CN114090959B - Random space-time interpolation method for runoff of river basin under constraint of river network structure - Google Patents
Random space-time interpolation method for runoff of river basin under constraint of river network structure Download PDFInfo
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Abstract
According to the river network structure constraint drainage basin runoff random space-time interpolation method, the area of a denesting water collecting area and a runoff sequence of each hydrologic site are obtained, and an EOF method is adopted to obtain a time main component and a space function; creating a new residual sequence after eliminating the linear correlation of the diameter flow sequence of each denesting water collecting area to the diameter flow sequence of the total outlet of the drainage basin, and deducing a corresponding time main component and a space function based on a CEOF method; and obtaining a radial flow random space-time interpolation sequence of any space point by utilizing the time main component and the space function decomposed by the EOF and CEOF methods, and evaluating the radial flow interpolation precision. According to the method, by introducing different-order time main components and space functions, the multi-basin runoff space-time variation law is flexibly described, redundant information of runoff correlations of different water collecting areas caused by basin hydrologic similarity is effectively removed, random space-time two-dimensional interpolation of runoff sequences is realized, and the interpolation precision of a traditional EOF method is improved.
Description
Technical Field
The invention relates to a basin runoff space-time interpolation method, in particular to a basin runoff random space-time interpolation method under the constraint of a river network structure, and belongs to the technical field of basin hydrologic analysis.
Background
The acquisition of the complete runoff quantity sequence of the river basin is indispensable to hydrologic researches such as water conservancy infrastructure planning, water resource management, flood or drought prediction and the like.
However, in reality, due to incomplete recording or information loss caused by accidents or artificial reasons, huge threats are caused to the reliability of hydrologic design work, so that interpolation of drainage basin runoff missing data is needed.
Under the complex actions of the natural runoff confluence process and the river network structure underlying factors, the runoff situation of the river basin presents obvious space region difference and time fluctuation characteristics, so that the conventional empirical orthogonal function (Empirical orthogonal function; EOF) method is difficult to effectively describe the runoff time sequence evolution mode of a part of areas, and further the condition of low interpolation precision of the conventional EOF method is caused.
On one hand, under the influence of a river network structure, hydrologic similarity exists at a spatial neighboring point in a river basin yielding and converging process, namely, the nested superposition effect exists at different neighboring points of the runoffs in the river basin, so that high correlation possibly exists in runoff sequences in different regions of the river basin, and the problem of how to weaken the influence of statistical autocorrelation and separate various runoff time sequence evolution modes to improve the interpolation efficiency of the traditional EOF method still cannot be fully solved; on the other hand, watershed runoff sequence interpolation has two-dimensional properties in time and space.
Therefore, there is a need to address the problem of steering from a single temporal or spatial dimension to spatio-temporal two-dimensional synchronous interpolation.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a river basin runoff random space-time interpolation method under the constraint of a river network structure.
In order to achieve the above object, the present invention adopts the following technical scheme:
a random space-time interpolation method for runoff in river basin under the constraint of river network structure comprises the following steps:
s1, extracting area nesting relation of water collecting areas of known M sites under the constraint of river basin river network structures, and calculating de-embedding of the known sitesArea omega of water collecting region i And a sequence of runoff volumes Q (t, ω) of de-nested catchments i )；
S2, the runoff sequences Q (t, omega) of different stations in the river basin are processed i ) Carrying out homogenization treatment to obtain a homogenized flow sequence X (t, omega) i )；
S3, adopting an EOF method, and regarding the homogenized flow sequence X (t, omega) i ) Calculating the different denesting water collection zone outlets i e (1., M) and j e (1, space variance-covariance matrix cov between M) Q (ω i ,ω j )；
Decompose X (t, omega) i ) Obtaining the time main component psi of the uniform flow sequence k (t); k=1..m and spatial function β k (ω i )；
S4, by eliminating the runoff sequence Q (t, omega) of each denesting water collecting area i ) Linear correlation of the runoff sequence Q (t, Ω) of the total outlet of the watershed, creating a new residual sequence Q (r) (t,ω i ) The method comprises the steps of carrying out a first treatment on the surface of the Omega is the water collection area of the total outlet of the drainage basin;
application of EOF decomposition to Q (r) (t,ω i ) Steps S2 and S3 are carried out, and the corresponding time principal component phi after homogenization is redefined and calculated under the condition that the 1 st order time principal component is forced to be exactly equal to the runoff sequence of the total outlet of the river basin k (t) a CEOF method;
s5, carrying out normalization processing on the time main components obtained by decomposition based on the EOF and CEOF methods, so that the time main components with different orders all meet the conditions that the mean value is 0, the variance is 1, and the time main components are marked as psi' k (t) calculating normalized ψ' k (t) corresponding spatial function beta k ' omega (l)), obtaining a radial flow random space-time interpolation sequence Q (t, omega (l)) of any sub-drainage basin omega (l) of the total outlet distance l of the relative drainage basins on the river network;
s6, calculating the relative interpretation variance of the time principal components of different orders on the interpolation sequenceAnd evaluating the runoff interpolation accuracy of different space points on the river network structure.
