CN111898258B - Two-dimensional drought disaster assessment method driven by hydrologic cycle variation - Google Patents

Two-dimensional drought disaster assessment method driven by hydrologic cycle variation Download PDF

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CN111898258B
CN111898258B CN202010691987.1A CN202010691987A CN111898258B CN 111898258 B CN111898258 B CN 111898258B CN 202010691987 A CN202010691987 A CN 202010691987A CN 111898258 B CN111898258 B CN 111898258B
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尹家波
郭生练
王俊
顾磊
熊丰
邓乐乐
田晶
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Abstract

The invention discloses a two-dimensional drought disaster assessment method under the drive of hydrologic cycle variation, which comprises the following steps: firstly, collecting basin meteorological hydrological data; acquiring a future meteorological sequence by a quantile deviation correction method based on M global climate modes, and considering the influence of global climate change on the future drought; taking the water-heat balance of watershed water circulation into consideration by using a Budyko equation, taking the characteristic parameters of a Fei-Pai formula as covariates, and considering the influence of the activity of the human underlying surface; a two-variable drought event joint probability distribution function under a non-uniform condition is constructed, and a self-adaptive non-uniform two-variable drought disaster assessment method based on hydrothermal coupling balance under the comprehensive driving of climate change and underlying surface human activities is provided based on a most probable combination mode of drought duration and intensity. The invention considers the underlying surface condition and the non-consistency characteristics of hydrological series, and can provide important reference basis with strong operability for the management and planning of basin water resources.

Description

Two-dimensional drought disaster assessment method driven by hydrologic cycle variation
Technical Field
The invention relates to the technical field of hydrologic disaster assessment, in particular to a two-dimensional drought disaster assessment method under the drive of hydrologic cycle variation.
Background
Drought disasters are one of the most common natural disasters in the world, and seriously threaten grain safety, water supply safety and ecological safety. China is one of the most seriously affected areas by drought disasters, and the deep knowledge of the development rule and the influence mechanism of China has important practical significance. Due to the random nature of the occurrence, scholars at home and abroad usually describe the risks quantitatively by a hydrological frequency analysis method, for example, Yuan Qian et al (2008) explores the probability distribution and the recurrence characteristics of the duration of the extreme drought based on an analytic method and a simulation method. However, the method is based on the traditional univariate frequency analysis means, and the correlation among the attributes of the drought event is difficult to accurately describe. In fact, drought events are often characterized by multiple attributes, such as duration, severity, and intensity, and multivariate hydrological frequency analysis methods have been applied to multidimensional drought risk assessment in recent years. For example, the Yaopisti et al (2019) determines an optimal probability distribution function based on the Markov Monte Carlo method, and analyzes the joint occurrence frequency of the duration and the intensity of drought in the Huaihe river basin in China.
The inventor of the present application finds that the method of the prior art has at least the following technical problems in the process of implementing the present invention:
due to the influence of global climate change and human activities, the hydrologic cycle process is significantly changed, the drought disaster situation is aggravated, and the consistency assumption in the traditional frequency analysis is challenged. The global climate mode is an effective tool for evaluating the influence of future climate change on water circulation, and scholars propose that the inconsistent evolution characteristics of the drought event are analyzed by simulating the future meteorological hydrological situation, and how to select a proper physical factor as an explanatory variable becomes a research difficulty. The water-heat balance equation Budyko formula considers the water balance and the energy balance of an area, can better reflect the influence of human activities on the underlying surface condition and the yield convergence characteristic, but the existing literature fails to adopt the method to consider the future climate change and the two-dimensional drought disaster characteristic under the comprehensive driving of the underlying surface, is difficult to accurately reflect the non-uniform change characteristic of the hydrologic process under the changing environment, and restricts the scientific evaluation of the drought disaster under the driving of hydrologic cycle variation.
Disclosure of Invention
The invention provides a two-dimensional drought disaster assessment method under the drive of hydrologic cycle variation, which is used for solving or at least partially solving the technical problem that the assessment effect is poor due to the fact that the method in the prior art is difficult to accurately reflect the non-uniform variation characteristics of the hydrologic process in a changing environment.
