Calculation method of meteorological drought to hydrological drought propagation time based on exponential decay function

Abstract

The application discloses a meteorological drought to hydrological drought propagation time calculation method based on an exponential decay function, and particularly relates to the following steps: step 1, collecting measured precipitation data in a target basin; step 2, constructing a time equation required for meteorological drought to hydrological drought propagation based on an exponential decay response and a precipitation runoff data sequence; step 3, identifying meteorological drought and hydrological drought events in the target basin, extracting precipitation and runoff sequences corresponding to each drought event, and a complete meteorological-hydrological drought propagation event; and step 4, for any meteorological-hydrological drought propagation event, extracting runoff data, substituting the runoff data into the equation in step 2, and obtaining the time required for meteorological drought to hydrological drought propagation in the meteorological-hydrological drought propagation event. The application is suitable for drought propagation analysis under the conditions of basins in different climate regions, provides a scientific basis for comparison and risk assessment of drought characteristics between regions, and provides a quantitative reference for early drought warning.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hydrology and meteorology, and particularly relates to a meteorological drought to hydrological drought propagation time calculation method based on an exponential decay function. BACKGROUND

[0002] Drought is a complex natural disaster process, which usually includes different stages such as meteorological drought, agricultural drought, and hydrological drought. Among them, the propagation process from meteorological drought to hydrological drought is an important link in the formation and evolution of basin drought, and is of key significance to water resource regulation and drought risk management. However, existing researches mostly use statistical correlation analysis or empirical lag method to estimate drought propagation time, which is difficult to fully reflect the nonlinear relationship between the underlying surface conditions, runoff process and meteorological factors in the basin.

[0003] Traditional methods often only perform linear fitting based on the time lag between the standardized precipitation index (SPI) and the standardized runoff index (SRI), without considering the attenuation characteristics of meteorological drought signals in the hydrological response of the basin, resulting in large uncertainty in the estimation results of the propagation time. In addition, the climate characteristics, soil hydrological conditions and vegetation coverage in different regions have a significant impact on the transmission rate of drought signals, and the existing methods lack a unified calculation framework, making it difficult to realize the quantification and comparability analysis of drought propagation.

[0004] Therefore, there is an urgent need for a calculation method that can reflect the attenuation law of meteorological drought signals in the hydrological system of the basin, so as to more accurately identify the propagation process and propagation time of meteorological drought to hydrological drought, and provide a scientific basis for regional drought warning and water resource management. SUMMARY

[0005] The application provides a meteorological drought to hydrological drought propagation time calculation method based on an exponential decay function.

[0006] Technical scheme: The meteorological drought to hydrological drought propagation time calculation method based on an exponential decay function, specifically comprises the following steps:

[0007] Step 1: Collect the measured precipitation data in the target basin, calculate the target basin surface precipitation, and form a continuous precipitation runoff data sequence of the target basin;

[0008] Step 2: Based on the exponential decay response and the continuous precipitation runoff data sequence, a time required for the propagation of meteorological drought to hydrological drought is constructed Equation;

[0009] Step 3: Identify the meteorological drought and hydrological drought events in the target basin, extract the precipitation and runoff sequences corresponding to each drought event, and the complete meteorological-hydrological drought propagation event;

[0010] Step 4: Extracting runoff data for any one meteorological-hydrological drought propagation event, substituting into the equation in Step 2 to obtain the time required for meteorological drought to hydrological drought propagation in the meteorological-hydrological drought propagation event .

[0011] Further, Step 1 further comprises pre-processing the collected data, specifically: interpolating and removing missing values and outliers in the data sequence respectively.

[0012] Further, the Thiessen polygon method is used to calculate the target basin precipitation in Step 1.

[0013] Further, Step 2 is specifically:

[0014] Step 2.1: Calculate the initial runoff brought by single precipitation at time t :

[0015] ;

[0016] Wherein, a, b are empirical parameters, represents the precipitation at time t;

[0017] Step 2.3: Based on the initial runoff and exponential decay kernel function, calculate the runoff generated by the pulse at time :

[0018] ;

[0019] Wherein, is the exponential decay kernel function, the expression is:

[0020] ;

[0021] Wherein, is the decay time, e is the natural constant, is the decay coefficient of runoff;

[0022] Step 2.4: Based on the runoff generated by the pulse at time in Step 2.3, construct the time equation required for meteorological drought to hydrological drought propagation :

[0023] ;

[0024] Wherein, is the runoff when hydrological drought is reached, is the initial runoff.

