CN107977729B - Multivariable standardized drought index design method - Google Patents

Multivariable standardized drought index design method Download PDF

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CN107977729B
CN107977729B CN201710748967.1A CN201710748967A CN107977729B CN 107977729 B CN107977729 B CN 107977729B CN 201710748967 A CN201710748967 A CN 201710748967A CN 107977729 B CN107977729 B CN 107977729B
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drought
mmsdi
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precipitation
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张强
李勤
黄庆忠
史培军
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Beijing Normal University
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Abstract

The invention relates to a multivariable standardized drought index design method, which is characterized in that on the basis of the design of a conventional MSDI drought index, precipitation amount and potential evapotranspiration amount are taken as common influence factors to be added into the design process of the MSDI drought index, and the difference value PPET between precipitation P and potential evapotranspiration PET is used for replacing precipitation variable in the conventional MSDI drought index as one of two variables and Soil Humidity variable Soil Humidity, namely SH, as a combined distribution variable; and estimating through position division proposed by Gringorten based on non-parametric joint distribution to obtain the MMSDI drought index. The MMSDI is added with a potential evapotranspiration variable on the basis of considering precipitation and soil humidity, and a meteorological agricultural comprehensive drought index comprehensively considering the influence of precipitation, potential evapotranspiration and soil humidity on meteorological drought, agricultural drought and meteorological agricultural comprehensive drought is established.

Description

Multivariable standardized drought index design method
Technical Field
The invention relates to the technical field of meteorological prediction, in particular to a multivariable standardized drought index design method.
Background
Drought is one of the most serious and complicated natural disasters at present. The drought has long duration and wide influence range, and has great influence on national economy. Drought is internationally classified into meteorological drought, agricultural drought, hydrographic drought, and socioeconomic drought. Among them, weather drought generally refers to a phenomenon of water shortage caused by long unbalanced time of precipitation and evaporation, and is also a common disaster type. Whereas agricultural drought reflects the degree to which the water content of the soil is less than the water demand of the plants. The drought monitoring system can early warn the beginning and duration of drought, the severity, the spatial distribution and the like, and is an important reference basis for the nation to take disaster prevention and reduction countermeasures.
At present, the weather drought common indexes include indexes such as a standardized rainfall index (SPI), a Pelmer drought index (PDSI), and a SPEI. After the United states drought monitoring is carried out by Guttman by using SPI and PDSI, the characteristic spectrum of the PDSI is found to change along with the change of places, and the SPI index does not change. However, the SPI only considers precipitation and cannot measure the influence of other climate factors on drought. The applicability of the SPEI index in Chinese drought monitoring is comprehensively analyzed by Wangling and the like by using methods such as goodness-of-fit inspection and the like, and the SPEI index is considered to be capable of describing drought more accurately than the SPI index. At the same time, SPEI has a multi-time scale characteristic compared to PDSI.
For agricultural drought monitoring research, the main indexes include a K index, a Palmer index, a precipitation range percentage, a standardized soil moisture content index (SSMI) and the like. Wangjinsong, etc]The research shows that the K index has better effect in the meteorological drought and agricultural drought monitoring in northwest regions. The capacity of SSMI to characterize regional drought was confirmed by wang et al.
The influence of weather and agricultural drought on social economy and the interaction of the weather and agricultural drought are non-independent and hysteresis. Hao et al proposed a multivariable MSDI index based on meteorological and agricultural drought and was used for drought studies in California, USA. The MSDI index integrates the characteristics of the SPI and the SSI index, takes the information of precipitation, soil humidity and the like into consideration, and has the characteristic of multiple time scales. Since the SPI index only considers the effects of precipitation, there are limitations in drought monitoring, and thus the application of MSDI is also limited. In order to comprehensively consider the influence of rainfall, evapotranspiration and soil humidity on drought, the method improves the MSDI comprehensive drought index provided by Hao and the like on the basis of summarizing the existing drought monitoring index construction theory to create the MMSDI index.
