Karst area runoff yield and confluence calculation method considering spatial differences of underlying surface

Abstract

The application discloses a kind of karst area runoff yield and confluence calculation method considering underlying surface spatial difference, comprising the following steps: step 1, data collection and pretreatment;Step 2, karst area runoff yield threshold distribution calculation;Step 3, karst area runoff yield calculation;Step 4, karst area confluence calculation.The method disclosed in the application, based on the spatial distribution difference of underlying surface condition in karst area, the characteristics that karst area runoff yield threshold is generally small and unevenly distributed, uses statistical curve to represent the distribution of karst area runoff yield threshold, and calculates the runoff yield and confluence of karst area accordingly, solves the problem that karst area runoff yield and confluence calculation is not accurate and not high in precision in the past, improves the accuracy of karst area runoff yield and confluence calculation, improves the precision of karst area runoff simulation prediction, wide applicability, has strong engineering significance.

Description

Technical Field

[0001] This invention belongs to the field of karst runoff generation and runoff calculation technology, specifically relating to a karst runoff generation and runoff calculation method that considers the spatial differences of the underlying surface. Background Technology

[0002] Approximately 17% of the global population lives in karst regions. With economic and social development, the demand for water resources in karst areas is increasing, making runoff simulation and forecasting in these regions increasingly important. Karst regions possess unique watershed characteristics. The development of caves, conduits, fissures, and pores creates special water storage media and groundwater systems. The dual structure and openness of the watershed result in spatiotemporal instability of its area. These unique watershed characteristics contribute to the complexity of hydrological features in karst regions. The watershed contains two water systems: surface water and groundwater, which constantly interact. In most cases, the groundwater system accounts for a larger proportion. The outflow process is highly nonlinear, and floods in the watershed often exhibit steep rises and slow falls. These complex hydrological processes lead to low accuracy in runoff simulation and forecasting in karst regions.

[0003] Due to various factors, the development of karst hydrological models is relatively recent. Currently, commonly used runoff generation and runoff calculations in karst areas can be mainly divided into two types: one uses existing lumped hydrological models, and the other uses distributed hydrological models to calculate the runoff in each unit and then calculates the runoff using hydraulic methods. Due to limitations in observation methods and technology, data on runoff and groundwater in karst areas are scarce, which restricts the application of distributed hydrological models in karst areas. Therefore, lumped methods are often used for runoff generation and runoff calculations in karst areas. However, commonly used runoff generation and runoff calculation methods cannot consider the spatial distribution differences of underlying surface conditions in karst areas and cannot reflect the uneven runoff generation and runoff thresholds in karst areas. This leads to problems such as low accuracy of karst hydrological models, poor application of runoff generation and runoff calculation methods in karst areas, and limited application scope. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating runoff generation and confluence in karst areas that takes into account spatial differences in the underlying surface, so as to solve the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention discloses a method for calculating runoff generation and confluence in karst areas considering spatial differences in the underlying surface. The method includes the following steps:

[0007] Step 1: Data Collection and Preprocessing: Collect hydrological and meteorological data for the target karst area, including precipitation data from each rain gauge station and evaporation data from each evaporation station in the basin; calculate the basin-wide average precipitation P using the Thiessen polygon method based on the distribution of rain gauge stations. tThe average evaporation rate E of the watershed was obtained by calculating and processing the evaporation data using the Thiessen polygon method based on the distribution of evaporation sites. t ;

[0008] Step 2, Calculation of runoff threshold distribution in karst areas: Based on the non-uniform distribution of runoff thresholds in karst areas, a statistical curve is used to characterize the distribution of runoff thresholds in karst areas. The formula for calculating the runoff threshold distribution curve in karst areas is as follows:

[0009]

[0010] In the formula, is the proportion of runoff-producing area in the karst region, f is the area of ​​the runoff-producing portion of the karst region, FR is the total area of ​​the karst region; SSK is the runoff threshold at a single point in the karst region, SKMM is the maximum runoff threshold at a single point in the karst region; kweb is the non-uniformity index of the runoff threshold distribution curve in the karst region.