[0025] Further, the method further comprises: calculating the time ​Decay coefficient of runoff in the equation Solving; in particular:

[0026] According to step 2.3, the runoff equation under the discrete time sequence is established:

[0027] ;

[0028] Wherein, is the fitting residual; n is the maximum decay time;

[0029] The parameters a and b in the runoff equation under the discrete time sequence and the decay coefficient are fitted by using the nonlinear least squares method, and the objective function is:

[0030] ;

[0031] The simulated runoff sequence after fitting the parameters is evaluated.

[0032] Further, for any meteorological-hydrological drought propagation event, the initial runoff is the instantaneous flow at the beginning of the drought event or the average value of the previous several months; is the minimum value of the runoff during the meteorological-hydrological drought propagation event.

[0033] Further, the step 3 is specifically:

[0034] Calculate the standardized precipitation index SPI;

[0035] Calculate the standardized runoff index SRI;

[0036] Identify drought events: set the starting threshold x of meteorological drought events and the starting threshold y of hydrological drought events, and take the first time when SPI falls below x to the time when SPI and SRI both recover to the corresponding starting threshold as a complete meteorological-hydrological drought propagation event.

[0037] Further, the standardized precipitation index SPI is calculated, specifically: for the monthly precipitation data of the target basin, the gamma distribution is used for fitting to generate the probability density function; select several month time scales, and convert the precipitation into dimensionless SPI values conforming to the standard normal distribution through probability integration;

[0038] Calculate the standardized runoff index, specifically: for the monthly runoff data of the target basin, based on the gamma distribution, select several month time scales to standardize the runoff into SRI values.

[0039] A computer device comprises a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the steps of the meteorological drought to hydrological drought propagation time calculation method based on the exponential decay function when executing the computer program.

[0040] A computer readable storage medium for storing a program, wherein the program is executed to implement the steps of the meteorological drought to hydrological drought propagation time calculation method based on the exponential decay function.

[0041] Advantages:

[0042] 1. The present application introduces a decay function model to describe the attenuation process of meteorological drought signals in the hydrological system of a basin, establishes a dynamic response relationship between meteorological drought and hydrological drought, and realizes the quantitative calculation of drought propagation time. It can depict the step-by-step attenuation characteristics of meteorological drought signals in the precipitation-soil-runoff system, and significantly improve the physical rationality of the propagation time estimation.

[0043] 2. The present application provides a unified calculation framework that can be applied to drought propagation analysis under different climate zones and basin conditions, provides a scientific basis for drought characteristic comparison and risk assessment between regions, and provides a quantitative reference for early drought warning. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a flowchart of the present application;

[0045] Figure 2 is a graph of the time-varying trend of the exponential decay kernel function, wherein figure (a) is a graph of the time-varying trend of the exponential decay kernel function in the Yellow River source area, and figure (b) is a graph of the time-varying trend of the exponential decay kernel function in the Yangtze River source area;

[0046] Figure 3 is a simulation accuracy graph of the rainfall-runoff empirical formula, wherein figure (a) is a comparison graph of measured and simulated values in the Yellow River source area using the method of the present application; and figure (b) is a comparison graph of measured and simulated values in the Yangtze River source area using the method of the present application;

[0047] Figure 4 is a histogram and probability distribution function (PDF) graph of meteorological to hydrological drought propagation time , wherein figure (a) is a histogram and probability distribution function graph of meteorological to hydrological drought propagation time in the Yellow River source area using the method of the present application; and figure (b) is a histogram and probability distribution function graph of meteorological to hydrological drought propagation time in the Yangtze River source area using the method of the present application. DETAILED DESCRIPTION

[0048] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application illustrate embodiments of the application and to explain them without imposing on the application undue limitations.

[0049] The present application aims to provide a meteorological drought to hydrological drought propagation time calculation method based on exponential decay function, by constructing the decay function relationship between precipitation and runoff, establishing the quantitative identification and analysis process of drought propagation process, realizing the scientific estimation of meteorological drought to hydrological drought propagation time, so as to solve the problem of imperfect drought propagation mechanism description and insufficient propagation time identification precision in the prior art.