In order to solve the technical problem, the invention provides a two-dimensional drought disaster assessment method under the drive of hydrologic cycle variation, which comprises the following steps:
s1: acquiring basic meteorological hydrological data, wherein the meteorological hydrological data comprise M global climate mode simulation data, meteorological data and flow series of basin control hydrological stations;
s2: acquiring a weather simulation series under M groups of weather change scenes based on basic weather hydrological data and a quantile deviation correction method;
s3: driving a pre-constructed basin hydrological model through a meteorological simulation series under M groups of climatic change scenes, and simulating to obtain a basin hydrological process under a future scene, wherein the basin hydrological process under the future scene comprises M groups of runoff long sequences of each sub-basin in a research area in a historical period and a future period;
s4: obtaining standardized runoff indexes based on M groups of runoff length sequences of each sub-watershed in a historical period and a future period in a research area, and extracting drought duration characteristic values and drought intensity characteristic values corresponding to the M groups of runoff length sequences through a run theory;
s5: establishing a watershed hydrothermal coupling equilibrium equation, calibrating characteristic parameters of the hydrothermal coupling equilibrium equation, and analyzing the correlation between the characteristic parameters and a standardized runoff index;
s6: establishing a time-varying edge distribution function and a joint probability distribution function under a non-uniform condition based on a hydrothermal coupling equilibrium equation and by adopting characteristic parameters in the hydrothermal coupling equilibrium equation as covariates;
s7: and (4) according to the time-varying edge distribution function and the joint distribution function established in the S6, finding the most possible combination scene of the drought duration and the drought intensity in the given recurrence period, and taking the most possible combination scene as the result of disaster evaluation.
In one embodiment, S2 specifically includes:
and calculating the difference between the output variable of the global climate modes GCMs and the observed weather variable on each quantile, and removing the difference on each quantile of future scenes output by the global climate modes to obtain future corrected GCMs climate predictions, namely the weather simulation series under M groups of climate change scenes.
In one embodiment, S3 specifically includes:
s3.1: calibrating and screening an optimal hydrological model as a basin hydrological model through actually measured meteorological and hydrological data;
s3.2: and inputting the obtained meteorological simulation series under the M groups of climatic change scenes into an optimal hydrological model, and simulating to obtain the watershed hydrological process under the future scene.
In one embodiment, S3.1 specifically includes: inputting the actually measured meteorological sequence into four hydrological models of Xinanjiang, GR4J, HMETS and HBV, using KGE efficiency coefficient as maximum target, defining each model by SCEUA method, selecting the model with the highest KGE efficiency coefficient as the optimal hydrological model,
wherein,
Figure BDA0002589635080000031
wherein r represents the Pearson linear correlation coefficient of the simulated sequence and the measured sequence, α represents the ratio of the variance of the simulated sequence and the measured sequence, β represents the ratio of the mean of the simulated sequence and the measured sequence, and the KGE efficiency coefficient is in the range of (— infinity, 1), wherein when KGE is 1, the simulated sequence completely coincides with the measured sequence.
In one embodiment, S4 specifically includes:
s4.1: in the historical period, each monthly runoff is first fitted by probability distribution:
Figure BDA0002589635080000032
in the formula, F (r) represents the cumulative probability distribution function of P-III distribution, alpha, beta and omega are the shape, scale and position parameters of the P-III distribution, and then the standardized runoff index in the historical time interval and the SRI index long sequence in the historical time interval are obtained through the inverse standardization process, wherein the standardized runoff index is the SRI index value: sri (r) ═ Φ-1(F(r))；
S4.2: for a future time period, inputting the simulated monthly runoff into P-III distribution determined by a historical reference period to obtain cumulative distribution probability, and then carrying out reverse standardization on the obtained cumulative distribution probability to obtain an SRI index sequence of the future time period;
s4.3: by utilizing M groups of long sequences of the SRI indexes in the historical time period and the SRI index sequences in the future time period of the drainage basin, on the basis of the run-length theory, respectively extracting the drought duration and the drought intensity characteristic value of the M groups of long sequences of the SRI indexes in the historical time period and the drought duration and the drought intensity characteristic value of the M groups of SRI index sequences in the future time period.
In one embodiment, S5 specifically includes:
s5.1: calculating potential evapotranspiration through a Peneman formula, and obtaining actual evapotranspiration of a drainage basin through a water volume balance equation; the Peneman formula is as follows:
Figure BDA0002589635080000033
in the formula: PET is latent evapotranspiration (mm/d); Δ represents the slope of the saturated water pressure curve (kPa/DEG C); rnNet radiation for the earth's surface; g is soil heat flux; gamma is a dry-wet table constant; t ismeanRepresents the daily average temperature; u. of2Two meters near-ground wind speed; e.g. of the typesRefers to the saturated water pressure; e.g. of the typeaThe actual water pressure is referred to;
s5.2: selecting a time window with certain time, calibrating an annual average hydrothermal coupling equilibrium equation characteristic parameter w by a least square method, analyzing the correlation between the parameter w and a drought index SRI sequence, and verifying the reliability of the parameter w as an drought sequence interpretation variable; the annual average hydrothermal coupling equilibrium equation is as follows:
Figure BDA0002589635080000041
in the formula, ET is the actual evapotranspiration to fully consider the energy balance and the moisture balance of the land-atmosphere system, and the parameter w is used to reflect the change of the underlying surface characteristics.
