A Budyko method for analyzing the mechanism of water-heat coupling in a watershed

Abstract

The present invention relates to a new Budyko framework for analyzing the mechanism of water-heat coupling in a watershed, and belongs to the technical field of water-heat coupling analysis in a watershed. The method of the present invention comprises: obtaining and preprocessing data of the historical period and the research period of the research watershed; calibrating the model structure index of the new Budyko framework using the data of the historical period of the research watershed, and calculating the actual evapotranspiration of the research watershed year by year in the research period in combination with the data of the research period; calculating the actual evapotranspiration and the model structure index of the research watershed year by year in the research period by combining the new Budyko framework and other Budyko formulas; estimating the interval of the actual evapotranspiration of the research watershed year by year using the results of the actual evapotranspiration of the research watershed year by year using different Budyko formulas; and quantifying the relationship between the model structure indexes of different Budyko formulas year by year using the results of the model structure indexes of different Budyko formulas. The present invention can effectively solve the problems that the model structure index of the Budyko formula cannot be calibrated when the watershed lacks data, the actual evapotranspiration of the watershed cannot be measured, and the water-heat coupling of the watershed is difficult to evaluate, and has important practical significance for accurately estimating the surface evapotranspiration of the watershed in remote areas.

Description

Technical Field

[0001] The invention relates to a method for mining the coupling relationship among actual evapotranspiration, potential evapotranspiration and precipitation in a watershed, and in particular to a new Budyko framework that takes into account coordination and harmony with other Budyko methods. Background Art

[0002] The actual evapotranspiration of a watershed year by year is mainly determined by the balance between atmospheric water supply and atmospheric evaporation demand, which constitutes Budyko's basic hypothesis on the water-heat coupling relationship of a watershed. Atmospheric water supply is usually expressed by annual precipitation in a watershed, and atmospheric evaporation demand is usually expressed by annual potential evapotranspiration in a watershed. The Budyko hypothesis describes the interaction between the climate, hydrology and underlying surface of a watershed with only two meteorological variables, becoming a powerful tool for understanding the complex relationship between climate, vegetation and soil in a watershed. The Budyko hypothesis is widely used in watershed evapotranspiration research because of its concise expression and clear physical meaning.

[0003] Based on the Budyko hypothesis, many scholars have proposed simple models to describe the water-heat coupling mechanism between actual evapotranspiration, annual precipitation and potential evapotranspiration in the basin. Representative models include the Fu Baopu formula proposed based on the physical meaning of basin hydrometeorology and the Mezentsev-Choudhury-Yang water-heat coupling equation that considers the impact of basin precipitation and net radiation spatial heterogeneity on basin evapotranspiration. These two methods attribute the contribution of various possible factors that affect the water-heat coupling control parameters of the basin to the model structure index. Although the two Budyko models have similar curve forms and both comply with energy and water boundary conditions, there is an inherent incompatibility between the two models. There are two problems when jointly solving the actual annual evapotranspiration of the basin and the model structure index: 1) If the model structure index of the two methods is assumed to be equal, there will be a contradiction that the annual precipitation is equal to the annual potential evapotranspiration when jointly solving; 2) If the model structure index of the two methods is assumed to be unequal, the actual annual evapotranspiration of the basin and the model structure index cannot be directly jointly solved. It is necessary to calibrate the model structure index in advance with data such as annual runoff, annual precipitation, net radiation of crop surface, hygrometer constant, slope of the relationship curve between saturated water vapor pressure and temperature, air temperature, ground wind speed, air saturated water vapor pressure, actual air vapor pressure, etc. in multiple basins, and then solve the actual annual evapotranspiration of the basin. The availability and collection of calibration data and the calibration of the model structure index have largely restricted the promotion and application of these two methods.

