CN106597575A - Precipitation spatial interpolation method based on cross validation and two-dimensional Gaussian distribution weighting - Google Patents
Precipitation spatial interpolation method based on cross validation and two-dimensional Gaussian distribution weighting Download PDFInfo
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Abstract
The invention discloses a precipitation spatial interpolation method based on cross validation and two-dimensional Gaussian distribution weighting, and the method comprises the steps: determining the coordinates and elevation values of all rainfall stations in an interpolation region and the coordinates and elevation values of to-be-interpolated points in the interpolation region; calculating the distance and elevation difference between any two rainfall stations in the interpolation region, and determining the maximum value of the distances between all stations in the interpolation region and the maximum value of the elevation differences between all stations in the interpolation region; optimizing optimal weighted parameter values through optimization according to the rainfall observation data of all rainfall stations in the interpolation region and the maximum value of the distances and the maximum value of the elevation differences between all stations; and calculating the rainfall time sequence estimation value of each to-be-interpolated point, thereby obtaining the rainfall spatial interpolation data in the interpolation region. The method gives consideration to the impact on rainfall distribution from distance and elevation factors, is simple and convenient for calculation, and guarantees the operation efficiency.
Description
Technical field
The present invention relates to geographical and hydro science field, more particularly to a kind of to be based on cross validation and dimensional gaussian distribution
Entitled spatial interpolation method for precipitation.
Background technology
Precipitation interpolation method is widely used in the space interpolation to rainfall station-observed data and analyzes, to obtain region drop
Water yield space distribution situation, can provide significant data and support for flood control, drought resisting etc..At present, insert in the precipitation space being widely used
Value method mainly has：Nearest neighbor method, anti-distance method, Trend simulating method and Kriging technique etc..Nearest neighbor method is called Thiessen polygon method,
Its interpolation result Spatial Variation is undesirable.Inverse distance weight is a kind of accurate interpolation method, easily by data point cluster
Affect, a kind of isolated point data as a result often occur and be distributed apparently higher than the "goose egg" formula of ambient data point.Trend simulating method is to be based on
Regression analyses principle, can produce smooth curved surface, but cannot ensure accuracy of the result on known point.Kriging technique is based on ground
Reason statistics, can produce more natural spatial distribution result, but arithmetic speed is slower.
The impact of relative distance factor pair spatial distribution of precipitation between rainfall website is only considered more than above Precipitation Interpolation, and
Have ignored the impact of landform.Especially for the mountain area that landform is more complicated, precipitation is largely affected by elevation change.
Research shows, in Precipitation in Mountain Area amount and elevation variation tendency in gradient.Therefore, it is necessary while examining in precipitation Interpolation Process
Consider the impact of distance and Elevation factor to rainfall distribution.This especially analyzes significant to Precipitation in Mountain Area quantity space.
The content of the invention
In view of this, it is an object of the invention to propose one kind based on cross validation and the entitled precipitation of dimensional gaussian distribution
Quantity space interpolation method, to consider the impact of distance and Elevation factor to rainfall distribution simultaneously.
The present invention provide based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution include with
Lower step：
Determine the seat of the coordinate and height value of all rainfall websites and the point of the interpolation in interpolation area in interpolation area
Mark and height value；
Distance and depth displacement between any two rainfall website in interpolation area are calculated, and determines all stations in interpolation area
The maximum of the maximum of distance and depth displacement two-by-two between point；
According to high apart from maximum value two-by-two between all precipitation station point precipitation observation data and all websites in interpolation area
Path difference maximum, optimization obtains optimal weighting parameter value；
Calculate distance and depth displacement between each interpolation point and rainfall website in interpolation area；
According between all websites two-by-two apart from maximum value depth displacement maximum, optimal weighting parameter value and each interpolation
Distance and depth displacement between point and rainfall website, calculates precipitation time serieses estimated value on each interpolation point, so as to be inserted
Spatial Interpolation of Rainfall data in value region.
In some embodiments of the invention, it is described determine interpolation area in all rainfall websites coordinate and height value with
And the interpolation point in interpolation area coordinate and height value the step of include：
Basic data is collected, the basic data includes：Interpolation area scope, Law of DEM Data, rainfall website
Coordinate position and rainfall website precipitation discharge observation data sequence；
Basic data according to collecting is determined in interpolation area in the height value and interpolation area of all rainfall websites
Interpolation point coordinate and height value.
