Runoff estimation method considering vegetation interception under non-uniform rainfall conditions

Abstract

The application discloses a runoff estimation method considering vegetation interception under non-uniform rainfall conditions, and steps include: step 1, establishing a vegetation interception model to calculate the interception process; step 2, establishing an infiltration model to calculate the infiltration process; and step 3, establishing a runoff generation model to obtain the runoff generation process under the non-uniform rainfall conditions. The method is verified to be accurate in the runoff generation model through a numerical solution. The method further perfects the simulation of the rainfall-runoff process, and can predict the single-width flow at a runoff outlet of a mountain slope only by using the rainfall intensity under the natural rainfall intensity.

Description

Technical Field

[0001] This invention belongs to the field of agricultural hydrological process analysis technology, and relates to a method for estimating runoff considering vegetation interception under non-uniform rainfall conditions. Background Technology

[0002] Under natural rainfall conditions, vegetation can significantly and continuously alter rainfall-runoff hydrological processes. When there is vegetation cover, some rainwater reaches the ground directly through gaps, while the rest is intercepted by the leaves and stems of the vegetation. The interception capacity of vegetation gradually weakens with the duration of rainfall. The intercepted water drips back to the surface after overcoming surface tension. Therefore, accurately predicting runoff processes under vegetation interception is essential. Existing runoff prediction models either fail to quantify or ignore the interception effect of vegetation, making it impossible for runoff models to accurately predict runoff processes under vegetation growth. Therefore, establishing a runoff model that considers vegetation interception under non-uniform rainfall conditions is highly necessary. Summary of the Invention

[0003] The purpose of this invention is to provide a runoff estimation method that considers vegetation interception under non-uniform rainfall conditions, which solves the problems of unreasonable runoff generation model settings, inconvenient operation, and difficulty in accurately predicting runoff processes under vegetation growth in the prior art.

[0004] The technical solution adopted in this invention is a method for estimating runoff considering vegetation interception under non-uniform rainfall conditions, which is implemented according to the following steps:

[0005] Step 1: Establish a vegetation interception model to calculate the interception process;

[0006] Step 2: Establish an infiltration model to calculate the infiltration process;

[0007] Step 3: Establish a runoff generation model to obtain the runoff generation process under non-uniform rainfall conditions.

[0008] The beneficial effects of this invention are that it first establishes a vegetation interception model, then an infiltration model under the influence of interception, and finally a runoff generation model. The accuracy of the runoff generation model is verified through numerical solutions. This method further improves the simulation of the rainfall-runoff generation process, as it only requires rainfall intensity at the natural rainfall intensity level to predict the unit width flow rate at the hillside outfall. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating the overall calculation process of the method of this invention;

[0010] Figure 2 This is a calculation diagram of the retention process used in the method of this invention;

[0011] Figure 3This is a calculation diagram of the infiltration process used in the method of this invention;

[0012] Figure 4 This is the runoff process calculation diagram used in the method of this invention. Detailed Implementation

[0013] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0014] Reference Figure 1 The method for estimating runoff considering vegetation interception under non-uniform rainfall conditions of the present invention is implemented according to the following steps:

[0015] Step 1: Establish a vegetation interception model to calculate the interception process.

[0016] Reference Figure 2 The specific process is as follows:

[0017] Vegetation intercepts precipitation, and the interception rate varies over time. Generally, the interception rate is highest before rainfall occurs and gradually decreases after rainfall begins. This decline in the interception rate can be described by an exponential function. The expression for the vegetation interception rate is:

[0018] Int = C·Int m exp(-kt), (1)

[0019] In equation (1), Int is the vegetation interception rate, with the unit symbol being cm / min; C is the vegetation coverage, with the unit symbol being cm. 2 / cm 2 t represents the rainfall duration, with the unit symbol being min; Int m is the maximum vegetation interception rate, with the unit symbol cm / min; k is the raindrop retention coefficient.