[0004] The reason for the above problems is that the model structure indexes in the two Budyko methods are incompatible with each other, and the difference in parameterization of the underlying soil and vegetation biophysical properties that affect the actual evapotranspiration of the basin makes it difficult to connect them. In order to fully connect the existing Budyko method with the law of the formation of actual evapotranspiration in the basin, provide a boundary condition for estimating the actual evapotranspiration of the basin for the existing Budyko method, and provide a communication bridge between the existing Budyko methods, a new Budyko framework that can connect with other Budyko methods and can be self-contained is invented. Summary of the invention

[0005] In view of the limitations of the prior art, the present invention provides a Budyko method for analyzing the water-heat coupling mechanism of a watershed, including the following technical features:

[0006] T1: Establish a new Budyko framework to analyze the mechanism of water-heat coupling in the basin, in which the sum of the annual potential evapotranspiration index and the annual precipitation index in the numerator is greater than the mean of the annual potential evapotranspiration index and the annual precipitation index in the denominator by 1;

[0007] T2: The new Budyko framework is coordinated with other Budyko formulas and can be used as boundary conditions for other Budyko formulas to jointly solve the actual evapotranspiration and model structure index of the basin year by year;

[0008] T3: The new Budyko framework does not require data calibration, and the results of the combined solution of other Budyko formulas can be used to estimate the interval of actual evapotranspiration in the basin year by year;

[0009] T4: The new Budyko framework and the results of the simultaneous solution of other Budyko formulas can be used to quantify the relationship between the structural indices of other different Budyko formula models.

[0010] As a further preferred technical solution, the T1 is specifically:

[0011]

[0012] Wherein, ET is the actual evapotranspiration of the study basin during the study period (mm / year), P is the annual precipitation of the study basin during the study period (mm / year), ET0 is the annual potential evapotranspiration of the study basin during the study period (mm / year), n is the model structure index describing the water-heat coupling mechanism, the sum of the index of ET0 and the index of P in the numerator is n+1, and the average of the index of ET0 and the index of P in the denominator is n.

[0013] As a further preferred technical solution, T2, the coordination of the new Budyko framework with other Budyko formulas means that the new Budyko framework and other Budyko formulas can be solved jointly without contradiction, and the new Budyko framework and other Budyko formulas can be used as boundary conditions for each other to jointly solve the actual evapotranspiration of the basin year by year and the model structure index, specifically:

[0014] It can be combined with the Budyko formula to solve the actual evapotranspiration of the basin and the model structure index year by year:

[0015]

[0016] The first formula is the Budyko formula. The actual evapotranspiration ET of the basin year by year and the model structure index n are the quantities to be determined. The nonlinear equation system composed of the above two formulas can be solved by iteration method, Aitkin method or Newton-Raphson method to obtain the actual evapotranspiration ET of the basin year by year. F and the model structure index n F ;

[0017] It can be used together with the Budyko Mezentsev-Choudhury-Yang water-heat coupling equation to solve the actual evapotranspiration and model structure index of the basin year by year:

[0018]

[0019] The first equation is the Budyko Mezentsev-Choudhury-Yang water-heat coupling equation. The actual evapotranspiration ET of the basin year by year and the model structure index n are the quantities to be determined. The nonlinear equation system composed of the above two equations can be solved by iteration method, Aitkin method or Newton-Raphson method to obtain the actual evapotranspiration ET of the basin year by year. M and the model structure index n M .

[0020] As a further preferred technical solution, the T3, the Budyko new framework does not require data calibration, and the results of the simultaneous solution of other Budyko formulas can be used to estimate the interval of actual evapotranspiration in the basin year by year, specifically:

[0021] ET∈[min(ET F , E.T. M ), max(ET F , E.T. M )]

[0022] Where ET is the actual annual evapotranspiration of the study basin during the study period (mm / year), [min(ET F , E.T. M ), max(ET F , E.T.M )] is the range of actual evapotranspiration in the basin estimated by using the new Budyko framework and other Budyko formulas to solve the problem.

