CN108053049A - A kind of random interpolation Runoff Forecast method of hydrology based on Budyko theories - Google Patents
A kind of random interpolation Runoff Forecast method of hydrology based on Budyko theories Download PDFInfo
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Abstract
The invention discloses a kind of random interpolation Runoff Forecast methods of the hydrology based on Budyko theories, comprise the following steps：Determine basin to be predicted, the basin is divided into multiple sub-basins；Spatial prediction is carried out deeply to each sub-basin mean annual runoff using Budyko theories, obtains Annual Runoff Prediction value, the certainty ingredient as runoff；Using the random interpolation method of the hydrology to multiple sub-basin mean annual runoff prediction deviations into row interpolation, the randomness ingredient as runoff；It is coupled using the certainty ingredient with randomness ingredient, obtains finally predicting runoff.The present invention improves Runoff Forecast precision, a kind of new idea and method is provided for runoff plot for predicting the depth of runoff of Cross Some Region Without Data and explaining the spatial distribution characteristic of runoff.
Description
Technical field
The present invention relates to a kind of random interpolation Runoff Forecast method of the hydrology based on Budyko theories, more particularly, to no money
Expect Runoff Forecast, runoff spatial distribution characteristic and the law-analysing field in area, belong to Hydrology and Water Resources technical field.
Background technology
Water resource spatial distribution characteristic, the prediction that can be used for disclosing basin using the footpath flow graphization research of spatial interpolation technology
The mean annual runoff of Cross Some Region Without Data, this is the research of one of hydrological basic problem and large-scale system optimum
Hot spot.From based on observation precipitation and potential evapotranspiration send out different, basin outlet runoff observe be subject to entire basin precipitation with
The collective effect of underground properties rather than the characteristics of Runoff for only representing certain point, thus the space interpolation of runoff is not only by measured path
Flow valuve controls, also related with the Regional Hydrologic characteristic of River.
For hydrological certainty angle, the runoff process in basin is the important component of Regional Hydrologic Cycle,
Response of the distributed rainfall-runoff model energy runoff simulation to precipitation, the Runoff Simulation result of model also explain its regional space
The regularity of distribution.However this method is largely dependent upon the availability of data set.In view of Hydrometeorological Factors and underlay
The interpolation method of the runoff plot of region feature can make up the deficiency of distributed model to a certain extent, and it is gentle to establish runoff for another example
Space interpolation is carried out as the empirical relation of the controlling elements such as, land use and landform.But empirical relation is only applicable to specific stream
Domain can not empirical tests and directly apply to other similar to basin.Budyko is theoretical to be used as a kind of relatively simple semiempirical
Formula, is commonly used to the water balance problem in land face of the estimation for many years under scale, quantitative analysis Regional Precipitation be converted into evapotranspiration and
The ratio of runoff predicts the utilized water resources and Change of Runoff of Cross Some Region Without Data.However Budyko theories can be described preferably
The hydrology-Meteorological Characteristics on large watershed scale, also there are relatively large deviations for runoff or evaporation prediction to specific basin or area.For
Improve the precision of Budyko Regional Hydrologic Forecasting Methodologies, many researchs attempt to establish parameter of curve and Land-Use/vegetation,
The relation of landform, abnormal climate etc., however not yet Budyko predicted values and the deviation of basin measuring runoff are united as region
Meter characteristic accounts for.
Statistical nature similitude of the geo-statistic interpolation method (Kriging regression) based on area variable, the change of specific position
Amount estimate is the weighted array of all sample areas variate-values.The variable space similitude of traditional geo-statistic interpolation method by
Variation function based on the point of space Euclidean distance between describes.Kriging regression is as a kind of minimum dispersion linear unbiased estimator
Method makes predicted value and the variance of measured value minimum.According to the different disposal to Deterministic Trends value, Kriging regression can divide
For different types.It is general if ordinary kriging interpolation (Ordinary Kriging) is using unknown constant as Deterministic Trends value
Kriging regression (Universal Kriging) is using the regression equation of space coordinates as Deterministic Trends, block Ke Lijin
(block-kriging) be different from the conventional kriging method such as ordinary kriging interpolation, being boxed area variate-value of estimation and
It is non-to be directed to a point valuation, thus put and replaced with the variation function of point by putting with square variation function.
