CN113946796A - Drought propagation time calculation method based on conditional probability high space-time resolution - Google Patents

Drought propagation time calculation method based on conditional probability high space-time resolution Download PDF

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CN113946796A
CN113946796A CN202111161033.0A CN202111161033A CN113946796A CN 113946796 A CN113946796 A CN 113946796A CN 202111161033 A CN202111161033 A CN 202111161033A CN 113946796 A CN113946796 A CN 113946796A
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黄生志
李逸飞
马川惠
冷国勇
王韩叶
方伟
邓铭江
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Xian University of Technology
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Abstract

The invention discloses a drought propagation time calculation method based on conditional probability high space-time resolution, which comprises the following steps of: step 1: collecting specified precipitation data and soil humidity data, and processing the precipitation data and the soil humidity data into a ten-day scale sequence to obtain gridding precipitation data and soil humidity data with high spatial resolution; step 2: calculating a standardized precipitation index; calculating a standardized soil humidity index; and step 3: establishing a combined distribution with the best dependence between the standardized rainfall index and the standardized soil humidity index; and 4, step 4: calculating the probability of agricultural drought under different levels of meteorological drought conditions, and setting a threshold interval; and if the probability of the agricultural drought reaches the threshold value requirement, obtaining the propagation time from the meteorological drought to the agricultural drought. The method improves the calculation precision of the drought propagation time, and can provide guidance for agricultural water resource management and agricultural drought prevention.