In one embodiment, S6 specifically includes:
step S6.1: constructing a time-varying edge distribution function; representing the drought characteristic quantity by X, wherein the drought characteristic quantity comprises duration D and intensity S, and adopting a gamma distribution function as an edge distribution function of the drought duration and the intensity, wherein the probability density function of the gamma distribution function under the consistent condition is as follows:
Figure BDA0002589635080000042
wherein alpha and beta represent shape and scale parameters respectively.
S6.2: constructing a two-variable time-varying drought joint probability distribution function; for any scene under the M groups of climatic scenes of the drainage basin, selecting a G-HCopula function as a joint probability distribution function of drought duration and drought intensity, and replacing the parameter theta of the Copula function by a time-varying parameter
Figure BDA0002589635080000043
Figure BDA0002589635080000044
Wherein,
Figure BDA0002589635080000045
for the Copula joint distribution function,
Figure BDA0002589635080000046
the range is (1, ∞); u. oft,vtRespectively, duration D and intensity S edge distribution functions,
Figure BDA0002589635080000047
in one embodiment, S7 specifically includes:
and (3) calculating the most possible combination scene of drought duration and drought intensity in a given recurrence period, and taking the OR recurrence period as a measurement index of the drought, wherein the measurement index is defined as: t isor t(dt,st)＝1/[1-Ft(dt,st)]；
In the formula, Tor t(dt,st) A time-varying OR joint recurrence period, in units of years; the most probable combination pattern of duration and intensity of drought refers to the combination (d) of the greatest joint probability density function on the contour line during the recurrence period*(t),s*(t)), solving by constructing the following equation:
Figure BDA0002589635080000048
wherein,
Figure BDA0002589635080000049
a time-varying edge distribution function representing the D and S variables,
Figure BDA00025896350800000410
representing a time-varying parameter; f. oft(dt,st) A density function representing a time-varying joint distribution function of duration D and intensity S;
Figure BDA0002589635080000051
a density function representing a time-varying Copula joint distribution function;
Figure BDA0002589635080000052
and
Figure BDA0002589635080000053
respectively represent
Figure BDA0002589635080000054
And
Figure BDA0002589635080000055
is used as a density function of the edge distribution function.
One or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:
according to the two-dimensional drought disaster assessment method under the drive of hydrologic cycle variation, the non-uniformity characteristics of hydrologic series under the influence of climate variation and human underlying surface activities are fully considered, the characteristic parameters in the hydrothermal coupling equilibrium equation are used as covariates, the non-uniformity of the hydrologic series is considered to construct a time-varying edge distribution function and a joint probability distribution function, the method has strong physical significance and a statistical basis, the change characteristics of future drought under the drive of hydrologic cycle variation can be effectively represented, and therefore the disaster assessment effect is improved.
Furthermore, the method combines a climate multi-mode set, a hydrological model, a hydrothermal balance equation, a most probable combination scenario method and the drainage basin drought, can provide important reference basis with strong operability for drainage basin drought assessment and early warning under a changing environment, and provides engineering reference value for dealing with future climate disasters and scientifically making emission reduction strategies.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a detailed flow diagram of the method of the present invention;
FIG. 2 is a schematic diagram of run-length theory;
FIG. 3 is a schematic diagram of the Budyko hydrothermal equilibrium equation.
Detailed Description
The invention aims to overcome the defects in the prior art, the influence of climate change on future drought is considered based on a Global Climate Mode Set (GCMs), the water heat balance of watershed water circulation is considered by adopting a Budyko equation, the influence of underlying surface human activities on drought is represented by taking characteristic parameters of a Fupu formula as covariates, a time-varying Copula model is constructed by considering the non-uniformity of hydrologic series, and the two-dimensional drought disaster evaluation method under the drive of hydrologic circulation variation is provided based on the most possible combination mode of drought duration and intensity.
