Hydrological parameter transplanting method, small watershed flood forecasting method, equipment, medium and product

Abstract

The invention discloses a hydrological parameter transplanting method, a small watershed flood forecasting method, equipment, a medium and a product, and relates to the technical field of hydrological forecasting and hydrological parameter determination. According to the method, firstly, space unit division is carried out on a research area, then a similar area is determined for each space unit, and hydrological parameters of enough first-class space units in the similar areas are determined by adopting a parameter mapping mode; according to the method, hydrological parameter transplantation is carried out based on parameter mapping and spatial interpolation modes, hydrological parameters of different space units of a small watershed are determined, and the problem that the hydrological parameters of different space units of the small watershed cannot be determined due to data scarcity and insufficient field observation is solved. The hydrological parameters are difficult to quantify accurately, and accurate determination of the hydrological parameters is realized.

Description

Technical Field

[0001] The present application relates to the technical field of hydrological forecasting and hydrological parameter determination, and particularly to a method for transplanting hydrological parameters, a method for flood forecasting in small watersheds, equipment, a medium, and a product. Background Art

[0002] Flood forecasting in small watersheds is an important research direction in the field of disaster prevention and mitigation. However, in practical applications, it faces many challenges. First, due to the small area and significant local characteristics of small watersheds, their hydrological processes (such as rainfall infiltration, surface runoff generation, and confluence processes) have strong spatio-temporal heterogeneity. Traditional methods that rely on long-term historical data to determine parameters often do not work well in such areas. Specifically, the key parameters involved in the model are difficult to accurately quantify due to scarce data and insufficient on-site observations. How to obtain a reasonable and accurate parameter field has always been a technical problem in this field. Summary of the Invention

[0003] The purpose of the present application is to provide a method for transplanting hydrological parameters, a method for flood forecasting in small watersheds, equipment, a medium, and a product, which can solve the defect that it is difficult to accurately quantify hydrological parameters due to scarce data and insufficient on-site observations through the transplantation method, and achieve the accurate determination of hydrological parameters.

[0004] To achieve the above purpose, the present application provides the following solutions.

[0005] In the first aspect, the present application provides a method for transplanting hydrological parameters, including:

[0006] Dividing the research area into spatial units and obtaining the environmental variables of each spatial unit;

[0007] According to the environmental variables of each spatial unit, determining the similar regions of each spatial unit, and taking the spatial units with the number of similar regions greater than a preset threshold as the first type of spatial units, and taking the spatial units with the number of similar regions not greater than the preset threshold as the second type of spatial units;

[0008] According to the environmental variables of each first-type spatial unit, the environmental variables and hydrological parameters of the similar regions of each first-type spatial unit, determining the hydrological parameter mapping values of each first-type spatial unit by using the parameter mapping method;

[0009] According to the hydrological parameter mapping values of each first-type spatial unit, determining the hydrological parameter mapping values of each second-type spatial unit by using the spatial interpolation method.

[0010] In the second aspect, a method for flood forecasting in small watersheds is provided, including:

[0011] Taking the small watershed as the research area and using the above-mentioned hydrological parameter transplantation method, the hydrological parameters of the small watershed are obtained;

[0012] Inputting the hydrological parameters of the small watershed into the distributed hydrological model to simulate the runoff and confluence of the small watershed;

[0013] Determining the flood risk of the small watershed based on the runoff and confluence simulation results.

[0014] In a third aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the above-mentioned hydrological parameter transplantation method or the above-mentioned small watershed flood forecasting method.

[0015] In a fourth aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the above-mentioned hydrological parameter transplantation method or the above-mentioned small watershed flood forecasting method.

[0016] In a fifth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the above-mentioned hydrological parameter transplantation method or the above-mentioned small watershed flood forecasting method

[0017] According to the specific embodiments provided by the present application, the present application has the following technical effects.

[0018] The present application provides a hydrological parameter transplantation method, a small watershed flood forecasting method, a device, a medium, and a product. The present application first divides the research area into spatial units, then determines the similar areas for each spatial unit, uses the parameter mapping method to determine the hydrological parameters for the first type of spatial units with sufficient similar areas, and uses the spatial interpolation method to determine the hydrological parameters for the second type of spatial units with insufficient similar areas. The present application performs hydrological parameter transplantation based on the parameter mapping and spatial interpolation methods to determine the hydrological parameters of different spatial units in the small watershed, solves the defect that it is difficult to accurately quantify hydrological parameters due to data scarcity and insufficient on-site observations, and realizes the accurate determination of hydrological parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0020] Figure 1 It is a schematic flowchart of a hydrological parameter transplantation method provided by an embodiment of the present application.