[0011] Step 3, Calculation of Karst Area Outflow: Based on the distribution of runoff thresholds in karst areas, the portion of rainfall exceeding the runoff threshold generates rapid outflow. The rapid outflow rate in karst areas is calculated based on the different runoff thresholds in different regions. Based on the distribution of runoff thresholds in karst areas, the slow outflow rate in karst areas is calculated using the slow outflow coefficient. The runoff rate in karst areas is the sum of the rapid outflow rate and the slow outflow rate in karst areas.

[0012] Step 4: Calculation of runoff in karst areas: Calculate the runoff based on the rapid outflow and slow outflow of the karst areas to obtain the rapid outflow runoff and slow outflow runoff of the karst areas. The runoff in the karst areas is the sum of the rapid outflow runoff and slow outflow runoff of the karst areas.

[0013] Furthermore, the calculation process for the rapid outflow from the karst area mentioned in step 3 is as follows:

[0014] First, the maximum runoff threshold currently reached in the karst region at the initial stage of the watershed is calculated as follows:

[0015]

[0016] In the formula, AK is the maximum runoff threshold currently reached in the karst area under the initial state, SK is the average runoff threshold already reached in the karst area under the initial state, and SKM is the average runoff threshold in the karst area.

[0017] According to formula (1), the average runoff threshold SKM in the karst area is:

[0018] SKM = SKMM / (1 + kweb)(3)

[0019] Then, based on the average evaporation rate E of the watershed area calculated in step 1... t The potential evapotranspiration capacity of the karst area is calculated as follows:

[0020] E p =E t ·K (4)

[0021] In the formula, E p K represents the potential evapotranspiration capacity of the karst area, and K is the conversion factor for the potential evapotranspiration capacity of the karst area.

[0022] The average precipitation P of the watershed area calculated in step 1 t The net rainfall is calculated as follows:

[0023] PE = max(0, P t -E p (5)

[0024] In the formula, PE represents the net rainfall replenished to the karst area;

[0025] Finally, based on the runoff threshold distribution, the rapid outflow rate in the karst area was calculated as follows:

[0026]

[0027] In the formula, R kq For rapid outflow in karst areas;

[0028] The calculation process for the slow outflow rate in the karst area mentioned in step 3 is as follows:

[0029] R ks = kkg·(SK+PE-R) kq (7)

[0030] In the formula, R ks denoted as , where kkg is the karst slow outflow rate and kkg is the karst slow outflow coefficient.

[0031] Furthermore, the runoff calculation in step 4 adopts the linear reservoir method; the calculation process for the rapid outflow runoff and slow outflow runoff in the karst area is as follows:

[0032] The rapid outflow volume of the karst area is:

[0033]

[0034] In the formula, Q kq,t Let Q be the rapid outflow and sinking flow rate of the karst region at time t. kq,t-1 Let a be the rapid outflow and sinking flow rate of the karst region at time t-1. kq R is the coefficient for the rapid karst flow regression. kq,t The rapid outflow rate of the karst area at time t;

[0035] The slow outflow volume of the karst area is:

[0036]

[0037] In the formula, Q ks,t Q is the slow outflow rate of the karst region at time t. ks,t-1 Let a be the slow outflow and sinking flow rate of the karst region at time t-1. ks R is the coefficient for the regression of slow karst flows. ks,t The flow rate of the karst region at time t is the slow outflow rate.

[0038] The beneficial effects of this invention are as follows: This invention provides a method for calculating runoff generation and runoff in karst areas that considers spatial differences in underlying surface conditions. Based on the spatial distribution differences in underlying surface conditions in karst areas, and the generally small and unevenly distributed runoff generation thresholds, this invention uses statistical curves to characterize the distribution of runoff generation thresholds in karst areas, and calculates the runoff generation and runoff volume in karst areas accordingly. The method described in this invention solves the problems of inaccuracy and low precision in previous runoff generation and runoff calculations in karst areas, improves the accuracy of runoff generation and runoff calculations in karst areas, enhances the accuracy of runoff simulation and forecasting in karst areas, has wide applicability, and has strong engineering significance.