Random interpolation method is the common interpolation method of hydrometeorological areas's variable, especially precipitation, evaporates so
Spatial point process.Such method is such as meant that the horizontal discharge series mistake for having ignored basin applied to runoff interpolation
Journey using the continuous runoff process in space as space dot characteristics, thus is lost the Spatial Variation of runoff, may result in
The excessively high estimation of runoff.
It is influenced along river flowing water stream by nested water system planning, is the continuous overall process in space, there is nest relation
Basin upstream and downstream catchment area and adjacent no waterpower relation basin Interpolation Process difference, thus traditional geo-statistic
Interpolation method is not suitable for runoff Interpolation Process.It is, the Euclidean distance used in traditional Interpolation Process is in most cases not
Can the space length of the net watershed suitable for runoff Interpolation Process well definition.In view of the influence of water system planning,
Gottschalk develops a set of random interpolation method of the runoff hydrology, at the same consider runoff space relationship overall permanence and
Basin is classified the collective effect of water system planning, has redefined the calculating of basin space length, put variation function between by
The variation function in basin replaces, and adds water balance constraint.But the statistical method does not consider that region is average for many years
The Deterministic Trends component that annual flow climate and underlying surface influence, while the work of forefathers also indicates that while considers area variable
Random and certainty rule, and it is had into preferable applicability applied to hydrometeorological geo-statistic field simultaneously.
The content of the invention
Goal of the invention：It is existing in the prior art in order to solve the problems, such as, it predicts the depth of runoff of Cross Some Region Without Data and analyzes runoff
Spatial distribution characteristic, improve Runoff Forecast precision, the present invention provides a kind of hydrology based on Budyko theories random interpolation footpath
Flow Forecasting Methodology.
Technical solution：A kind of random interpolation Runoff Forecast method of hydrology based on Budyko theories, comprises the following steps：
(1) sub-basin to be predicted and multiple known sub-basins are determined；It is actual by each known sub-basin of hydrometric station observation
Mean annual runoff depth R's (x)；It is pre- that space is carried out to each known sub-basin mean annual runoff using Budyko theories
It surveys, obtains mean annual runoff depth predicted value Rd(x), the certainty ingredient as sub-basin runoff to be predicted；
(2) by R (x) and Rd(x) difference is as mean annual runoff prediction deviation；Utilize the random interpolation method of the hydrology
To multiple known sub-basin mean annual runoff prediction deviations into row interpolation, known sub-basin depth of runoff deviation interpolation knot is obtained
Fruit Rs *(x), the randomness ingredient as sub-basin runoff to be predicted；
(3) coupled using the certainty ingredient with randomness ingredient, obtain the final prediction runoff of sub-basin to be predicted：
R*(x)=Rd(x)+Rs *(x) (1)
In formula, R*(x) the final prediction runoff at sub-basin x to be predicted is represented.
Preferably, in step (1), mean annual precipitation, actual evapotranspiration, potential evapotranspiration hair amount, profit are counted respectively
Spatial prediction is carried out to mean annual runoff with Budyko theories：
P-E=Rd(x) (3)
Formula (4) is obtained by formula (2) and (3)：
Wherein, P, E, E0、Rd(x) be respectively mean annual precipitation, actual evapotranspiration, potential evapotranspiration hair amount and
The depth of runoff (mm) of budyko predictions；ω is parameters of formula, and ω value ranges are (1, ∞), and ω values are bigger, and precipitation is converted into
The ratio of runoff is lower.
Preferably, in step (2), using the random interpolation method of the hydrology to mean annual runoff prediction deviation into row interpolation
Including：On the basis of block kriging interpolation methods, consider the basin distance of basin water system planning feature, increase simultaneously
Basin water Constraints of Equilibrium, as continuous process spatially, predictor formula is the depth of runoff deviation of prediction：
In formula, Rs *(A0) it is sub-basin depth of runoff deviation to be predicted, Rs(Ai) it is that i-th of area is AiKnown sub-basin
The depth of runoff deviation being calculated, Λ are weight matrix, RsIt is depth of runoff deviation matrix, Rs *(A0) it is Rs(A0) estimate,
Middle A0It is the cellar area of prediction, E [R is required according to minimum dispersion linear unbiased estimators *(A0)-Rs(A0)]=0 calculate weight matrix
Λ：
C(ui,uj) be sub-basin known to each pair fitting covariance function value, C0(ui,u0) it is u to be asked0Position and every
A known sub-basin uiThe fitting covariance function value at place, λiFor the weight of corresponding each known sub-basin at sub-basin x to be predicted
Value, μ is Lagrange coefficient, and substitution formula (3) obtains the predicted value of depth of runoff deviation after weight matrix is calculated.