Description

Drought propagation time calculation method based on conditional probability high space-time resolution
Technical Field
The invention belongs to the technical field of drought management and coping, and particularly relates to a drought propagation time calculation method based on conditional probability high space-time resolution.
Background
Drought is an extreme natural disaster caused by long-term shortage of rainfall, and the influence of drought on agricultural production is particularly serious. The yield reduction of the grains caused by drought accounts for more than 60% of the grain loss caused by various natural disasters. In the source of agricultural drought, severe agricultural drought is often caused after the occurrence of weather drought due to the lack of irrigation facilities in weather drought, particularly in rain-fed agricultural areas. Determining the propagation time from weather to agricultural drought has great significance for early warning of agricultural drought;
the method is characterized in that firstly, the theory of the method is incomplete, a correlation coefficient method is generally adopted to capture the dependence relationship between an atmospheric system and a soil system, and the propagation time is determined through the maximum correlation coefficient of a weather drought index sequence with a certain time scale and an agricultural drought index sequence with a fixed time scale. In addition, the traditional method only can provide the whole and general propagation time from the meteorological drought to the agricultural drought, the propagation process of the drought under the stress of the meteorological drought of different levels cannot be reflected, and finally, the traditional method is rough in the aspect of describing the time-space precision of the propagation time, and the propagation time obtained by taking months and sites as units can obviously not meet the requirement of actual agricultural drought early warning. How to determine an evaluation method which has a complete theoretical basis and high space-time resolution and can reflect the propagation time from meteorological drought to agricultural drought at different levels is an urgent problem to be solved in the process of establishing an early agricultural drought early warning platform.
Disclosure of Invention
The invention aims to provide a drought propagation time calculation method based on conditional probability and high space-time resolution, and solves the problems that the actual agricultural drought early warning and the method theory integrity of the existing agricultural drought propagation time evaluation method need to be further improved.
The technical scheme adopted by the invention is that,
a drought propagation time calculation method based on conditional probability high space-time resolution comprises the following steps:
step 1: collecting designated precipitation data and soil humidity data, processing the precipitation data and the soil humidity data into a ten-day scale sequence, and processing the precipitation data and the soil humidity data by adopting a spatial interpolation method to obtain gridded precipitation data and soil humidity data with high spatial resolution;
step 2: calculating a standardized precipitation index based on the meshed precipitation data to represent meteorological drought; calculating a standardized soil humidity index based on the gridded soil humidity data to represent agricultural drought;
and step 3: establishing combined distribution with the best dependence relationship between the standardized rainfall index and the standardized soil humidity index through a Copula theory;
and 4, step 4: obtaining a conditional probability formula based on the joint distribution, calculating the probability of causing agricultural drought under different levels of meteorological drought conditions through the conditional probability formula, and setting a threshold interval; and judging whether the probability of the occurrence of the agricultural drought reaches the threshold requirement, if the probability of the occurrence of the agricultural drought does not reach the threshold requirement, adjusting the threshold interval to judge whether the probability reaches the threshold again, and if the probability of the occurrence of the agricultural drought reaches the threshold requirement, obtaining the propagation time from the meteorological drought to the agricultural drought.
The present invention is also characterized in that,
in step 2: the calculation of the standardized precipitation index specifically comprises the following steps: calculating the probability corresponding to the gridded precipitation data and the soil humidity data by using a double-parameter gamma distribution function, then carrying out normal standardization treatment on the probability value to obtain a standardized precipitation index, and obtaining drought characteristics under different time scales according to the standardized precipitation index; the calculation of the standardized soil humidity index specifically comprises the following steps: and calculating the average value and the standard deviation of the gridding soil humidity sequence, and then subtracting the soil humidity average value from the soil humidity data and dividing the soil humidity average value by the soil humidity standard deviation to obtain the standardized soil humidity index.
In step 3, the joint distribution calculation formula is as follows (6):
FSPI-i,SSMI-j(spi,ssmi)＝P(SPI-i<spi,SSMI-j<ssmi)＝C(F1(spi),F2(ssmi))(6)，
wherein SPI-i and SSMI-j are respectively a standardized precipitation sequence and a standardized soil humidity sequence, FSPI-i,SSMI-jFor the joint distribution to be established, i and j are the time scales corresponding to SPI and SSMI, respectively, F1And F2The edge distribution function for SPI and SSMI sequences, respectively.
Step 3 is specifically that the edge distribution of the standardized precipitation index and the standardized soil humidity index is fitted by adopting normal distribution, then the joint distribution is fitted by adopting five Copula functions of Gaussian, Gumbel, Frank, Clayton and Student, and the fitting goodness of the five Copula functions is checked by adopting the minimum Euclidean square distance as a criterion, so that the joint distribution function with the best fitting effect is screened out.
In step 4, calculating the conditional probability of causing agricultural drought under different levels of meteorological drought conditions as the following formulas (7), (8) and (9):
and (3) medium drought scene:
Figure BDA0003289971270000041
heavy drought scenario:
Figure BDA0003289971270000042
extremely drought scene:
Figure BDA0003289971270000043
wherein, Pm-n，Ps-nAnd Ps-nThe probability of causing agricultural drought under moderate, severe and extreme drought conditions of meteorological drought respectively, n is the time length of the standardized soil humidity index lagging the standardized rainfall index, C is a Copula function, and P is a probability function.