In the step S1, the following steps are performed:
a1, area omega of denesting water collecting area i Is calculated by (1):
defining the water collecting area of the total outlet of the drainage basin as omega, wherein the runoff quantity sequence of the total outlet is represented as Q (t, omega); under the constraint of river basin river network structure, extracting the denesting water collecting area omega of M stations in the river basin i ；i＝1,...,M：
The method meets the following conditions:
where s represents the number of all stations upstream of station i, A i Representing the actual total water collection area of site i; if there is no known site upstream of site i under the river network structure, ω i Exactly equal to A i ；
A2, diameter flow sequence of denesting water collecting area Q (t, omega) i ) Is calculated by (1):
the net flow value of the inflow upstream of the zone is subtracted from the actual flow observation,
if there is no known site upstream of site i under the river network structure, Q (t, ω i )＝Q(t,A i )。
The sequence of runoff amounts Q (t, ω) in step S2 described above i ) The homogenization treatment comprises centralization and standardization;
i.e. the instantaneous flow integral of each spatial point u in the de-nested collection zone above the outlet, can be deduced as a uniform flow sequence X (t, ω) i )：
The centering is as follows:
the standardization is as follows:
wherein m is Q (ω i ) Representing the annual average radial flow value, sigma, of a de-nesting collection zone Q (ω i ) Representing standard deviation of runoffs of the denesting water collecting area; m is m Q (ω i )、σ Q (ω i ) Estimated from the runoff logging data already present at the site.
The EOF method in the step S3 includes:
B1、X(t,ω i ) A set of biorthogonal sequences linearly decomposed into spatial and temporal functions:
in the formula, the time main component psi k (t); k=1.., M and space function beta k (ω i ) Are all threshold values balloon(s) infinity of the two points, + -infinity) is included, beta k (ω i ) Representing a certain k-order time principal component ψ k (t); k=1.., M is at the weight coefficient set of arbitrary denesting water collecting area, satisfy:
wherein the flow sequence of homogenization X (t, omega) of any de-nested water collection region i ) Can be regarded as a linear combination of function values of the projection of the amplitude function of different orders on the zone weight vector;
b2, calculating a homogenized flow sequence X (t, ω) i ) Is a spatial variance-covariance matrix cov of (2) Q (ω i ,ω j )：
For centralization:
for standardization: equation (8) is converted into a spatial correlation coefficient ρ (ω) i ,ω j ) Is a matrix of (a):
cov Q (ω i ,ω j )＝σ Q (ω i )σ Q (ω j )ρ(ω i ,ω j )＝ρ(ω i ,ω j ) (9)
b3, solve beta k (ω i )：
In the formula, scalar lambda k The method comprises the steps of carrying out a first treatment on the surface of the k=1, 2..m is a characteristic value, typically ordered progressively decreasing in order of value as λ k ≥λ k+1 ；
B4, calculating the time main component psi k (t)：
Wherein the characteristic value lambda k Also denoted as psi k Variance value of (t), i.eλ k The larger the value, the representation ψ k (t) description of the original sequence Q (t, ω) i ) The greater the capacity of the system, the less the runoff information is lost.