In order to achieve the technical effects, the main inventive concept of the invention is as follows:
firstly, collecting basin meteorological hydrological data; acquiring a future meteorological sequence by a quantile deviation correction method based on M global climate modes, and considering the influence of global climate change on the future drought; taking the water-heat balance of watershed water circulation into consideration by using a Budyko equation, taking the characteristic parameters of a Fei-Pai formula as covariates, and considering the influence of the activity of the human underlying surface; a two-variable drought event joint probability distribution function under a non-uniform condition is constructed, and a self-adaptive non-uniform two-variable drought disaster assessment method based on hydrothermal coupling balance under the comprehensive driving of climate change and underlying surface human activities is provided based on a most probable combination mode of drought duration and intensity. The invention considers the underlying surface condition and the non-consistency characteristics of hydrological series, and can provide important reference basis with strong operability for the management and planning of basin water resources.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method comprises the steps of acquiring meteorological information such as future rainfall, air temperature, relative humidity and wind speed of a basin by a quantile deviation correction method based on a Global Climate Model Set (GCMs), combining the meteorological scene with a hydrological model to acquire runoff information of the basin in a changing environment, calculating a drought index and extracting a drought characteristic index, considering the hydrothermal balance of basin water circulation based on a Budyko equation, constructing a time-varying Copula model by taking characteristic parameters of the equation as covariates and considering the inconsistency of hydrological series, and providing a self-adaptive non-consistency two-variable drought disaster assessment method under the drive of water circulation variation, wherein the specific flow is shown in figure 1 in detail.
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings, and the method of the invention specifically comprises the following steps:
s1: acquiring basic meteorological hydrological data, wherein the meteorological hydrological data comprises M global climate mode simulation data, meteorological data and a flow series of basin control hydrological stations.
The meteorological data comprise data such as daily precipitation, air temperature, wind speed, relative humidity, sunshine duration and the like.
S2: based on basic meteorological hydrological data and a quantile deviation correction method, a meteorological simulation series under M sets of climatic change scenes is obtained.
In one embodiment, S2 specifically includes:
and calculating the difference between the output variable of the global climate modes GCMs and the observed weather variable on each quantile, and removing the difference on each quantile of future scenes output by the global climate modes to obtain future corrected GCMs climate predictions, namely the weather simulation series under M groups of climate change scenes.
Specifically, a quantile deviation correction method is adopted to correct the GCMs output, and a future meteorological sequence is obtained; specifically, the difference of the GCMs output variable and the observed meteorological variable on each quantile (0.01-0.99) is calculated, and the difference is removed from each quantile of the future GCMs output scene to obtain the future corrected GCMs climate prediction.
For example, the air temperature (wind speed, relative humidity, sunshine duration) is corrected as follows:
Tadj,d＝TGCM,d+(Tobs,Q-TGCM，ref,Q) (1)
the precipitation is corrected as follows:
Padj,d＝PGCM,d×(Pobs,Q/PGCM,ref,Q) (2)
in the formula, T and P represent air temperature (wind speed, relative humidity, sunshine duration) and precipitation, adj represents a corrected sequence, obs represents observation data, ref and fut represent a historical reference period and a future prediction period, respectively, d represents day data, and Q represents quantiles.
S3: the method comprises the steps of driving a pre-constructed basin hydrological model through a meteorological simulation series under M groups of climatic change scenes, and simulating to obtain a basin hydrological process under a future scene, wherein the basin hydrological process under the future scene comprises M groups of runoff long sequences of each sub-basin in a research area in a historical period and a future period.
In one embodiment, S3 specifically includes:
s3.1: calibrating and screening an optimal hydrological model as a basin hydrological model through actually measured meteorological and hydrological data;
s3.2: and inputting the obtained meteorological simulation series under the M groups of climatic change scenes into an optimal hydrological model, and simulating to obtain the watershed hydrological process under the future scene.
Wherein, S3.1 specifically includes: inputting the actually measured meteorological sequence into four hydrological models of Xinanjiang, GR4J, HMETS and HBV, using KGE efficiency coefficient as maximum target, defining each model by SCEUA method, selecting the model with the highest KGE efficiency coefficient as the optimal hydrological model,
Figure BDA0002589635080000071
wherein r represents the Pearson linear correlation coefficient of the simulated sequence and the measured sequence, α represents the ratio of the variance of the simulated sequence and the measured sequence, β represents the ratio of the mean of the simulated sequence and the measured sequence, and the KGE efficiency coefficient is in the range of (— infinity, 1), wherein when KGE is 1, the simulated sequence completely coincides with the measured sequence.
And selecting a model with the highest KGE efficiency coefficient, and representing the nonlinear relation of the drainage basin precipitation and the runoff.