In some embodiments of the invention, the distance and height calculated in interpolation area between any two rainfall website
Path difference, and include the step of determine in interpolation area between all websites maximum D and E of distance and depth displacement two-by-two：
Based on the coordinate and height value of each rainfall website in interpolation area, calculated using range formula and depth displacement formula
To any two rainfall site distance from dijWith depth displacement eij, and further compare any two rainfall site distance from dijWith
Depth displacement eij, so that it is determined that maximum D and E of distance and depth displacement two-by-two between all websites of interpolation area.
In some embodiments of the invention, it is described according to all precipitation station point precipitations observation data in interpolation area and
Two-by-two apart from maximum value depth displacement maximum between all websites, optimizing the step of obtaining optimal weighting parameter value includes：
Based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area, to each
Precipitation station point carries out Gaussian function weighted sum precipitation Interpolate estimation；
Precipitation value is surveyed as reference with each rainfall website, the root-mean-square of corresponding precipitation station point precipitation Interpolate estimation is assessed
Error mean；
It is optimal weighting parameter combination to choose the minimum parameter combination of root-mean-square error average, so as to obtain optimal weighting ginseng
Numerical value.
In some embodiments of the invention, it is described based on cross-validation method, with all rainfall websites in interpolation area
Based on precipitation discharge observation data, wrap the step of carry out Gaussian function weighted sum precipitation Interpolate estimation to each precipitation station point
Include：
Based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area, adopt respectively
Gaussian function is carried out with different dimensional gaussian distribution parameter combinations with other precipitation station point precipitations to each rainfall website to add
Power and precipitation Interpolate estimation, wherein, dimensional gaussian distribution function expression isFormula
In, g (dist, elev) is dimensional gaussian distribution functional value；Dist and elev are respectively two independent variables, wherein dist and elev
Difference two factors of influence of respective distances and elevation；C1And C2Respectively dimensional gaussian distribution function parameter.
In some embodiments of the invention, it is described that precipitation value is surveyed as reference with each rainfall website, assess corresponding rain
The step of root-mean-square error average of amount website precipitation Interpolate estimation, includes：
Wherein,Be using cross-validation method all precipitation station point dewatering data sequence interpolation results are calculated it is equal
Square error average；N is interpolation area rainfall website sum；M is the precipitation measurement length of time series of each rainfall website；It is k-th time serieses precipitation estimated value to rainfall website i；PikFor the k-th time serieses precipitation of rainfall website i
Discharge observation value, PjkFor k-th time serieses precipitation observation of rainfall website j；wijTo give the interpolation weight of rainfall website j
Weight values；And dijHomogenization distance and actual range respectively between rainfall website i and j；And eijRespectively rainfall website i
Homogenization depth displacement and actual depth displacement between j；D and E are respectively between all websites of interpolation area distance and depth displacement two-by-two
Maximum；CdAnd CeRespectively two-dimensional Gaussian function considers the weighting parameters of distance and Elevation factor.
In some embodiments of the invention, it is described according between all websites two-by-two apart from maximum value depth displacement maximum,
Distance and depth displacement between optimal weighting parameter value and each interpolation point and rainfall website, calculates precipitation on each interpolation point
The step of time serieses estimated value, includes：
To any interpolation point x, its k-th time serieses precipitation interpolation calculation formula：
Wherein,For k-th time serieses precipitation interpolation result of interpolation point x；wxjTo give inserting for rainfall website j
Value weighted value；And dxjHomogenization distance and actual range between respectively interpolation point x and rainfall website j；And exjRespectively
For homogenization depth displacement and actual depth displacement between interpolation point x and rainfall website j；C'dAnd Ce' be respectively determine optimum add
Weight parameter is combined.
Described in above as can be seen that the present invention provide based on cross validation and the entitled precipitation of dimensional gaussian distribution
Quantity space interpolation method carries out precipitation interpolation weight and estimates and cross-validation method optimization weighting parameters based on dimensional gaussian distribution, together
When consider the impact to rainfall distribution of distance and Elevation factor, calculating process is easy, it is ensured that operation efficiency.Compared to existing skill
Art, the present invention has the advantages that：(1) while considering the impact of distance and elevation, interpolation result can reflect precipitation with height
The space distribution rule of Cheng Bianhua；(2) optimal weighting parameter is determined based on cross-validation method, has ensured the reliability of interpolation result
Property；(3) mountain area precipitation station point precipitation observation data space interpolation analysis are particularly well-suited to, and obtain high spatial resolution grid
Precipitation data.