Disclosure of Invention
The invention aims to solve the technical problem that the invention provides a multivariable standardized drought index design method, and potential evapotranspiration variables are added to establish a meteorological agricultural comprehensive drought index which comprehensively considers the influence of rainfall, potential evapotranspiration and soil humidity on meteorological drought, agricultural drought and meteorological agricultural comprehensive drought.
The invention adopts the following technical scheme for solving the technical problems:
a multivariable standardized drought index design method is characterized in that on the basis of design of a conventional MSDI (modified Multi-data acquisition) drought index, precipitation amount and potential evapotranspiration amount are used as common influence factors to be added into a MSDI (modified Multi-data acquisition) drought index design process, a difference value P-PET (P-polyethylene terephthalate) based on precipitation P and potential evapotranspiration PET is recorded as PPET, a precipitation variable in the conventional MSDI drought index is replaced and used as one of two variables and a Soil Humidity variable Soil Humidity, recorded as SH, and used as a joint distribution variable; and estimating through position division proposed by Gringorten based on non-parametric joint distribution to obtain the MMSDI drought index.
Respectively representing the difference PPET based on the precipitation P and the potential evapotranspiration PET as variables X and Y, establishing an MMSDI index based on the precipitation, the potential evapotranspiration and the soil humidity, and then representing the combined distribution of the variables X and Y as follows:
P(X≤x，Y≤y)＝p (1)
where X and Y represent samples, and X and Y represent specific values that need to be satisfied, namely:
P(PPET≤ppet，SH≤sh)＝p (2)
wherein, PPET and SH represent corresponding samples, PPET and SH represent specific values required to be satisfied, and p represents the joint distribution probability of the variable X and the variable Y.
The MMSDI may be defined based on the joint distribution probability p as:
Figure GDA0003319141410000021
wherein the content of the first and second substances,
Figure GDA0003319141410000022
is a standard normal distribution function; the MMSDI drought index is derived from the joint probabilities of the variables, and the drought is characterized on different time scales.
Based on non-parametric joint distribution, the empirical binary joint probability is estimated through a position division formula proposed by Gringorten:
Figure GDA0003319141410000031
where n is the number of observations, mkIs a relationship pair (x)i，yi) In xi≤xkAnd yi≤yk(i is not less than 1 and not more than n) number of events, xiAnd yiRefers to the ith observation, xkAnd ykRefers to the kth value that satisfies the condition. When the joint probability in the formula (4) is derived, the joint probability can be used as an input value to the formula (3) to obtain the MMSDI value.
The partitioning of the MMSDI drought index into various types of drought event classes is shown in the following table:
table drought index grade dividing table
Figure GDA0003319141410000032
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the MMSDI is added with a potential evapotranspiration variable on the basis of considering precipitation and soil humidity, and a meteorological agricultural comprehensive drought index comprehensively considering the influence of precipitation, potential evapotranspiration and soil humidity on meteorological drought, agricultural drought and meteorological agricultural comprehensive drought is established. The key point is that the consideration of potential evapotranspiration factors is increased, and the meteorological agricultural drought strength is comprehensively analyzed from a multi-variable angle.
The method is based on a non-parametric joint distribution concept, the difference value of rainfall and potential evapotranspiration is used as an independent variable to form a joint distribution model of two parameters with the soil humidity variable, and the MMSDI index is obtained through joint probability derivation, so that the influence of distribution hypothesis is avoided to a limited extent, the calculated amount of fitting parameter distribution is reduced remarkably, and the calculation efficiency is improved greatly.
Drawings
FIG. 1 is a diagram comparing MSDI and MMSDI methods;
FIG. 2 is a 3 month and 6 month scale 2014 POD, FAR, CSI, EOD;
FIG. 3 is a graph of percentage of SPEI, SSI, MMSDI monitoring accuracy.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the invention provides a multivariable standardized drought index design method.A comprehensive drought index MMSDI newly proposed by the method is added with a potential evapotranspiration variable on the basis of considering precipitation and soil humidity, and a meteorological agricultural comprehensive drought index comprehensively considering the influence of precipitation, potential evapotranspiration and soil humidity on meteorological drought, agricultural drought and meteorological agricultural comprehensive drought is established. The key point is that the consideration of potential evapotranspiration factors is increased, and the meteorological agricultural drought strength is comprehensively analyzed from a multi-variable angle.