The CEOF method in step S4 includes:
first according to the sequence of runoffs Q (t, ω) for each de-nested header i ) Linear correlation with the runoff sequence Q (t, Ω) of the total outlet of the basin, generating a new residual sequence Q (r) (t,ω i )：
Application of EOF method to residual sequence Q (r) (t,ω i ) Calculate Q (r) (t,ω i ) Variance-covariance matrix of (2) to obtain time principal component
Defining the condition: time principal component phi of CEOF method k (t); k=1.., M is as follows:
the 1 st order conditional amplitude function is the flow field outlet flow sequence, i.e. φ 1 (t)＝Q(t,Ω)；
The 2 nd to M th order conditional amplitude functions are in turn equal to the M-1 amplitude functions determined by the residual sequence, i.e
The calculation of the radial-flow random space-time interpolation sequence Q (t, Ω (l)) in the above step S5 includes:
calculating normalized time principal component psi' k (t) corresponding space function beta' k (Ω(l))：
For centralization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)]σ Q (13)
for standardization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)] (14)
wherein ρ represents a correlation coefficient, σ Q Represents the standard deviation of the basin Ω (l) runoff;
will be beta' k (Ω (l)) and ψ' k And (t) substituting the formula (6) to derive a random space-time interpolation calculation formula, wherein the random space-time interpolation calculation formula is as follows:
wherein m is Q Mean diameter flow value over years for basin Ω (l); m is m Q 、σ Q The correlation coefficient rho is estimated from the radial flow record data existing in the place or is subjected to a spatial interpolation method(e.g., kriging, inverse distance weighting, etc.).
The evaluation of the interpolation accuracy in the step S6 includes:
c1, calculate K time principal components, i.e. { ψ' 1 (t),ψ′ 2 (t)，...,ψ′ K (t) } the relative interpretation variance for a certain river basin Ω (l) runoff sequence is:
wherein Ω (l) is the area of the water collection region of the sub-basin upstream of the basin at a distance l from the outlet of the basin, ρ [ Q (t, Ω (l) ], ψ ]' k (t)]Q (t, Ω (l)) and ψ k A correlation coefficient between (t);
when k=m, the original sequence of runoffs for the site can be fully reconstructed, i.eThe larger the representation the more original data information is retained; usually only a few (K<M) the time main component can avoid redundant information on one hand and achieve rapid convergence of the runoff interpolation accuracy of the flow field on the other hand;
c2, calculating the precision of the radial flow random space-time interpolation sequence by adopting an efficiency coefficient index;
for example, NSE efficiency coefficient (Nash-Sutcliffe):
wherein NSE is [ - ] infinity, 1]By measuring the estimate (Q esi,t ) And observation series (Q) obs,t ) Evaluating the consistency degree of the (2);
log nsellog efficiency coefficient (Nash-Shuffle):
in the formula, ln (·) represents a natural logarithm function;
KGE efficiency coefficient (Kling-Gupta):
wherein: KGE represents a decomposed form of the NSE coefficient, comprising three parts, in turn, the Pearson correlation r, mean deviation (μ esi /μ obs ) And relative variability (sigma) esi /σ obs ) Is a measure of (2);
and C3, calculating the statistical characteristic parameter theta of the radial flow random space-time interpolation sequence by adopting a relative deviation index RE (%) esi Statistical characteristic parameters theta compared to the original data sequence obs Is defined as the deviation:
assuming an unbiased reference of 100%, then
Where Θ represents a general symbol of the above statistical feature parameter.
Further, the statistical characteristic parameters include average value, standard deviation, median, minimum value and maximum value.
The invention has the advantages that:
the invention relates to a river basin runoff random space-time interpolation method under the constraint of a river network structure,
(1) By considering the area nesting relation of different water collecting areas in the river network structure constraint downflow area, the runoff sequence which accords with the hydrologic similarity of the river basin and retains the hydrologic characteristics of the different water collecting areas is effectively extracted;
(2) By decomposing the runoff space-time sequences of multiple (hydrological) stations of the river basin, redundant information of runoff correlations of different water collecting areas caused by the hydrologic similarity of the river basin is effectively removed, the independent separation and extraction of time main components and space function change characteristics of the runoff sequences of the river basin are realized, the time and space change rules of the runoff sequences of the river basin are conveniently diagnosed respectively, and the evolution forms of various time main components at various space points in the river basin are intuitively identified;
(3) The relative representativeness of the main components and the space functions of each order in explaining the space-time variation rules of different runoffs along the river network structure is flexibly reflected by introducing the strong and weak information of the runoff correlations of different water collecting areas under the river network structure, and the accuracy of the traditional EOF method in the runoff space-time sequence interpolation of the river basin runoff can be better improved under the principle that the loss of the original data information is least as the order of the main components and the space functions of the input time is increased, so that the two-dimensional random interpolation of the runoff sequence time and space is realized.
