阅读说明：本技术 一种复杂地形区域的降水数据空间插值方法及计算机存储介质 (Rainfall data spatial interpolation method for complex terrain area and computer storage medium ) 是由 杨大文 杜灿勋 唐莉华 刘勇 孙子日哈 王宇涵 徐定辉 严冬 于 2021-09-09 设计创作，主要内容包括：本申请公开了一种复杂地形区域的降水数据空间插值方法,包括：根据辅助站点与目标网格的距离分别获取每个辅助站点的距离权重；根据辅助站点中的站点与站点间以目标网格为中心所形成的角度,计算距离方向权重；根据辅助站点的多年平均月降水数据及海拔高程数据,拟合得到降水高程梯度；根据拟合得到的降水高程梯度,计算辅助站点到目标网格路径上的第一平均降水高程梯度；利用距离方向权重和第一平均降水高程梯度对目标网格的多年平均月降水数据进行插值,得到目标网格的多年平均月降水数据的插值。由于采用降水-高程梯度关系对距离方向权重进行修正,可以估计降水随地形的变化,提高了降水空间插值的精度。(The application discloses a precipitation data spatial interpolation method for a complex terrain area, which comprises the following steps: respectively acquiring the distance weight of each auxiliary station according to the distance between the auxiliary station and the target grid; calculating distance direction weight according to an angle formed by the sites in the auxiliary sites and the target grid as the center; fitting to obtain a precipitation elevation gradient according to the average monthly precipitation data and the elevation data of the auxiliary station for many years; calculating a first average rainfall elevation gradient from the auxiliary station to a target grid path according to the rainfall elevation gradient obtained by fitting; and interpolating the average monthly rainfall data of the target grid by using the distance direction weight and the first average rainfall elevation gradient to obtain the interpolation of the average monthly rainfall data of the target grid. Because the weight of the distance direction is corrected by adopting the precipitation-elevation gradient relation, the change of the precipitation along with the terrain can be estimated, and the precision of the precipitation spatial interpolation is improved.)

1. A method for spatial interpolation of precipitation data of a complex terrain area comprises the following steps:

dividing a region to be processed comprising a plurality of sites into more than two grids, and performing the following processing by taking one grid as a target grid:

determining the sites within a preset range from the target grid as auxiliary sites;

respectively acquiring the distance weight of each auxiliary station according to the distance between the auxiliary station and the target grid;

calculating distance direction weight according to an angle formed by the sites in the auxiliary sites and the target grid as the center;

fitting to obtain a precipitation elevation gradient according to the average monthly precipitation data and the elevation data of the auxiliary station for many years;

calculating a first average rainfall elevation gradient from the auxiliary station to a target grid path according to the rainfall elevation gradient obtained by fitting;

and interpolating the average monthly rainfall data of the target grid by using the distance direction weight and the first average rainfall elevation gradient to obtain the interpolation of the average monthly rainfall data of the target grid.

2. The method of spatial interpolation of precipitation data according to claim 1, the method further comprising:

calculating the uncertainty of the interpolation of the average monthly rainfall data of a plurality of years according to the distance from the auxiliary station to the target grid;

and calculating the average uncertainty of the interpolation of the average monthly rainfall data of the years according to the uncertainty of the interpolation of the average monthly rainfall data of the years.

3. The method of spatial interpolation of precipitation data according to claim 2, said calculating an average uncertainty of an interpolation of annual average monthly precipitation data, comprising:

calculating a second average precipitation elevation gradient from one of the auxiliary stations to the other station according to the precipitation elevation gradient;

and calculating the average uncertainty of the interpolation of the average monthly rainfall data of the years by using the second average rainfall elevation gradient.

4. The method of spatial interpolation of precipitation data according to claim 3, said calculating uncertainty of the interpolation of the annual average monthly precipitation data according to the distance of the auxiliary sites to the target grid, comprising:

and fitting the relation between the semi-variation function and the corresponding distance by adopting a preset mathematical model.

5. The method of spatial interpolation of precipitation data according to claim 4, wherein the mathematical model is a spherical model or an exponential model.

6. The method of spatial interpolation of precipitation data according to claim 3, further comprising:

and quantifying the average uncertainty of the annual average monthly rainfall data interpolation.