[0050] As shown in Figure 1 , the method of the present application comprises the following steps:

[0051] Step S1: data collection and compilation. Collect long series of monthly scale measured precipitation and cross section runoff data in the target basin, and interpolate and remove the missing values and abnormal values in the data sequence respectively.

[0052] The precipitation and runoff data required by the present embodiment should have continuity and consistency; for precipitation data, the target basin rainfall is calculated by using the Thiessen polygon method, and the continuous rainfall runoff data sequence of the target basin is formed.

[0053] Step S2: formula parameter fitting. Based on the quality controlled measured precipitation and runoff data, the parameters in the formula based on exponential decay response and empirical precipitation-runoff relationship are estimated and fitted by using nonlinear least squares method, and the fitting quality is evaluated.

[0054] Step S2.1: the meteorological drought to hydrological drought propagation time calculation method is as follows:

[0055] For the initial runoff brought by single precipitation p at time t , it is assumed that the precipitation pulse generates the initial runoff in the unit time scale according to the empirical relationship:

[0056] (1)

[0057] Where a, b > 0 are empirical parameters, which are obtained by fitting the observation data.

[0058] For subsequent time, the runoff generated by each pulse is attenuated in the form of an exponential decay kernel function:

[0059] (2)

[0060] (3)

[0061] where e is a natural constant; is the decay coefficient of runoff, is the exponential decay kernel function, indicating that the total runoff of the basin is a linear superposition of the contributions of historical precipitation pulses.

[0062] The above relationships are combined to obtain the runoff expression under the discrete time series:

[0063] (4)

[0064] where is the fitting residual, reflecting the uncertainty of precipitation input and the influence of other water sources (such as snowmelt, groundwater) on runoff; n is the maximum decay time, set to 1 year for short-term drought propagation time, i.e. n = 11 months.

[0065] Based on equations (2) and (3), the time required for meteorological drought to hydrological drought propagation can be derived as :

[0066] (5)

[0067] where is the runoff when hydrological drought is reached, is the initial runoff.

[0068] Step S2.2: Based on the measured precipitation and runoff data, the parameters a and b in equation (4) and the decay coefficient are fitted using the nonlinear least squares method, and the objective function is to minimize the sum of squared residuals:

[0069] (6)

[0070] Step S2.3: The Nash efficiency coefficient (NSE) is used to evaluate the runoff sequence simulated after parameter fitting, to verify the applicability and accuracy of the model.

[0071] Step S3: Drought event identification. Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI) are used to identify meteorological drought and hydrological drought events in the basin, and the corresponding precipitation and runoff sequences of each drought event, as well as the start and end time range of the event, are extracted.

[0072] Step S3.1: Calculate the Standardized Precipitation Index (SPI). For the monthly precipitation data of the study area, the gamma distribution is used for fitting to generate the probability density function; select a 3-month time scale, and convert the precipitation to dimensionless SPI values that conform to the standard normal distribution through probability integration.

[0073] Step S3.2: Calculate the standardized runoff index (SRI). Based on the gamma distribution assumption, the monthly runoff data of the study area is standardized to SRI values by selecting a 3-month time scale.

[0074] Step S3.3: Identify drought events. Set the SPI value below -0.5 as the starting condition for meteorological drought events, and the SRI value below -0.5 as the starting condition for hydrological drought events. Considering that meteorological drought usually occurs earlier than hydrological drought, i.e., there is a propagation time lag, a complete meteorological-hydrological drought propagation event is defined as: from the first time SPI falls below -0.5 (meteorological drought begins) to the time when both SPI and SRI recover to above -0.5 (drought ends).

[0075] Step S4: Drought propagation time calculation. According to the precipitation and runoff data within the time range of the extracted meteorological drought to hydrological drought propagation event, the lag time index of meteorological drought to hydrological drought propagation is calculated, and the uncertainty of the result is analyzed.

[0076] Step S4.1: Based on the selected complete meteorological-hydrological drought propagation event, determine the drought runoff and the initial runoff : where the initial runoff takes the instantaneous flow at the beginning of the drought propagation event or the average value of the previous month; the drought runoff takes the minimum value of the runoff during the meteorological to hydrological drought propagation process; then use formula (5) to calculate of each complete meteorological-hydrological drought propagation event.

[0077] Step S4.2: Calculate the average, median, and confidence interval information of all propagation events .

