CN108874750A - A kind of Calculation of Area Rainfall uncertainty estimation method - Google Patents
A kind of Calculation of Area Rainfall uncertainty estimation method Download PDFInfo
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Abstract
The invention discloses a kind of Calculation of Area Rainfall uncertainty estimation methods.It is assumed that Calculation of Area Rainfall error Normal Distribution, and it is standardized, in conjunction with《Standardized normal distribution function table》The corresponding relationship of middle fraction and quantile carries out mathematical description to Calculation of Area Rainfall uncertainty.Meanwhile based on station method empirical equation is taken out, in known drainage area, dispersed elevation, precipitation station number and calculation interval, the anti-fraction that pushes away is 90% calculating error.Finally, bringing the calculating error of fraction 90% into Calculation of Area Rainfall uncertainty description formula, inquire into using calculated value as the conditional distribution function of the areal rainfall of condition, quantization Calculation of Area Rainfall is uncertain.
Description
Technical field
The present invention relates to hydrologic forecast prediction field more particularly to a kind of Calculation of Area Rainfall uncertainty estimation methods.
Background technique
Due to the limitation of the complexity of natural hydrologic process and human knowledge's level, so that can not during flood forecasting
Avoid there are many uncertainties, so as to cause the uncertainty of flood forecasting result, bring risk for Flood Control Dispatch.Cause
This carries out and forecasts uncertain quantization method research, and the uncertainty of each element, has highly important during quantized prediction
Realistic meaning.As the most important input element of Flood Forecasting Model, the estimation precision of basin face mean rainfall is greatly determined
The quality of final forecast result.Since website laying condition etc. limits, although the density of rainfall observation website is continuing to increase,
But existing rainfall website still can not accomplish comprehensive laying to a basin, therefore inevitably need to pass through Field in Limited Rain
The observation rainfall at amount station calculates basin face mean rainfall.In order to ensure the computational accuracy of face mean rainfall, hydrologist and statistics
Scholar has developed many areal rainfall difference calculation methods, such as gram in golden difference, Thiessen polygon calculating method.Nevertheless, by
In the influence for the conditions such as watershed unit, landforms, spatially distributed rainfall be uneven, the calculating of areal rainfall is uncertain inevitable.
Therefore, carry out the research of Calculation of Area Rainfall uncertainty quantization method, have important practical significance.
Summary of the invention
It is an object of the present invention to solution the deficiencies in the prior art, the present invention provides a kind of Calculation of Area Rainfall uncertainty and estimates
Meter method, it is assumed that Calculation of Area Rainfall error Normal Distribution, and it is standardized, it is based on standardized normal distribution fraction
With the relationship of quantile, mathematical description is carried out to Calculation of Area Rainfall uncertainty；Corresponding fraction is pushed away using empirical equation is counter
Calculate error；In conjunction with fraction, error and the probabilistic mathematical expression formula of Calculation of Area Rainfall are calculated, inquires into the item of areal rainfall
Part probability distribution realizes the probabilistic quantization of Calculation of Area Rainfall with this.
In order to solve the above-mentioned technical problem, the technical scheme is that：A kind of Calculation of Area Rainfall uncertainty estimation side
Method, which is characterized in that include the following steps：
Step 1：The probabilistic description of Calculation of Area Rainfall, to any moment t, it is assumed that the calculating relative error ε of areal rainfall
(t) Normal Distribution, the corresponding relationship of combined standard normal distribution fraction and quantile, to Calculation of Area Rainfall uncertainty
Carry out mathematical description；
Step 2：Formula is counter to be pushed away, counter to be pushed to the prediction error calculation formula for determining fraction according to existing empirical equation；
Step 3：In conjunction with step 1 and step 2, inquire into calculated valueFor the areal rainfall of conditionProbability distribution,
It is uncertain to quantify Calculation of Area Rainfall.