7. The method of spatial interpolation of precipitation data according to claim 6, wherein quantifying the average uncertainty of the interpolation of the mean monthly precipitation data over a plurality of years comprises:

and calculating the variance of the interpolation of the average monthly rainfall data of the target grid for many years.

8. The method of spatial interpolation of precipitation data according to claim 1, the method further comprising:

calculating the ratio of the daily precipitation observation value and the daily precipitation climate value of the target grid;

performing spatial interpolation on the ratio by adopting a distance direction weighting interpolation method to obtain spatial interpolation of the ratio;

and calculating the interpolation of the daily precipitation data of the target grid according to the daily precipitation climate value of the target grid and the spatial interpolation of the ratio.

9. The method of spatial interpolation of precipitation data of claim 8, further comprising:

and calculating the average uncertainty of the target grid daily precipitation data interpolation by using the ratio of the daily precipitation observation value to the daily precipitation climate value of the target grid.

10. A computer storage medium having a computer program stored thereon, which when executed by a processor implements a method of spatial interpolation of precipitation data as claimed in any one of claims 1 to 9.

Technical Field

The present disclosure relates to, but not limited to, hydrology and water resource and hydraulic engineering technologies, and more particularly, to a method for spatial interpolation of precipitation data in a complex terrain area and a computer storage medium.

Background

Precipitation is the subject of both hydrology and meteorology research. The hydrology field mainly studies the space-time distribution and the transformation rule of rainfall on the ground surface. The space-time distribution of rainfall determines the surface water resource amount and the disaster characteristics of flooding, drought and the like. The basin hydrological model is a mathematical structure established for simulating the basin hydrological process, the simulated hydrological phenomenon is called a prototype, and the model is a generalization of the physical and logical processes of the prototype. The accuracy of precipitation data has a significant influence on the runoff simulation result of the hydrological model.

The rainfall station directly observes the rainfall, the rainfall observation mode has a history of more than 100 years, and rainfall station networks of different scales are formed in countries in the world at present. With the development of satellite communication technology, a wider range of precipitation data can be obtained by utilizing indirect precipitation observation modes such as meteorological satellites and weather radars. However, because there are many unavoidable interference factors in the process of data collection and data inversion by meteorological satellites, and the weather radar needs to effectively deal with potential error influences such as ground clutter and beam occlusion, the accuracy of the indirect rainfall observation mode is still limited in general.

Therefore, the rainfall station in the related art is still an indispensable rainfall observation means, and the rainfall station still plays a fundamental role in the whole rainfall observation system. However, for a complicated terrain area, due to uneven distribution and limited coverage of rainfall stations, in the process of observing rainfall, a rainfall data spatial interpolation method is required to expand rainfall observation of a point scale to a surface scale. Common spatial interpolation methods include the Thiessen polygon method, the Crithn interpolation method, the inverse distance weight method (IDW), the distance direction weight method (ADW), and the like.

Since precipitation is significantly affected by terrain, especially in complex terrain areas, spatial interpolation methods in the related art all have different degrees of uncertainty, thereby affecting the accuracy of observing precipitation.

Disclosure of Invention

In view of this, the embodiments of the present invention provide the following solutions.

The following is a summary of the subject matter described in detail herein. This summary is not intended to limit the scope of the claims.

The embodiment of the invention provides a precipitation data spatial interpolation method for a complex terrain area, which comprises the following steps:

dividing a region to be processed comprising a plurality of sites into more than two grids, and performing the following processing by taking one grid as a target grid:

determining the sites within a preset range from the target grid as auxiliary sites;

respectively obtaining the distance weight of each auxiliary station according to the distance between the auxiliary station and the target grid;

calculating distance direction weight according to an angle formed by the sites in the auxiliary sites and the target grid as the center;

fitting to obtain a precipitation elevation gradient according to the average monthly precipitation data and the elevation data of the auxiliary station for many years;

calculating a first average rainfall elevation gradient from the auxiliary station to a target grid path according to the rainfall elevation gradient obtained by fitting;

and interpolating the average monthly rainfall data of the target grid by using the distance direction weight and the first average rainfall elevation gradient to obtain the interpolation of the average monthly rainfall data of the target grid.

In one illustrative example, the method further comprises:

calculating the uncertainty of the interpolation of the average monthly rainfall data of a plurality of years according to the distance from the auxiliary station to the target grid;

and calculating the average uncertainty of the interpolation of the average monthly rainfall data of the years according to the uncertainty of the interpolation of the average monthly rainfall data of the years.