The method has high space-time resolution, can reflect the propagation time from meteorological drought to agricultural drought under the meteorological drought stress of different levels, improves the calculation precision of the drought propagation time, can identify the drought propagation time under the high space-time resolution of the ten-day scale, can reflect the drought propagation process under the meteorological drought stress of different levels, and can provide guidance for agricultural water resource management and agricultural drought prevention.
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FIG. 1 is a schematic flow chart of a method for calculating drought propagation time based on conditional probability high spatiotemporal resolution according to the present invention.
Detailed Description
The method for calculating the drought propagation time based on the conditional probability high space-time resolution is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in FIG. 1, the invention provides a drought propagation time calculation method based on conditional probability high spatiotemporal resolution.
The invention provides a method for calculating the propagation time from weather drought to agricultural drought based on a Copula theory and a conditional probability model, which comprises the following steps:
step 1: collecting designated precipitation data and soil humidity data, processing the precipitation data and the soil humidity data into a ten-day scale sequence, and processing the precipitation data and the soil humidity data by adopting a spatial interpolation method to obtain the meshed precipitation data and soil humidity data with high spatial resolution; as an example, the spatial resolution here is chosen to be 0.25 °.
Step 2: calculating a standardized rainfall index (SPI) to represent weather drought on the basis of the meshed rainfall data; calculating a standardized soil humidity index (SSMI) based on the gridded soil humidity data to represent agricultural drought;
and step 3: establishing combined distribution with the best dependence relationship between the standardized rainfall index and the standardized soil humidity index through a Copula theory;
and 4, step 4: obtaining a conditional probability formula based on the joint distribution, calculating the probability of causing agricultural drought under different levels of meteorological drought conditions through the conditional probability formula, and setting a threshold interval; and judging whether the probability of the occurrence of the agricultural drought reaches the threshold requirement, if the probability of the occurrence of the agricultural drought does not reach the threshold requirement, adjusting the threshold interval to judge whether the probability reaches the threshold again, and if the probability of the occurrence of the agricultural drought reaches the threshold requirement, obtaining the propagation time from the meteorological drought to the agricultural drought.
The invention relates to a drought propagation time calculation method based on conditional probability high space-time resolution; in step 2: the process of calculating the SPI index can be summarized as follows, after a precipitation sequence is obtained, the probability corresponding to the precipitation sequence is calculated by using a two-parameter Gamma distribution function, finally, the probability value is subjected to normal standardization processing to obtain the SPI index, the SPI index captures the variable time scale of meteorological drought, and by utilizing the characteristic, the drought characteristics under different time scales can be obtained; for the SSMI index, because the drought-describing principle is similar to that of the SPI index, the agricultural drought state under a certain fixed time scale can be obtained, and the obtained information can be used for further establishing the combined distribution of the meteorological drought index and the agricultural drought index sequence. Furthermore, the drought-rating criteria for SPI and SSMI indices are shown in table 1 below:
TABLE 1 SPI and SSMI index drought grade division Standard
Figure BDA0003289971270000061
The invention relates to a drought propagation time calculation method based on conditional probability high space-time resolution; in step 3: the establishment of the joint distribution of the SPI and the SSMI indexes by utilizing the Copula theory can be further subdivided into the following processes, firstly, the edge distribution of two drought indexes is fitted by adopting normal distribution, and then, the joint distribution is fitted by adopting five Copula functions of Gaussian, Cumbel, Frank, Clayton and Student, wherein the basic characteristics of the five Copula functions are shown in the following table:
TABLE 2 basic information of five candidate copula functions
Figure BDA0003289971270000062
Figure BDA0003289971270000071
The invention adopts the European square distance (SED) minimum as a criterion to check the fitting goodness of each Copula function, thereby screening out a combined distribution function with the best fitting effect, wherein the calculation formula of the SED is SED ═ (CUV-C)2In the formula, CUV represents an empirical value of two-dimensional joint distribution, and C represents a theoretical value of the Copula function.
The invention provides a drought propagation time calculation method based on Copula theory and a conditional probability model; in step 4: the conditional probability formula for causing agricultural drought under different levels of meteorological drought is calculated as follows:
and (3) medium drought scene:
Figure BDA0003289971270000072
heavy drought scenario:
Figure BDA0003289971270000073
extremely drought scene:
Figure BDA0003289971270000081
in the formula Pm-n，Ps-nAnd P iss-nThe probability of causing agricultural drought under moderate, severe and extreme drought conditions of meteorological drought respectively, wherein n represents the time length of the SSMI sequence lagging the SPI sequence, and the value range is 1-33 ten days. According to the formula, the probability matrix P under moderate weather drought conditions corresponding to a certain grid point when n is 1-33td respectively can be calculatedmAnd probability matrix P under severe weather drought and extreme weather drought conditionss，Pe。