Further, step 1 includes the following steps：
Step 1.1：It is assumed that Calculation of Area Rainfall valueRelative error ε (t) Normal Distribution it is as follows：
In formula,It is true face average rainfall；σ is the standard deviation of Calculation of Area Rainfall error.
Step 1.2：According to above-mentioned it is assumed that Calculation of Area Rainfall value can be inquired intoUnder known conditions, true face is averaged rain
AmountCondition distribution it is as follows：
In formula, Φ is the probability function of standardized normal distribution.
Step 1.3：It is assumed that standardized variable u is as follows：
In formula, standardized variable u obeys standardized normal distribution, then can inquire《Standardized normal distribution function table》,
Inquire into the corresponding quantile-u of a certain level of significance α (confidence level is η=1- α)α/2(t)、uα/2(t) and probability α/2, (1- α/
2) (schematic diagram is shown in Fig. 2) passes through inquiry by taking unilateral quantile as an example《Standardized normal distribution function table》, available：
Φ(uα/2(t))=α/2 1- (4)
According to above formula, the definition of combining standardized variable u can be pushed away：
In formula, EηThe allowable error of η is taken for fraction, then areal rainfallCondition distribution can be rewritten as：
Further, step 2 is specially：
In conjunction with station method empirical equation is taken out, the anti-fraction that pushes away is 90% Calculation of Area Rainfall error E90%It is as follows：
E90%=0.099 × N-1.166×A0.3×H0.155×T-0.197 (7)
In formula, N is the quantity (station) for studying area's precipitation station；A is research area's area (km2)；H is research area's dispersed elevation
(m)；T is that duration of raining is long (h), wherein N=12；A=805；H=479；T=1.
Further, step 3 is specially：
When fraction takes 90%, inquiry《Standardized normal distribution function table》It is found that unilateral quantile uα/2(t)=
1.64.In conjunction with above formula, it can push away and be able to calculated valueFor the areal rainfall of conditionCondition distribution it is as follows：
The beneficial effects obtained by the present invention are as follows：A kind of Calculation of Area Rainfall uncertainty estimation method provided by the invention, knot
It closes fraction to be described with quartile point correspondence opposite rainfall calculating uncertainty, and method empirical equation in station is counter to be pushed away based on taking out
The calculating error of 90% fraction, and then it is uncertain to quantify Calculation of Area Rainfall.
Detailed description of the invention
Fig. 1 is a kind of flow chart of Calculation of Area Rainfall uncertainty estimation method of the present invention；
Fig. 2 is standardized normal distribution probability density function schematic diagram；
Fig. 3 is the Calculation of Area Rainfall uncertainty schematic diagram of certain hydrometric station rainfall；
Fig. 4 is certain the 6th period of hydrometric station rainfall areal rainfall conditional probability density function figure.
Specific embodiment
With reference to the accompanying drawings and detailed description, the present invention is furture elucidated, it should be understood that following specific embodiments are only
For illustrating the present invention rather than limiting the scope of the invention.
Below with reference to example, the present invention will be further explained.
As Figure 1-Figure 4, a kind of Calculation of Area Rainfall uncertainty estimation method, which is characterized in that include the following steps：
Step 1：The probabilistic description of Calculation of Area Rainfall, to any moment t, it is assumed that the calculating error ε (t) of areal rainfall takes
From normal distribution, the corresponding relationship of combined standard normal distribution fraction and quantile carries out Calculation of Area Rainfall uncertainty
Mathematical description；
Step 2：Formula is counter to be pushed away, counter to be pushed to the prediction error calculation formula for determining fraction according to existing empirical equation；
Step 3：In conjunction with step 1 and step 2, inquire into calculated valueFor the areal rainfall of conditionProbability distribution,
It is uncertain to quantify Calculation of Area Rainfall.
Specific implementation process is as follows：A kind of Calculation of Area Rainfall uncertainty estimation method, includes the following steps：
(1) assume Calculation of Area Rainfall valueRelative error ε (t) Normal Distribution it is as follows：
In formula,It is true face average rainfall；σ is the standard deviation of Calculation of Area Rainfall error.