S4: obtaining a standardized runoff index based on M groups of runoff length sequences of each sub-watershed in the research area in a historical period and a future period, and extracting a drought duration characteristic value and a drought intensity characteristic value corresponding to the M groups of runoff length sequences through a run theory.
And (3) calculating and obtaining M groups of Standardized Runoff Indexes (SRI) by using the Runoff length sequences of the M groups of the drainage basin obtained in the step (3), and extracting corresponding drought characteristic values (drought duration and drought intensity) by a run theory.
In one embodiment, S4 specifically includes:
s4.1: and calculating the normalized runoff index (SRI). And (3) calculating the standardized runoff index SRI by using the M groups of runoff length sequences of the sub-watersheds in the research area in the historical period and the future period, which are obtained in the step (3). In the historical period, firstly, fitting the runoff of each month through probability distribution:
Figure BDA0002589635080000081
wherein F (r) represents the cumulative probability distribution function of P-III distribution, and alpha, beta and omega are the shape, scale and position parameters of the P-III distribution respectively. Then, the historical period SRI index value can be obtained by the inverse normalization process:
SRI(r)＝Φ-1(F(r)) (5)
s4.2: and for a future time period, inputting the simulated monthly runoff into the P-III distribution determined by the historical reference period to obtain the cumulative distribution probability, and then carrying out reverse standardization on the obtained cumulative distribution probability to obtain the SRI index sequence of the future time period.
S4.3: by utilizing M groups of long sequences of the SRI indexes in the historical time period and the SRI index sequences in the future time period of the drainage basin, on the basis of the run-length theory, respectively extracting the drought duration and the drought intensity characteristic value of the M groups of long sequences of the SRI indexes in the historical time period and the drought duration and the drought intensity characteristic value of the M groups of SRI index sequences in the future time period.
Among them, the P-III (Pearson type III) distribution function is used in this example.
S5: establishing a watershed hydrothermal coupling equilibrium equation, calibrating characteristic parameters of the hydrothermal coupling equilibrium equation, and analyzing the correlation between the characteristic parameters and the standardized runoff index.
In one embodiment, S5 specifically includes:
s5.1: calculating potential evapotranspiration through a Peneman formula, and obtaining actual evapotranspiration of a drainage basin through a water volume balance equation; the Peneman formula is as follows:
Figure BDA0002589635080000091
in the formula: PET is latent evapotranspiration (mm/d); Δ represents the slope of the saturated water pressure curve (kPa/DEG C); rnNet radiation for the earth's surface; g is soil heat flux; gamma is a dry-wet table constant; t ismeanRepresents the daily average temperature; u. of2Two meters near-ground wind speed; e.g. of the typesRefers to the saturated water pressure; e.g. of the typeaThe actual water pressure is referred to;
s5.2: selecting a time window with certain time, calibrating an annual average hydrothermal coupling equilibrium equation characteristic parameter w by a least square method, analyzing the correlation between the parameter w and a drought index SRI sequence, and verifying the reliability of the parameter w as an drought sequence interpretation variable; the annual average hydrothermal coupling equilibrium equation is as follows:
Figure BDA0002589635080000092
in the formula, ET is the actual evapotranspiration to fully consider the energy balance and the moisture balance of the land-atmosphere system, and the parameter w is used to reflect the change of the underlying surface characteristics.
Specifically, the penman formula and the water balance equation are conventional methods, and the implementation principle thereof will not be described in detail here. The units and meanings of the parameters are as follows: PET is the possible evapotranspiration (mm/d); Δ represents the slope of the saturated water pressure curve (kPa/DEG C); rnNet surface radiation (MJ/(m d)); g is the soil heat flux (MJ/(m2 × d)); γ is the dry-wet table constant (kPa/. degree. C.); t ismeanRepresents the daily average temperature (. degree. C.); u. of22 meters high wind speed (m/s); e.g. of the typesSaturated water gas pressure (kPa); e.g. of the typeaRefers to the actual water gas pressure (kPa). In the formula (7), ET is actual evapotranspiration, and is obtained by adopting the difference value between the annual precipitation (P) and the annual runoff; the equation can fully consider the energy balance and the moisture balance of a land-atmosphere system, and the parameter w can better reflect the characteristic change of the underlying surface; the w value can be obtained by inputting PET, ET and P through the equation.
In particular, the present embodiment selects a time window of 11 years.
S6: based on a hydrothermal coupling equilibrium equation, and by adopting characteristic parameters in the hydrothermal coupling equilibrium equation as covariates, a time-varying edge distribution function and a joint probability distribution function under a non-uniformity condition are established.