Description of the drawings
Fig. 1 is the embodiment of the present invention based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution
Schematic flow sheet；
Fig. 2 is the two-dimensional Gaussian function distribution schematic diagram of the embodiment of the present invention；
Fig. 3 is interpolation area scope, DEM elevations and the rainfall website location drawing of the embodiment of the present invention；
Fig. 4 is the interpolation area stress and strain model figure of the embodiment of the present invention；
Fig. 5 is interpolation area interpolation point (interpolation grid center) coordinate position of the embodiment of the present invention；
Fig. 6 is distributed for the two-dimensional Gaussian function for embodiment precipitation interpolation that the optimization of the embodiment of the present invention determines, its
Middle C 'dWith C 'eRespectively 0.9 and 1.1；
Fig. 7 (a) is each precipitation station correspondence grid-based monitoring average annual precipitation figure, Fig. 7 in the interpolation area of the embodiment of the present invention
B () assigns average annual Rainfall distribution figure in each interpolation grid that power interpolation is obtained based on dimensional gaussian distribution.
Specific embodiment
To make the object, technical solutions and advantages of the present invention become more apparent, below in conjunction with specific embodiment, and reference
Accompanying drawing, the present invention is described in more detail.
It should be noted that the statement of all uses " first " and " second " is for distinguishing two in inventive embodiments
The entity of same names non-equal or the parameter of non-equal, it is seen that " first " " second " should not manage only for the convenience of statement
Solution is the restriction to inventive embodiments, and subsequent embodiment is no longer illustrated one by one to this.
It is described based on cross validation and the entitled precipitation quantity space of dimensional gaussian distribution as one embodiment of the present of invention
The step of interpolation method mainly includes the step of determining weighting parameters and Interpolate estimation：First, based on interpolation area space number
In the case of collecting with pretreatment, optimized parameter estimation is carried out to dimensional gaussian distribution function based on cross-validation method, it is determined that
Optimal weighting parameter；Then, distance and the whole interpolation area of two factor pairs of elevation are considered using the optimal weighting parameter for determining
Precipitation carries out spatial interpolation prediction.Cross-validation method can efficiently determine optimal weighting parameter, be the reliability of final interpolation result
Property provide technical guarantee；Meanwhile, power is assigned based on dimensional gaussian distribution function and considers distance and Elevation factor to precipitation quantity space
The impact of distribution, has the higher suitability especially for Precipitation in Mountain Area quantity space interpolation analysis.
Referring to Fig. 1, it is the embodiment of the present invention based on cross validation and the entitled precipitation quantity space of dimensional gaussian distribution
The schematic flow sheet of interpolation method.Specifically, it is described to be inserted based on cross validation and the entitled precipitation quantity space of dimensional gaussian distribution
Value method may comprise steps of：
Step 101：Basic data is collected and processed.
In the step, basic data is collected first, the basic data includes：Interpolation area scope, digital elevation model
(DEM) the precipitation discharge observation data sequence of data, the coordinate position of rainfall website and rainfall website；Then according to the base collected
Plinth data determine the height value of all rainfall websites in interpolation area, and interpolation point (grid element center) in interpolation area
Coordinate and its corresponding height value.Wherein, the precipitation discharge observation data of the rainfall website can select precipitation station as needed
The precipitation discharge observation data of point, can be daily rainfall, all rainfalls, moon rainfall, season rainfall, annual rainfall etc., such as
2000-2010 day data sequence.It is determined that interpolation point coordinate and height value when, need consider interpolation result spatial discrimination
Rate requires to divide interpolation grid, such as 1km grids.
Step 102：Rainfall website is analyzed apart from the discrepancy in elevation.In this step, any two precipitation station in interpolation area is calculated
Distance and depth displacement between point, and determine in interpolation area between all websites maximum D and E of distance and depth displacement two-by-two.
Based on the coordinate and height value of each rainfall website in step 101, calculated using range formula and depth displacement formula
To any two rainfall site distance from dijWith depth displacement eij, and further compare any two rainfall site distance from dijWith
Depth displacement eij, so that it is determined that maximum D and E of distance and depth displacement two-by-two between all websites in interpolation area.