The random space-time interpolation method for the runoff of the river is suitable for the river with the surface river runoff as the main characteristic, and besides the application result shown in the embodiment, the random space-time interpolation method for the runoff of the river is particularly suitable for the water collecting area of the river, which lacks historical hydrologic flow observation data, and provides an effective random space-time interpolation method for the runoff, which is transplanted to a non-data area from the runoff information of a known site, and can be flexibly expanded to space-time two-dimensional synchronous interpolation from single-dimensional interpolation according to the spatial interpolation result information of different runoffs of the non-data area, so that powerful theory and data basis are provided for the water conservancy industry to engage in the hydrologic analysis of the river and the water resource management decision, and the random space-time interpolation method has strong practicability and wide applicability.
Drawings
FIG. 1 shows the results of two homogenization treatments, namely, the centralization and standardization of the measured runoff sequence.
Fig. 2 is a2 nd order spatial function determined by eof+ normalization methods.
FIG. 3 is the principal component of order 2 time solved by EOF+ centering and EOF+ normalization methods.
FIG. 4 shows the 2 nd order spatial function (FIG. b) for the EOF+ centering and EOF+ normalization methods and the 2 nd order temporal principal component (FIG. a) solved by the EOF+ centering method.
Fig. 5 is an interpolation of the correlation coefficient ρ between runoff and the time principal component of order 1 (eof+ normalization method) along the total outlet distance l of the basin.
FIG. 6 is a graph comparing interpolation results of CEOF+ normalization method with original measured sequences.
Fig. 7 shows the variation of the relative interpretation variance of different interpolation methods with time of different orders.
Fig. 8 is a graph showing the comparison of evaluation index values of the effects of different interpolation methods.
Detailed Description
The invention is described in detail below with reference to the drawings and the specific embodiments.
The river basin runoff random space-time interpolation method under the constraint of the river network structure in the embodiment comprises the following steps:
s1, extracting area nesting relations of different water collecting areas of known M sites under the constraint of river basin river network structures, and calculating the area omega of the denesting water collecting areas of the known sites i Diameter flow sequence Q (t, omega) of denesting water collecting area i )：
A1, area omega of denesting water collecting area i Is calculated by (1):
defining the water collecting area of the total outlet of the drainage basin as omega, and defining the runoff sequence of the total outlet as Q (t, omega); under the constraint of river basin river network structure, extracting the denesting water collecting area omega of M stations in the river basin i ；i＝1,...,M：
The method meets the following conditions:
where s represents the number of all stations upstream of station i, A i Representing the actual total water collection area of site i; if there is no known site upstream of site i under the river network structure, ω i Exactly equal to A i 。
A2, diameter flow sequence of denesting water collecting area Q (t, omega) i ) Is calculated by (1):
i.e. the actual flow observation minus the net flow value of the inflow upstream of the zone,
if there is no known site upstream of site i under the river network structure, Q (t, ω i )＝Q(t,A i )。
S2, Q (t, omega) of long sequence runoff of different stations in the river basin at each moment t i ) The homogenization treatment, in particular the optional centring or standardisation treatment, i.e. the de-nesting of the water collection area omega above the outlet i The instantaneous flow integral for each spatial point u within can be deduced as a uniform flow sequence (a centered or normalized flow sequence):
the centering is as follows:
the standardization is as follows:
wherein m is Q (ω i ) Representing the annual average radial flow value, sigma, of a de-nesting collection zone Q (ω i ) Representing standard deviation of runoffs of the denesting water collecting area; m is m Q (ω i )、σ Q (ω i ) Estimated from the runoff logging data already present at the site.
As shown in figure 1, 23 stations in the river basin are selected to divide the water collecting area according to the runoff data condition of the stations in the river basin of China. Taking the total outlet of the drainage basin as an example, two sequence homogenization treatment results of centralization and standardization are shown.
S3, adopting an Empirical Orthogonal Function (EOF) method, and for a centralized (or standardized) flow sequence X (t, omega) i ) Computing different denesting zone outlets i e (1., M) and j e (1, space variance-covariance matrix cov between M) Q (ω i ,ω j ) Decompose X (t, omega) i ) Obtaining a centralised (or normalised) flow sequenceTime principal component ψ k (t); k=1..m and spatial function β k (ω i ). The method comprises the following steps:
B1、X(t,ω i ) A set of biorthogonal sequences linearly decomposed into spatial and temporal functions:
in the formula, the time main component psi k (t); k=1.., M and space function beta k (ω i ) Are all threshold values balloon(s) infinity of the two points, + -infinity) is included, beta k (ω i ) Representing a certain k-order time principal component ψ k (t); k=1.., M at any de-nesting water collection area omega i The weight coefficient set of (2) satisfies:
in which the water collecting area omega is arbitrarily de-nested i Is a centralised (or normalised) flow sequence X (t, ω) i ) Can be seen as a linear combination of the function values of the different order of the projection of the amplitude function onto the zone weight vector.