In an exemplary embodiment, the calculating an average uncertainty of the interpolation of the annual average monthly precipitation data comprises:

calculating a second average precipitation elevation gradient from one of the auxiliary stations to the other station according to the precipitation elevation gradient;

and calculating the average uncertainty of the interpolation of the average monthly rainfall data of the years by using the second average rainfall elevation gradient.

In one illustrative example, the calculating an uncertainty of the interpolation of the annual average monthly precipitation data as a function of the distance of the secondary site to the target grid comprises:

and fitting the relation between the semi-variation function and the corresponding distance by adopting a preset mathematical model.

In an illustrative example, the mathematical model is a spherical model or an exponential model.

In one illustrative example, the method further comprises:

and quantifying the average uncertainty of the annual average monthly rainfall data interpolation.

In one illustrative example, the quantifying the average uncertainty in interpolating the multi-year average monthly precipitation data comprises:

and calculating the variance of the interpolation of the average monthly rainfall data of the target grid for many years.

In one illustrative example, the method further comprises:

calculating the ratio of the daily precipitation observation value and the daily precipitation climate value of the target grid;

performing spatial interpolation on the ratio by adopting a distance direction weighting interpolation method to obtain spatial interpolation of the ratio;

and calculating the interpolation of the daily precipitation data of the target grid according to the daily precipitation climate value of the target grid and the spatial interpolation of the ratio.

In one illustrative example, the method further comprises:

and calculating the average uncertainty of the target grid daily precipitation data interpolation by using the ratio of the daily precipitation observation value to the daily precipitation climate value of the target grid.

In another aspect, an embodiment of the present invention further provides a computer storage medium, where a computer program is stored, and when the computer program is executed by a processor, the method for spatial interpolation of precipitation data is implemented.

According to the rainfall data spatial interpolation method for the complex terrain area, the distance direction weight is corrected according to the rainfall data-elevation gradient relation, the problem that the weight of densely distributed stations is overlarge can be avoided, the change condition of the rainfall data along with the terrain is estimated, and the precision of the rainfall data spatial interpolation is improved. Moreover, based on the geostatistical method, under the condition that the influence of the distance, the elevation and the station distribution characteristics on the rainfall space variability is considered, the uncertainty of interpolation results is quantified.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

Drawings

The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the example serve to explain the principles of the invention and not to limit the invention.

FIG. 1 is a flow chart of a distance direction weighted precipitation space interpolation method according to an embodiment of the present invention;

FIG. 2 is a diagram of a verification area in accordance with an embodiment of the present invention;

FIG. 3 is a schematic diagram of a site path according to an embodiment of the present invention;

FIG. 4a is a schematic view of the elevation gradient of precipitation in a study area for an average of 7 months over a plurality of years according to an embodiment of the present invention;

FIG. 4b is a schematic view of the elevation gradient of precipitation in a study area over a number of years in 10 months on average according to an embodiment of the present invention;

FIG. 5 is a diagram of a multi-year average month-half-variance function of an example of the present invention taking into account both distance and elevation;

FIG. 6a is an example of a years average 7 month precipitation interpolation according to the present invention;

FIG. 6b is a schematic diagram of the variance of the multi-year average 7-month precipitation interpolation of the example of the present invention;

FIG. 7 is a graphical illustration of a semi-variogram of the climate value ratio of an exemplary daily precipitation to a daily precipitation of the present invention;

FIG. 8a is an example interpolation of 10/1/2010 precipitation;

FIG. 8b is a schematic diagram of the variance of the interpolation of the 10/1/2010 precipitation;

FIG. 9a is a schematic diagram of MAAE cross-validation results of interpolation of site precipitation without consideration of elevation according to an example of the present invention.

FIG. 9b is a schematic diagram illustrating MAAE cross-validation results of station precipitation interpolation with consideration of elevation according to an example of the present invention.

FIG. 10 is a schematic diagram illustrating the improvement of MAAE in elevation taken into account in accordance with an example of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the embodiments and features of the embodiments in the present application may be arbitrarily combined with each other without conflict.