[0039] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the method flow described in this invention;

[0041] Figure 2 This is a schematic diagram for calculating the yield of karst areas;

[0042] Figure 3 This is a schematic diagram comparing the simulated and measured values ​​of the watershed outlet flow. Detailed Implementation

[0043] This invention discloses a method for calculating runoff generation and confluence in karst areas that considers spatial differences in the underlying surface, such as... Figure 1 As shown, it includes the following steps:

[0044] Step 1: Data Collection and Preprocessing: Collect hydrological and meteorological data for the target karst area, including precipitation data (PP) from various rain gauge stations in the watershed. t =(P 1,t ,P 2,t ,…P m,t ), m is the number of rainfall stations; evaporation data EE of each evaporation station in this watershed t =(E 1,t E 2,t ,…E n,t), where n represents the number of evaporation stations; the collected hydrological data undergoes a "three-fold review," including reliability review, consistency review, and representativeness review. Then, based on the distribution of rainfall stations, the Thiessen polygon method is used to calculate and process the precipitation data to obtain the basin-wide average precipitation P. t The average evaporation rate E of the watershed was obtained by calculating and processing the evaporation data using the Thiessen polygon method based on the distribution of evaporation sites. t .

[0045] Step 2: Calculation of runoff generation threshold distribution in karst areas: Due to the significant spatial differences in the underlying surface of karst areas, the runoff generation threshold distribution is uneven. Based on the characteristics of the overall small and uneven distribution of runoff generation thresholds in karst areas, a statistical curve is used to characterize the distribution of runoff generation thresholds. The formula for calculating the runoff generation threshold distribution curve is as follows:

[0046]

[0047] In equation (1), FR is the proportion of runoff-producing area in the karst region, f is the area of ​​the runoff-producing portion of the karst region, and FR is the total area of ​​the karst region; SSK is the runoff threshold at a single point in the karst region, SKMM is the maximum runoff threshold at a single point in the karst region; kweb is the non-uniformity index of the runoff threshold distribution curve in the karst region. The larger the kweb value, the more uneven the runoff threshold distribution. If kweb = 0, the runoff thresholds are consistent within the karst region.

[0048] Step 3, Calculation of karst area yield: (e.g.) Figure 2 As shown, based on the distribution of runoff generation thresholds in karst areas, the portion of rainfall exceeding the runoff generation threshold generates rapid outflow. The rapid outflow rate in karst areas is calculated based on the different runoff generation thresholds in different regions.

[0049] The specific process is as follows: First, calculate the maximum runoff threshold currently reached in the karst region at the initial stage of the watershed:

[0050]

[0051] In equation (2), AK is the maximum runoff threshold currently reached in the karst area under the initial state, SK is the average runoff threshold already reached in the karst area under the initial state, and SKM is the average runoff threshold in the karst area.

[0052] According to formula (1), the average runoff threshold SKM in the karst area is:

[0053] SKM = SKMM / (1 + kweb) (3)

[0054] Then, based on the average evaporation rate E of the watershed area calculated in step 1... t The potential evapotranspiration capacity of the karst area is calculated as follows:

[0055] Ep =E t ·K (4)

[0056] In equation (4), E p K represents the potential evapotranspiration capacity of the karst area, and K is the conversion factor for the potential evapotranspiration capacity of the karst area.

[0057] The average precipitation P of the watershed area calculated in step 1 t The net rainfall is calculated as follows:

[0058] PE = max(0, P t -E p (5)

[0059] In equation (5), PE represents the net rainfall in the karst region.

[0060] Finally, the rapid outflow rate in the karst area was calculated based on the runoff threshold distribution:

[0061]

[0062] In equation (6), R kq For rapid outflow in karst areas.

[0063] Based on the runoff threshold distribution in karst areas, the slow outflow rate in karst areas is calculated using the slow outflow coefficient. The slow outflow rate in karst areas is:

[0064] R ks = kkg·(SK+PE-R) kq (7)

[0065] In equation (7), R ks denoted as , where kkg is the karst slow outflow rate and kkg is the karst slow outflow coefficient.

[0066] The karst region's yield is the rapid outflow rate R from the karst region. kq With slow outflow R in karst areas ks sum.