B2, calculating the flow sequence X (t, omega) i ) Is a spatial variance-covariance matrix cov of (2) Q (ω i ,ω j )：
For centralization:
for standardization: equation (8) is converted into a spatial correlation coefficient ρ (ω) i ,ω j ) Is a matrix of (a):
cov Q (ω i ,ω j )＝σ Q (ω i )σ Q (ω j )ρ(ω i ,ω j )＝ρ(ω i ,ω j ) (9)。
b3, solve beta k (ω i )：
In the formula, scalar lambda k The method comprises the steps of carrying out a first treatment on the surface of the k=1, 2..m is a characteristic value, typically ordered progressively decreasing in order of value as λ k ≥λ k+1 ；
As shown in fig. 2, taking the EOF (normalized) determined 2 nd order spatial function as an example, the triangle size reflects the magnitude of the absolute value of the spatial function. From the graph results, the spatial functions obtained by decomposition have obvious differences in the watershed, and reflect the change condition of the spatial distribution of the runoff of the watershed.
B4, calculating the time main component psi k (t)：
Wherein the characteristic value lambda k Also denoted as psi k Variance value of (t), i.eλ k The larger the value, the representation ψ k (t) description of the original sequence Q (t, ω) i ) The greater the capacity of the system, the less the runoff information is lost.
As shown in fig. 3, taking eof+ centering and eof+ normalization methods as examples, the 2 nd order time principal component solved by both methods is shown. The results represent a time-evolution of the river basin measured runoff sequence.
S4, eliminating each denesting water collecting area omega i The method comprises the steps of carrying out a first treatment on the surface of the i=1.. the original observed flow sequence of M versus the runoff sequence Q of the total outlet of the basin (t, Ω) creates a new set of residual sequences Q (r) (t,ω i ) Substituted Q (t, ω) i ) Applying EOF decomposition to Q (r) (t,ω i ) Steps S2 and S3 are carried out, and the corresponding time principal components in the two cases of centralization and standardization are redefined and calculated under the condition that the flow sequence of the 1 st order time principal component is forced to be exactly equal to the total outlet of the drainage basinφ k (t) a decomposition method under condition CEOF (Complex Empirical orthogonal function). The method comprises the following steps:
in the CEOF process, the water collection region ω is first of all nested according to each i The method comprises the steps of carrying out a first treatment on the surface of the i=1.. the sequence of runoffs Q (t, ω) of M i ) Linear correlation with the runoff sequence Q (t, Ω) of the total outlet of the basin, generating a new set of residual sequences Q (r) (t,ω i )：
Applying EOF decomposition to residual sequence Q (r) (t,ω i ) Calculate Q (r) (t,ω i ) Variance-covariance matrix (for the centering process) or correlation coefficient matrix (for the normalization process), solving to obtain a time principal component
Defining the condition: time principal component phi of CEOF method k (t); k=1.., M is as follows:
the 1 st order conditional amplitude function is the flow field outlet flow sequence, i.e. φ 1 (t)＝Q(t,Ω)；
The 2 nd to M th order conditional amplitude functions are in turn equal to the M-1 amplitude functions determined by the residual sequence, i.e
As shown in fig. 4 (a, b), taking the ceof+centering and ceof+normalization methods as examples, the results of the 2 nd order time principal component solved by the two methods are shown, and the 2 nd order spatial function obtained by the ceof+centering method is given.