[0020] To analyze the impact of different rainfall intensities on the interception process, the rainfall time was divided into several smaller time intervals. This allows us to assume that the rainfall intensity is constant within a small time interval (tb, t). p Correspondingly, the interception process is also divided into two sub-processes: Sub-process A is the period when the rainfall intensity equals the interception rate, t≤t0, that is, all rainwater is intercepted by vegetation; Sub-process B is the period when the interception rate decreases exponentially, t>t0, that is, after the vegetation intercepts the excess rainwater, it can fall to the ground in the form of water droplets.

[0021] To obtain the critical time t0, the rainfall is calculated using the average rainfall intensity. Based on the assumptions of subprocess A, the expression for cumulative rainfall is:

[0022]

[0023] In equation (2), C is the vegetation cover, in cm. 2 / cm 2 ; It is the average rainfall intensity before t0, in cm / min; t s The time at which the rejection rate and the approximate rejection rate intersect in equation (1) is expressed in minutes.

[0024] The expression for the average rainfall intensity before t0 is:

[0025]

[0026] In equation (3), r t t represents the rainfall intensity at time t, expressed in cm / min.

[0027] At the time intersection point t=t s The expression for the retention rate at this time intersection is:

[0028]

[0029] Combining equations (2) and (4), we have:

[0030]

[0031]

[0032] Substituting equation (3) into equation (6), we get:

[0033]

[0034] The solution t0 of equation (7) is obtained by the bisection method, and t is obtained by combining equations (3) and (5). s The value;

[0035] The expression for the interception process of the rainfall event is as follows:

[0036]

[0037] Int = C·Int m exp(-k(t-Δt int )), t>t0, (9)

[0038] In equation (9), Δt int Δt is the time difference between the interception times, expressed in minutes; int =t0-t s ,

[0039] From then on, the vegetation interception model was established.

[0040] Step 2: Establish an infiltration model to calculate the infiltration process, referring to... Figure 3 The specific process is as follows:

[0041] Because vegetation may not completely cover the ground, some rainwater falls directly onto the soil surface. Meanwhile, the remaining rainwater, after being intercepted by vegetation, immediately infiltrates the soil upon reaching the ground. When the average rainfall intensity exceeds the vegetation's interception capacity, the intercepted water drips onto the soil surface. The infiltration rate increases over time before runoff begins, and surface runoff begins when the net rainfall intensity exceeds the infiltration capacity.

[0042] The Philips method is used to represent the infiltration process, and the expression is:

[0043]

[0044] In equation (10), Inf is the infiltration rate, in cm / min; S is the permeation rate, in cm / min. 1 / 2 ;

[0045] The original Philip equation only applies to the infiltration process of accumulated water. By modification, it can be applied to the infiltration process under the influence of interception processes during non-uniform rainfall. Therefore, the expression for the infiltration rate at the time of water accumulation is:

[0046] In equation (11), This is the average rainfall intensity, expressed in cm / min; t p t1 represents the duration of water accumulation, in minutes; t1 is the intersection of the original Philip equation and the average rainfall intensity, in cm / min.

[0047] t p The previous expression for average rainfall intensity was:

[0048]

[0049] The expression for the cumulative infiltration amount before the water accumulation time is:

[0050]

[0051] Combining equations (11) and (13), we obtain equations (14) and (15):

[0052]

[0053]

[0054] abortion time t p By solving equation (15), and then combining equations (12) and (13), t1 can be solved.

[0055] The expression for the infiltration process under non-uniform rainfall conditions is as follows:

[0056] Inf = r(1-C), t ≤ t0 (16)

[0057] Inf = rC·Int m exp(-k(t-Δt int )), t0 <t<t p (17)

[0058]

[0059] In equation (18), Δt inf It is the infiltration time difference, in minutes; Δt inf =t p -t1.

[0060] From this point on, the infiltration model was completed.