[0078] In one embodiment of the present application, the Yangtze River source area and the Yellow River source area are taken as research cases, specifically:

[0079] Step S1: Collect the measured precipitation data of the target basin. Among them, 13 stations in the Yellow River source area obtained monthly precipitation data from 1961 to 2020; 18 stations in the Yangtze River source area obtained monthly precipitation data from 1961 to 2016. At the same time, the monthly runoff data of Tangnaihe hydrological station at the outlet section of the Yellow River source area from 1961 to 2020, and the monthly runoff data of Zhi Men Da hydrological station at the outlet section of the Yangtze River source area from 1961 to 2016 are collected. The basin rainfall is calculated by using the Thiessen polygon method, and the runoff sequence is subjected to data quality control, and finally a continuous and consistent precipitation-runoff data sequence is constructed.

[0080] Step S2: Based on the quality-controlled measured precipitation and runoff data, the three empirical parameters a, b and a in equation (4) are estimated and fitted by using the nonlinear least squares method, and the fitting target is to minimize the sum of squares of residuals. The parameter fitting results of the two study areas are shown in Table 1, and the variation trend of the exponential decay kernel function with time is shown in Figure 2 The simulation results of the empirical formula of precipitation-runoff after the determination of the empirical parameters are evaluated by using the Nash efficiency coefficient (NSE), and the simulation results are shown in Figure 3 The NSE of the simulated runoff in the Yellow River source area is 0.81, and that in the Yangtze River source area is 0.88.

[0081] Table 1

[0082]

[0083] Step S3: Based on the quality-controlled areal precipitation data, the standardized precipitation index (SPI) is calculated. First, the gamma distribution is used to fit the data to generate the probability density function; select a 3-month time scale, and convert the precipitation to dimensionless standard normal distribution variables (i.e. SPI values) by probability integration. Similarly, assuming that the runoff follows the gamma distribution, the monthly runoff data is converted to standardized runoff index (SRI) values by selecting the same time scale. The SPI value below -0.5 is regarded as the beginning of meteorological drought event, and the SRI value below -0.5 is regarded as the beginning of hydrological drought event. Considering that meteorological drought usually occurs earlier than hydrological drought, i.e. there is a time lag in drought propagation, a complete meteorological-hydrological drought propagation event is defined as: from the first time SPI falls below -0.5 (the beginning of meteorological drought) to the time when both SPI and SRI recover to above -0.5 (the end of drought). The identification results of meteorological-hydrological drought events in the Yellow River source area are shown in Table 2, and the identification results of meteorological-hydrological drought events in the Yangtze River source area are shown in Table 3. A total of 60 meteorological-hydrological drought propagation events are identified in the Yellow River source area from 1961 to 2020, most of which start in December of each year to January of the next year, and most of which start in January to February. The average duration is 4.5 months, and the multi-year average cumulative intensity of SPI and SRI is 2.83 and 2.27 respectively. A total of 56 propagation events are identified in the Yangtze River source area from 1961 to 2016, most of which start in December to January of the next year, and most of which start in January to February. The average duration is 5 months, and the multi-year average cumulative intensity of SPI and SRI is 2.71 and 2.19 respectively.

[0084] Table 2

[0085]

[0086] Table 3

[0087]

[0088] Step S4: Calculate the propagation time of each event based on all the identified meteorological-hydrological drought propagation events Firstly, the drought runoff and the initial runoff in formula (5) need to be determined. The initial runoff is the instantaneous runoff or the average value of the previous month at the beginning of the drought propagation event (SPI <-0.5); the drought runoff is the minimum value of the runoff during the meteorological-hydrological drought propagation process. The statistical results of and in each event are shown in Table 4: the average drought runoff of all events in the Yellow River source region is 172.44 m 3 / s, and the average initial runoff is 318.52 m 3 / s; the average drought runoff of all events in the Yangtze River source region is 66.32 m 3 / s, and the average initial runoff is 145.86 m 3 / s.

[0089] Table 4

[0090]

[0091] In this embodiment, formula (5) is used to calculate the of all meteorological-hydrological drought propagation events, and the statistical results are shown in Table 5: the average value of the propagation time in the Yellow River source region is 0.84 months, and the median is 0.95 months; the average value of the propagation time in the Yangtze River source region is 0.73 months, and the median is 0.79 months. The histogram and probability distribution function (PDF) of the propagation time in the two basins of the study area are shown in Figure 4 .