[0023] As a further preferred technical solution, T4, the Budyko new framework and other Budyko formula simultaneous solution results can be used to quantify the relationship between other different Budyko formula model structure indexes, specifically:

[0024] n f =n m +n F -n M

[0025] Where n f represents the model structure index of the Budyko-Fu Baopu formula, n m represents the model structure index of the Budyko Mezentsev-Choudhury-Yang hydrothermal coupling equation, n F -n M represents the model structure index result obtained by solving the Budyko new framework and the Budyko Fu Baopu formula and the Budyko Mezentsev-Choudhury-Yang hydrothermal coupling equation respectively. f With n m quantitative relationship.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The present invention provides a new Budyko framework for analyzing the mechanism of water-heat coupling in a watershed. Compared with the weak connection ability of the traditional Budyko framework, the new Budyko framework provided by the present invention has three characteristics: 1) it can be used as the boundary condition of the water-heat coupling law in the actual evapotranspiration of the watershed, and can be combined with other Budyko methods to solve the actual evapotranspiration of the watershed, without the need to collect calibration data in a time-consuming and laborious manner; 2) it can be used as a medium for exploring the relationship between different Budyko methods, and can be combined with other Budyko methods to form a nonlinear closed equation group to solve the quantitative relationship between the model structure indexes of different Budyko methods; 3) compared with the linear segmentation of water-heat coupling in the traditional Budyko formula, this framework further embodies the nonlinear segmentation mechanism of water-heat coupling in the estimation of actual evapotranspiration of the watershed by using the non-integer power of the product of potential evapotranspiration and precipitation in the numerator, and can be self-contained and independently applied. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical features of the present invention, the drawings used in the embodiments of the present invention will be described in detail below. It is obvious that the drawings are only part of the embodiments of the present invention and should not be regarded as limiting the scope of the present invention.

[0029] Figure 1 A flow chart of a method in an embodiment of the present invention; DETAILED DESCRIPTION

[0030] In order to make the technical solutions and beneficial effects of the present invention more understandable, the purpose, technical features and characteristics of the embodiments of the present invention are described in detail and clearly in combination with the drawings in the embodiments of the present invention. It is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. For ordinary technicians in this field, all other embodiments obtained by referring to the embodiments of the present invention without creative work should be within the protection scope of the present invention.

[0031] Please refer to Figure 1 , Figure 1 The technical flow chart in the embodiment provided by the present invention includes the following steps:

[0032] S1 obtains and preprocesses the data of the historical period and the research period of the study basin;

[0033] S2 uses historical data of the study basin to calibrate the model structure index of the new Budyko framework, and combines the data of the study period to calculate the actual evapotranspiration of the basin year by year during the study period;

[0034] S3 combines the new Budyko framework with other Budyko formulas to calculate actual evapotranspiration and model structure index year by year during the study period in the study basin;

[0035] S4 uses the actual evapotranspiration results of the basin year by year in different Budyko formulas in S3 to estimate the range of the actual evapotranspiration of the basin year by year;

[0036] S5 uses the year-by-year model structure index results of different Budyko formulas in S3 to quantify the relationship between the year-by-year model structure indexes of different Budyko formulas.

[0037] In S1, the data obtained for the historical period and the research period of the study basin include: the daily average wind speed u (m / s) at 2 meters, the daily average actual water vapor pressure e a(kPa), digital elevation model, daily precipitation (mm / d), daily average surface pressure (kPa), daily average air temperature (℃), daily average relative humidity (%), daily minimum temperature (℃), daily maximum temperature (℃), actual sunshine hours (hr), possible maximum sunshine hours (hr), these data can be downloaded from the National Meteorological Science Data Center, surface albedo MODIS product MCD43A3 (dimensionless), can be downloaded from the NASA Data Management Center, daily runoff value of the basin outlet hydrological station (mm / d), can be obtained through the National Hydrological Yearbook compilation data;

[0038] The preprocessing includes: extracting the boundary of the research basin and the number of grids according to the digital elevation model, data spatial interpolation and clipping;

[0039] The preprocessing also includes the calculation of annual precipitation in the historical period of the study basin and the study period, specifically:

[0040]

[0041] In the formula, G represents the number of grid points of precipitation data after spatial interpolation in the study basin, y represents the year number of the historical period or the study period, and D y represents the number of days in year y, P gdy represents the daily precipitation (mm / d) at the g-th grid point in the study basin on the d-th day of the y-th year, P y represents the precipitation in the whole study basin in year y (mm / year);

[0042] The preprocessing also includes the calculation of the annual runoff of the study basin during the historical period and the study period, specifically:

[0043]