[0061] Step 3: Establish a runoff generation model to obtain the runoff generation process under non-uniform rainfall conditions. Specifically, the runoff generation process is described using a kinematic wave model, as shown in the following expression:

[0062]

[0063] Q(x,t)=αh(x,t) β (20)

[0064] r e =r-Int-Inf, (21)

[0065] Where Q is the unit width flow rate, measured in cm. 2 / min; h is the runoff depth in cm; x is the slope length in cm; α is a parameter representing the slope and roughness; β is the flow pattern index; r e It is the net rainfall reaching the earth's surface, expressed in cm / min;

[0066] For ease of calculation, β is approximated as 2, in (t b The expression for the time period t is:

[0067]

[0068] In equation (22), q and q b It is t and t b The flow rate at any given time is expressed in cm / min.

[0069] In non-uniform rainfall events, due to r eThe numerical relationship between -q(t) and q(t) is different, and the solution of equation (22) may change. There are four scenarios in total, which are described below:

[0070] Scenario 1: r e >q, integrating equation (22), we have:

[0071]

[0072] The solution to equation (23) is as follows:

[0073]

[0074] In equation (24), w t It is a comprehensive terrain parameter, w t =α / L;

[0075] The expressions for the unit width flow rate and runoff depth in Scenario 1 are as follows:

[0076]

[0077]

[0078] Scenario 2: 0 <r e b Integrating equation (22), we have:

[0079]

[0080] The solution to equation (27) is as follows:

[0081]

[0082] The expressions for the unit width flow rate and runoff depth in scenario 2 are as follows:

[0083]

[0084]

[0085] Scenario 3: r e =0, integrating equation (22), we have:

[0086]

[0087] The solution to equation (31) is as follows:

[0088]

[0089] The expressions for the unit width flow rate and runoff depth in scenario 3 are as follows:

[0090] ​

[0091]

[0092] Scenario 4: r = 0, integrating equation (22), we have:

[0093]

[0094] The solution to equation (35) is as follows:

[0095]

[0096] The expressions for the unit width flow rate and runoff depth in scenario 4 are as follows:

[0097]

[0098]

[0099] Among them, t u It is the time when the rainfall stopped, in minutes; q u It is the flow velocity when the rainfall stops, measured in cm / min.

[0100] Experimental verification:

[0101] To verify the correctness of the physics-based method, this invention employs a numerical simulation-based method (i.e., the Preissmann scheme) to simulate the runoff generation process using an example. The results are as follows: Figure 4 As shown in Table 1, the parameters used in both methods are shown in Table 1. Rainfall intensity is generated from a random sequence, 0 <r<0.15。

[0102] Table 1. Model Calculation Parameters

[0103]

[0104] By inputting the parameters in Table 1, the analytical solution and numerical solution of the flow generation model established in this invention are compared. For example... Figure 4 As shown, the correlation coefficient R 2 ≥0.92 indicates that the runoff generation model established by the method of the present invention has high accuracy in predicting the runoff generation process under vegetation growth conditions.

