Runoff attribution method based on hydrological water and heat coupling budyko framework

Abstract

The application discloses a runoff attribution method based on a catchment water-heat coupling Budyko framework, and specifically comprises the following steps: firstly, collecting yearly runoff data of a control hydrological station of a research catchment, catchment area data and daily meteorological data of internal and surrounding meteorological stations of the catchment in a research period; calculating multi-year average runoff, multi-year average surface precipitation, multi-year average surface potential evapotranspiration and parameter values of the catchment water-heat coupling Budyko framework under multi-year average conditions; calculating multi-year average runoff, multi-year average surface precipitation, multi-year average surface potential evapotranspiration and parameter values of the catchment water-heat coupling Budyko framework of each sliding window, and determining a reference period and a change period; attributing runoff change, solving elastic coefficients of runoff to different factors influencing the runoff; and calculating runoff change attribution contribution rates of each sliding window in the change period relative to the reference period.

Description

Technical Field

[0001] This invention belongs to the field of watershed hydrothermal coupling analysis technology, and relates to a runoff attribution method based on the Budyko framework of watershed hydrothermal coupling. Background Technology

[0002] Water resources, as a vital resource essential for the survival of all life on Earth, play an irreplaceable role. Precipitation, runoff, and evaporation are all important forms of water resources, and the hydrological cycle has undergone significant changes against the backdrop of current global change. There are two main reasons for these changes: climate change and changes in the underlying surface caused by human activities. Therefore, quantitative research on the impacts of climate change (such as precipitation and evaporation) and underlying surface changes on runoff is of great significance.

[0003] Methods for runoff attribution analysis mainly include the double cumulative curve method, the distributed hydrological model method, and the Budyko framework-based method. The double cumulative curve method is computationally simple but overly subjective and lacks physical meaning; the distributed hydrological model method has clear physical meaning but is computationally overly complex; the Budyko framework-based method, compared to the previous two methods, has certain physical meaning and is relatively simple to calculate. Many existing methods based on the Budyko framework exist, but the physical meaning of most formulas is not very clear. There is a need to establish a watershed hydrothermal coupling Budyko framework that is convenient to use, structurally simple, and has clear physical meaning, in order to analyze the causes of runoff variation. Therefore, proposing a runoff attribution method based on a watershed hydrothermal coupling Budyko framework is of great significance. Summary of the Invention

[0004] The purpose of this invention is to provide a runoff attribution method based on the watershed hydrothermal coupling Budyko framework. This method can simply and efficiently calculate the quantitative attribution contribution rate of watershed runoff changes.

[0005] The technical solution adopted in this invention is a runoff attribution method based on the Budyko framework of watershed hydrothermal coupling, which specifically includes the following steps:

[0006] Step 1: Determine the study basin and study period, and collect annual runoff data and basin area data controlled by the hydrological stations in the study basin during the study period; collect daily meteorological data from meteorological stations inside and around the study basin during the study period.

[0007] Step 2: Using the annual runoff data from the control hydrological stations in the study basin collected in Step 1 during the study period, calculate the multi-year average runoff; using the daily meteorological data from meteorological stations inside and around the study basin collected in Step 1 during the study period, calculate the annual areal precipitation and potential evapotranspiration of the basin, as well as the multi-year average areal precipitation and multi-year average potential evapotranspiration.

[0008] Step 3: Using the sliding window method, process the annual areal precipitation and potential evapotranspiration calculated in Step 2 and the annual runoff collected in Step 1 to obtain the multi-year average runoff, multi-year average areal precipitation and multi-year average potential evapotranspiration for each sliding window, and determine the base period and the period of change.

[0009] Step 4: Construct the watershed hydrothermal coupling Budyko framework. Utilize the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in Step 2, and combine this with the least squares method to calculate the parameter values ​​of the multi-year average watershed hydrothermal coupling Budyko framework. Simultaneously, use the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window calculated in Step 3 to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window.

[0010] Step 5: Attribute the runoff variation under the watershed hydrothermal coupling Budyko framework constructed in Step 4. Using the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2 and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, solve the elasticity coefficient of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework.

[0011] Step 6: Using the elasticity coefficients calculated in Step 5, the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, and combined with the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 3 for each sliding window, calculate the runoff change attribution contribution rate of each sliding window relative to the baseline period during the change period.

[0012] The invention is further characterized by:

[0013] The specific process of step 2 is as follows:

[0014] Step 2.1: Using the annual runoff data and watershed area data controlled by the hydrological stations during the study period collected in Step 1, the multi-year average runoff is calculated. The specific calculation formula is as follows:

[0015]

[0016] In the formula, R is the multi-year average runoff, in mm. i Let m be the runoff in year i. 3n represents the length of the study period in years; F represents the catchment area controlled by the hydrological station, in km². 2 ;

[0017] Step 2.2: Using the daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, calculate the daily potential evapotranspiration for each meteorological station according to the Penman-Monteith formula, and sum them to obtain the annual potential evapotranspiration for each meteorological station. Finally, calculate the annual areal potential evapotranspiration of the study basin during the study period using the arithmetic mean method, and then calculate the multi-year average areal potential evapotranspiration. The specific calculation formula is as follows:

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, ET 0,i,j,k The potential evapotranspiration of the k-th weather station on the j-th day of the i-th year, mm / d; Δ i,j,k Let be the slope of the saturated water vapor pressure curve at the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;R n,i,j,k The net radiation of the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 G i,j,k Let be the soil heat flux density at the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 ;γ i,j,k Let be the wet / dry constant of the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;T i,j,k Let e ​​be the average temperature at the k-th meteorological station on the j-th day of the i-th year, in °C; s,i,j,k Let e ​​be the saturated water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; a,i,j,k The actual water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; u 2,i,j,k Let ET be the average wind speed at 2m on day j of year i at the k-th weather station, in m / s; 0,i,k The potential evapotranspiration of the k-th weather station in year i, mm; m i E represents the number of days in the i-th year. 0,i The potential evapotranspiration of the watershed in year i is in mm; The average potential evapotranspiration over many years is measured in mm; l represents the number of meteorological stations within and around the study basin.

[0023] Step 2.3: Using the daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, calculate the annual areal precipitation and the multi-year average areal precipitation of the basin. The specific calculation formula is as follows:

[0024]

[0025]

[0026]

[0027] In the formula: P i Let be the areal precipitation in year i, in mm; The average annual precipitation over many years, in mm; pre i,k Let be the precipitation at the k-th meteorological station in the i-th year, in mm; i,j,k Let be the precipitation at the k-th meteorological station on the j-th day of the i-th year, in mm;

[0028] The specific process of step 3 is as follows:

[0029] Step 3.1: Determine the length of the sliding window using the sliding window method. Then, perform a sliding average calculation on the annual areal precipitation and potential evapotranspiration calculated in Step 2, and the annual runoff collected in Step 1. This yields the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window. The specific calculation formulas are as follows:

[0030]

[0031]

[0032]

[0033] In the formula: P c,g Let the isal precipitation in year g of the c-th sliding window be in mm; R represents the multi-year average areal precipitation for the c-th sliding window, in mm. c,g Let the runoff in the c-th sliding window in the g-th year be mm; E represents the multi-year average runoff volume for the c-th sliding window, in mm. 0,c,g The potential evapotranspiration of the c-th sliding window in the g-th year is in mm. Let be the multi-year average surface potential evapotranspiration of the c-th sliding window, in mm; h be the length of the sliding window.

[0034] Step 3.2: Determine the first sliding window as the baseline period, and each of the remaining sliding windows as a change period.

[0035] The specific process of step 4 is as follows:

[0036] Step 4.1: Construct the watershed hydrothermal coupling Budyko framework. In this framework, the parameter v represents the coefficient of the distribution ratio among actual evapotranspiration, precipitation, and runoff, which can clearly reflect the relationship between various physical variables. The specific formula is as follows:

[0037]

[0038] Where: R is the runoff under multi-year average conditions, mm; E0 is the potential evapotranspiration of the watershed under multi-year average conditions, mm; P is the watershed precipitation under multi-year average conditions, mm; v is the parameter of the watershed hydrothermal coupling Budyko framework.

[0039] Step 4.2: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in Step 2 into the Budyko framework formula (12) for watershed hydrothermal coupling, and calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework using the least squares method. The specific formula for the least squares method is as follows:

[0040]

[0041] Where: R is the runoff under the multi-year average conditions calculated using formula (12), in mm; The multi-year average runoff volume calculated in step 2 is in mm;

[0042] Step 4.3: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration of each sliding window obtained in Step 3 into the watershed hydrothermal coupling Budyko framework formula (12), and use the least squares method to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window. The specific formula for the least squares method is as follows:

[0043]

[0044] In the formula: R c The runoff volume (in mm) is the multi-year average runoff volume under the c-th sliding window condition calculated using formula (12); Let v be the multi-year average runoff of the c-th sliding window, in mm. c For the parameter values ​​of the Budyko framework for watershed hydrothermal coupling in the c-th sliding window;

[0045] The specific process of step 5 is as follows:

[0046] Step 5.1, based on the watershed hydrothermal coupling Budyko framework, the factors determining the runoff variation are: precipitation, potential evapotranspiration and parameters;

[0047] Step 5.2: Utilize the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the parameters of the multi-year average watershed hydrothermal coupling Budyko framework calculated in Step 4. The elasticity coefficients of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework are solved, and the specific formulas are as follows:

[0048]

[0049]

[0050]

[0051] In the formula, ε P This is the elasticity coefficient of runoff to precipitation; ε is the elastic coefficient of runoff with respect to potential evapotranspiration; v The elastic coefficients of runoff on the parameters of the watershed hydrothermal coupling Budyko framework; This is the partial derivative of runoff with respect to precipitation; This is the partial derivative of runoff with respect to potential evapotranspiration; This represents the partial derivative of runoff with respect to the parameters of the watershed hydrothermal coupling Budyko framework.