Constructing a univariate probability distribution function of drought characteristics (drought duration and drought intensity) under a non-uniform condition by combining a water-heat coupling equilibrium equation and taking w in the equation as a covariate based on the drought characteristic series in the step 4; selecting a Gumbel-Hougard Copula (G-HCopula for short) function which is well fitted to a drought characteristic series related structure as a joint probability distribution function, and establishing the joint probability distribution function based on the Copula under the condition of non-uniformity by still adopting w as a covariate aiming at the non-uniformity of the drought duration and the drought intensity related structure.
In one embodiment, S6 specifically includes:
step S6.1: constructing a time-varying edge distribution function; representing the drought characteristic quantity by X, wherein the drought characteristic quantity comprises duration D and intensity S, and adopting a gamma distribution function as an edge distribution function of the drought duration and the intensity, wherein the probability density function of the gamma distribution function under the consistent condition is as follows:
Figure BDA0002589635080000101
wherein alpha and beta represent shape and scale parameters respectively.
In the time-varying parametric model, α and β are no longer constant values and vary from time period to time period with covariates. For the time-varying moment of the edge distribution function at the time t, a scale parameter α is assumedtShape parameter betatAll by way of explanation of variable wtIs expressed by a monotonic function of:
Figure BDA0002589635080000102
in the formula: g (-) represents a monotonic connecting function, the concrete form passes through a statistical parameter thetaXIs determined; when theta isX∈R,g(θX)＝θX(R characterizes the real number set) when θXWhen > 0, then g (theta)X)＝ln(θX)；wtRepresenting the value of the covariate at time t, alphai(i ═ 1, 2; 10,20) represents the parameters of the model. Then the probability density function of the gamma distribution under non-uniform conditions is:
Figure BDA0002589635080000103
s6.2: constructing a two-variable time-varying drought joint probability distribution function; for any scene under M groups of climatic scenes in the drainage basin, selecting a G-HCopula function as the duration of droughtAnd replacing the parameter theta of the Copula function with a time-varying parameter by using a combined probability distribution function of the drought intensity
Figure BDA0002589635080000104
Figure BDA0002589635080000105
Wherein,
Figure BDA0002589635080000106
for the Copula joint distribution function,
Figure BDA0002589635080000107
the range is (1, ∞); ut, vt are the duration D, intensity S edge distribution functions respectively,
Figure BDA0002589635080000108
based on the definition of Copula function, the non-uniform two-variable Copula function can be expressed as:
Figure BDA0002589635080000109
in the formula: ft(dt,st) A time-varying joint distribution function representing D and S;
Figure BDA0002589635080000111
and
Figure BDA0002589635080000112
representing the time-varying edge distribution function and the time-varying parameters of the D and S variables, respectively. Further, the parameters of the time-varying Copula function are expressed as covariates w:
Figure BDA00025896350800001111
in the formula: gc(. to) represents the join function of the copula function; when in use
Figure BDA0002589635080000113
When (for G-HCopula),
Figure BDA0002589635080000114
b0,b1respectively, the parameters of the model.
S7: and (4) according to the time-varying edge distribution function and the joint distribution function established in the S6, finding the most possible combination scene of the drought duration and the drought intensity in the given recurrence period, and taking the most possible combination scene as the result of disaster evaluation.
And (4) solving the most possible combination situation in a given recurrence period to evaluate the influence of climate change and underlying human activities on the future drought situation of the watershed.
In one embodiment, S7 specifically includes:
and (3) calculating the most possible combination scene of drought duration and drought intensity in a given recurrence period, and taking the OR recurrence period as a measurement index of the drought, wherein the measurement index is defined as:
Tor t(dt,st)＝1/[1-Ft(dt,st)] (14)
in the formula, Tor t(dt,st) A time-varying OR joint recurrence period, in units of years; the most probable combination pattern of duration and intensity of drought refers to the combination (d) of the greatest joint probability density function on the contour line during the recurrence period*(t),s*(t)), solving by constructing the following equation:
Figure BDA0002589635080000115
and in order to obtain a reasonable design value combination, selecting the most probable event of the drought event as the design value, namely the most probable combination mode, wherein the most probable combination mode specifically referring to the drought duration and the intensity refers to the combination with the maximum joint probability density function on the contour line of the recurrence period. f. oft(dt,st) A density function representing a time-varying joint distribution function of duration D and intensity S;
Figure BDA0002589635080000116
a density function representing a time-varying Copula joint distribution function;
Figure BDA0002589635080000117
and
Figure BDA0002589635080000118
respectively represent
Figure BDA0002589635080000119
And
Figure BDA00025896350800001110
is used as a density function of the edge distribution function.