(2) according to above-mentioned it is assumed that Calculation of Area Rainfall value can be inquired intoUnder known conditions, true face mean rainfallCondition distribution it is as follows：
In formula, Φ is the probability function of standardized normal distribution.
(3) assume that standardized variable u is as follows：
In formula, standardized variable u obeys standardized normal distribution, then can inquire《Standardized normal distribution function table》,
Inquire into the corresponding quantile-u of a certain level of significance α (confidence level is η=1- α)α/2(t)、uα/2(t) and probability α/2, (1- α/
2) (schematic diagram is shown in Fig. 2) passes through inquiry by taking unilateral quantile as an example《Standardized normal distribution function table》, available：
Φ(uα/2(t))=α/2 1- (4)
According to above formula, the definition of combining standardized variable u can be pushed away：
In formula, EηThe allowable error of η is taken for fraction, then areal rainfallCondition distribution can be rewritten as：
(4) it combines and takes out station method empirical equation, the anti-Calculation of Area Rainfall error E for pushing away fraction and being 90%90%It is as follows：
E90%=0.099 × N-1.166×A0.3×H0.155×T-0.197 (7)
In formula, N is the quantity (station) for studying area's precipitation station；A is research area's area (km2)；H is research area's dispersed elevation
(m)；T is duration of raining length (h).
(5) when fraction takes 90%, inquiry《Standardized normal distribution function table》It is found that unilateral quantile uα/2(t)=
1.64.In conjunction with above formula, it can push away and be able to calculated valueFor the areal rainfall of conditionCondition distribution it is as follows：
Embodiment：Existing a certain drainage area A=805km2, basin dispersed elevation H=479m has precipitation station N in basin
=12, the material calculation (duration of raining length) of deterministic prediction model is T=1h.To a certain field rainfall in the basin into
The quantization of row Calculation of Area Rainfall uncertainty：
(1) assume Calculation of Area Rainfall valueRelative error ε (t) Normal Distribution it is as follows：
In formula,It is true face average rainfall；σ is the standard deviation of Calculation of Area Rainfall error.
(2) according to above-mentioned it is assumed that Calculation of Area Rainfall value can be inquired intoUnder known conditions, true face mean rainfallCondition distribution it is as follows：
In formula, Φ is the probability function of standardized normal distribution.
(3) assume that standardized variable u is as follows：
In formula, standardized variable u obeys standardized normal distribution, then can inquire《Standardized normal distribution function table》,
Inquire into the corresponding quantile-u of a certain level of significance α (confidence level is η=1- α)α/2(t)、uα/2(t) and probability α/2, (1- α/
2) (schematic diagram is shown in Fig. 2) passes through inquiry by taking unilateral quantile as an example《Standardized normal distribution function table》, available：
Φ(uα/2(t))=α/2 1- (4)
According to above formula, the definition of combining standardized variable u can be pushed away：
In formula, EηThe allowable error of η is taken for fraction, then areal rainfallCondition distribution can be rewritten as：
(4) it combines and takes out station method empirical equation, the anti-Calculation of Area Rainfall error E for pushing away fraction and being 90%90%It is as follows：
E90%=0.099 × N-1.166×A0.3×H0.155×T-0.197 (7)
In formula, N=12；A=805；H=479；T=1.
(5) when fraction takes 90%, inquiry《Standardized normal distribution function table》It is found that unilateral quantile uα/2(t)=
1.64.In conjunction with above formula, it can push away and be able to calculated valueFor the areal rainfall of conditionCondition distribution it is as follows：
(6) face mean rainfall can be quantified using above formula to any time tUncertainty, it is a certain with the basin
For the rainfall of field, the Calculation of Area Rainfall uncertainty schematic diagram (Fig. 3) of this rainfall is drawn, and by taking the 6th moment as an example, drawing should
When facet mean rainfall probability density function figure (Fig. 4).