[0044] In the formula, R dy represents the daily runoff (mm / d) of the outlet hydrological station of the study basin on the dth day of the yth year, R y represents the runoff at the outlet of the study basin in year y (mm / year);

[0045] The preprocessing also includes the calculation of potential evapotranspiration of the study basin in the historical period and the study period, specifically:

[0046]

[0047] Δ gdy To study the slope of the saturated water vapor pressure curve (kPa / ℃), γ gdy is the psychrometric constant (kPa / ℃) of the g-th grid on the d-th day of the y-th year in the study basin, e sgdyis the daily average saturated water vapor pressure (kPa) of the g-th grid on the d-th day of the y-th year in the study basin, e agdy The actual daily average water vapor pressure (kPa) and u gdy The daily average wind speed at 2 meters above the g-th grid in the y-th year and the d-th day of the study basin, R ngdy The net daily radiation value of the surface of the g-th grid in the y-th year and the d-th day of the basin is (MJ / (m 2 d)), which can be expressed as the daily value of net shortwave radiation (MJ / (m 2 d)) and the daily value of net longwave radiation (MJ / (m 2 d)) difference, G ngdy is the daily soil heat flux value of the g-th grid in the study basin on the d-th day of the y-th year (MJ / (m 2 d)), G on a daily scale ngdy Take 0;

[0048] The preprocessing also includes calculating actual evapotranspiration of the study basin in the historical period and the study period year by year based on the basin water balance, specifically:

[0049] ET y =P y -Ry

[0050] In the formula, ET y is the actual evapotranspiration of the study basin in year y (mm / year).

[0051] In S2, the model structure index of the Budyko new framework is calibrated using the historical data of the study basin, specifically:

[0052]

[0053] In the formula, Y represents the number of years in the historical period of the study basin. The Y nonlinear equations can be solved by iterative method, Aitkin method or Newton-Raphson method to obtain the annual model structure index {n y} 1≤y≤Y , then the model structure index of Budyko's new framework is

[0054] The actual evapotranspiration of the basin during the study period is calculated by combining the data of the study period as follows:

[0055]

[0056] Where K represents the number of years of the study period of the basin, ET k It represents the actual evapotranspiration in the kth year of the basin study period.

[0057] In S3, the combined Budyko new framework and other Budyko formulas are used to calculate the actual evapotranspiration and model structure index of the study basin during the study period. If the other Budyko formula is the Fu Baopu formula, specifically:

[0058]

[0059] Each of the K pairs of nonlinear equations above contains ET k and n k Two unknowns can be solved by iterative method, Aitkin method or Newton-Raphson method, and the result is {ET Fk} 1≤k≤K and {n Fk} 1≤k≤K ;

[0060] If the other Budyko formula is selected as the Mezentsev-Choudhury-Yang hydrothermal coupling equation, it is specifically:

[0061]

[0062] Each of the K pairs of nonlinear equations above contains ET k and n k Two unknowns can be solved by iterative method, Aitkin method or Newton-Raphson method, and the result is {ET Mk} 1≤k≤K and {n Mk} 1≤k≤K ;

[0063] In S4, the interval of the actual evapotranspiration of the basin year by year is estimated by using the actual evapotranspiration results of the basin in different Budyko formulas in S3, specifically:

[0064] {ET k ∈[min(ET Fk , E.T. Mk ), max(ET Fk , E.T. Mk )} 1≤k≤K

[0065] In S5, the relationship between the different Budyko formula year-by-year model structure index results in S3 is quantified, specifically:

[0066] {n fk =n mk +n Fk -n Mk} 1≤k≤K

[0067] Where nfk represents the model structure index of the Budyko formula in the kth year, n mk Represents the model structure index of the BudykoMezentsev-Choudhury-Yang hydrothermal coupling equation in the kth year.

[0068] The present invention proposes a new Budyko framework for analyzing the water-heat coupling mechanism of a watershed, which has the following characteristics: 1) the actual surface evapotranspiration of the watershed can be obtained conveniently and quickly using meteorological station or meteorological reanalysis data; 2) the invention extends the linear segmentation of the water-heat coupling mechanism of the watershed in the traditional Budyko framework to nonlinear segmentation; 3) the invention can be combined with other Budyko methods to analyze the actual evapotranspiration and water-heat coupling law of the watershed when there is no calibration data; 4) the invention can serve as a medium for evaluating other Budyko methods for calculating the actual evapotranspiration of the watershed when there is no calibration data; 5) the invention can serve as a boundary condition for other Budyko methods to estimate the model structure index when there is no calibration data.