[0052] The specific process of step 6 is as follows:

[0053] Step 6.1: Using the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 3 for each sliding window, calculate the changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​for each sliding window relative to the baseline period during the change period. The specific formulas are as follows:

[0054]

[0055]

[0056]

[0057]

[0058] In the formula, The multi-year average runoff of the first sliding window, i.e., the multi-year average runoff of the base period, in mm; Let be the multi-year average runoff of the c-th sliding window, in mm; ΔR c Let be the change in the multi-year average runoff volume of the c-th sliding window relative to the base period, in mm; The average annual precipitation for the first sliding window, in mm; Let ΔP be the multi-year average isal precipitation for the c-th sliding window, in mm; c Let be the change in the multi-year average isothermal precipitation for the c-th sliding window relative to the baseline period, in mm; The multi-year average surface potential evapotranspiration for the first sliding window, in mm; The multi-year average surface potential evapotranspiration for the c-th sliding window, mm; ΔE 0,c Let be the change in potential surface evapotranspiration of the c-th sliding window relative to the base period over many years, in mm; The parameters for the watershed hydrothermal coupling Budyko framework in the first sliding window; The parameters of the watershed hydrothermal coupling Budyko framework for the c-th sliding window; Δv c The change in the watershed hydrothermal coupling Budyko framework parameters for the c-th sliding window relative to the baseline period is denoted as .

[0059] Step 6.2: Using the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, as well as the multi-year average runoff change, multi-year average areal precipitation change, multi-year average potential evapotranspiration change, and watershed hydrothermal coupling Budyko framework parameter value changes for each sliding window of the change period relative to the base period calculated in Step 6.1, calculate the attribution contribution rate of runoff change for each sliding window of the change period relative to the base period. The specific formula is as follows:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] In the formula, ΔR P,c Let be the change in runoff caused by precipitation during the c-th sliding window, in mm; ΔR represents the change in runoff caused by potential evapotranspiration during the c-th sliding window, in mm. v,c ΔR represents the runoff variation caused by the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed, in mm.c 'The sum of runoff changes caused by the three influencing factors in the c-th sliding window, in mm; Con P,c The contribution rate of precipitation change to runoff change in the c-th sliding window; Let Con be the contribution rate of the potential evapotranspiration change in the c-th sliding window to the runoff change; v,c The contribution rate of the variation of the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed to the runoff variation;

[0068] The beneficial effects of this invention are that the runoff attribution method based on the watershed hydrothermal coupling Budyko framework provided by this invention has a simple calculation process, reasonable calculation results, and comprehensively considers the main factors affecting watershed runoff changes. Starting from the principle of watershed hydrothermal coupling changes, it has a certain physical mechanism and can provide scientific support for watershed ecological environment protection and the formulation of hydrological and water resources planning. Attached Figure Description

[0069] Figure 1 This is a flowchart of the runoff attribution method based on the watershed hydrothermal coupling Budyko framework of the present invention;

[0070] Figure 2 This is a schematic diagram showing the results of precipitation, potential evapotranspiration, and runoff at the Jinghe Zhangjiashan hydrological station in each sliding window of the watershed, based on the runoff attribution method of the watershed hydrothermal coupling Budyko framework in this invention.

[0071] Figure 3 This is a schematic diagram showing the parameter values ​​of the Budyko framework for each sliding window of the watershed ...

[0072] Figure 4 This is a schematic diagram showing the results of the sum of the runoff change in each sliding window of the control basin at Zhangjiashan Hydrological Station of the Jinghe River and the runoff change caused by three influencing factors in the runoff attribution method based on the watershed hydrothermal coupling Budyko framework of the present invention.

[0073] Figure 5 This is a schematic diagram showing the attribution contribution rate of runoff changes under the Budyko framework for each sliding window of the control basin of the Jinghe Zhangjiashan hydrological station in the embodiment of the runoff attribution method based on the watershed hydrothermal coupling of the present invention. Detailed Implementation

[0074] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0075] This invention relates to a runoff attribution method based on the watershed hydrothermal coupling Budyko framework, which specifically includes the following steps:

[0076] Step 1: Determine the study basin and study period, and collect annual runoff data from the hydrological stations controlling the study basin during the study period; collect daily meteorological data from meteorological stations within and around the study basin, and data on the basin area controlled by the hydrological stations during the study period.

[0077] Step 2: Using the annual runoff data from the control hydrological stations in the study area collected in Step 1, the multi-year average runoff is calculated. The specific calculation formula is as follows:

[0078]

[0079] In the formula, R is the multi-year average runoff, in mm. i Let m be the runoff in year i. 3 n represents the length of the study period in years; F represents the catchment area controlled by the hydrological station, in km². 2 ;

[0080] Using daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, the daily potential evapotranspiration of each meteorological station was calculated according to the Penman-Monteith formula. The annual potential evapotranspiration of each meteorological station was then summed. Finally, the annual areal potential evapotranspiration of the study basin during the study period was calculated using the arithmetic mean method. Next, the multi-year average areal potential evapotranspiration was calculated. The specific calculation formula is as follows:

[0081]

[0082]

[0083]

[0084]

[0085] Where: ET 0,i,j,k The potential evapotranspiration of the k-th weather station on the j-th day of the i-th year, mm / d; Δ i,j,k Let be the slope of the saturated water vapor pressure curve at the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;R n,i,j,k The net radiation of the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 G i,j,k Let be the soil heat flux density at the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 ;γ i,j,k Let be the wet / dry constant of the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;Ti,j,k Let e ​​be the average temperature at the k-th meteorological station on the j-th day of the i-th year, in °C; s,i,j,k Let e ​​be the saturated water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; a,i,j,k The actual water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; u 2,i,j,k Let ET be the average wind speed at 2m on day j of year i at the k-th weather station, in m / s; 0,i,k The potential evapotranspiration of the k-th weather station in year i, mm; m i E represents the number of days in the i-th year. 0,i The potential evapotranspiration of the watershed in year i is in mm; The average potential evapotranspiration over many years is measured in mm; l represents the number of meteorological stations within and around the study basin.