Preferably, the computational methods of weight matrix Λ：
Formula (4) is expressed as matrix form：C Λ=C0, thus weight matrix Λ is expressed as：
Λ=C-1C0. (7)
Wherein：
Wherein, Matrix C is the covariance function matrix of the point in sub-basin known to each pair, C0It is in sub-basin known to each pair
Point and sub-basin to be predicted in point covariance function matrix, uiFor the position of the point in known sub-basin, u0To be to be predicted
The position of point in sub-basin, μ are Lagrange coefficient.
Preferably, formula (5), (6) are the depth of runoff deviation expression formulas in a region to be predicted, if Interpolation Process is counted simultaneously
The depth of runoff deviation of M sub-basin is calculated, formula (5) is constant, and optimal weights matrix is：
And
Wherein LiIt is the weighted value for each known sub-basin of sub-basin known to i-th, μ*And μiIt is for Lagrange
Number, the C and C0For：
Wherein, matrix K is expressed as：
Matrix V and G are：
Wherein Δ AiIt is the catchment area of i-th of non-nested sub-basin, niFor each non-nested sub-basin Δ AiContained net
Lattice number, above-mentioned Matrix division are constrained including water balance, and water balance constraint is that the measured runoff in basin exit should
Equal to the sum of all sub-basin interpolation run-offs, it is expressed as：
RTIt is the measured runoff of basin outlet.
It preferably, will each non-nested known sub-basin Δ AiIt is divided into niA area be a grid, each Δ AiFootpath
Stream deflection forecast value is the linear combination that depth of runoff deviation is calculated in weight coefficient and known sub-basin, and formula (16) is further
It is expressed as：
Wherein, nTIt is the number of basic grid, rTIt is the measured path flow depth of basin outlet；
Basin distance is defined by Gottschalk, i.e., the desired value of the distance of all mesh points pair, is expressed as in basin：
Wherein, A, B represent two known sub-basins；A1And A2It is known sub-basin A, the drainage area of sub-basin B respectively,
u1、u2Respectively known sub-basin A, the position of known sub-basin B；
According to basin distance, experiment covariance function and the relational graph of basin distance are drawn out, A is supported based on basin1With
A2, theoretical covariance function Cov (A, B) is：
Wherein, CovpIt is a covariance function.
Preferably, by trial-and-error method calibration optimal mathematical model, experiment covariance function and the relational graph of basin distance are drawn
When only with pairwise independent known sub-basin.
Preferably, the sub-basin at least 40.
Advantageous effect：A kind of random interpolation Runoff Forecast method of hydrology based on Budyko theories provided by the invention is led to
Drift function outside the random interpolation of the increase hydrology is crossed, by the random interpolation method of the Budyko Runoff Forecast deviation application hydrology, by two
Kind method couples to form a kind of new random interpolation method of the runoff hydrology based on Budyko theories, and improves the estimation of runoff
Precision.This method can be applied to the compartmentalization of runoff element in hydrologic cycle, and the spatial distribution for providing runoff in specific basin is special
It levies and predicts the depth of runoff of Cross Some Region Without Data, theoretical compared to the more traditional Budyko and general random interpolation method of the hydrology improves
The precision of prediction of runoff provides a kind of new idea and method, preferably to carry out water resource rule for the research of footpath flow graphization
It draws management and provides scientific basis.
Description of the drawings
Fig. 1 is the flow chart of the random interpolation Runoff Forecast method of the hydrology the present invention is based on Budyko theories；
Fig. 2 is Basin of Huaihe River Bangbu more than landform drainage map；
Fig. 3 is Basin of Huaihe River Bangbu more than hydrometric station and sub-basin figure；
Fig. 4 is Basin of Huaihe River Budyko curves E/P~E0/ P relational graphs；
Fig. 5 is the experiment covariance of Huaihe River sub-basin depth of runoff and theoretical covariance function；
Fig. 6 is the experiment covariance of Huaihe River sub-basin depth of runoff deviation and theoretical covariance function；
Fig. 7 (a) embraces the actual measurement of uncut jade formula and prediction depth of runoff relation for Fu；
Fig. 7 (b) is the cross validation results of actual measurement~prediction depth of runoff of the random interpolation method of the hydrology；
Fig. 7 (c) be coupling process cross validation results (in figure dotted line be 1:1 line)；
Fig. 8 (a) predicts mean annual runoff spatial distribution map for Budyko methods；
Fig. 8 (b) predicts mean annual runoff spatial distribution map for the random interpolation method of the hydrology；
Fig. 8 (c) is that the random interpolation Runoff Forecast method of the hydrology based on Budyko theories predicts that mean annual runoff is empty
Between distribution map.