Specifically, if the coordinate of any two rainfall website is respectively (a1,b1) and (a2,b2), then the distance of the point-to-point transmission
Computing formula is：
If the elevation of any two rainfall website is respectively c1And c2, then two point height difference computing formula be：
E=| c1-c2| (2)
Step 103：Determine weighting parameters.
Precipitation discharge observation data sequence P based on the rainfall website collected in step 101jkIt is calculated with step 102
The all websites in interpolation area between two-by-two apart from maximum D, depth displacement maximum E optimization obtain optimal weighting parameter value C'dWith C 'e。
In the present invention, using cross-validation method, optimized parameter estimation is carried out to gaussian weighing function.Cross validation
(Cross Validation) is a kind of statistical analysis technique for verifying model prediction performance, and its basic thought is at certain
Initial data is grouped under meaning, used as training set (train set), another part is used as checking collection for a part
(validation set).It is trained with training the set pair analysis model first, recycles the precision of checking collection test training pattern, with
This is evaluated model performance.Therefore, based on cross validation, reference can be provided for determination optimal model parameters.
The present invention is shown in respectively formula (3) and figure for the entitled dimensional gaussian distribution function expression of precipitation interpolation and schematic diagram
Shown in 2.
In formula, g (dist, elev) is dimensional gaussian distribution functional value；Dist and elev are respectively two independent variables, wherein
Dist and elev difference two factors of influence of respective distances and elevation；C1And C2Respectively dimensional gaussian distribution function parameter.
From formula (3) and Fig. 2, the dimensional gaussian distribution is mainly by parameter C1And C2Determine.Typically with C1And C2Definitely
Value is closer to 0, and Gauss distribution curved surface is more precipitous；And with C1And C2Absolute value increases, and function distribution surface tends to flat.DANGSHEN
Number C1And C2One timing, the value of independent variable dist and elev is less, and Gaussian function numerical value g (dist, elev) is bigger.As dist and
When elev is 0, g (dist, elev) takes maximum 1.
Based on above cross-validation method and two-dimensional Gaussian function, the present invention considers distance and the depth displacement factor simultaneously, with two
Dimension gauss of distribution function g (dist, elev) value carries out precipitation interpolation and assigns power.Concrete weighting parameters are defined below：
Based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area, adopt respectively
Gaussian function is carried out with different dimensional gaussian distribution parameter combinations with other precipitation station point precipitations to each rainfall website i to add
Power and precipitation Interpolate estimation (not considering the impact of our station (i) rainfall value)；Then, precipitation value is surveyed with each rainfall website i
It is reference, assesses the root-mean-square error (RMSE) of corresponding rainfall website i precipitation Interpolate estimations, all rainfall websites is tried to achieve then
The RMSE averages of the precipitation Interpolate estimation of (n), i.e.,So
Afterwards, it is optimized parameter to choose the minimum parameter combination of mean square error average, and optimization computing formula is as follows：
Wherein,Be using cross-validation method all precipitation station point dewatering data sequence interpolation results are calculated it is equal
Square error average；N is interpolation area rainfall website sum；M be the precipitation measurement length of time series of each rainfall website (such as
M days)；It is k-th time serieses precipitation estimated value (not considering the impact of our station (i) rainfall value) to rainfall website i；
PikFor k-th time serieses precipitation observation of rainfall website i, PjkFor the k-th time serieses precipitation of rainfall website j
Observation；wijTo give the interpolation weight weight values of rainfall website j；And dijHomogenization distance respectively between rainfall website i and j
And actual range；And eijHomogenization depth displacement and actual depth displacement respectively between rainfall website i and j；D and E is respectively inserted
It is worth between all websites in region the maximum of distance and depth displacement two-by-two；CdAnd CeRespectively two-dimensional Gaussian function considers distance and height
The weighting parameters of Cheng Yinzi.It is optimal weighting parameter combination to choose the minimum parameter combination of root-mean-square error average, so as to obtain
Optimal weighting parameter value C'dWith C 'e。
Step 104：Interpolation point is analyzed apart from the discrepancy in elevation.In this step, each interpolation point and rain in interpolation area is calculated
Distance and depth displacement between amount website.Based on the coordinate and height value of each interpolation point in step 101, using range formula and height
Path difference formula calculate between each interpolation point and rainfall website apart from dxjWith depth displacement exj。
Specifically, if the coordinate of any one interpolation point and a rainfall website is respectively (a1,b1) and (a2,b2), then
The point-to-point transmission apart from computing formula is：
If the elevation of any one interpolation point and a rainfall website is respectively c1And c2, then the two point heights difference calculating
Formula is：
E=| c1-c2| (7)
Step 105：Space interpolation is estimated.