[0067] Step 4: Calculation of runoff in karst areas: The linear reservoir method is used to calculate the runoff based on the rapid outflow and slow outflow of the karst areas, respectively, to obtain the rapid outflow runoff and slow outflow runoff of the karst areas.

[0068] The rapid outflow and runoff volume in the karst area is:

[0069]

[0070] In equation (8), Q kq,t Let Q be the rapid outflow and sinking flow rate of the karst region at time t. kq,t-1 Let a be the rapid outflow and sinking flow rate of the karst region at time t-1. kqR is the coefficient for the rapid karst flow regression. kq,t The flow rate of the karst region at time t is the rapid outflow rate.

[0071] The slow outflow collection rate in the karst area is:

[0072]

[0073] In equation (9), Q ks,t Q is the slow outflow rate of the karst region at time t. ks,t-1 Let a be the slow outflow and sinking flow rate of the karst region at time t-1. ks R is the coefficient for the regression of slow karst flows. ks,t The flow rate of the karst region at time t is the slow outflow rate.

[0074] The runoff volume in a karst region is the sum of the rapid outflow runoff volume and the slow outflow runoff volume in the karst region, i.e., Q. k,t =Q kq,t +Q ks,t Q k,t Let t be the total runoff in the karst region at time t.

[0075] Example 1

[0076] This embodiment is a specific application example of the above method.

[0077] A watershed with karst development has a total area of ​​F. Spatially, it can be divided into a karst region (area FR) and a non-karst region (area F-FR). The runoff generation and runoff process in the karst region is calculated according to the above method and steps, while the runoff generation and runoff process in the non-karst region is calculated according to an existing mature model. The total runoff generation and runoff of the watershed is obtained by adding the runoff generation and runoff of the karst region and the non-karst region.

[0078] The specific process includes the following steps:

[0079] Step 1: Data Collection and Preprocessing: Collect hydrological and meteorological data for the karst area, including precipitation data from various rain gauge stations in the watershed. t =(P 1,t ,P 2,t ,…P m,t ), m is the number of rainfall stations; evaporation data EE of each evaporation station in this watershed t =(E 1,t E 2,t ,…E n,t ), where n represents the number of evaporation stations; the collected hydrological data undergoes a "three-fold review," including reliability review, consistency review, and representativeness review. Then, based on the distribution of rainfall stations, the Thiessen polygon method is used to calculate and process the precipitation data to obtain the basin-wide average precipitation P. tThe average evaporation rate E of the watershed was obtained by calculating and processing the evaporation data using the Thiessen polygon method based on the distribution of evaporation sites. t .

[0080] Step 2: Calculation of runoff generation threshold distribution in karst areas: Due to the significant spatial differences in the underlying surface of karst areas, the runoff generation threshold distribution is uneven. Based on the characteristics of the overall small and uneven distribution of runoff generation thresholds in karst areas, a statistical curve is used to characterize the distribution of runoff generation thresholds. The formula for calculating the runoff generation threshold distribution curve is as follows:

[0081]

[0082] In equation (1), FR is the proportion of runoff-producing area in the karst region, f is the area of ​​the runoff-producing portion of the karst region, and FR is the total area of ​​the karst region; SSK is the runoff threshold at a single point in the karst region, SKMM is the maximum runoff threshold at a single point in the karst region; kweb is the non-uniformity index of the runoff threshold distribution curve in the karst region. The larger the kweb value, the more non-uniform the distribution. If kweb = 0, the runoff thresholds are consistent within the karst region.

[0083] Step 3, Calculation of runoff in karst areas: Based on the runoff threshold distribution in karst areas, the portion of rainfall exceeding the runoff threshold generates rapid outflow. Calculate the rapid outflow in karst areas based on the different runoff thresholds in different regions.