[0092] Table 5

[0093]

[0094] In addition, it should be noted that each specific technical feature described in the above specific embodiments can be combined in any appropriate manner without contradiction. In order to avoid unnecessary repetition, the present application will not describe various possible combinations again.

Claims

1. A method for calculating the propagation time from meteorological drought to hydrological drought based on an exponential decay function, characterized in that, Specifically, Step 1: Collecting the precipitation data of the target basin, calculating the areal precipitation of the target basin, and forming the continuous precipitation runoff data sequence of the target basin; Step 2: Constructing the time needed for the propagation of meteorological drought to hydrological drought based on the exponential decay response and the continuous precipitation runoff data series Equation; Step 3: Identifying meteorological drought and hydrological drought events in the target basin, extracting the precipitation and runoff sequences corresponding to each drought event, and the complete meteorological-hydrological drought propagation event; Step 4: For any one meteorological-hydrological drought propagation event, extract the runoff data, substitute into the equation in Step 2, and obtain the time required for the meteorological drought to hydrological drought propagation in the meteorological-hydrological drought propagation event ; Step 2 is specifically: Step 2.1: Calculate the initial runoff from a single precipitation event at time t : ； wherein a, b are empirical parameters, represents the precipitation at time t; Step 2.3: Calculate the pulse of runoff based on the initial runoff and the exponential decay kernel function Runoff pulse generated at time t : ； wherein is an exponential decay kernel function, expressed as: ； wherein, is the decay time, e is the natural constant, is the decay coefficient for the runoff; Step 2.4: Based on step 2.3 The time required for the propagation of meteorological drought to hydrological drought is constructed based on the pulse of runoff at the moment Equation: ； wherein, to achieve the runoff at hydrological drought, is the initial runoff.

2. The method for calculating the meteorological drought to hydrological drought propagation time based on the exponential decay function according to claim 1, characterized in that, Step 1 also includes preprocessing the collected data, specifically: interpolating and removing missing values and outliers in the data sequence.

3. The method for calculating the meteorological drought to hydrological drought propagation time based on the exponential decay function according to claim 1, characterized in that, In step 1, the Thiessen polygon method is used to calculate the areal precipitation of the target basin.

4. The method for calculating the meteorological drought to hydrological drought propagation time based on the exponential decay function according to claim 1, characterized in that, The method also includes solving for time The decay coefficient of the runoff in the equation is solved; specifically: According to step 2.3, the runoff equation under discrete time sequence is established: ； wherein, is the fitting residual; n is the maximum decay time; The parameters a, b, and attenuation coefficient in the runoff equation for discrete time series are analyzed using the nonlinear least squares method. To perform the fitting, the objective function is: ； The simulated runoff sequence after parameter fitting is evaluated.

5. The method for calculating the propagation time from meteorological drought to hydrological drought based on an exponential decay function according to claim 1, characterized in that, For any meteorological-hydrological drought propagation event, the initial runoff the instantaneous flow at the beginning of the drought event or the average value of the previous months; is the minimum value of the runoff during the meteorological-hydrological drought propagation event.

6. The exponential-decay-function-based weather drought-to-hydrologic drought travel time calculation method of claim 1, wherein, The step 3 is specifically: Calculate the standardized precipitation index SPI; Calculate the standardized runoff index SRI; Identify drought events: Set the starting threshold x of meteorological drought events and the starting threshold y of hydrological drought events, and take the first time SPI falls below x to SPI and SRI both recover to the corresponding starting threshold as a complete meteorological-hydrological drought propagation event.

7. The method for calculating the meteorological drought to hydrological drought propagation time based on the exponential decay function according to claim 6, characterized in that, Calculate the standardized precipitation index SPI, specifically: For the monthly precipitation data of the target basin, use the gamma distribution to fit and generate the probability density function; select several monthly time scales, and convert the precipitation into dimensionless SPI values conforming to the standard normal distribution through probability integration; Calculate the standardized runoff index, specifically: For the monthly runoff data of the target basin, based on the gamma distribution, select several monthly time scales to standardize the runoff into SRI values.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The processor executes the computer program to implement the steps of the meteorological drought to hydrological drought propagation time calculation method based on the exponential decay function according to any one of claims 1-7.

9. A computer readable storage medium for storing a program, characterized in that, The program is executed to implement the steps of the meteorological drought to hydrological drought propagation time calculation method based on the exponential decay function according to any one of claims 1-7.

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