[0021] Figure 2 A structural schematic diagram of a computer device provided in an embodiment of the present application. Specific implementation manners

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part rather than all of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0023] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0024] A method for transplanting hydrological parameters, a small watershed flood forecasting method, a device, a medium, and a product of the present application are applicable to determining key hydrological parameter transplantation in small watersheds in data-scarce areas, and are particularly applicable to small watersheds with complex environmental conditions and insufficient on-site observation data, and can effectively improve the parameter estimation accuracy and the reliability of the hydrological model.

[0025] In an exemplary embodiment, a method for transplanting hydrological parameters is provided, as Figure 1 shown, including the following steps 101 - step 104.

[0026] Step 101, divide the research area into spatial units and obtain the environmental variables of each spatial unit.

[0027] Step 102, determine the similar areas of each spatial unit according to the environmental variables of each spatial unit, and regard the spatial units with the number of similar areas greater than the preset threshold as the first type of spatial units, and regard the spatial units with the number of similar areas not greater than the preset threshold as the second type of spatial units.

[0028] Step 103, according to the environmental variables of each first type of spatial unit, the environmental variables and hydrological parameters of the similar areas of each first type of spatial unit, determine the hydrological parameter mapping values of each first type of spatial unit by using the parameter mapping method.

[0029] Step 104, according to the hydrological parameter mapping values of each first type of spatial unit, determine the hydrological parameter mapping values of each second type of spatial unit by using the spatial interpolation method.

[0030] Implementing the above steps 101 - step 104 solves the defect that it is difficult to accurately quantify hydrological parameters due to data scarcity and insufficient on-site observation, and realizes the accurate determination of hydrological parameters.

[0031] In another exemplary embodiment, in step 101, GIS technology is used to divide the study area into spatial units, extract environmental variable characteristics, including elevation, slope, aspect, vegetation index, land use type, and soil type, and perform data preprocessing. Data preprocessing includes unifying spatial coordinates, handling outliers, and interpolating missing values.

[0032] In another exemplary embodiment, in step 103, the environmental variables of each similar area are used as independent variables, i.e., input features, and the hydrological parameters of the similar areas (including but not limited to soil saturated permeability Ks, wetting front suction potential ψ, and soil moisture difference Δθ) are used as outputs (Y), i.e., labels, to construct a training sample set of K training samples:

[0033] {(X1,Y1),(X2,Y2),…,(X K ,Y K )}

[0034] Support Vector Regression (SVR) aims to find a nonlinear mapping function f(X) to perform regression fitting on the training data with minimal structural risk (i.e., model complexity). This function can be expressed as:

[0035]

[0036] in:

[0037] f(X): support vector machine regression model;

[0038] A nonlinear mapping function that maps the input feature X to a high-dimensional feature space;

[0039] ω: weight vector in the high-dimensional feature space of the support vector machine regression model;

[0040] b: Bias term of the support vector machine regression model.

[0041] By introducing slack variables and ε-insensitive loss function, the following optimization problem is established:

[0042]

[0043] Constraints:

[0044]

[0045] Among them, ξ k and are two slack variables for the kth training sample, K is the number of training samples, C is the regularization parameter used to balance the model complexity and training error, ∈ is the error tolerance, and Y kis the label of the k-th training sample, is the input feature X of the k-th training sample k is the non-linear mapping function that maps the input feature X of the k-th training sample to a high-dimensional feature space. The superscript T represents the transpose

[0046] In another exemplary embodiment, for the second type of spatial units with a small number of non-existent similar regions, the present application uses the following formula to obtain hydrological parameters.

[0047]

[0048] where, Z n is the hydrological parameter mapping value of the second type of spatial unit n, Z j is the hydrological parameter mapping value of the first type of spatial unit j corresponding to the second type of spatial unit n, J n is the number of the first type of spatial units adjacent to the second type of spatial unit n, λ j is the interpolation weight coefficient of the first type of spatial unit j adjacent to the second type of spatial unit n; n = 1, 2,..., N, and N is the number of the second type of spatial units.