[0086] Using the daily meteorological data from meteorological stations within and around the study basin collected in step 1 during the study period, the annual areal precipitation and the multi-year average areal precipitation of the basin were calculated. The specific calculation formulas are as follows:

[0087]

[0088]

[0089]

[0090] In the formula: P i Let be the areal precipitation in year i, in mm; The average annual precipitation over many years, in mm; pre i,k Let be the precipitation at the k-th meteorological station in the i-th year, in mm; i,j,k Let be the precipitation at the k-th meteorological station on the j-th day of the i-th year, in mm;

[0091] Step 3: Determine the length of the sliding window using the sliding window method. Then, perform a sliding average calculation on the annual areal precipitation and potential evapotranspiration calculated in Step 2, and the annual runoff collected in Step 1. This yields the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window. The specific calculation formulas are as follows:

[0092]

[0093]

[0094]

[0095] In the formula: P c,g Let the isal precipitation in year g of the c-th sliding window be in mm; R represents the multi-year average areal precipitation for the c-th sliding window, in mm.c,g Let the runoff in the c-th sliding window in the g-th year be mm; E represents the multi-year average runoff volume for the c-th sliding window, in mm. 0,c,g The potential evapotranspiration of the c-th sliding window in the g-th year is in mm. Let be the multi-year average surface potential evapotranspiration of the c-th sliding window, in mm; h be the length of the sliding window; the first sliding window is defined as the base period, and each of the remaining sliding windows is a period of change;

[0096] Step 4: Construct the watershed hydrothermal coupling Budyko framework. In this framework, parameter v represents the coefficient of the distribution ratio between actual evapotranspiration, precipitation, and runoff. It is mainly related to underlying surface factors and can clearly reflect the relationship between various physical variables. The specific formula is as follows:

[0097]

[0098] Where: R is the runoff under multi-year average conditions, mm; E0 is the potential evapotranspiration of the watershed under multi-year average conditions, mm; P is the watershed precipitation under multi-year average conditions, mm; v is the parameter of the watershed hydrothermal coupling Budyko framework.

[0099] Step 4.2: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in Step 2 into the Budyko framework formula (12) for watershed hydrothermal coupling, and calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework using the least squares method. The specific formula for the least squares method is as follows:

[0100]

[0101] Where: R is the runoff under the multi-year average conditions calculated using formula (12), in mm; The multi-year average runoff volume calculated in step 2 is in mm;

[0102] Step 4.3: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration of each sliding window obtained in Step 3 into the watershed hydrothermal coupling Budyko framework formula (12), and use the least squares method to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window. The specific formula for the least squares method is as follows:

[0103]

[0104] In the formula: R c The runoff volume (in mm) is the multi-year average runoff volume under the c-th sliding window condition calculated using formula (12); Let v be the multi-year average runoff of the c-th sliding window, in mm. c For the parameter values ​​of the Budyko framework for watershed hydrothermal coupling in the c-th sliding window;

[0105] Step 5: Under the Budyko framework of watershed hydrothermal coupling, the factors affecting runoff change are mainly three variables: precipitation, potential evapotranspiration, and parameters. Therefore, the causes of runoff change can be mainly summarized as three factors: precipitation, potential evapotranspiration, and parameters.

[0106] The parameters of the multi-year average areal precipitation and multi-year average potential evapotranspiration calculated in step 2, and the multi-year average watershed hydrothermal coupling Budyko framework calculated in step 4 are used. The elasticity coefficients of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework are solved, and the specific formulas are as follows:

[0107]

[0108]

[0109]

[0110] In the formula, ε P This is the elasticity coefficient of runoff to precipitation; ε is the elastic coefficient of runoff with respect to potential evapotranspiration; v The elastic coefficients of runoff on the parameters of the watershed hydrothermal coupling Budyko framework; This is the partial derivative of runoff with respect to precipitation; This is the partial derivative of runoff with respect to potential evapotranspiration; This represents the partial derivative of runoff with respect to the parameters of the watershed hydrothermal coupling Budyko framework;

[0111] Step 6: Using the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​obtained in Step 3 for each sliding window, calculate the changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​for each sliding window relative to the baseline period during the change period. The specific formulas are as follows:

[0112]

[0113]

[0114]

[0115]

[0116] In the formula, The multi-year average runoff of the first sliding window, i.e., the multi-year average runoff of the base period, in mm; Let be the multi-year average runoff of the c-th sliding window, in mm; ΔR c Let be the change in the multi-year average runoff volume of the c-th sliding window relative to the base period, in mm; The average annual precipitation for the first sliding window, in mm; Let ΔP be the multi-year average isal precipitation for the c-th sliding window, in mm; c Let be the change in the multi-year average isothermal precipitation for the c-th sliding window relative to the baseline period, in mm; The multi-year average surface potential evapotranspiration for the first sliding window, in mm; The multi-year average surface potential evapotranspiration for the c-th sliding window, mm; ΔE 0,c Let be the change in potential surface evapotranspiration of the c-th sliding window relative to the base period over many years, in mm; The parameters for the watershed hydrothermal coupling Budyko framework in the first sliding window; The parameters of the watershed hydrothermal coupling Budyko framework for the c-th sliding window; Δv c The change in the watershed hydrothermal coupling Budyko framework parameters for the c-th sliding window relative to the baseline period is denoted as .