S5, carrying out normalization processing on the time main components obtained by decomposition based on the EOF and CEOF methods, so that the time main components with different orders all meet the conditions that the mean value is 0, the variance is 1, and the time main components are marked as psi' k (t) calculating normalized ψ' k (t) corresponding space function beta' k (Ω (l)) to obtain the total outlet distance l of the relative river basin on the river networkRadial flow random spatiotemporal interpolation sequence Q (t, Ω (l)) for any sub-basin Ω (l). The method comprises the following steps:
calculating normalized time principal component psi' k (t) corresponding space function beta' k (Ω(l))：
For centralization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)]σ Q (13)
for standardization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)] (14)
wherein ρ represents a correlation coefficient, σ Q Represents the standard deviation of the basin Ω (l) runoff;
will be beta' k (Ω (l)) and ψ' k And (t) substituting the formula (6) to derive a random space-time interpolation calculation formula, wherein the random space-time interpolation calculation formula is as follows:
wherein m is Q Mean diameter flow value over years for basin Ω (l); m is m Q 、σ Q And the correlation coefficient ρ is estimated from the existing runoff record data of the place or by spatial interpolation (such as kriging, inverse distance weighting, etc.).
Taking the statistical estimation result of the kriging method as an example, as shown in fig. 5, the interpolation result of the correlation coefficient ρ between the runoff and the time principal component of the 1 st order (eof+normalization method) along the total outlet distance l of the basin is shown.
As shown in fig. 6, taking the Jian station in the river basin as an example, the interpolation result of the station diameter flow sequence is shown. From the graph, the interpolation result calculated by the CEOF+standardization method has higher coincidence degree with the original actual measurement sequence, and the interpolation effect is better.
And for any sub-watershed Ω (l) of the relative watershed total outlet distance l to fall within the data-free region, the correlation coefficient ρ can be calculated by spatial interpolation.
S6, calculating the relative interpretation variance of the time principal components of different orders on the interpolation sequenceAnd evaluating the runoff interpolation accuracy of different space points on the river network structure. The method comprises the following steps:
c1, calculate K time principal components (i.e. { ψ' 1 (t),ψ′ 2 (t)，...,ψ′ K (t) } the relative interpretation variance for a certain river basin Ω (l) runoff sequence is:
wherein Ω (l) represents the catchment area of the sub-basin upstream of the basin at a distance l from the basin outlet; ρQ (t, Ω (l)), ψ' k (t)]Q (t, Ω (l)) and ψ k And (t) a correlation coefficient between them. When k=m, the original sequence of runoffs for the site can be fully reconstructed, i.eThe larger the representation the more original data information is retained. Usually only a few (K<M), on one hand, redundant information can be avoided, and on the other hand, rapid convergence of the flow field runoff interpolation accuracy is achieved.
As shown in fig. 7, the relative interpretation variance, which is the interpolation result of the four methods, gradually increases with the increase in the order of the principal component over time. The result shows that when the time principal component reaches the 2 nd order, 80% of the runoff amount sequence evolution information can be effectively described, and the interpolation effect of the CEOF method is verified to be superior to that of the traditional EOF method.
And C2, calculating the precision of the radial flow random space-time interpolation sequence by adopting an efficiency coefficient index.
For example, the Nash-Sutcliffe efficiency coefficient (NSE):
wherein NSE is [ - ] infinity, 1]By measuring the estimate (Q esi,t ) And observation series (Q obs,t ) And (3) evaluating the consistency degree of the two.
Logarithmic Nash-Shuffle efficiency coefficient (nsellog):
where ln (·) represents the natural logarithmic function.
Kling-Gupta efficiency coefficient (KGE):
wherein: KGE represents a decomposed form of the NSE coefficient, comprising three parts, in turn, the Pearson correlation r, mean deviation (μ esi /μ obs ) And relative variability (sigma) esi /σ obs ) Is a measure of (2).
And C3, calculating the statistical characteristic parameter Θ of the radial flow random space-time interpolation sequence by adopting a relative deviation index RE (%) (assuming that an unbiased reference is 100%) esi (including mean, standard deviation, median, minimum and maximum) compared to the original data sequence obs Is defined as the deviation:
where Θ represents a general symbol of the above statistical feature parameter.
As shown in fig. 8, taking the standard deviation and the median in the efficiency coefficient and the statistical characteristic parameter as examples, the different interpolation result evaluation index values prove that the CEOF method deviates by 100% from the standard line of the EOF method by the minimum, wherein the interpolation effect of the ceof+normalization is optimal.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be appreciated by persons skilled in the art that the above embodiments are not intended to limit the invention in any way, and that all technical solutions obtained by means of equivalent substitutions or equivalent transformations fall within the scope of the invention.