Based on D, E value determined in step 102, the optimal weighting parameter value C' determined in step 103dWith C 'e, Yi Jibu
The distance between each interpolation point and rainfall website and depth displacement in rapid 104, calculates precipitation time serieses on each interpolation point
Estimated value.Finally, Spatial Interpolation of Rainfall data in interpolation area are obtained.
To any interpolation point x, shown in its k-th time serieses precipitation interpolation calculation formula such as formula (8-11)：
Wherein,For k-th time serieses precipitation interpolation result of interpolation point x；wxjTo give inserting for rainfall website j
Value weighted value；And dxjHomogenization distance and actual range between respectively interpolation point x and rainfall website j；And exjPoint
Homogenization depth displacement that Wei be between interpolation point x and rainfall website j and actual depth displacement；C'dWith C 'eThe optimum for respectively determining
Weighting parameters are combined.
Below, using present invention offer based on cross validation and the entitled Spatial Interpolation of Rainfall side of dimensional gaussian distribution
Method is applied to certain mountain area rainfall, and to it space interpolation is carried out, and comprises the following steps that：
1) basic data is collected and processed：As shown in figure 3, collect obtaining regional extent (i.e. interpolation area scope), the DEM
Altitude data, the positional information (X, Y) of known rainfall website and precipitation discharge observation data sequence.Wherein, 89 rainfall are collected altogether
Site location, and the intra day ward observation data sequence of each website 2003-2012 (10 years).In this step, it is considered to empty
Between resolution requirement grid division (as shown in Figure 4), it is determined that with the position that each grid element center is the region interpolation point, such as Fig. 5
It is shown, so as to obtain the coordinate (X, Y) of corresponding each interpolation point；And determine each rainfall website and to be inserted with reference to DEM altitude datas
The height value of value point corresponding coordinate.
2) rainfall website is analyzed apart from the discrepancy in elevation：Based on each precipitation station point coordinates and height value in 1) step, using formula (1-2)
Be calculated any two site distance from and depth displacement, and compare in determination interpolation area between all websites distance and elevation two-by-two
Poor maximum D and E, respectively 717 and 2000.
3) weighting parameters are determined：Based on the 2) result of calculation of step and each precipitation station point precipitation observation that 1) step is collected
Data sequence, and optimal weighting parameter value C ' is obtained based on calculation expression (4-5) optimizationdWith C 'e, respectively 0.9 and 1.1.Phase
Answer function distribution as shown in Figure 6.
4) interpolation point is analyzed apart from the discrepancy in elevation：Based on the 1) each interpolation point coordinates that step determines and height value, using formula
(6-7) between each interpolation point of analytical calculation and rainfall website apart from dxjWith depth displacement exj。
5) space interpolation is estimated：Based on D, E value and optimal weighting parameter value C' that determine respectively in second step and the 3rd stepd
=0.9, C'e=1.1, and the distance and depth displacement 4) between each interpolation point that step is calculated and rainfall website, using formula (8-
11) 2003-2012 intra day ward time sequential values on each interpolation point are estimated day by day.Finally give 2003- in interpolation area
Intra day ward space interpolation data in 2012.
By the further finishing analysis of 10 year day DS, each interpolation point correspondence grid of the interpolation area can be obtained
Average annual precipitation distribution is as shown in Fig. 7 (b).Fig. 7 (a) illustrates the average annual precipitation of each rainfall site location correspondence interpolation grid point
Amount measured value situation.Contrast Fig. 7 (a) and (b) rainfall distribution, show dividing based on cross validation and dimensional Gaussian for present invention offer
The entitled spatial interpolation method for precipitation of cloth can preferably estimate the space distribution situation of the region annual precipitation, and obtain high-altitude
Between resolution grid precipitation data, for hydrology and water conservancy related application analysis.