After obtaining the probability matrix, determining the propagation time from weather drought to agricultural drought according to whether the probability value exceeds a certain proper threshold, taking a moderate drought scene as an example, the specific method is that firstly, a threshold s is preset to be 0.8, and P is determinedmMaximum value of (P)maxThen, judging PmaxWhether the probability value exceeds 0.7 or not, and if so, further judging PmaxJudging whether a preset threshold value s is exceeded or not (s is equal to 0.8), if so, obtaining a fixed threshold value s of 0.8, and judging P from n is equal to 1m-nWhether the drought Propagation Time (PT) is equal to or greater than a determined threshold value, and if yes, determining the drought Propagation Time (PT) to be n; if PmaxIf the threshold value is less than the initial threshold value s, the threshold value requirement is lowered, s-0.1 (k-0.79) is taken, and P is judged againmaxIf equal to or greater than the new preset threshold s, if satisfied the fixed threshold is s (k is 0.79), for PmThe matrix is judged from n being 1, PT is determined, and if P ismaxIf s is still less than the preset threshold value s, the threshold requirement is lowered again (s-0.1) until s is 0.7. Furthermore if P startsmaxLess than 0.7, directly with PmaxFor threshold, the propagation time PT is equal to PmaxThe value of n corresponds to the value. For probability matrix Ps，PeThe matrix adopts the same method to respectively obtain the transmission from severe weather drought and extreme weather drought to agricultural droughtBroadcasting time
The method for calculating the drought propagation time based on the conditional probability high spatiotemporal resolution is further described in detail by specific embodiments.
Taking the drought propagation time calculation under the moderate weather drought condition as an example, the provided method for calculating the drought propagation time based on the Copula theory and the conditional probability model comprises the following steps.
1. Collecting daily rainfall and soil humidity data, accumulating the rainfall data by the daily data to obtain a ten-day rainfall sequence, and averaging the daily soil data to obtain a ten-day soil humidity sequence. And carrying out spatial interpolation on the station data by ten days, or using mature related data products to obtain gridding data.
2. And (5) calculating the drought index.
The SPI index is first calculated using the formula:
Figure BDA0003289971270000091
Figure BDA0003289971270000092
in the formula: x a precipitation sequence with a certain time accumulation scale; alpha and beta are shape parameters and scale parameters of gamma distribution; f (x) is the cumulative precipitation probability distribution associated with the gamma function.
Figure BDA0003289971270000093
Figure BDA0003289971270000094
In the formula: s is a positive coefficient and a negative coefficient of probability density, and when f (x) >0.5, g (x) ═ 1-f (x), and S ═ 1; when f (x) <0.5, g (x) ═ f (x), S ═ 1; the specific values of the calculation parameters of the simplified approximate solution formula for converting the gamma distribution function into the cumulative frequency are that c0, c1, c2, d1, d2 and d3 are as follows: c 0-2.515517, c 1-0.802853, c 2-0.010328, d 1-1.432788, d 2-0.189269 and d 3-0.001308. The SPI drought index with the cumulative time scale of 4-36 days is calculated by the method in the embodiment.
The SSMI index was calculated using the formula:
Figure BDA0003289971270000101
in the formula: sm is the soil humidity value of a certain time scale,
Figure BDA0003289971270000102
and σ is the mean and standard deviation, respectively, of soil moisture over the time scale over years. The cumulative SSMI index of the present case is 3 th day.
3. And establishing joint distribution. The formula used is as follows:
FSPI-i,SSMI-j(spi,ssmi)＝P(SPI-i<spi,SSMI-j<ssmi)＝C(F1(spi),F2(ssmi))(6)，
in the formula FSPI-i,SSMI-jFor the established joint distribution, i and j are time scales corresponding to the SPI and the SSMI respectively, in this case, i takes 4-36 ten days, and j takes 3 ten days. F1And F2The edge distribution functions of the SPI and SSMI sequences, respectively, are normalized, so a normal distribution is selected as their edge distribution function. And C is a Copula function of connecting edge distribution, combines 5 Copula functions in the table 2, adopts the Euclidean distance minimum principle, selects the optimal fitting function, and respectively establishes the joint distribution between SPI-4-SPI-36 and SSMI-3.
4. The travel time is calculated. In this case, taking a moderate weather drought scenario as an example, the formula used is as follows:
Figure BDA0003289971270000103
in the formula Pm-nIn order to indicate the probability of agricultural drought caused by meteorological drought under the moderate drought condition, n represents the time length of the SSMI sequence lagging the SPI sequence, and the value range is 1-33 days. According to the formula, the probability matrix P under moderate weather drought conditions corresponding to a certain grid point when n is 1-33td respectively can be calculatedm。
Obtaining a probability matrix PmThereafter, as shown in the flowchart of fig. 1, the preset threshold s is 0.8 and P is determinedmMaximum value of (P)maxThen, judging PmaxWhether the probability value exceeds 0.7 or not, and if so, further judging PmaxJudging whether a preset threshold value s is exceeded or not (s is equal to 0.8), if so, obtaining a fixed threshold value s of 0.8, and judging P from n is equal to 1m-nWhether the drought Propagation Time (PT) is equal to or greater than a determined threshold value, and if yes, determining the drought Propagation Time (PT) to be n; if PmaxIf the threshold value is less than the initial threshold value s, the threshold value requirement is lowered, s-0.1 (k-0.79) is taken, and P is judged againmaxIf equal to or greater than the new preset threshold s, if satisfied the fixed threshold is s (k is 0.79), for PmThe matrix is judged from n being 1, PT is determined, and if P ismaxIf s is still less than the preset threshold value s, the threshold requirement is lowered again (s-0.1) until s is 0.7. Furthermore if P startsmaxLess than 0.7, directly with PmaxFor threshold, the propagation time PT is equal to PmaxThe value of n corresponds to the value.
The same method can be used for obtaining the drought propagation time under the severe weather drought and extreme weather drought conditions. And when the method is applied, the cumulative scale of the SSMI sequences can be adjusted as required to evaluate the drought propagation time of crops in a special period.
The invention relates to a drought propagation time calculation method based on conditional probability high space-time resolution; the evaluation method has high space-time resolution and can reflect the propagation time from meteorological drought to agricultural drought under different levels of meteorological drought stress, the calculation precision of the drought propagation time is improved, the drought propagation process under different levels of meteorological drought stress can be reflected, and the prevention and early warning efficiency of agricultural water resource management and agricultural drought is improved. Has certain practical significance.