Further, the most likely combination problem is solved by the lagrange multiplier method, and the following solving equation is constructed:
Figure BDA0002589635080000121
in the formula: lambda [ alpha ]tRepresenting the lagrange multiplier for the time state t. Function f of probability density to be madet(dt,st) Taking the maximum value, and letting the derivative be 0, the nonlinear equation for the most likely combination is obtained:
Figure BDA0002589635080000122
Figure BDA0002589635080000123
Figure BDA0002589635080000124
in the formula,
Figure BDA0002589635080000125
f′Dt(d) and f'St(s) are each independently
Figure BDA0002589635080000126
And
Figure BDA0002589635080000127
the derivative of (c). This equation can be solved by numerical methods (e.g., newton's method).
For a given OR recurrence period, respectively calculating the most possible combination situation of drought duration and drought intensity of M groups of research areas which change year by year, and then calculating the median of multi-model results, namely the long-period evolution process of the watershed hydrologic drought in the changing environment. And averaging the most probable combination scenes in the historical period and the future period respectively, and then taking the difference to further quantify the change of the future basin drought situation driven by hydrologic cycle variation.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (8)

1. A two-dimensional drought disaster assessment method driven by hydrologic cycle variation is characterized by comprising the following steps:
s1: acquiring basic meteorological hydrological data, wherein the meteorological hydrological data comprise M global climate mode simulation data, meteorological data and flow series of basin control hydrological stations;
s2: acquiring a weather simulation series under M groups of weather change scenes based on basic weather hydrological data and a quantile deviation correction method;
s3: driving a pre-constructed basin hydrological model through a meteorological simulation series under M groups of climatic change scenes, and simulating to obtain a basin hydrological process under a future scene, wherein the basin hydrological process under the future scene comprises M groups of runoff long sequences of each sub-basin in a research area in a historical period and a future period;
s4: obtaining standardized runoff indexes based on M groups of runoff length sequences of each sub-watershed in a historical period and a future period in a research area, and extracting drought duration characteristic values and drought intensity characteristic values corresponding to the M groups of runoff length sequences through a run theory;
s5: establishing a watershed hydrothermal coupling equilibrium equation, calibrating characteristic parameters of the hydrothermal coupling equilibrium equation, and analyzing the correlation between the characteristic parameters and a standardized runoff index;
s6: establishing a time-varying edge distribution function and a joint probability distribution function under a non-uniform condition based on a hydrothermal coupling equilibrium equation and by adopting characteristic parameters in the hydrothermal coupling equilibrium equation as covariates;
s7: and (4) according to the time-varying edge distribution function and the joint distribution function established in the S6, finding the most possible combination scene of the drought duration and the drought intensity in the given recurrence period, and taking the most possible combination scene as the result of disaster evaluation.
2. The disaster assessment method according to claim 1, wherein S2 specifically comprises:
and calculating the difference between the output variable of the global climate modes GCMs and the observed weather variable on each quantile, and removing the difference on each quantile of future scenes output by the global climate modes to obtain future corrected GCMs climate predictions, namely the weather simulation series under M groups of climate change scenes.
3. The disaster assessment method according to claim 1, wherein S3 specifically comprises:
s3.1: calibrating and screening an optimal hydrological model as a basin hydrological model through actually measured meteorological and hydrological data;
s3.2: and inputting the obtained meteorological simulation series under the M groups of climatic change scenes into an optimal hydrological model, and simulating to obtain the watershed hydrological process under the future scene.
4. The disaster assessment method according to claim 3, wherein S3.1 comprises in particular: inputting the actually measured meteorological sequence into four hydrological models of Xinanjiang, GR4J, HMETS and HBV, using KGE efficiency coefficient as maximum target, defining each model by SCEUA method, selecting the model with the highest KGE efficiency coefficient as the optimal hydrological model,
Figure FDA0003493250350000021
wherein r represents the Pearson linear correlation coefficient of the simulated sequence and the measured sequence, α represents the ratio of the variance of the simulated sequence and the measured sequence, β represents the ratio of the mean of the simulated sequence and the measured sequence, and the KGE efficiency coefficient is in the range of (— infinity, 1), wherein when KGE is 1, the simulated sequence completely coincides with the measured sequence.