As can be seen here, the present invention provide based on cross validation and the entitled Spatial Interpolation of Rainfall side of dimensional gaussian distribution
Method based on dimensional gaussian distribution carry out precipitation interpolation weight estimate and cross-validation method optimize weighting parameters, while consider distance and
Impact of the Elevation factor to rainfall distribution, calculating process is easy, it is ensured that operation efficiency.Compared to prior art, present invention tool
Have the advantages that：(1) while considering the impact of distance and elevation, interpolation result can reflect the space that precipitation changes with elevation
The regularity of distribution；(2) optimal weighting parameter is determined based on cross-validation method, has ensured the reliability of interpolation result；(3) it is particularly suitable
In mountain area precipitation station point precipitation observation data space interpolation analysis, and obtain high spatial resolution grid precipitation data.
Those of ordinary skill in the art should be understood：The discussion of any of the above embodiment is exemplary only, not
It is intended to imply that the scope of the present disclosure (including claim) is limited to these examples；Under the thinking of the present invention, above example
Or can also be combined between the technical characteristic in different embodiments, step can be realized with random order, and be existed such as
Many other changes of upper described different aspect of the invention, for simple and clear their no offers in details.Therefore, it is all
Within the spirit and principles in the present invention, any omission, modification, equivalent, improvement for being made etc. should be included in the present invention's
Within protection domain.
Claims (7)
1. it is a kind of to be based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution, it is characterised in that to include
Following steps：
Determine in interpolation area the coordinate of the coordinate and height value of all rainfall websites and the point of the interpolation in interpolation area and
Height value；
Calculate distance and depth displacement between any two rainfall website in interpolation area, and determine in interpolation area between all websites
The maximum of the maximum of distance and depth displacement two-by-two；
Observed between data and all websites two-by-two apart from maximum value depth displacement according to all precipitation station point precipitations in interpolation area
Maximum, optimization obtains optimal weighting parameter value；
Calculate distance and depth displacement between each interpolation point and rainfall website in interpolation area；
According between all websites two-by-two apart from maximum value depth displacement maximum, optimal weighting parameter value and each interpolation point with
Distance and depth displacement between rainfall website, calculates precipitation time serieses estimated value on each interpolation point, so as to obtain interpolation area
Spatial Interpolation of Rainfall data in domain.
2. according to claim 1 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, the coordinate and height value and the interpolation in interpolation area for determining all rainfall websites in interpolation area
The step of coordinate and height value of point, includes：
Basic data is collected, the basic data includes：Interpolation area scope, Law of DEM Data, the seat of rainfall website
The precipitation discharge observation data sequence of cursor position and rainfall website；
Basic data according to collecting determines treating in the height value and interpolation area of all rainfall websites in interpolation area
The coordinate and height value of interpolation point.
3. according to claim 1 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, the distance and depth displacement calculated in interpolation area between any two rainfall website, and determine interpolation area
Between interior all websites two-by-two maximum D and E of distance and depth displacement the step of include：
Based on the coordinate and height value of each rainfall website in interpolation area, calculate and take office using range formula and depth displacement formula
Two rainfall site distances of meaning are from dijWith depth displacement eij, and further compare any two rainfall site distance from dijAnd elevation
Difference eij, so that it is determined that maximum D and E of distance and depth displacement two-by-two between all websites of interpolation area.
4. according to claim 1 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, described observe between data and all websites two-by-two apart from pole according to all precipitation station point precipitations in interpolation area
Big value, depth displacement maximum, optimizing the step of obtaining optimal weighting parameter value includes：
Based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area, to each rainfall
Website carries out Gaussian function weighted sum precipitation Interpolate estimation；
Precipitation value is surveyed as reference with each rainfall website, the root-mean-square error of corresponding precipitation station point precipitation Interpolate estimation is assessed
Average；
It is optimal weighting parameter combination to choose the minimum parameter combination of root-mean-square error average, so as to obtain optimal weighting parameter
Value.
5. according to claim 4 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, it is described based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area,
The step of carrying out Gaussian function weighted sum precipitation Interpolate estimation to each precipitation station point includes：
Based on cross-validation method, based on the precipitation discharge observation data of all rainfall websites in interpolation area, it is respectively adopted not
Same dimensional gaussian distribution parameter combination carries out Gaussian function weighted sum to each rainfall website with other precipitation station point precipitations
Precipitation Interpolate estimation, wherein, dimensional gaussian distribution function expression isFormula
In, g (dist, elev) is dimensional gaussian distribution functional value；Dist and elev are respectively two independent variables, wherein dist and elev
Difference two factors of influence of respective distances and elevation；C1And C2Respectively dimensional gaussian distribution function parameter.