Claims (5)

1. A drought propagation time calculation method based on conditional probability high space-time resolution is characterized by comprising the following steps:
step 1: collecting designated precipitation data and soil humidity data, processing the precipitation data and the soil humidity data into a ten-day scale sequence, and processing the precipitation data and the soil humidity data by adopting a spatial interpolation method to obtain the meshed precipitation data and soil humidity data with certain spatial resolution;
step 2: calculating a standardized precipitation index based on the meshed precipitation data to represent meteorological drought; calculating a standardized soil humidity index based on the gridded soil humidity data to represent agricultural drought;
and step 3: establishing combined distribution with the best dependence relationship between the standardized rainfall index and the standardized soil humidity index through a Copula theory;
and 4, step 4: obtaining a conditional probability formula based on the joint distribution, calculating the probability of causing agricultural drought under different levels of meteorological drought conditions through the conditional probability formula, and setting a threshold interval; and judging whether the probability of the occurrence of the agricultural drought reaches the threshold requirement, if the probability of the occurrence of the agricultural drought does not reach the threshold requirement, adjusting the threshold interval to judge whether the probability reaches the threshold again, and if the probability of the occurrence of the agricultural drought reaches the threshold requirement, obtaining the propagation time from the meteorological drought to the agricultural drought.
2. The method for calculating the drought propagation time based on the conditional probability high spatiotemporal resolution as claimed in claim 1, wherein in step 2: the calculation of the standardized precipitation index specifically comprises the following steps: calculating the probability corresponding to the gridded precipitation data and the soil humidity data by using a double-parameter gamma distribution function, then carrying out normal standardization treatment on the probability value to obtain a standardized precipitation index, and obtaining drought characteristics under different time scales according to the standardized precipitation index; the calculation of the standardized soil humidity index specifically comprises the following steps: and calculating the average value and the standard deviation of the gridding soil humidity sequence, and then subtracting the soil humidity average value from the soil humidity data and dividing the soil humidity average value by the soil humidity standard deviation to obtain the standardized soil humidity index.
3. The method for calculating the drought propagation time based on the conditional probability high spatiotemporal resolution as claimed in claim 1, wherein in step 3, the joint distribution calculation formula is as follows (6):
FSPI-i,SSMI-j(spi,ssmi)＝P(SPI-i<spi,SSMI-j<ssmi)＝C(F1(spi),F2(ssmi)) (6)，
wherein, FSPI-i,SSMI-jFor the joint distribution to be established, i and j are the time scales corresponding to SPI and SSMI, respectively, F1And F2The edge distribution function for SPI and SSMI sequences, respectively.
4. The method of claim 1, wherein in step 3, the method for calculating drought propagation time based on conditional probability high spatio-temporal resolution is implemented by first fitting the edge distribution of the normalized precipitation index and the normalized soil humidity index by using normal distribution, then fitting the joint distribution by using five Copula functions of gaussian, gunbel, frank, cleton and student, and checking the goodness of fit of the five Copula functions by using the least squared euclidean distance as a criterion, thereby screening out the joint distribution function with the best fitting effect.
5. The method for calculating the drought propagation time based on the conditional probability high spatial-temporal resolution as claimed in claim 1, wherein in step 4, the conditional probabilities of causing agricultural drought under different levels of meteorological drought conditions are calculated as shown in the following formulas (7), (8) and (9):
and (3) medium drought scene:
Figure FDA0003289971260000021
heavy drought scenario:
Figure FDA0003289971260000031
extremely drought scene:
Figure FDA0003289971260000032
wherein, Pm-n，Ps-nAnd Ps-nThe probability of causing agricultural drought under moderate, severe and extreme drought conditions of meteorological drought respectively, n is the time length of the standardized soil humidity index lagging the standardized rainfall index, C is a Copula function, and P is a probability function.
CN202111161033.0A 2021-09-30 2021-09-30 Drought propagation time calculation method based on conditional probability high space-time resolution Pending CN113946796A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115310796A (en) * 2022-07-29 2022-11-08 西安理工大学 Method and system for determining propagation relationship among different types of drought
CN115331215A (en) * 2022-10-18 2022-11-11 水利部交通运输部国家能源局南京水利科学研究院 Three-dimensional identification and matching method and device for drought event

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115310796A (en) * 2022-07-29 2022-11-08 西安理工大学 Method and system for determining propagation relationship among different types of drought
CN115331215A (en) * 2022-10-18 2022-11-11 水利部交通运输部国家能源局南京水利科学研究院 Three-dimensional identification and matching method and device for drought event

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