Specific embodiment
The invention will be further described in the following with reference to the drawings and specific embodiments.
For the present embodiment using more than Basin of Huaihe River Bangbu 40 sub-basins as experiment sample, Basin of Huaihe River is the sixth-largest water of China
System, the weather transition region having a common boundary positioned at Chinese north and south, western moist climate is changed to from the warm temperate zone of east.Basin population is close
Degree is big, is one of the Main Agricultural area of China, will consume great lot of water resources every year to maintain industrial or agricultural and domestic water.Per capita
The 1/5 of water resource and the water resource deficiency average national level of unit area, it is often more important that more than half water resource by mistake
Degree exploitation, the recommendation far above international inland river utilize horizontal (30%).In addition very high rainfall concentration degree, it is meant that annual
Precipitation has sizable ratio to concentrate in short some months so that basin is highly prone to the invasion and attack of drought and waterlogging.Frequently drought
Damage caused by waterlogging evil has also opened the difficulty that water resource utilizes and flood control measure is implemented wide.Topographic map is shown in Fig. 2, and hydrometric station and sub-basin are shown in Fig. 3,
The following Basin of Huaihe River area 121,000km in Bangbu2, river network obtains by the data packet that national geographic information system provides, should
Basin upstream totally 40 sub-basins, hydrometeorological data system was from 1961 to 2000, wherein independent sub-basin is 27,
And 13 nested sub-basins.The sub-basin in the research area the north such as Zhongmou County, Zhuan Qiao, accomplish, the arid coefficient (E of Zhoukou City0/P)
Relatively high has been more than 1.3, and more to moisten such as Mei Shanshuiku, horizontally-arranged head, the arid coefficient of Huangchuan small for each sub-basin in south
In 0.8, mean annual runoff deep about 400mm, the 1000mm of the minimum northern 90mm close to Yellow River basin to Mountain Areas of Southern,
The more southern bigger in time and space variability the north of Basin of Huaihe River runoff.
The present embodiment is theoretical pre- by Experimental comparison Budyko for 1961 to 2000 Basin of Huaihe River of totally 40 years
Three kinds of moulds of random interpolation Runoff Forecast method of the hydrology based on Budyko theories of survey, the random interpolation method of the hydrology and the present invention
The prediction result of type, so as to prove the advantageous effect of this method.As shown in Figure 1, including four parts, it is right using Budyko theories
Mean annual runoff carries out spatial prediction, and the random interpolation method prediction mean annual runoff of the hydrology is theoretical based on Budyko
The random interpolation coupling process of the hydrology, cross validation evaluates different model prediction results.
1. Fu embraces uncut jade formula Runoff Forecast, the actual evapotranspiration root of hair in each basin is according to mean annual water balance formula (E=
P-R) acquire, averagely water balance factors are shown in Table 1 to each known sub-basin 1961-2000 for many years, bent according to formula (1) Budyko
Line E/P~E0/ P relational graphs as shown in Figure 4, in figure two boundary lines be respectively arid area water balance control (E=P) and
Energy balance control (the E=E of humid region0).The Budyko curve shapes of Basin of Huaihe River determine by parameter ω, each sub-basin
ω values acquire according to formula (2) and are listed in table 1, the scopes of ω values from the 1.43 to the 3.16 of Jiang Jia collection basin of yellow tail river valley,
Average is 2.32.