[0117] Using the multi-year average areal precipitation and multi-year average potential evapotranspiration calculated in step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in step 4, as well as the calculated changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​for each sliding window of the change period relative to the baseline period, the attribution contribution rate of runoff change for each sliding window of the change period relative to the baseline period is calculated. The specific formula is as follows:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] In the formula, ΔRP,c Let be the change in runoff caused by precipitation during the c-th sliding window, in mm; ΔR represents the change in runoff caused by potential evapotranspiration during the c-th sliding window, in mm. v,c ΔR′ represents the runoff variation caused by the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed, in mm. c The sum of runoff changes caused by the three influencing factors in the c-th sliding window, in mm; Con P,c The contribution rate of precipitation change to runoff change in the c-th sliding window; Let Con be the contribution rate of the potential evapotranspiration change in the c-th sliding window to the runoff change; v,c The contribution rate of the variation of the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed to the runoff variation;

[0126] Example

[0127] Taking the Jinghe Zhangjiashan Hydrological Station's controlled watershed as an example, the technical process is as follows: Figure 1 As shown, please follow these steps:

[0128] Step 1: First, collect basic data: Collect annual runoff data from the Zhangjiashan Hydrological Station on the Jinghe River from 1988 to 2019; collect daily meteorological data from 40 meteorological stations within and around the basin controlled by the Zhangjiashan Hydrological Station on the Jinghe River from 1988 to 2019, including daily precipitation, wind speed, maximum temperature, minimum temperature, average relative humidity, and sunshine duration; collect data on the basin area controlled by the Zhangjiashan Hydrological Station.

[0129] Step 2: Using the annual runoff data from the Zhangjiashan Hydrological Station on the Jinghe River collected in Step 1 for 1988-2019, the multi-year average runoff is calculated. The specific calculation formula is as follows:

[0130]

[0131] In the formula, R is the multi-year average runoff, in mm. i Let m be the runoff in year i. 3 ; n represents the length of the study period in years, here n is 32; F represents the catchment area controlled by the Zhangjiashan hydrological station, in km². 2 ;

[0132] Using daily meteorological data collected in Step 1 from 1988 to 2019 from 40 meteorological stations within and around the Jinghe River basin controlled by the Zhangjiashan Hydrological Station, the daily potential evapotranspiration of each meteorological station was calculated according to the Penman-Monteith formula. The annual potential evapotranspiration of each station was then summed. Finally, the annual areal potential evapotranspiration of the study basin during the study period was calculated using the arithmetic mean method. Next, the multi-year average areal potential evapotranspiration was calculated. The specific calculation formula is as follows:

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[0135]

[0136]

[0137] Where: ET 0,i,j,k The potential evapotranspiration of the k-th weather station on the j-th day of the i-th year, mm / d; Δ i,j,k Let be the slope of the saturated water vapor pressure curve at the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;R n,i,j,k The net radiation of the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 G i,j,k Let be the soil heat flux density at the k-th meteorological station on the j-th day of the i-th year, in MJ·m -2 ·d -1 ;γ i,j,k Let be the wet / dry constant of the k-th meteorological station on the j-th day of the i-th year, in kPa·℃. -1 ;T i,j,k Let e ​​be the average temperature at the k-th meteorological station on the j-th day of the i-th year, in °C; s,i,j,k Let e ​​be the saturated water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; a,i,j,k The actual water vapor pressure at the k-th meteorological station on the j-th day of the i-th year, in kPa; u 2,i,j,k Let ET be the average wind speed at 2m on day j of year i at the k-th weather station, in m / s; 0,i,k The potential evapotranspiration of the k-th weather station in year i, mm; m i E represents the number of days in the i-th year. 0,i The potential evapotranspiration of the watershed in year i is in mm; The average potential evapotranspiration over many years is represented in mm; l represents the number of meteorological stations within and around the study basin, which is 40 here.

[0138] Using the daily precipitation data collected in Step 1 from 1988 to 2019 from 40 meteorological stations within and around the Jinghe River basin controlled by the Zhangjiashan Hydrological Station, the annual areal precipitation and the multi-year average areal precipitation of the basin were calculated. The specific calculation formulas are as follows:

[0139]

[0140]

[0141]

[0142] In the formula: P i Let be the areal precipitation in year i, in mm; The average annual precipitation over many years, in mm; pre i,k Let be the precipitation at the k-th meteorological station in the i-th year, in mm; i,j,k Let be the precipitation at the k-th meteorological station on the j-th day of the i-th year, in mm;

[0143] Step 3: Based on the Loess Plateau literature, the sliding window is set to 11 years. Using the sliding window method, the annual areal precipitation and potential evapotranspiration calculated in Step 2 from 1998 to 2019 are processed with the annual runoff collected in Step 1 from 1998 to 2019 to obtain the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window. The specific calculation formulas are as follows:

[0144]

[0145]

[0146]

[0147] In the formula: P c,g Let the isal precipitation in year g of the c-th sliding window be in mm; R represents the multi-year average areal precipitation for the c-th sliding window, in mm. c,g Let the runoff in the c-th sliding window in the g-th year be mm; E represents the multi-year average runoff volume for the c-th sliding window, in mm. 0,c,g The potential evapotranspiration of the c-th sliding window in the g-th year is in mm. Let be the multi-year average potential evapotranspiration of the c-th sliding window, in mm; h be the length of the sliding window, which is 11 here; the number of sliding windows is 22.