5. The disaster assessment method according to claim 1, wherein S4 specifically comprises:
s4.1: in the historical period, each monthly runoff is first fitted by probability distribution:
Figure FDA0003493250350000022
in the formula, F (r) represents the cumulative probability distribution function of P-III distribution, alpha, beta and omega are the shape, scale and position parameters of the P-III distribution, and then the standardized runoff index in the historical time interval and the SRI index long sequence in the historical time interval are obtained through the inverse standardization process, wherein the standardized runoff index is the SRI index value: sri (r) ═ Φ-1(F(r))；
S4.2: for a future time period, inputting the simulated monthly runoff into P-III distribution determined by a historical reference period to obtain cumulative distribution probability, and then carrying out reverse standardization on the obtained cumulative distribution probability to obtain an SRI index sequence of the future time period;
s4.3: by utilizing M groups of long sequences of the SRI indexes in the historical time period and the SRI index sequences in the future time period of the drainage basin, on the basis of the run-length theory, respectively extracting the drought duration and the drought intensity characteristic value of the M groups of long sequences of the SRI indexes in the historical time period and the drought duration and the drought intensity characteristic value of the M groups of SRI index sequences in the future time period.
6. The disaster assessment method according to claim 1, wherein S5 specifically comprises:
s5.1: calculating potential evapotranspiration through a Peneman formula, and obtaining actual evapotranspiration of a drainage basin through a water volume balance equation; the Peneman formula is as follows:
Figure FDA0003493250350000023
in the formula: PET is potential evapotranspiration, in mm/d; Δ represents the slope of the saturated water pressure curve in units of kPa/DEG C; rnNet radiation for the earth's surface; g is soil heat flux; gamma is a dry-wet table constant; t ismeanRepresents the daily average temperature; u. of2Two meters near-ground wind speed; e.g. of the typesRefers to the saturated water pressure; e.g. of the typeaThe actual water pressure is referred to;
s5.2: selecting a time window with certain time, calibrating an annual average hydrothermal coupling equilibrium equation characteristic parameter w by a least square method, analyzing the correlation between the parameter w and a drought index SRI sequence, and verifying the reliability of the parameter w as an drought sequence interpretation variable; the annual average hydrothermal coupling equilibrium equation is as follows:
Figure FDA0003493250350000031
in the formula, ET is the actual evapotranspiration to fully consider the energy balance and the moisture balance of the land-atmosphere system, and the parameter w is used to reflect the change of the underlying surface characteristics.
7. The disaster assessment method according to claim 1, wherein S6 specifically comprises:
s6.1: constructing a time-varying edge distribution function; representing the drought characteristic quantity by X, wherein the drought characteristic quantity comprises duration D and intensity S, and adopting a gamma distribution function as an edge distribution function of the drought duration and the intensity, wherein the probability density function of the gamma distribution function under the consistent condition is as follows:
Figure FDA0003493250350000032
wherein alpha and beta respectively represent shape and scale parameters;
s6.2: constructing a two-variable time-varying drought joint probability distribution function; for any scene under the M groups of climatic scenes of the drainage basin, selecting a G-H Copula function as a joint probability distribution function of drought duration and drought intensity, and replacing a parameter theta of the Copula function by a time-varying parameter
Figure FDA0003493250350000033
Figure FDA0003493250350000034
Wherein,
Figure FDA0003493250350000035
for the Copula joint distribution function,
Figure FDA0003493250350000036
the range is (1, ∞); u. oft,vtRespectively, duration D and intensity S edge distribution functions,
Figure FDA0003493250350000037
8. the disaster assessment method according to claim 1, wherein S7 specifically comprises:
and (3) calculating the most possible combination scene of drought duration and drought intensity in a given recurrence period, and taking the OR recurrence period as a measurement index of the drought, wherein the measurement index is defined as: t isor t(dt，st)＝1/[1-Ft(dt，st)]；
In the formula, Tor t(dt，st) A time-varying OR joint recurrence period, in units of years; the most probable combination pattern of duration and intensity of drought refers to the combination (d) of the greatest joint probability density function on the contour line during the recurrence period*(t),s*(t)), solving by constructing the following equation:
Figure FDA0003493250350000038
wherein,
Figure FDA0003493250350000041
a time-varying edge distribution function representing the D and S variables,
Figure FDA0003493250350000042
the time-varying parameter is represented by,
Figure FDA0003493250350000043
a Copula joint distribution function is obtained; f. oft(dt,st) A density function representing a time-varying joint distribution function of duration D and intensity S;
Figure FDA0003493250350000044
a density function representing a time-varying Copula joint distribution function;
Figure FDA0003493250350000045
and
Figure FDA0003493250350000046
respectively represent
Figure FDA0003493250350000047
And
Figure FDA0003493250350000048
is used as a density function of the edge distribution function.
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