Claims (8)
1. The random space-time interpolation method for the runoff of the river basin under the constraint of the river network structure is characterized by comprising the following steps of:
s1, extracting area nesting relation of water collecting areas of known M sites under the constraint of river basin river network structures, and calculating the area omega of the denesting water collecting areas of the known sites i And a sequence of runoff volumes Q (t, ω) of de-nested catchments i )；
S2, the runoff sequences Q (t, omega) of different stations in the river basin are processed i ) Carrying out homogenization treatment to obtain a homogenized flow sequence X (t, omega) i )；
S3, adopting an EOF method, and regarding the homogenized flow sequence X (t, omega) i ) Calculating the different denesting water collection zone outlets i e (1., M) and j e (1, space variance-covariance matrix cov between M) Q (ω i ,ω j )；
Decompose X (t, omega) i ) Obtaining the time main component psi of the uniform flow sequence k (t); k=1..m and spatial function β k (ω i )；
S4, by eliminating the runoff sequence Q (t, omega) of each denesting water collecting area i ) Linear correlation of the runoff sequence Q (t, Ω) of the total outlet of the watershed, creating a new residual sequence Q (r) (t,ω i ) The method comprises the steps of carrying out a first treatment on the surface of the Omega is the water collection area of the total outlet of the drainage basin;
application of EOF decomposition to Q (r) (t,ω i ) Steps S2 and S3 are carried out, and the corresponding time principal component phi after homogenization is redefined and calculated under the condition that the 1 st order time principal component is forced to be exactly equal to the runoff sequence of the total outlet of the river basin k (t) a CEOF method;
s5, carrying out normalization processing on the time main components obtained by decomposition based on the EOF and CEOF methods, so that the time main components with different orders all meet the conditions that the mean value is 0, the variance is 1, and the time main components are marked as psi' k (t) calculating normalized ψ' k (t) corresponding space function beta' k (Ω (l)) to obtain any sub-basin of the total outlet distance l of the relative basin on the river networkA radial-flow random spatiotemporal interpolation sequence Q (t, Ω (l));
s6, calculating the relative interpretation variance of the time principal components of different orders on the interpolation sequenceAnd evaluating the runoff interpolation accuracy of different space points on the river network structure.
2. The method according to claim 1, wherein in step S1:
a1, area omega of denesting water collecting area i Is calculated by (1):
defining the water collecting area of the total outlet of the drainage basin as omega, wherein the runoff quantity sequence of the total outlet is represented as Q (t, omega); under the constraint of river basin river network structure, extracting the denesting water collecting area omega of M stations in the river basin i ；i＝1,...,M：
The method meets the following conditions:
where s represents the number of all stations upstream of station i, A i Representing the actual total water collection area of site i; if there is no known site upstream of site i under the river network structure, ω i Exactly equal to A i ；
A2, diameter flow sequence of denesting water collecting area Q (t, omega) i ) Is calculated by (1):
the net flow value of the inflow upstream of the zone is subtracted from the actual flow observation,
if there is no known site upstream of site i under the river network structureQ (t, ω) i )＝Q(t,A i )。
3. The method according to claim 1, wherein the sequence of runoffs Q (t, ω i ) The homogenization treatment comprises centralization and standardization;
i.e. the instantaneous flow integral of each spatial point u in the de-nested collection zone above the outlet, can be deduced as a uniform flow sequence X (t, ω) i )：
The centering is as follows:
the standardization is as follows:
wherein m is Q (ω i ) Representing the annual average radial flow value, sigma, of a de-nesting collection zone Q (ω i ) Representing standard deviation of runoffs of the denesting water collecting area; m is m Q (ω i )、σ Q (ω i ) Estimated from the runoff logging data already present at the site.
4. The method according to claim 1, wherein the EOF method in step S3 comprises:
B1、X(t,ω i ) A set of biorthogonal sequences linearly decomposed into spatial and temporal functions:
in the formula, the time main component psi k (t); k=1.., M and space function beta k (ω i ) Are all threshold values balloon(s) infinity of the two points, + -infinity) is included, beta k (ω i ) Representing a certain k-order time principal component ψ k (t)；k=1.., M is at the weight coefficient set of arbitrary denesting water collecting area, satisfy:
wherein the flow sequence of homogenization X (t, omega) of any de-nested water collection region i ) Can be regarded as a linear combination of function values of the projection of the amplitude function of different orders on the zone weight vector;
b2, calculating a homogenized flow sequence X (t, ω) i ) Is a spatial variance-covariance matrix cov of (2) Q (ω i ,ω j )：
For centralization:
for standardization: equation (8) is converted into a spatial correlation coefficient ρ (ω) i ,ω j ) Is a matrix of (a):
cov Q (ω i ,ω j )＝σ Q (ω i )σ Q (ω j )ρ(ω i ,ω j )＝ρ(ω i ,ω j ) (9)
b3, solve beta k (ω i )：
In the formula, scalar lambda k The method comprises the steps of carrying out a first treatment on the surface of the k=1, 2..m is a characteristic value, typically ordered progressively decreasing in order of value as λ k ≥λ k+1 ；
B4, calculating the time main component psi k (t)：
In the middle ofCharacteristic value lambda k Also denoted as psi k Variance value of (t), i.eλ k The larger the value, the representation ψ k (t) description of the original sequence Q (t, ω) i ) The greater the capacity of the system, the less the runoff information is lost.