[0148] The first sliding window is designated as the baseline period, and each subsequent sliding window represents a period of change; the calculation results of step 3 are as follows: Figure 2 As shown.

[0149] Step 4: Construct the watershed hydrothermal coupling Budyko framework. In this framework, parameter v represents the coefficient of the distribution ratio between actual evapotranspiration, precipitation, and runoff, which is mainly related to underlying surface factors and can clearly reflect the relationship between various physical variables. The specific formula is as follows:

[0150]

[0151] Where: R is the runoff under multi-year average conditions, mm; E0 is the potential evapotranspiration of the watershed under multi-year average conditions, mm; P is the watershed precipitation under multi-year average conditions, mm; v is the parameter of the watershed hydrothermal coupling Budyko framework.

[0152] Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in step 2 into the watershed hydrothermal coupling Budyko framework formula (12), and combine the least squares method to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework. The calculated value here is 8.31. The specific formula for the least squares method is as follows:

[0153]

[0154] Where: R is the runoff under the multi-year average conditions calculated using formula (12), in mm; The multi-year average runoff volume calculated in step 2 is in mm;

[0155] Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration of each sliding window obtained in step 3 into the watershed hydrothermal coupling Budyko framework formula (12), and combine the least squares method to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window. The specific formula of the least squares method is as follows:

[0156]

[0157] In the formula: R c The runoff volume (in mm) is the multi-year average runoff volume under the c-th sliding window condition calculated using formula (12); Let v be the multi-year average runoff of the c-th sliding window, in mm. c The parameter values ​​for the hydrothermal coupling of the c-th sliding window watershed in the Budyko framework are calculated as follows: Figure 3 As shown;

[0158] Step 5: Under the Budyko framework of watershed hydrothermal coupling, the factors affecting runoff change are mainly three variables: precipitation, potential evapotranspiration, and parameters. Therefore, the causes of runoff change can be mainly summarized as three factors: precipitation, potential evapotranspiration, and parameters.

[0159] The parameters of the multi-year average areal precipitation and multi-year average potential evapotranspiration calculated in step 2, and the multi-year average watershed hydrothermal coupling Budyko framework calculated in step 4 are used. The elasticity coefficients of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework are solved, and the specific formulas are as follows:

[0160]

[0161]

[0162]

[0163] In the formula, ε P The elasticity coefficient of runoff to precipitation is calculated to be 1.94. ε is the elasticity coefficient of runoff to potential evapotranspiration, calculated here as -0.945; v The elastic coefficient of runoff on the watershed hydrothermal coupling Budyko framework parameters is calculated here as -0.945; The partial derivative of runoff with respect to precipitation is given by 0.108; The partial derivative of runoff with respect to potential evapotranspiration is calculated here to be -0.0255; The partial derivative of runoff with respect to the parameters of the watershed hydrothermal coupling Budyko framework is calculated here to be -3.25;

[0164] Step 6: Using the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​obtained in Step 3 for each sliding window, calculate the changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​for each sliding window relative to the baseline period during the change period. The specific formulas are as follows:

[0165]

[0166]

[0167]

[0168]

[0169] In the formula, The multi-year average runoff of the first sliding window, i.e., the multi-year average runoff of the base period, in mm; Let be the multi-year average runoff of the c-th sliding window, in mm; ΔR cLet be the change in the multi-year average runoff volume of the c-th sliding window relative to the base period, in mm; The average annual precipitation for the first sliding window, in mm; Let ΔP be the multi-year average isal precipitation for the c-th sliding window, in mm; c Let be the change in the multi-year average isothermal precipitation for the c-th sliding window relative to the baseline period, in mm; The multi-year average surface potential evapotranspiration for the first sliding window, in mm; The multi-year average surface potential evapotranspiration for the c-th sliding window, mm; ΔE 0,c Let be the change in potential surface evapotranspiration of the c-th sliding window relative to the base period over many years, in mm; The parameters for the watershed hydrothermal coupling Budyko framework in the first sliding window; The parameters of the watershed hydrothermal coupling Budyko framework for the c-th sliding window; Δv c The change in the watershed hydrothermal coupling Budyko framework parameters for the c-th sliding window relative to the baseline period is denoted as .

[0170] Step 6.2: Using the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, along with the calculated changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​for each sliding window of the change period relative to the baseline period, calculate the attributable contribution rate of runoff change for each sliding window of the change period relative to the baseline period. The specific formula is as follows:

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] In the formula, ΔR P,c Let be the change in runoff caused by precipitation during the c-th sliding window, in mm; ΔR represents the change in runoff caused by potential evapotranspiration during the c-th sliding window, in mm. v,cΔR′ represents the runoff variation caused by the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed, in mm. c The sum of runoff changes caused by the three influencing factors in the c-th sliding window, in mm; Con P,c The contribution rate of precipitation change to runoff change in the c-th sliding window; Let Con be the contribution rate of the potential evapotranspiration change in the c-th sliding window to the runoff change; v,c Let ΔR′ be the contribution rate of the variation in the parameters of the hydrothermal coupling Budyko framework in the c-th sliding window watershed to the runoff variation. c and ΔR c The calculation results are as follows Figure 4 As shown; Con v,c The calculation results are as follows Figure 5 As shown.