[0084] The specific process is as follows: First, calculate the maximum runoff threshold currently reached in the karst region at the initial stage of the watershed:

[0085]

[0086] In equation (2), AK is the maximum runoff threshold currently reached in the karst region under the initial state, SK is the average runoff threshold already reached in the karst region under the initial state, and SKM is the average runoff threshold in the karst region. According to equation (1), the average runoff threshold SKM in the karst region is:

[0087] SKM = SKMM / (1 + kweb) (3)

[0088] Then, based on the average evaporation rate E of the watershed area calculated in step 1... t The potential evapotranspiration capacity of the karst area is calculated as follows:

[0089] E p =E t ·K (4)

[0090] In equation (4), E p K represents the potential evapotranspiration capacity of the karst area, and K is the conversion factor for the potential evapotranspiration capacity of the karst area.

[0091] The average precipitation P of the watershed area calculated in step 1t The net rainfall is calculated as follows:

[0092] PE = max(0, P t -E p (5)

[0093] In equation (5), PE represents the net rainfall in the karst region.

[0094] Finally, the rapid outflow rate in the karst area was calculated based on the runoff threshold distribution:

[0095]

[0096] In equation (6), R kq For rapid outflow in karst areas.

[0097] Based on the runoff threshold distribution in karst areas, the slow outflow rate in karst areas is calculated using the slow outflow coefficient. The slow outflow rate in karst areas is:

[0098] R ks = kkg·(SK+PE-R) kq (7)

[0099] In equation (7), R ks denoted as , where kkg is the karst slow outflow rate and kkg is the karst slow outflow coefficient.

[0100] The karst region's yield is the rapid outflow rate R from the karst region. kq With slow outflow R in karst areas ks sum;

[0101] Step 4: Calculation of runoff in karst areas: The linear reservoir method is used to calculate the runoff based on the rapid outflow and slow outflow of the karst areas, respectively, to obtain the rapid outflow runoff and slow outflow runoff of the karst areas.

[0102] The rapid outflow and runoff volume in the karst area is:

[0103]

[0104] In equation (8), Q kq,t Let Q be the rapid outflow and sinking flow rate of the karst region at time t. kq,t-1 Let a be the rapid outflow and sinking flow rate of the karst region at time t-1. kq R is the coefficient for the rapid karst flow regression. kq,t The flow rate of the karst region at time t is the rapid outflow rate.

[0105] The slow outflow collection rate in the karst area is:

[0106]

[0107] In equation (9), Qks,t Q is the slow outflow rate of the karst region at time t. ks,t-1 Let a be the slow outflow and sinking flow rate of the karst region at time t-1. ks R is the coefficient for the regression of slow karst flows. ks,t The flow rate of the karst region at time t is the slow outflow rate.

[0108] The runoff volume in a karst region is the sum of the rapid outflow runoff volume and the slow outflow runoff volume in the karst region, i.e., Q. k,t =Q kq,t +Q ks,t Q k,t Let t be the total runoff in the karst region at time t.

[0109] Step 5: For non-karst areas, existing and mature rainfall-runoff basin models (such as the Xin'anjiang model, Sacramento model, water tank model, TOPKAPI model, etc.) are used to calculate the runoff volume Q of the non-karst area at time t. b,t .

[0110] Step 6: The total discharge at the outlet of this basin is equal to the sum of the discharges from the karst and non-karst areas, i.e., Q. c,t =Q k,t +Q b,t Q c,t The calculated watershed outlet flow rate (which may be referred to as "simulated value" or "calculated value").

[0111] The simulated value Q of the basin outlet discharge during a flood event in the basin. c,t Compared with the measured value Q t A comparison was made, such as Figure 3 As shown, the accuracy of the simulation results was evaluated using the relative error of the flood peak, the relative error of the flood volume, and the coefficient of determination. The relative error of the flood peak was -4.9%, the relative error of the flood volume was 10.1%, and the coefficient of determination was 0.75, indicating that the simulation process is in high agreement with the measured flow process and meets the accuracy requirements of the "Hydrological Information Forecasting Standard (GB / T22482-2008)".

[0112] This invention proposes a method for calculating runoff generation and confluence in karst areas that considers spatial differences in the underlying surface. It uses a parabolic linear statistical distribution to describe the spatial non-uniformity of the runoff generation threshold in karst areas, and calculates both rapid and slow karst outflows separately, thereby improving the accuracy and precision of runoff generation and confluence calculations in karst areas.