The ω values of all known sub-basins (make the Budyko predicted values of evapotranspiration and put down for many years according to non-linear fitting method
The standard error of mean minimum i.e. MAE minimums of both measured values that equal water balance obtains) full basin ω values such as Fig. 4 institutes for acquiring
Show, the ω values of the fitting are 2.213, and the ω averages with 40 basins are sufficiently close to.ω=2.213 are substituted into formula 2, are obtained：
The certainty ingredient of as runoff expressed by the formula, arid coefficient (E0/ P) smaller, the footpath in corresponding basin
Flow depth is bigger, and it is more arid that the larger depth of runoff in the north in Fig. 4 illustrates that these sub-basins compare other basins.It is average for many years
Budyko prediction depth of runoff and prediction deviation that year precipitation, reality/potential evapotranspiration hair and formula (20) represent, average mistake
Difference etc. is given in Table 1, and the evaluation of prediction result is provided by table 2.Budyko predicts the standard error of mean MAE of depth of runoff
For 94mm, root-mean-square error RMSE is 112mm, wherein the absolute error of yellow tail river sub-basin is up to 328.03mm, Xi County
The minimum 23.77mm of error in basin, relative error maximum are Xinzheng sub-basin 91mm, basin measured path flow depth of about standing
81.6%, the 36.94mm of the minimum big vast flood control reservoir of sound account for the 4.99% of measured path flow depth.
Each sub-basin Hydrometeorological Factors in 1 Huaihe River of table and prediction depth of runoff
2 three kinds of methods of table are in the Runoff Forecast result of Basin of Huaihe River
2. hydrology random device as a comparison, is directly applied to each son in Huaihe River by the random interpolation method of the hydrology of depth of runoff
The Runoff Forecast in basin, experiment covariance are calculated by following formula：
Wherein,Represent the measured path flow depth (mm) of all known sub-basins, d is the ground system between known sub-basin two-by-two
Count distance.For the geo-statistic distance between sub-basin known to difference is obtained, Basin of Huaihe River is divided into the grid that 40 rows × 50 arrange, by
All known sub-basins of formula (18) are to the geo-statistic distance of (i.e. known sub-basin A and B, amount to 820 couples) by known sub-basin A
Being averaged for distance is worth between the grid two-by-two contained by B, according to the distance between sub-basin known two-by-two being obtained and phase
Experiment covariance C (d) is obtained by formula (21) in the measured path flow depth in each basin answered, and then draws basin distance and experiment association
The relational graph of variance, in the step using the experiment covariance function in pairwise independent basin and corresponding basin distance simultaneously
The average value that experiment covariance function is acquired in every 50km spacing is plotted in figure, as shown in figure 5, experiment covariance function is optimal
Fitting function is：
C (d)=600000 × exp (- d/28.62) (22)
The exponential function of fitting is for the theoretical covariance function in calculation formula (19), Matrix C, C shown in formula (22)0,
K, V and G can also be accordingly calculated using matlab programs, and thus weight coefficient matrix is obtained, and then obtain Basin of Huaihe River
Runoff interpolation result, prediction error provided by table 1.Directly utilize the average of the random interpolation method prediction depth of runoff of the hydrology
Error MAE is 134mm, and root-mean-square error RMSE176mm, maximum absolute error is yellow tail river valley (448mm), minimum definitely to miss
Difference is to ring big vast flood control reservoir basin (3mm).It can be seen that interpolation error is big compared with the prediction error of Budyko theories, footpath is illustrated
The spatial distribution for determining measuring runoff of the certainty ingredient bigger of stream, and this also affects its space interpolation precision.
3. the random interpolation method of the hydrology based on Budyko theories, empty by the certainty components utilising for removing footpath fluid space
Interpolation method can be corrected Runoff Forecast the random error of spatial autocorrelation.Fu is embraced into uncut jade formula for table first
Show the i.e. external drift function R of certainty ingredient of runoffd *(x), the deviation of runoff measured value and predicted value is as random element,
Predicted that interpolation result is shown in Table 1 using the random interpolation method of the hydrology.
Experiment covariance R between known sub-basin two-by-twos *(x) see Fig. 6 with the relational graph of corresponding basin distance, refer to as follows
Number function is as its best fit equation：
C (d)=3000 × exp (- d/48.34) (23)
Matrix C, C are calculated using matlab programs by formula (23) and formula (11)~(15)0, K, V and G, so
Weight coefficient matrix is calculated afterwards and then the predicted value of runoff deviation is obtained.The interpolation method is directed to the space bias of runoff,
By Fu embrace uncut jade formula Runoff Forecast value be superimposed the runoff deviation interpolative prediction result finally obtain Basin of Huaihe River runoff it is pre-
Survey result.The coupling prediction method result of the runoff is still provided by table 1 and 2, and for distinct methods Runoff Forecast precision into
Comparison is gone.This method is that standard error of mean MAE is 47mm, root-mean-square error RMSE69mm using result in 40 basins,
Maximum absolute error is yellow tail river valley (236mm), and least absolute error is Jiang Jia collection basin (1.5mm).