Fig. 1 is a flowchart of a precipitation data spatial interpolation method for a complex terrain area according to an embodiment of the present invention, as shown in fig. 1, including: dividing a region to be processed comprising a plurality of sites into more than two grids, and performing the following processing by taking one grid as a target grid;

step 101, determining a station within a preset range from a target grid as an auxiliary station;

in an exemplary embodiment, taking the Yangtze river upstream drainage basin as the area to be processed, 396 stations are used altogether, wherein Digital Elevation Model (Digital Elevation Model) data, srtm (stub radio localization session) data with the original precision of 90m is used. For each grid of the area to be processed, the 8 closest sites to the target grid may be selected as secondary sites.

102, respectively obtaining the distance weight of each auxiliary station according to the distance between the auxiliary station and a target grid;

in one illustrative example, step 102 can be obtained by equation (1):

in formula (1), x is the distance between the target grid (m, n) and the station i; according to the distribution of the flow field sites upstream of the Yangtze river, in the embodiment of the application, x is assumed₀The value is 400 km; s is a correction coefficient, and may take a value of 4, for example, according to an actual application scenario.

103, calculating distance direction weight according to an angle formed by the sites in the auxiliary sites and the sites by taking the target grid as the center;

in one illustrative example, step 103 can be obtained by equation (2):

w_(m,n),i＝w_0(m,n),i(1+a_(m,n),i) (2)

the adjustment coefficient in formula (2) can be obtained by formula (3):

in the formula (3), cos θ_m,n(i, j) represents the angle formed by the ith and jth stations centered on the target grid (m, n), as shown in FIG. 3; nog denotes the number of sites used; w is a_0(m,n),jIndicating the distance weight of the jth site.

Step 104, fitting to obtain a precipitation elevation gradient according to the average monthly precipitation data and the altitude elevation data of the auxiliary station;

in an exemplary embodiment, the precipitation elevation gradient is fitted by selecting the 5 nearest sites to the target grid based on the correlation between the annual average monthly precipitation data and the elevation data.

Step 105, calculating a first average rainfall elevation gradient from the auxiliary station to the target grid path according to the rainfall elevation gradient obtained by fitting;

in one illustrative example, step 105 can be obtained by equation (4):

in the formula (4), ele (u)_m,n) And ele (u)_g) Respectively representing the target mesh u_m,nAnd elevation data for station g, Nop representing the number of grids on the path. Fig. 3 shows the path from site s2 to the target grid (m, n). slope_jThe elevation gradient of the precipitation for the jth grid on the path.

And 106, interpolating the multi-year average monthly rainfall data of the target grid by using the distance direction weight and the first average rainfall elevation gradient to obtain the interpolation of the multi-year average monthly rainfall data of the target grid.

In one illustrative example, step 106 can be obtained by equation (5):

in the formula (5), w_g(u_m,n) Indicating the g-th site to target grid u for interpolation_m,nDistance direction weight of (1); nog denotes the number of sites used for interpolation; s (u)_g,u_m,n) Representing the g-th site to grid u_m,nAnd (5) averaging the elevation gradient of the rainfall, and calculating the formula (4).

In an illustrative example, interpolation of the years' average 7 month precipitation data for the target grid is shown in FIG. 6 a.

According to the embodiment of the invention, the distance direction weight is corrected according to the precipitation-elevation gradient relation, so that the change condition of precipitation data along with the terrain can be estimated, the problem that the weight of densely distributed stations is greatly influenced is avoided, and the precision of precipitation space interpolation is improved.

In an illustrative example, a method of an embodiment of the present invention further includes:

calculating the uncertainty of the interpolation of the average monthly rainfall data of a plurality of years according to the distance from the auxiliary station to the target grid;

and calculating the average uncertainty of the interpolation of the average monthly rainfall data of the years according to the uncertainty of the interpolation of the average monthly rainfall data of the years.

In an exemplary embodiment, the calculating an average uncertainty of the interpolation of the annual average monthly precipitation data comprises:

and calculating a second average precipitation elevation gradient from one of the auxiliary stations to the other station according to the precipitation elevation gradient.

The second average precipitation elevation gradient may be obtained by equation (6):

in formula (6), Nop represents the number of meshes on a path; ele (u)_i+ h) and ele (u)_i) Two for a distance hElevation of individual sites; slope_jThe elevation gradient of the precipitation for the jth grid on the path.

The average uncertainty of the interpolation of the annual average monthly rainfall data can be obtained by equation (7):

in the formula (7), n (h) is the number of station pairs with a mutual distance of h; p (u)_i+ h) and P (u)_i) The average monthly rainfall data of many years.