6. according to claim 4 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, described survey precipitation value as reference with each rainfall website, corresponding precipitation station point precipitation Interpolate estimation is assessed
Root-mean-square error average the step of include：
Wherein,It is all precipitation station point dewatering data sequence interpolation results are calculated root-mean-square using cross-validation method
Error mean；N is interpolation area rainfall website sum；M is the precipitation measurement length of time series of each rainfall website；For
K-th time serieses precipitation estimated value to rainfall website i；PikFor k-th time serieses precipitation discharge observation of rainfall website i
Value, PjkFor k-th time serieses precipitation observation of rainfall website j；wijTo give the interpolation weight weight values of rainfall website j；
And dijHomogenization distance and actual range respectively between rainfall website i and j；And eijRespectively between rainfall website i and j
Homogenization depth displacement and actual depth displacement；D and E are respectively between all websites of interpolation area the maximum of distance and depth displacement two-by-two
Value；CdAnd CeRespectively two-dimensional Gaussian function considers the weighting parameters of distance and Elevation factor.
7. according to claim 1 based on cross validation and the entitled spatial interpolation method for precipitation of dimensional gaussian distribution,
Characterized in that, it is described according between all websites two-by-two apart from maximum value depth displacement maximum, optimal weighting parameter value and each
Distance and depth displacement between interpolation point and rainfall website, on each interpolation point of calculating the step of precipitation time serieses estimated value
Including：
To any interpolation point x, its k-th time serieses precipitation interpolation calculation formula：
Wherein,For k-th time serieses precipitation interpolation result of interpolation point x；wxjTo give the interpolation weight of rainfall website j
Weight values；And dxjHomogenization distance and actual range between respectively interpolation point x and rainfall website j；And exjRespectively treat
Homogenization depth displacement and actual depth displacement between interpolation point x and rainfall website j；C′dWith C 'eThe optimal weighting ginseng for respectively determining
Array is closed.
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Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107393001A (en) * | 2017-07-26 | 2017-11-24 | 新疆金风科技股份有限公司 | The complementing method and equipment in SRTM data invalids region |
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| CN107393001A (en) * | 2017-07-26 | 2017-11-24 | 新疆金风科技股份有限公司 | The complementing method and equipment in SRTM data invalids region |
| CN107393001B (en) * | 2017-07-26 | 2019-01-29 | 新疆金风科技股份有限公司 | The complementing method and equipment in SRTM data invalid region |
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| CN111123408B (en) * | 2019-11-26 | 2022-02-18 | 深圳震有科技股份有限公司 | Method, system and storage medium for predicting precipitation distribution based on GIS |
| CN111340950A (en) * | 2020-02-18 | 2020-06-26 | 云南师范大学 | Digital elevation model reconstruction method and device |
| CN111340950B (en) * | 2020-02-18 | 2023-09-15 | 云南师范大学 | Digital elevation model reconstruction method and device |
| CN113282883A (en) * | 2021-02-04 | 2021-08-20 | 河海大学 | Comprehensive interpolation method for day-by-day rainfall data |
| CN112800634A (en) * | 2021-04-07 | 2021-05-14 | 水利部交通运输部国家能源局南京水利科学研究院 | Rainfall estimation method and system coupling dry-wet state identification and multi-source information fusion |
| CN112800634B (en) * | 2021-04-07 | 2021-06-25 | 水利部交通运输部国家能源局南京水利科学研究院 | Rainfall estimation method and system coupling dry-wet state identification and multi-source information fusion |
| CN113239136A (en) * | 2021-05-17 | 2021-08-10 | 北京车和家信息技术有限公司 | Data processing method, device, equipment and medium |
| CN113239136B (en) * | 2021-05-17 | 2023-12-19 | 北京车和家信息技术有限公司 | Data processing method, device, equipment and medium |
| CN113779505A (en) * | 2021-09-09 | 2021-12-10 | 华能西藏雅鲁藏布江水电开发投资有限公司 | Rainfall data spatial interpolation method for complex terrain area and computer storage medium |
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