4. the runoff spatial prediction comparison of three kinds of methods, as shown in table 2, the water proposed by the present invention based on Budyko theories
Literary random interpolation Runoff Forecast method has considered the certainty and random element of space runoff, is reduced available for systematicness empty
Between runoff prediction error, compare Budyko theoretical methods and directly using the two methods of random interpolation of the hydrology, the present invention proposes
Method obtained Runoff Forecast mean absolute error MAE and root-mean-square error RMSE significantly reduce.Such as yellow tail river valley
The 328mm that is predicted by Budyko theoretical methods of worst error and be directly reduced to using the 448mm of the random interpolative prediction of the hydrology
236mm.The cross validation results coefficient of determination that table 2 provides0.93 has been increased to by 0.81 and 0.54.
The correlativity figure of Runoff Forecast and measured value is provided by Fig. 7, and the two that the method for the present invention calculating is drawn is related to close
System reaches 0.95, with 1:The irrelevance of 1 line is minimum.By comparison, Budyko theoretical methods and directly apply the hydrology with the machine transplanting of rice
It is poor (coefficient R 2 be respectively 0.58 and 0.82) that correlativity is surveyed~predicted to the runoff that value method obtains, particularly after two
Kind method has substantially over-evaluated runoff low value, underestimates runoff high level (as seen from Figure 7).
(it is Budyko theoretical, the random interpolation of the hydrology and coupling side proposed by the present invention respectively by above-mentioned three kinds of Forecasting Methodologies
Method) the runoff spatial distribution map of Basin of Huaihe River drawn as shown in figure 8, the Basin of Huaihe River runoff distribution map of three kinds of methods have it is bright
Significant difference is other, and first two method substantially underestimates the northern depth of runoff compared with arid area compared with the method for the present invention, also illustrates this
The reasonability of invention.Method proposed by the present invention considered runoff space Integral Characteristic and river network to runoff
It influences, while combines the certainty and Uncertainty of runoff, the random character of runoff is particularly added into Forecasting Methodology
The considerations of scope, be conducive to improve space runoff precision of prediction, also the prediction for other hydrology variables provide it is a kind of newly
Idea and method.
Claims (8)
1. a kind of random interpolation Runoff Forecast method of hydrology based on Budyko theories, which is characterized in that comprise the following steps：
(1) entire basin is divided into multiple sub-basins, the sub-basin includes known sub-basin and sub-basin to be predicted, determines to treat
Predict sub-basin and multiple known sub-basins；The actual mean annual runoff of each known sub-basin is obtained by hydrometric station observation
Deep R (x)；Spatial prediction is carried out to each known sub-basin mean annual runoff using Budyko theories, is obtained average for many years
Annual flow depth predicted value Rd(x), the certainty ingredient as sub-basin runoff to be predicted；
(2) by R (x) and Rd(x) difference is as mean annual runoff prediction deviation；Using the random interpolation method of the hydrology to more
A known sub-basin mean annual runoff prediction deviation obtains known sub-basin depth of runoff deviation interpolation result R into row interpolations *
(x), the randomness ingredient as sub-basin runoff to be predicted；
(3) coupled using the certainty ingredient with randomness ingredient, obtain the final prediction runoff of sub-basin to be predicted：
R*(x)=Rd(x)+Rs *(x) (1)
In formula, R*(x) the final prediction runoff at sub-basin x to be predicted is represented.
2. the random interpolation Runoff Forecast method of the hydrology according to claim 1 based on Budyko theories, which is characterized in that
In step (1), mean annual precipitation, actual evapotranspiration, potential evapotranspiration hair amount are counted respectively, using Budyko theories to more
Annual annual flow carries out spatial prediction：
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Formula (4) is obtained by formula (2) and (3)：
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<mo>=</mo>
<mi>P</mi>
<mo>&CenterDot;</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
<mi>P</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>&omega;</mi>
</msup>
<mo>)</mo>
</mrow>
<mfrac>
<mn>1</mn>
<mi>&omega;</mi>
</mfrac>
</msup>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, P, E, E0、Rd(x) it is respectively mean annual precipitation, actual evapotranspiration, potential evapotranspiration hair amount and budyko
The depth of runoff of prediction；ω is parameters of formula, and ω value ranges are (1, ∞), and ω values are bigger, and precipitation is converted into the ratio of runoff
It is lower.