The method is based on a non-parametric joint distribution concept, the difference value of rainfall and potential evapotranspiration is used as an independent variable to form a joint distribution model of two parameters with the soil humidity variable, and the MMSDI index is obtained through joint probability derivation, so that the influence of distribution hypothesis is avoided to a limited extent, the calculated amount of fitting parameter distribution is reduced remarkably, and the calculation efficiency is improved greatly.
MSDI is an index for representing meteorological agricultural comprehensive drought based on data of precipitation and soil humidity, and the method is an extension of an SPI method which is widely used at present and is a two-dimensional variable model based on precipitation and soil humidity. SPEI index[15]Compared with SPI, the influence of rainfall and potential evapotranspiration on drought is comprehensively considered, and a plurality of researches show that the SPEI has applicability in China, based on the principle, the influence of the rainfall, the potential evapotranspiration and Soil Humidity on drought is comprehensively considered, based on the difference value (P-PET, noted as PPET) of the rainfall (P) and the Potential Evapotranspiration (PET) to replace the rainfall variable in the original MSDI as one of two variables and the other Soil Humidity variable (Soil Humidity, noted as SH) as combined distribution variables, respectively expressed as variables X and Y, the MMSDI index based on the rainfall, the potential evapotranspiration and the Soil Humidity is established,the joint distribution of the variables X and Y can be expressed as:
P(X≤x，Y≤y)＝p (1)
where X and Y represent samples, and X and Y represent specific values that need to be satisfied, namely:
P(PPET≤ppet，SH≤sh)＝p (2)
wherein, PPET and SH represent corresponding samples, PPET and SH represent specific values to be satisfied, and p represents the joint distribution probability of a variable X (the difference value of precipitation and potential evapotranspiration, PPET) and a variable Y (soil humidity, SH). Thus, the MMSDI can be defined based on the joint distribution probability p as:
Figure GDA0003319141410000051
wherein the content of the first and second substances,
Figure GDA0003319141410000052
is a standard normal distribution function. Thus, similar to SPEI, MMSDI can be derived from the joint probabilities of the variables and can characterize drought on different time scales (e.g., 1 month, 3 months, 6 months, 12 months, etc.).
To avoid assumptions about distribution and to reduce the computation of fitting parameter distributions, the citation herein is based on a non-parametric joint distribution concept. The empirical binary joint probability can be estimated by the location partition formula proposed by grinporten:
Figure GDA0003319141410000053
where n is the number of observations, mkIs a relationship pair (x)i，yi) In xi≤xkAnd yi≤yk(i is not less than 1 and not more than n) number of events, xiAnd yiRefers to the ith observation, xkAnd ykRefers to the kth value that satisfies the condition. When the joint probability in the formula (4) is derived, the joint probability can be used as an input value to the formula (3) to obtain the MMSDI value.
The MMSDI index refers to the unified standard adopted by Hao and the like for the classification of various drought event grades, and is shown in Table 1.
TABLE 1 drought index rating Scale
Figure GDA0003319141410000061
For example, SPEI, SSI, MSDI and MMSDI are four indicators characterizing the spatial distribution of drought levels. The drought spatial distribution represented by MSDI is basically consistent with that of MMSDI, but the regions shown in red boxes are greatly different, and the drought spatial distribution represented by MSDI is mainly characterized in that the drought level represented by MSDI is higher than that represented by SPEI or SSI, and the drought level represented by MMSDI is closer to that of SPEI.
The drought distribution monitored by the SPEI is not monitored by the MSDI, and the drought is more accurately monitored by the MMSDI. The drought conditions monitored by MSDI in 2014 are mainly different from MMSDI in that the monitored drought range is large, and the other difference is that the drought level is high compared with the MSDI monitoring result.