5. The method according to claim 1, wherein the CEOF process in step S4 comprises:
first according to the sequence of runoffs Q (t, ω) for each de-nested header i ) Linear correlation with the runoff sequence Q (t, Ω) of the total outlet of the basin, generating a new residual sequence Q (r) (t,ω i )：
Application of EOF method to residual sequence Q (r) (t,ω i ) Calculate Q (r) (t,ω i ) Variance-covariance matrix of (2) to obtain time principal component
Defining the condition: time principal component phi of CEOF method k (t); k=1.., M is as follows:
the 1 st order conditional amplitude function is the flow field outlet flow sequence, i.e. φ 1 (t)＝Q(t,Ω)；
The 2 nd to M th order conditional amplitude functions are in turn equal to the M-1 amplitude functions determined by the residual sequence, i.e
6. The method according to claim 1, wherein the calculation of the radial flow random spatio-temporal interpolation sequence Q (t, Ω (l)) in step S5 comprises:
calculating normalized time principal component psi' k (t) corresponding space function beta' k (Ω(l))：
For centralization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)]σ Q (13)
for standardization:
β′ k (Ω(l))＝ρ[Q(t,Ω(l)),ψ′ k (t)] (14)
wherein ρ represents a correlation coefficient, σ Q Represents the standard deviation of the basin Ω (l) runoff;
will be beta' k (Ω (l)) and ψ' k And (t) substituting the formula (6) to derive a random space-time interpolation calculation formula, wherein the random space-time interpolation calculation formula is as follows:
wherein m is Q Mean diameter flow value over years for basin Ω (l); m is m Q 、σ Q And the correlation coefficient ρ is estimated from the runoff record data existing at the site or by spatial interpolation.
7. The method according to claim 1, wherein the evaluation of the interpolation accuracy of step S6 includes:
c1, calculate K time principal components, i.e. { ψ' 1 (t),ψ′ 2 (t)，...,ψ′ K (t) } the relative interpretation variance for a certain basin Ω (l) runoff sequence is:
wherein Ω (l) is the area of the water collection region of the sub-basin upstream of the basin at a distance l from the outlet of the basin, ρ [ Q (t, Ω (l) ], ψ ]' k (t)]Q (t, Ω (l)) and ψ k A correlation coefficient between (t);
when k=m, the original runoff sequence for the site can be fully re-weightedThe structure, i.e The larger the representation the more original data information is retained; usually only a few (K<M) the time main component can avoid redundant information on one hand and achieve rapid convergence of the runoff interpolation accuracy of the flow field on the other hand;
c2, calculating the precision of the radial flow random space-time interpolation sequence by adopting an efficiency coefficient index;
for example, NSE efficiency coefficient:
wherein NSE is [ - ] infinity, 1]By measuring the estimate (Q esi,t ) And observation series (Q) obs,t ) Evaluating the consistency degree of the (2);
log nsellog efficiency coefficient:
in the formula, ln (·) represents a natural logarithm function;
KGE efficiency coefficient:
wherein: KGE represents a decomposed form of the NSE coefficient, comprising three parts, in turn, the Pearson correlation r, mean deviation (μ esi /μ obs ) And relative variability (sigma) esi /σ obs ) Is a measure of (2);
c3, calculating runoff by adopting the relative deviation index RE (%)Statistical characteristic parameter theta of random space-time interpolation sequence esi Statistical characteristic parameters theta compared to the original data sequence obs Is defined as the deviation:
assuming an unbiased reference of 100%, then
Where Θ represents a general symbol of the above statistical feature parameter.
8. The method of claim 7, wherein the statistical characteristic parameters comprise mean, standard deviation, median, minimum and maximum.
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