3. the random interpolation Runoff Forecast method of the hydrology according to claim 1 based on Budyko theories, which is characterized in that
In step (2), mean annual runoff prediction deviation is included into row interpolation using the hydrology random interpolation method：In block
On the basis of kriging interpolation methods, the basin distance of basin water system planning feature is considered, while increase basin water balance about
Beam, as continuous process spatially, predictor formula is the depth of runoff deviation of prediction：
<mrow>
<msup>
<msub>
<mi>R</mi>
<mi>s</mi>
</msub>
<mo>*</mo>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>R</mi>
<mi>s</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mi>&Lambda;</mi>
<mi>T</mi>
</msup>
<msub>
<mi>R</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, Rs *(A0) it is sub-basin depth of runoff deviation to be predicted, Rs(Ai) it is that i-th of area is AiKnown sub-basin calculate
Obtained depth of runoff deviation, Λ are weight matrix, RsIt is depth of runoff deviation matrix, Rs *(A0) it is Rs(A0) estimate, wherein A0
It is the cellar area of prediction；E [R are required according to minimum dispersion linear unbiased estimators *(A0)-Rs(A0)]=0 calculate weight matrix Λ：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>&mu;</mi>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mi>n</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
C(ui,uj) be every sub-basin fitting covariance function value, C0(ui,u0) it is u to be asked0Position and each known son
Basin uiThe fitting covariance function value at place, λiFor sub-basin A to be predicted0Locate the weighted value of corresponding each known sub-basin, μ is
Lagrange coefficient, substitution formula (5) obtains the predicted value of depth of runoff deviation after weight matrix is calculated.
4. the random interpolation Runoff Forecast method of the hydrology according to claim 3 based on Budyko theories, which is characterized in that
The computational methods of weight matrix Λ：
Formula (4) is expressed as matrix form：C Λ=C0, thus weight matrix Λ is expressed as：
Λ=C-1C0. (7)
Wherein：
<mrow>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>&Lambda;</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&lambda;</mi>
<mi>n</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>&mu;</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, Matrix C is the covariance function matrix of the point in sub-basin known to each pair, C0It is the point in sub-basin known to each pair
With the covariance function matrix of the point in sub-basin to be predicted, uiFor the position of the point in known sub-basin, u0For subflow to be predicted
The position of point in domain, μ are Lagrange coefficient.
5. the random interpolation Runoff Forecast method of the hydrology according to claim 4 based on Budyko theories, which is characterized in that
Formula (5), (6) are the depth of runoff deviation expression formulas of a sub-basin to be predicted, if Interpolation Process calculates M sub-basin simultaneously
Depth of runoff deviation, formula (5) is constant, and optimal weights matrix is：
And
Wherein LiIt is weighted value of i-th of basin to be predicted for each known sub-basin, μ*And μiFor Lagrange coefficient,
The C and C0For：
Wherein, matrix K is expressed as：
Matrix V and G are：
<mrow>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
<mi>r</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
<mi>r</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
<mi>r</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>G</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>&Delta;A</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<msub>
<mi>&Delta;A</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>n</mi>
</msub>
<mo>,</mo>
<msub>
<mi>&Delta;A</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msup>
<mi>&mu;</mi>
<mi>i</mi>
</msup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein Δ AiThe catchment area of i-th of non-nested sub-basin, the non-nested sub-basin refer to there is no comprising or by comprising
The sub-basin of relation, niFor each non-nested sub-basin Δ AiContained meshes number, above-mentioned Matrix division include water balance
Constraint, water balance constraint are that the measured runoff in basin exit should be equal to the sum of all sub-basin interpolation run-offs, table
It is shown as：
<mrow>
<msub>
<mi>R</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</msubsup>
<msub>
<mi>&Delta;A</mi>
<mi>i</mi>
</msub>
<mi>r</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;A</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
RTIt is the measured runoff of basin outlet.