[0069] It should be noted that the above embodiments are only used to illustrate the technical solutions and implementation processes of the present invention, rather than to limit them. Although the above embodiments describe the basic ideas and technical features of the present invention in detail, for those of ordinary skill in the art, some features of the technical solutions can be modified or equivalently replaced according to the ideas of the present invention, but these changes essentially cannot deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A Budyko method for analyzing the water-heat coupling mechanism of a watershed, characterized in that: Features include: T1: Establish a new Budyko framework to analyze the mechanism of water-heat coupling in the basin. The sum of the annual potential evapotranspiration index and the annual precipitation index in the numerator of the new Budyko framework is greater than the mean of the annual potential evapotranspiration index and the annual precipitation index in the denominator by 1. The new framework is specifically: Wherein, ET is the actual evapotranspiration of the study basin during the study period, in mm / year; P is the annual precipitation of the study basin during the study period, in mm / year; ET0 is the annual potential evapotranspiration of the study basin during the study period, in mm / year; n is the model structure index describing the water-heat coupling mechanism; the sum of the index of ET0 and the index of P in the numerator is n+1; the mean of the index of ET0 and the index of P in the denominator is n; T2: The new Budyko framework is coordinated with other Budyko formulas and can be used as boundary conditions for other Budyko formulas to jointly solve the actual evapotranspiration and model structure index of the basin year by year, specifically: It can be combined with the Budyko formula to solve the actual evapotranspiration of the basin and the model structure index year by year: The first formula is the Budyko formula. The actual evapotranspiration ET of the basin year by year and the model structure index n are the quantities to be determined. The nonlinear equation system composed of the above two formulas can be solved by iteration method, Aitkin method or Newton-Raphson method to obtain the actual evapotranspiration ET of the basin year by year. F and the model structure index n F ; It can be used together with the Budyko Mezentsev-Choudhury-Yang water-heat coupling equation to solve the actual evapotranspiration and model structure index of the basin year by year: The first equation is the Budyko Mezentsev-Choudhury-Yang water-heat coupling equation. The actual evapotranspiration ET of the basin year by year and the model structure index n are the quantities to be determined. The nonlinear equation system composed of the above two equations can be solved by iteration method, Aitkin method or Newton-Raphson method to obtain the actual evapotranspiration ET of the basin year by year. M and the model structure index n M ; T3: The new Budyko framework does not require data calibration, and the results of the combined solution of other Budyko formulas can be used to estimate the interval of actual evapotranspiration in the basin year by year; T4: The new Budyko framework and the results of the simultaneous solution of other Budyko formulas can be used to quantify the relationship between the structural indices of other different Budyko formula models.

2. The method according to claim 1, characterized in that The T3, the Budyko new framework, and other Budyko formulas can be used to estimate the interval of actual evapotranspiration in the basin year by year without data calibration, specifically: AND∈[min(AND F ,AND M ), max(ET F ,AND M )] Where ET is the actual annual evapotranspiration of the study basin during the study period, in mm / year, [min(ET F , E.T. M ), max(ET F , E.T. M )] is the range of actual evapotranspiration in the basin estimated by using the new Budyko framework and other Budyko formulas to solve the problem.

3. The method according to claim 1, characterized in that: The T4, the Budyko new framework and other Budyko formula simultaneous solution results can be used to quantify the relationship between other different Budyko formula model structure indexes, specifically: n f =n m +n F -n M Where n f represents the model structure index of the Budyko-Fu Baopu formula, n m represents the model structure index of the Budyko Mezentsev-Choudhury-Yang hydrothermal coupling equation, n F -n M represents the model structure index result obtained by solving the Budyko new framework and the Budyko Fu Baopu formula and the Budyko Mezentsev-Choudhury-Yang hydrothermal coupling equation respectively. f With n m quantitative relationship.

Images