Claims

1. A runoff attribution method based on the Budyko framework of watershed hydrothermal coupling, characterized in that, Specifically, the steps include the following: Step 1: Determine the study basin and study period, and collect annual runoff data and basin area data controlled by the hydrological stations in the study basin during the study period; collect daily meteorological data from meteorological stations inside and around the study basin during the study period. Step 2: Using the annual runoff data from the control hydrological stations of the study basin collected in Step 1 during the study period, calculate the multi-year average runoff; using the daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, calculate the annual areal precipitation and potential evapotranspiration of the basin, as well as the multi-year average areal precipitation and multi-year average potential evapotranspiration; the specific process of Step 2 is as follows: Step 2.1: Using the annual runoff data and watershed area data controlled by the hydrological stations during the study period collected in Step 1, the multi-year average runoff is calculated. The specific calculation formula is as follows: （1）； In the formula, The average runoff over many years, in mm; For the first i Annual runoff, m 3 ; n The length of the study period in years; The drainage area controlled by the hydrological station, in km² 2 ; Step 2.2: Using the daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, calculate the daily potential evapotranspiration for each meteorological station according to the Penman-Monteith formula, and sum them to obtain the annual potential evapotranspiration for each meteorological station. Finally, calculate the annual areal potential evapotranspiration of the study basin during the study period using the arithmetic mean method, and then calculate the multi-year average areal potential evapotranspiration. The specific calculation formula is as follows: （2）； （3）； （4）； （5）； In the formula: For the first i Year j Heavenly k Potential evapotranspiration at each weather station, mm / d; For the first i Year j Heavenly k The slope of the saturated vapor pressure curve of each meteorological station, kPa·℃ -1 ; For the first i Year j Heavenly k Net radiation of each weather station, MJ·m -2 ·d -1 ; For the first i Year j Heavenly k Soil heat flux density at each weather station, MJ·m -2 ·d -1 ; For the first i Year j Heavenly k The wet / dry constant of each weather station, kPa·℃ -1 ; For the first i Year j Heavenly k The average temperature at each weather station, in °C; For the first i Year j Heavenly k The saturated vapor pressure of each weather station, in kPa; For the first i Year j Heavenly k The actual water vapor pressure at each weather station, in kPa; For the first i Year j Heavenly k The average wind speed at 2m from each weather station, in m / s; For the first i Year k Potential evapotranspiration at one weather station, mm; For the first i The number of days in a year; For the first i Potential evapotranspiration over the basin area in [year], mm; The multi-year average potential evapotranspiration, mm; To study the number of meteorological stations within and around the basin; Step 2.3: Using the daily meteorological data from meteorological stations within and around the study basin collected in Step 1 during the study period, calculate the annual areal precipitation and the multi-year average areal precipitation of the basin. The specific calculation formula is as follows: （6）； （7）； （8）； In the formula: For the first i Annual areal precipitation, mm; The average annual precipitation is measured in mm. For the first i Year k Rainfall at each weather station, in mm; For the first i Year j Heavenly k Rainfall at each weather station, in mm; Step 3: Using the sliding window method, process the annual areal precipitation and potential evapotranspiration calculated in Step 2 and the annual runoff collected in Step 1 to obtain the multi-year average runoff, multi-year average areal precipitation and multi-year average potential evapotranspiration for each sliding window, and determine the base period and the period of change. Step 4: Construct the watershed hydrothermal coupling Budyko framework. Utilize the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in Step 2, and combine this with the least squares method to calculate the parameter values ​​of the multi-year average watershed hydrothermal coupling Budyko framework. Simultaneously, use the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window calculated in Step 3 to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window. Step 5: Attribute the runoff variation under the watershed hydrothermal coupling Budyko framework constructed in Step 4. Using the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2 and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, solve the elasticity coefficient of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework. Step 6: Using the elasticity coefficients calculated in Step 5, the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, and combined with the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 3 for each sliding window, calculate the runoff change attribution contribution rate of each sliding window relative to the baseline period during the change period.

2. The runoff attribution method based on the watershed hydrothermal coupling Budyko framework according to claim 1, characterized in that, The specific process of step 3 is as follows: Step 3.1: Determine the length of the sliding window using the sliding window method. Then, perform a sliding average calculation on the annual areal precipitation and potential evapotranspiration calculated in Step 2, and the annual runoff collected in Step 1. This yields the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration for each sliding window. The specific calculation formulas are as follows: （9）； （10）； （11）； In the formula: For the first c The first sliding window g Annual areal precipitation, mm; For the first c The multi-year average areal precipitation for each sliding window, in mm; For the first c The first sliding window g Annual runoff, mm; For the first c The multi-year average runoff of the sliding window, in mm; For the first c The first sliding window g Potential evaporation per unit area per year, mm; For the first c The multi-year average surface potential evapotranspiration of a sliding window, mm; The length of the sliding window; Step 3.2: Determine the first sliding window as the baseline period, and each of the remaining sliding windows as a change period.