6. the random interpolation Runoff Forecast method of the hydrology according to claim 5 based on Budyko theories, which is characterized in that
It will each non-nested sub-basin Δ AiIt is divided into niA area be a grid, each Δ AiRunoff deflection forecast value be weight system
The linear combination of depth of runoff deviation is calculated in number and known sub-basin, and formula (16) is further represented as：
<mrow>
<msub>
<mi>R</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
<msubsup>
<mi>&lambda;</mi>
<mi>j</mi>
<mi>i</mi>
</msubsup>
<mi>r</mi>
<mo>(</mo>
<msub>
<mi>A</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>n</mi>
<mi>T</mi>
</msub>
<msub>
<mi>r</mi>
<mi>T</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, nTIt is the number of basic grid, rTIt is the measured path flow depth of basin outlet；
Geo-statistic distance between sub-basin A, B for defined by Gottschalk, i.e., the distance of all mesh points pair in basin
Desired value is expressed as：
<mrow>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>,</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>&Integral;</mo>
<msub>
<mo>&Integral;</mo>
<mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
</mrow>
</msub>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>du</mi>
<mn>1</mn>
</msub>
<msub>
<mi>du</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, A, B represent two known sub-basins；A1And A2It is the drainage area of known sub-basin A, B respectively, u1、u2Respectively
The position at known sub-basin A, B midpoint；
According to basin distance, experiment covariance function and the relational graph of basin distance are drawn out, A is supported based on basin1And A2, reason
It is by covariance function Cov (A, B)：
<mrow>
<mi>C</mi>
<mi>o</mi>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>,</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>&Integral;</mo>
<msub>
<mo>&Integral;</mo>
<mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
</mrow>
</msub>
<msub>
<mi>Cov</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
<mo>|</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
<msub>
<mi>du</mi>
<mn>1</mn>
</msub>
<msub>
<mi>du</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>19</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, CovpIt is a covariance function.
7. the random interpolation Runoff Forecast method of the hydrology according to claim 6 based on Budyko theories, which is characterized in that
By trial-and-error method calibration optimal mathematical model, only with par wise irrelevance when drawing experiment covariance function and the relational graph of basin distance
Known sub-basin.
8. the random interpolation Runoff Forecast method of the hydrology according to claim 1 based on Budyko theories, it is characterised in that：
The known sub-basin at least 40.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109816249A (en) * | 2019-01-28 | 2019-05-28 | 云南电网有限责任公司 | A kind of Watershed Runoff hydrologic condition fine evaluation method |
| CN110377989A (en) * | 2019-07-08 | 2019-10-25 | 武汉大学 | Two Variational Design flood calculation method of nonuniformity based on hydrothermal reaction coupling balance |
| CN113254861A (en) * | 2021-06-23 | 2021-08-13 | 中山大学 | Method and device for calibrating hydrological model parameters in data-free area and terminal equipment |
| CN114090959A (en) * | 2021-11-22 | 2022-02-25 | 黄河水利委员会黄河水利科学研究院 | Random space-time interpolation method for river network structure constrained drainage basin runoff |
| CN115203625A (en) * | 2022-07-29 | 2022-10-18 | 应急管理部国家减灾中心 | Drought and waterlogging index data missing value interpolation method and device |
| CN116882565A (en) * | 2023-07-07 | 2023-10-13 | 兰州大学 | River basin runoff variation prediction method |
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| CN110377989A (en) * | 2019-07-08 | 2019-10-25 | 武汉大学 | Two Variational Design flood calculation method of nonuniformity based on hydrothermal reaction coupling balance |
| CN110377989B (en) * | 2019-07-08 | 2022-08-05 | 武汉大学 | Non-uniformity two-variable design flood calculation method based on hydrothermal coupling balance |
| CN113254861A (en) * | 2021-06-23 | 2021-08-13 | 中山大学 | Method and device for calibrating hydrological model parameters in data-free area and terminal equipment |
| CN113254861B (en) * | 2021-06-23 | 2021-09-24 | 中山大学 | Method and device for calibrating hydrological model parameters in data-free area and terminal equipment |
| CN114090959A (en) * | 2021-11-22 | 2022-02-25 | 黄河水利委员会黄河水利科学研究院 | Random space-time interpolation method for river network structure constrained drainage basin runoff |
| CN114090959B (en) * | 2021-11-22 | 2024-03-22 | 黄河水利委员会黄河水利科学研究院 | Random space-time interpolation method for runoff of river basin under constraint of river network structure |
| CN115203625A (en) * | 2022-07-29 | 2022-10-18 | 应急管理部国家减灾中心 | Drought and waterlogging index data missing value interpolation method and device |
| CN116882565A (en) * | 2023-07-07 | 2023-10-13 | 兰州大学 | River basin runoff variation prediction method |
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