the inverse distance weighted method after adding the terrain has a certain change, the spatial change of the interpolation results of the kriging method after adding the terrain is relatively small, and the value range and spatial distribution of the interpolation results of the geographical weighted regression method after adding the terrain have a certain change.

[0120] The results of each interpolation method were evaluated through a unified cross-check and accuracy verification method. The results show that the Kriging method considering elevation is slightly better than the inverse distance weighted method considering elevation, while the geographically weighted regression method considering terrain has the best interpolation accuracy.

[0121] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A rainstorm interpolation method considering the terrain factors of the mountain torrent area basin, characterized by: include: Data preparation, including basin basic data, thematic data and basin precipitation data; After detecting the precipitation data of the basin, the basin was divided into three typical floods, and the three typical floods in the basin were interpolated using the inverse distance weighted method with terrain factors, the kriging method, and the geographically weighted regression method. Among them, the inverse distance weighted method considering the terrain is used to determine the distance and elevation weights. First, the weight determination of the inverse distance weighted method considering the terrain is considered, including the allocation of weights on horizontal distance and vertical distance; The above methods were cross-validated to obtain the average relative error, mean absolute error and root mean square error, and the characteristics of the rainstorm interpolation method and its applicability in the watershed were obtained.

2. A rainstorm interpolation method considering topographic factors of mountain torrent areas according to claim 1, characterized in that: The three typical floods in the basin include whether the rainfall in 1 hour is greater than 16 mm, whether the rainfall in 12 hours is greater than 30 mm, and whether the rainfall in 24 hours is greater than 16 mm; In formula (1): S i The ratio of the rainfall in the i-th period to the average rainfall in the rainstorm; n is the number of periods; V t The larger the value, the more uneven the distribution of rainstorm time is; In formula (2): t m is the time of occurrence of the main rain peak; T is the rainfall duration; C p The larger the value, the later the rain peak appears; In formula (3): α i is the Thiessen polygon area weight factor; α i is the rainfall at the ith rainfall station; P i is the basin surface rainfall; n has the same meaning as formula (1), V p The larger the value, the more uneven the spatial distribution of heavy rain is.

3. A rainstorm interpolation method considering terrain factors in mountain torrent areas according to claim 1, characterized in that: The interpolation calculation process of the inverse distance weighted method considering terrain involves the allocation of weights on horizontal distance and vertical distance, including: First, calculate the distance from the unknown point to the sampling point, and determine each sampling point based on the neighborhood search range and the maximum and minimum number of sampling points; calculate the horizontal distance and vertical elevation difference from the interpolation point to each sampling point; Secondly, according to the horizontal distance and relative elevation from the interpolation point to each sample point and the selected power function, the horizontal distance weight and vertical distance weight of each sampling point are calculated respectively; Where λ di is the weight of the horizontal distance at sample point i, W D is the weight of horizontal distance relative to vertical distance. i is the horizontal distance from the interpolation point to the sampling point; λzi is the weight of the vertical distance at the sample point i, W Z is the weight of vertical distance relative to horizontal distance; z i is the vertical distance from the point to be interpolated to the sampling point, that is, the elevation difference; finally, the value of the point to be interpolated is calculated by weighted summation based on the values ​​of each sampling point and its corresponding weight; Where P(x0,y0) is the point to be interpolated, λ di and λ zi is the horizontal distance weight coefficient and the vertical distance weight coefficient, P(x i ,y i ) is the measured value of sample point i.

4. A rainstorm interpolation method considering terrain factors in mountain torrent areas according to claim 1, characterized in that: The calculation formula of the inverse distance weighted method considering terrain is as follows: in, Where W D , W Z are the weights of the influence of distance and elevation on precipitation, their sum is 1, P i is the precipitation at observation station i, d i is the distance between the point to be estimated and observation station i, in km, and P is the rainfall at the station to be estimated; i is the elevation difference between the point to be estimated and observation station i, in meters.

5. The rainstorm interpolation method considering the terrain factors of the mountain torrent area according to claim 1 is characterized by: The calculation formula of the ordinary kriging method considering terrain is as follows: The prerequisite for using cokriging interpolation is that the N regionalized variables Zk(x) (k=1,2...N) satisfy the assumption of second-order stationarity, that is, the mathematical expectation of Zk(x) exists in the entire study area and is a constant, that is, for any x: E[Z k (x)]=m k (8) In the entire study area, the covariance of Zk(x) exists and is stable, that is, it only depends on the distance h between variables and has nothing to do with x: The[Z k (x), Z k (x+h)]=C(h) (9) When h=0, the above equation becomes Var[Z k x)]=C(0), that is, the variance of Zk(x) exists and is constant. Then under the assumption of second-order stationarity, the expectation of the co-regionalization variable is: E[Z k (x)]=m k E[Z k ′(x)]=m k ′(k' is the variable other than k among N variables) Second-order stationarity is a special case of the eigenvalue hypothesis, that is, if the second-order stationarity hypothesis is satisfied, the eigenvalue hypothesis must be satisfied; conversely, if the eigenvalue hypothesis is satisfied, the second-order stationarity hypothesis may not be satisfied. In coordinating ordinary kriging with an auxiliary variable, the estimate of any position to be interpolated X0 can be obtained using the following formula: In the formula, Z1 is the main variable, Z2 is the auxiliary variable, n is the number of measured points of variable Z1 in the neighborhood of the interpolation point x0, m is the number of measured points of variable Z2 in the neighborhood of the interpolation point x0, a i is the weight coefficient, indicating that the spatial sample point x i The observed value Z1(x i ) for the estimated value The contribution degree of the spatial sample point x j The observed value Z2(x j ) for the estimated value degree of contribution.

6. A rainstorm interpolation method considering terrain factors in mountain torrent areas according to claim 1, characterized in that: The calculation formula of the geographically weighted regression method with elevation factor considering the influence of terrain is as follows: P i =b 0i +b xi X i +b yi Y i +b zi Z i (11) Medium X i , Y i , Z i are the X coordinate, Y coordinate and elevation of point i, respectively, 0i is the constant term in the local regression coefficient, β xi , β yi , β zi is the regression coefficient at point i; P i is the spatial coordinate of the point to be interpolated The coefficient of determination R was used for geographically weighted regression considering the influence of terrain. 2 And root mean square error RMSE to evaluate model accuracy; Where: V oi is the measured value at sample point i; V pi is the predicted value at point i; n is the total number of sample points; R 2 Between 0 and 1, the closer it is to 1, the higher the stability of the model; the smaller the RMSE, the higher the accuracy of the model prediction.

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