3. The runoff attribution method based on the watershed hydrothermal coupling Budyko framework according to claim 2, characterized in that, Step 4 is described in detail below: Step 4.1: Construct the watershed hydrothermal coupling Budyko framework, in which the parameters... v The coefficient representing the distribution ratio among actual evapotranspiration, precipitation, and runoff is given by the following formula: （12）； In the formula: The runoff volume is the average runoff volume over many years, in mm. The potential evapotranspiration over the watershed under multi-year average conditions is in mm; The watershed surface precipitation under multi-year average conditions is expressed in mm. The parameters are for the watershed hydrothermal coupling Budyko framework; Step 4.2: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration calculated in Step 2 into the Budyko framework formula (12) for watershed hydrothermal coupling, and calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework using the least squares method. The specific formula for the least squares method is as follows: （13）； In the formula: The runoff volume under the multi-year average conditions calculated using formula (12) is in mm; The multi-year average runoff volume calculated in step 2 is in mm; Step 4.3: Substitute the multi-year average runoff, multi-year average areal precipitation, and multi-year average potential evapotranspiration of each sliding window obtained in Step 3 into the watershed hydrothermal coupling Budyko framework formula (12), and use the least squares method to calculate the parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window. The specific formula for the least squares method is as follows: （14）； In the formula: The first one calculated using formula (12) c Runoff volume under multi-year average conditions of a sliding window, in mm; For the first c The multi-year average runoff of the sliding window, in mm; For the first c The parameter values ​​of the sliding window watershed hydrothermal coupling Budyko framework.

4. The runoff attribution method based on the watershed hydrothermal coupling Budyko framework according to claim 3, characterized in that, The specific process of step 5 is as follows: Step 5.1, based on the watershed hydrothermal coupling Budyko framework, the factors determining the runoff variation are: precipitation, potential evapotranspiration and parameters; Step 5.2: Utilize the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the parameters of the multi-year average watershed hydrothermal coupling Budyko framework calculated in Step 4. The elasticity coefficients of runoff to different factors affecting runoff under the watershed hydrothermal coupling Budyko framework are solved, and the specific formulas are as follows: （15）； （16）； （17）； In the formula, This is the elasticity coefficient of runoff to precipitation; The elastic coefficient of runoff to potential evapotranspiration; The elastic coefficients of runoff on the parameters of the watershed hydrothermal coupling Budyko framework; This is the partial derivative of runoff with respect to precipitation; This is the partial derivative of runoff with respect to potential evapotranspiration; This represents the partial derivative of runoff with respect to the parameters of the watershed hydrothermal coupling Budyko framework.

5. The runoff attribution method based on the watershed hydrothermal coupling Budyko framework according to claim 4, characterized in that, The specific process of step 6 is as follows: Step 6.1: Using the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and the parameters of the watershed hydrothermal coupling Budyko framework for each sliding window calculated in Step 3, calculate the changes in multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and the watershed hydrothermal coupling Budyko framework parameters for each sliding window relative to the baseline period during the change period. The specific formulas are as follows: （18）； （19）； （20）； （21）； In the formula, The multi-year average runoff of the first sliding window, i.e., the multi-year average runoff of the base period, in mm; For the first c The multi-year average runoff of the sliding window, in mm; For the first c The change in multi-year average runoff volume relative to the baseline period for each sliding window, in mm; The average annual precipitation for the first sliding window, in mm; For the first c The multi-year average areal precipitation for each sliding window, in mm; For the first c The change in multi-year average areal precipitation relative to the baseline period for each sliding window, in mm; The multi-year average surface potential evapotranspiration for the first sliding window, in mm; For the first c The multi-year average surface potential evapotranspiration of a sliding window, mm; For the first c The change in potential surface evapotranspiration of a sliding window relative to the multi-year average of the baseline period, in mm; The parameters for the watershed hydrothermal coupling Budyko framework in the first sliding window; For the first c The parameter values ​​of the watershed hydrothermal coupling Budyko framework for each sliding window; For the first c The change in parameters of the watershed hydrothermal coupling Budyko framework relative to the baseline period for each sliding window; Step 6.2: Using the multi-year average areal precipitation, multi-year average potential evapotranspiration calculated in Step 2, and the multi-year average watershed hydrothermal coupling Budyko framework parameter values ​​calculated in Step 4, as well as the multi-year average runoff, multi-year average areal precipitation, multi-year average potential evapotranspiration, and watershed hydrothermal coupling Budyko framework parameter values ​​changes for each sliding window of the change period relative to the base period calculated in Step 6.1, calculate the attribution contribution rate of runoff change for each sliding window of the change period relative to the base period. The specific formula is as follows: （22）； （23）； （24）； （25）； （26）； （27）； （28）； In the formula, Let be the change in runoff caused by precipitation during the c-th sliding window, in mm; Let be the runoff change caused by the potential evapotranspiration of the c-th sliding window, in mm; The change in runoff caused by the hydrothermal coupling Budyko framework parameters in the c-th sliding window watershed is expressed in mm. Let be the sum of the runoff changes caused by the three influencing factors in the c-th sliding window, in mm; The contribution rate of precipitation change to runoff change in the c-th sliding window; The contribution rate of the potential evapotranspiration change in the c-th sliding window to the runoff change; The contribution rate of the variation in the parameters of the hydrothermal coupling Budyko framework in the c-th sliding window watershed to the runoff variation.

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