For areas with complex terrain, the effect of elevation changes at the site on the spatial variability of precipitation may be further considered. In this case, the average uncertainty of the interpolation of the multi-year average monthly precipitation data using the second average precipitation elevation gradient can be obtained by equation (8):

in the formula (8), ele (u)_i+ h) and ele (u)_i) All represent elevation in elevation; s (u)_i,u_i+ h) represents the second average precipitation elevation gradient, see equation (6).

In one illustrative example, the calculating an uncertainty of the interpolation of the annual average monthly precipitation data as a function of the distance of the secondary site to the target grid comprises:

and fitting the relation between the half-variation function and the corresponding distance by adopting a preset mathematical model, and drawing a fitting curve (shown as a curve in the attached figure 5) of the average months of years.

In one illustrative example, half-variogram values are calculated for months 1 to 12, respectively, using the annual average monthly precipitation data for 396 sites upstream of the Yangtze river. Dividing the interval into 22 intervals in 100km unit according to the distribution of the used stations, and finally dividing each intervalThe value is all within the intervalA total of 22 can be obtained by the arithmetic mean ofValues and corresponding distances h, for each pair of discrete points (as shown by the discrete points in fig. 5). The spatial variation of the precipitation is generally analyzed by using a theoretical variation function model such as a spherical model or an exponential model with the lump metal effect.

In an illustrative example, the mathematical model is a spherical model or an exponential model.

In an exemplary embodiment, the spherical model and the exponential model fit the semi-variogram versus distance, which can be obtained by equations (9) and (10), respectively:

in formulae (9) and (10), C₀Representing a lump value reflecting a variation feature that cannot be characterized due to insufficient sampling density, or an error derived from observation; a represents a variable range value and represents a spatial correlation scale, and generally, if the distance between sampling points is less than the distance, the correlation of observed data is strong; c₀+ C denotes the base value, C and C₀Can reflect that the spatial variability of the variables is caused by spatial correlation processes or random effects.

Fitting the half-variogram values with a spherical or exponential model with the lump effect, respectivelyAnd the corresponding distance h, the index model is better fitted in the area upstream of the Yangtze river, so that the index model is preferably selectedAnd (5) fitting the model. The initial parameter values in the exponential model are estimated by visually observing the distribution of the variation function values of the sample, and the more reasonable initial values of the parameters of the exponential model are further determined by a trial calculation mode. According to the practical application scenario, the value of the gold value C0 can be 0.5, the value of the variable range a can be 1900, and the value of the base station C can be 400.

In an illustrative example, a method of an embodiment of the present invention further includes:

and quantifying the average uncertainty of the annual average monthly rainfall data interpolation.

In one illustrative example, the quantifying the average uncertainty in interpolating the multi-year average monthly precipitation data comprises:

and calculating the variance of the interpolation of the average monthly rainfall data of the target grid for many years.

The variance can be obtained by equation (11):

the uncertainty quantification of the mean monthly precipitation data interpolation results over the years is shown in figure 6 b.

In an illustrative example, a method of an embodiment of the present invention further includes:

calculating the ratio of the daily precipitation observation value and the daily precipitation climate value of the target grid;

in an exemplary instance, the temporal-spatial variability of precipitation data is greater on a daily scale, and precipitation data for the same day in different years may have significantly different precipitation-elevation gradients. Therefore, the result of interpolation of the average precipitation data of each month (1-12) of a plurality of years is used as the precipitation climate value of each month in the research area, and meanwhile, the ratio of the precipitation observation value of each month to the precipitation climate value of each month in the target grid is further calculated on the assumption that the precipitation climate value of the scale of each month is equal to the precipitation climate value of each month divided by the corresponding number of days.

The ratio can be obtained by equation (12):

in the formula (12), x_cli(u_i) Representing a site u_iThe daily precipitation climate value of the location; x (u)_i) Representing daily precipitation observations.

And carrying out spatial interpolation on the ratio by adopting a distance direction weighting interpolation method to obtain the spatial interpolation of the ratio.

In an illustrative example, given that the spatial distribution of daily scale precipitation climate values already includes the effect of terrain variations on precipitation, the elevation is not considered when spatially interpolating the ratio.

The spatial interpolation of the ratio can be obtained by equation (13):

and calculating the interpolation of the daily precipitation data of the target grid according to the daily precipitation climate value of the target grid and the spatial interpolation of the ratio.