The present invention is described Calculation of Area Rainfall uncertainty by the relationship of fraction and quantile, and is based on experience
Formula inquires into the calculating error of 90% fraction, and it is uncertain to quantify Calculation of Area Rainfall on this basis.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of Calculation of Area Rainfall uncertainty estimation method, which is characterized in that include the following steps：
Step 1：The probabilistic description of Calculation of Area Rainfall, to any moment t, it is assumed that the relative error ε (t) of Calculation of Area Rainfall value
Normal Distribution, the corresponding relationship of combined standard normal distribution fraction and quantile, to Calculation of Area Rainfall uncertainty into
Row mathematical description；
Step 2：Formula is counter to be pushed away, counter to be pushed to the prediction error calculation formula for determining fraction according to existing empirical equation；
Step 3：In conjunction with step 1 and step 2, inquires into using Calculation of Area Rainfall value as the probability distribution of the areal rainfall of condition, quantify face
Rainfall calculates uncertain.
2. a kind of Calculation of Area Rainfall uncertainty estimation method according to claim 1, which is characterized in that step 1 is specific
Include the following steps：
Step 1.1：It is assumed that Calculation of Area Rainfall valueRelative error ε (t) Normal Distribution it is as follows：
In formula,It is true face average rainfall；σ is the standard deviation of Calculation of Area Rainfall error.
Step 1.2：According to above-mentioned it is assumed that Calculation of Area Rainfall value can be inquired intoUnder known conditions, true face mean rainfallCondition distribution it is as follows：
In formula, Φ is the probability function of standardized normal distribution；
Step 1.3：It is assumed that standardized variable u is as follows：
In formula, standardized variable u obeys standardized normal distribution, then can inquire《Standardized normal distribution function table》, inquire into
A certain level of significance α, confidence level η, corresponding quantile-uα/2(t)、uα/2(t) and probability α/2, (α/2 1-), pass through
Inquiry《Standardized normal distribution function table》, available：
Φ(uα/2(t))=α/2 1- (4)
According to above formula, the definition of combining standardized variable u can be pushed away：
In formula, EηThe allowable error of η=1- α is taken for fraction, then areal rainfallCondition distribution can be rewritten as：
Wherein, t is the moment, and σ is the standard deviation of Calculation of Area Rainfall error.
3. a kind of Calculation of Area Rainfall uncertainty estimation method according to claim 1, which is characterized in that step 2 is specific
For：
In conjunction with station method empirical equation is taken out, the anti-fraction that pushes away is 90% Calculation of Area Rainfall error E90%It is as follows：
E90%=0.099 × N-1.166×A0.3×H0.155×T-0.197 (7)
In formula, N is the quantity for studying area's precipitation station；A is research area's area；H is research area's dispersed elevation；T is that duration of raining is long.
4. a kind of Calculation of Area Rainfall uncertainty estimation method according to claim 3, which is characterized in that step 3 is specific
For：
When fraction takes 90%, inquiry《Standardized normal distribution function table》It is found that unilateral quantile uα/2(t)=1.64；Knot
Box-like (7), can push away and be able to calculated valueFor the areal rainfall of conditionCondition distribution it is as follows：
Wherein, Φ is the probability function of standardized normal distribution.
5. a kind of Calculation of Area Rainfall uncertainty estimation method according to claim 3, which is characterized in that the N=12,
A=805.
6. a kind of Calculation of Area Rainfall uncertainty estimation method according to claim 4, which is characterized in that H=479, T=
1。
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| CN109709015A (en) * | 2018-12-25 | 2019-05-03 | 河海大学 | It is a kind of can the preferential flow phenomenon of quantitative description kinematic infiltration method |
| CN110895354A (en) * | 2019-12-04 | 2020-03-20 | 中国水利水电科学研究院 | Surface rainfall calculation method based on dynamic adjustment of Thiessen polygon |
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Application publication date: 20181123 |