Claims

1. A method for estimating runoff considering vegetation interception under non-uniform rainfall conditions, characterized in that, Follow these steps to implement the procedure: Step 1: Establish a vegetation interception model to calculate the interception process. The specific process is as follows: The expression for vegetation interception rate is: ，(1) In equation (1), Int It is the vegetation interception rate, with the unit symbol being cm / min; C It refers to vegetation cover, with the unit symbol being cm. 2 / cm 2 ; t This refers to the duration of rainfall, expressed in minutes. Int m It is the maximum vegetation interception rate, with the unit symbol being cm / min; k It is the raindrop retention coefficient; The rainfall time is divided into several smaller time periods, and the rainfall intensity is assumed to be constant within a small time period. t b , t p Correspondingly, the interception process is also divided into two smaller processes: Subprocess A is the period when the rainfall intensity equals the interception rate. t ≤ t 0, meaning all rainwater is intercepted by vegetation; subprocess B is the period when the interception rate decreases exponentially. t > t 0 means that excess rainwater trapped by vegetation can fall to the ground in the form of water droplets; To obtain the critical time t 0. Using average rainfall intensity to calculate rainfall, based on the assumptions of subprocess A, the expression for cumulative rainfall is: ，(2) In equation (2), C It refers to vegetation cover, measured in cm. 2 / cm 2 ; yes t The average rainfall intensity before 0, in cm / min; t s The time at which the rejection rate and the approximate rejection rate intersect in equation (1) is expressed in minutes. t The expression for the average rainfall intensity before 0 is: ，(3) In equation (3), r t yes t Rainfall intensity at any given time, expressed in cm / min; Intersection of Time t = t s The expression for the retention rate at this time intersection is: ，(4) Combining equations (2) and (4), we have: ，(5) ，(6) Substituting equation (3) into equation (6), we get: ，(7) Solution of equation (7) t 0 is obtained through the bisection method, and by combining equations (3) and (5) we get t s The value; The expression for the interception process of the rainfall event is as follows: ， t≤t 0，(8) ， t > t 0，(9) In equation (9), Δ t int It is the time difference of the interception time, in minutes; Δ t int = t 0- t s Thus, the vegetation interception model was established; Step 2: Establish an infiltration model to calculate the infiltration process. The specific process is as follows: The Philips method is used to represent the infiltration process, and the expression is: ，(10) In equation (10), Inf It is the infiltration rate, measured in cm / min; S It is the permeation rate, measured in cm / min. 1 / 2 ; The expression for the infiltration rate at the moment of water accumulation is: ，(11) In equation (11), This is the average rainfall intensity, expressed in cm / min; t p This is the duration of water accumulation, expressed in minutes. t 1 represents the intersection of the original Philip equation and the average rainfall intensity, expressed in cm / min. t p The previous expression for average rainfall intensity was: ，(12) The expression for the cumulative infiltration amount before the water accumulation time is: ，(13) Combining equations (11) and (13), we obtain equations (14) and (15): ，(14) (15) abortion time t p By solving equation (15), and then combining equations (12) and (13), we can obtain the solution. t 1, The expression for the infiltration process under non-uniform rainfall conditions is as follows: ， t≤t 0(16) ， t 0< t < t p (17) ， t > t p (18) In equation (18), Δ t inf It is the infiltration time difference, in minutes; Δ t inf = t p - t 1; From this point on, the infiltration model is complete; Step 3: Establish a runoff generation model to obtain the runoff generation process under non-uniform rainfall conditions. The specific process is as follows: The flow generation process is described using a motion wave model, as shown in the following expression: ，(19) ，(20) ，(21) in, Q It is the unit width flow rate, measured in cm. 2 / min; h This refers to the runoff depth, expressed in cm. x This is the slope length, in cm; α These are parameters representing slope and roughness; β It is a water flow pattern index; r e It is the net rainfall reaching the earth's surface, expressed in cm / min; For ease of calculation, β Approximately 2, in ( t b , t The expression for the time period is: ，(22) In equation (22), q and q b yes t and t b The flow rate at any given time is expressed in cm / min.

2. The method for estimating runoff considering vegetation interception under non-uniform rainfall conditions according to claim 1, characterized in that, In non-uniform rainfall events, due to r e - q ( t The solution to equation (22) will change depending on the numerical relationship between the two conditions. There are four scenarios in total, which are described as follows: Scenario 1: r e > q Integrating equation (22), we have: ，(23) The solution to equation (23) is as follows: ，(24) In equation (24), w t It is a comprehensive set of terrain parameters. w t = α / L ; The expressions for the unit width flow rate and runoff depth in Scenario 1 are as follows: ，(25) ，(26) Scenario 2: 0 r e < q b Integrating equation (22), we have: ，(27) The solution to equation (27) is as follows: ，(28) The expressions for the unit width flow rate and runoff depth in scenario 2 are as follows: ，(29) ，(30) Scenario 3: r e =0, integrating equation (22), we have: ，(31) The solution to equation (31) is as follows: ，(32) The expressions for the unit width flow rate and runoff depth in scenario 3 are as follows: ，(33) ，(34) Scenario 4: r =0, integrating equation (22), we have: ，(35) The solution to equation (35) is as follows: ，(36) The expressions for the unit width flow rate and runoff depth in scenario 4 are as follows: ，(37) ，(38) in, t u This is the time when the rainfall stopped, in minutes. q u It is the flow velocity when the rainfall stops, measured in cm / min.

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