The interpolation of the daily precipitation data of the target grid can be obtained by equation (14):

x_ADW(u_m,n)＝x_cli(u_m,n)×ratio_ADW(u_m,n) (14)

in an illustrative example, interpolation of target grid 2010, 10 months, 1 day precipitation data is shown in FIG. 8 a.

In an illustrative example, a method of an embodiment of the present invention further includes:

and calculating the average uncertainty of the target grid daily precipitation data interpolation by using the ratio of the daily precipitation observation value to the daily precipitation climate value of the target grid.

In one illustrative example, the semi-variogram may be obtained by equation (15):

in formula (15), ratio (u)_i+ h) and ratio (u)_i) Respectively representing the ratio values, daily scales, of two stations at a mutual distance hThe fitting of the empirical expression of (a) is consistent with the monthly scale.

On a daily scale, according to a precipitation interpolation method and an error quantification method on the daily scale, after the half variogram of each day is obtained, as some stations in a research area have missing measurement conditions in certain time intervals, the half variogram of each day of a month is averaged to obtain the average half variogram of each day of the month in many years. Fitting the half-variogram values likewise with a spherical or exponential model with the lump effect, respectivelyAnd the corresponding distance h, the exponential model fitting is better, so the exponential model fitting is preferred. And estimating initial parameter values in the exponential model by visually observing the distribution of the variation function values of the sample, and further determining more reasonable initial parameter values of the exponential model by a trial calculation mode. According to the practical application scenario, the value of the gold value C0 may be 0, the value of the variable range a may be 20, and the value of the base station C may be 400.

The average uncertainty of the target grid daily precipitation data interpolation is quantified and can be obtained by equation (16): ,

in equation (16):when the station g arrives at the target grid u_m,nWhen the distance of (d) is h, the empirical fitting value of the half-variogram of the interpolation result of Ratio.

In an exemplary embodiment, the result of the average uncertainty quantification of the target grid daily precipitation data interpolation is shown in fig. 8 b.

The embodiment of the invention also provides a computer storage medium, wherein a computer program is stored in the computer storage medium, and when being executed by a processor, the computer program realizes the precipitation data spatial interpolation method.

The embodiment of the invention compares the error of the interpolation result under the two conditions of considering the elevation and not considering the elevation. Specifically, a leave-one-out cross inspection method is used, aiming at grids where 396 stations are located at the upstream of the Yangtze river, rainfall at each grid is obtained by other 8 stations closest to the grid through an ADW interpolation method under the condition that elevation elements are not considered and the elevation elements are considered. And based on the actually measured data of the station, the two results are tested, and the test index is the monthly mean absolute error (MAAE). Fig. 9a, 9b show MAAE cross-validation results in two cases, respectively. Overall, in most areas of the study area, both interpolation results MAAE are small, which is shown in that in the grid where 396 sites are used, when elevation is not considered, 145 sites with MAAE smaller than 5mm are occupied, and the total number of sites with MAAE smaller than 15mm is 351; when elevation is considered, 159 sites are occupied for MAAE less than 5mm, 354 are occupied for MAAE less than 15 mm. In the case of considering elevation, the interpolation effect of the grid with 60.6% of the sites is better than that in the case of not considering elevation elements. As shown in fig. 10, it can be seen that the sites with improved MAAE are mainly distributed in mountainous areas. The interpolation method after considering the elevation elements is more reasonable in mountainous areas with complex terrain. Table 1 shows the percentage of the number of stations in each elevation interval in which MAAE is improved after the elevation elements are considered.

TABLE 1 improvement of the error after interpolation of elevation factors in different elevation intervals

The specific gravity of improvement is smaller in low altitude areas, but as the elevation increases, the specific gravity of improvement tends to increase. The improved specific gravity is the largest in an elevation interval of 2500-3500 m in altitude. By combining the analysis, the ADW interpolation method considering the elevation elements is more reasonable, and the accuracy of the interpolation result is higher.

It will be understood by those of ordinary skill in the art that all or some of the steps of the methods, systems, functional modules/units in the devices disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. In a hardware implementation, the division between functional modules/units mentioned in the above description does not necessarily correspond to the division of physical components; for example, one physical component may have multiple functions, or one function or step may be performed by several physical components in cooperation. Some or all of the components may be implemented as software executed by a processor, such as a digital signal processor or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.