[0113] Finally, it should be noted that the above description is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred arrangement, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for calculating runoff generation and confluence in karst areas considering spatial differences in underlying surfaces, characterized in that, The method includes the following steps: Step 1: Data Collection and Preprocessing: Collect hydrological and meteorological data for the target karst area, including precipitation data from various rain gauge stations and evaporation data from various evaporation stations in the watershed; calculate the average precipitation over the watershed using the Thiessen polygon method based on the distribution of rain gauge stations. The average evaporation rate of the watershed was calculated by processing the evaporation data using the Thiessen polygon method based on the distribution of evaporation sites. ; Step 2, Calculation of runoff threshold distribution in karst areas: Based on the non-uniform distribution of runoff thresholds in karst areas, a statistical curve is used to characterize the distribution of runoff thresholds in karst areas. The formula for calculating the runoff threshold distribution curve in karst areas is as follows: (1) In the formula, FR represents the proportion of runoff-producing area in the karst region, f is the area of ​​the runoff-producing portion of the karst region, and FR is the total area of ​​the karst region. The threshold for single-point runoff generation in karst areas. This represents the maximum runoff threshold at a single point in the karst region. It is the non-uniformity index of the runoff generation threshold distribution curve in karst areas; Step 3, Calculation of Karst Area Outflow: Based on the distribution of runoff thresholds in karst areas, the portion of rainfall exceeding the runoff threshold generates rapid outflow. The rapid outflow rate in karst areas is calculated based on the different runoff thresholds in different regions. Based on the distribution of runoff thresholds in karst areas, the slow outflow rate in karst areas is calculated using the slow outflow coefficient. The runoff rate in karst areas is the sum of the rapid outflow rate and the slow outflow rate in karst areas. Step 4: Calculation of runoff in karst areas: Calculate the runoff based on the rapid outflow and slow outflow of the karst areas to obtain the rapid outflow runoff and slow outflow runoff of the karst areas. The runoff in the karst areas is the sum of the rapid outflow runoff and slow outflow runoff of the karst areas.

2. The method for calculating runoff generation and confluence in karst areas considering spatial differences in underlying surfaces, as described in claim 1, is characterized in that... The calculation process for the rapid outflow rate in the karst area mentioned in step 3 is as follows: First, the maximum runoff threshold currently reached in the karst region at the initial stage of the watershed is calculated as follows: (2) In the formula, This represents the maximum runoff threshold currently reached in the karst region under its initial conditions. This represents the average runoff generation threshold already achieved in the karst region under the initial conditions. This represents the average runoff threshold within the karst region. According to formula (1), the average runoff threshold in the karst area for: SKM = SKMM / (1 + kweb) (3) Then, based on the average evaporation rate of the watershed calculated in step 1... The potential evapotranspiration capacity of the karst area is calculated as follows: (4) In the formula, The potential evapotranspiration capacity of karst areas This is the conversion factor for potential evapotranspiration in karst areas; The average precipitation over the watershed calculated in step 1 The net rainfall is calculated as follows: (5) In the formula, To supplement the net rainfall in the karst area; Finally, based on the runoff threshold distribution, the rapid outflow rate in the karst area was calculated as follows: (6) In the formula, For rapid outflow in karst areas; The calculation process for the slow outflow rate in the karst area mentioned in step 3 is as follows: (7) In the formula, For slow outflow rates in karst areas, This represents the slow outflow coefficient of karst.

3. The method for calculating runoff generation and confluence in karst areas considering spatial differences in underlying surfaces, as described in claim 1, is characterized in that... The runoff calculation in step 4 uses the linear reservoir method; the calculation process for the rapid outflow runoff and slow outflow runoff in the karst area is as follows: The rapid outflow volume of the karst area is: (8) In the formula, for The rapid outflow and sinking volume of the karst area at all times for The rapid outflow and sinking volume of the karst area at all times The coefficient for rapid karst flow regression. for Rapid outflow from karst areas at all times; The slow outflow volume of the karst area is: (9) In the formula, for The slow outflow and sinking volume of the karst area at all times for The slow outflow and sinking volume of the karst area at all times This represents the coefficient for the regression of slow karst flows. for Slow outflow rate in karst areas.

Images