Fig. 2 is POD, FAR, CSI and EOD curves of corresponding values of the meteorological drought and agricultural drought grids in the meteorological agricultural integrated drought grid at the 3 and 6 month scale, respectively, in 2014. Although the scales are different, the distribution conditions of POD, FAR, CSI and EOD are similar. The POD value is 1, namely the corresponding position of the grid which is dry in meteorological drought or agricultural drought in the meteorological agricultural comprehensive drought is also necessary to be dry, namely the meteorological agricultural comprehensive drought can monitor the occurrence of the meteorological drought or the agricultural drought. Both CSI and EOD are close to 1 and the value of EOD is greater than CSI; the CSI is close to 1, which indicates that weather drought or agricultural drought occurs and the proportion of the weather agricultural comprehensive drought to the weather agricultural comprehensive drought is close to 1; EOD approaching 1 indicates that the ratio of the occurrence of meteorological drought or agricultural drought, the occurrence of meteorological agricultural comprehensive drought, the absence of meteorological drought and agricultural drought, and the absence of meteorological and agricultural drought to all cases approaches 1. A FAR of not 0 indicates that the meteorological-agricultural integrated drought is not only a simple addition of meteorological drought and agricultural drought, but also can monitor a drought area which cannot be monitored in meteorological drought or agricultural drought.
Fig. 3 reflects the comparison result between the drought area percentage of each province (directly governed city) with drought grade D4 monitored by the SPEI, SSI and MMSDI indexes in 1979-2014 and the disaster area percentage of crops, i.e., the percentage of the number of provinces in each province (directly governed city) in which the drought index monitoring is more accurate than the actual drought result. As can be seen from the figure, besides the drought monitoring result in a few years is more accurate than the SPEI or SSI, the MMSDI monitoring result is generally closer to the real drought situation than the SPEI and SSI indexes, wherein the MMSDI monitoring effect accounts for a larger percentage in 25 years of 1982, 1993, 1995, 2003 and 2010 of 1979-.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A multivariable standardized drought index design method is characterized in that the design method is based on MSDI drought index design, precipitation and potential evapotranspiration are added into the MSDI drought index design process as common influence factors, and estimation is carried out through position division proposed by Grignard based on non-parametric joint distribution to obtain an MMSDI drought index;
the MMSDI drought index is obtained by the following method:
MSDI is an index for representing meteorological agricultural comprehensive drought based on precipitation and Soil Humidity data, the MMSDI drought index is based on a difference value P-PET between precipitation P and potential evapotranspiration PET, is recorded as PPET, replaces a precipitation variable in the MSDI as one of two variables, and obtains a combined distribution variable together with a Soil Humidity variable, Soil Humidity, and SH;
respectively expressed as variables X and Y, and the MMSDI index based on precipitation, potential evapotranspiration and soil moisture is established, then the joint distribution of the variables X and Y is expressed as:
P(X≤x，Y≤y)＝p (1)
where X and Y represent samples, and X and Y represent specific values that need to be satisfied, namely:
P(PPET≤ppet，SH≤sh)＝p (2)
wherein PPET and SH represent corresponding samples, PPET and SH represent specific values required to be met, p represents a variable X, X is a difference value of precipitation and potential evapotranspiration, and PPET, a variable Y and a combined distribution probability of soil humidity SH;
the MMSDI is defined based on the joint distribution probability p as:
Figure FDA0003319141400000011
wherein the content of the first and second substances,
Figure FDA0003319141400000012
the MMSDI is derived from the joint probability of variables and can represent the drought on different time scales;
the empirical binary joint probability is estimated by the position partition formula proposed by grinporten:
Figure FDA0003319141400000013
where n is the number of observations, mkIs a relationship pair (x)i，yi) In xi≤xkAnd yi≤yk(i is not less than 1 and not more than n) number of events, xiAnd yiRefers to the ith observation, xkAnd ykRefers to the kth value that satisfies the condition; when the joint probability in the formula (4) is derived, the joint probability is used as an input value to the formula (3) to obtain the MMSDI value。
2. The method of claim 1, wherein the MMSDI drought index is classified into the following classes:
table drought index grade dividing table
Figure FDA0003319141400000014
Figure FDA0003319141400000021
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