[0049] In another exemplary embodiment, local correction is performed on the interpolation result and / or the mapping result. The correction amount of each spatial unit is calculated based on the limited adjacent measured points around itself. A small number of measured points are selected around the point to be corrected, the prediction residual is calculated, and correction is performed through inverse distance weighted interpolation (IDW):

[0050]

[0051] In the formula: Z' i is the corrected value of the hydrological parameter of spatial unit i, Z i is the mapping value of the hydrological parameter of spatial unit i, e f is the residual of the f-th measured point for local correction, e f = S(x f ) - Z(x f ), S(x f ) and Z(x f ) are respectively the measured value of the hydrological parameter and the mapping value of the hydrological parameter of the f-th measured point x f for local correction, d i,f is the spatial distance between the center of spatial unit i and the f-th measured point, p is the power exponent of the distance, and F is the total number of measured points for local correction.

[0052] Import the corrected parameter field into the hydrological model to calculate the runoff generation and concentration process of the small watershed. The model formulas include the cumulative infiltration amount I(t), the instantaneous infiltration rate f(t), the instantaneous runoff generation rate R(t), and the concentrated flow rate Q(t). The parameter test is evaluated using the Nash efficiency coefficient.

[0053]

[0054] Among them, NSE is the Nash efficiency coefficient, which is used to measure the model simulation accuracy. The value range is (∞, 1]. The closer it is to 1, the better the model prediction effect. Q obs (t) is the measured flow at time t. Q sim (t) is the simulated flow at time t. is the average value of the measured flow during the entire evaluation period. T' is the total number of flow data simulated by the model.

[0055] In an exemplary embodiment, a small watershed flood forecasting method is provided, including the following steps 201-step 203.

[0056] Step 201: Take the small watershed as the research area and use the above hydrological parameter transplantation method to obtain the hydrological parameters of the small watershed.

[0057] Step 202: Input the hydrological parameters of the small watershed into the distributed hydrological model to perform runoff generation and concentration simulation of the small watershed.

[0058] Step 20,3: Determine the flood risk of the small watershed based on the runoff generation and concentration simulation results.

[0059] In another exemplary embodiment, the above distributed hydrological model is used for the models of infiltration, runoff generation, and concentration processes.

[0060] 1. Infiltration

[0061] 1.1 Cumulative infiltration amount

[0062]

[0063] This equation generally needs to solve I through numerical iteration i (t), where K s is the soil saturated permeability (mm / h), ψ is the capillary pressure head at the wetting front (mm), Δθ is the difference between the saturated water content and the initial water content, Δθ = θ s - θ i , θ s is the saturated water content, θ i is the initial water content, I i (t) is the cumulative infiltration amount (mm) of the spatial unit i of the small watershed at time t.

[0064] 1.2, Instantaneous Infiltration Rate

[0065]

[0066] Where: f i (t) is the instantaneous infiltration rate (mm / h) of the spatial unit i in the small watershed at time t, and t is the time (h).

[0067] 2. Runoff Generation

[0068] Assume the rainfall intensity is P(t) (mm / h). If P(t) > f(t), then the rainfall amount exceeding the soil infiltration capacity is converted into surface runoff. That is

[0069] R i (t) = max{0, P i (t) - f i (t)}

[0070] Where: R i (t) is the instantaneous runoff generation rate of the spatial unit i in the small watershed at time t, and P i (t) is the rainfall intensity of the spatial unit i in the small watershed at time t, in mm / h.

[0071] 3. Confluence

[0072] If the watershed is divided into n units, and the area of each unit is A i (m 2 ), then the runoff generation q i (t) (m 3 / s) of this unit can be expressed as:

[0073]

[0074] Suppose the runoff generation of the i-th unit reaches the watershed outlet after a time delay T i . Then the watershed outlet flow Q out (t) can be expressed as:

[0075]

[0076] Among them, q i (t - T i ) is the runoff generation of the spatial unit i in the small watershed at time t - T i , A i is the area of the spatial unit i in the small watershed, R i (t - T i ) is the instantaneous runoff generation rate of the spatial unit i in the small watershed at time t - T i , Q out (t) is the watershed outlet flow at time t, I is the number of spatial units in the small watershed, and T iThe time delay for the runoff of the i-th unit to reach the basin outlet.

[0077] According to the specific embodiments provided by the present application, the present application has the following technical effects.

[0078] (1) The present application proposes a multi-source data fusion method applicable to data-scarce areas to improve the accuracy of parameter estimation. By combining remote sensing data and through data enhancement and feature optimization, the data integrity and spatial representativeness are improved, breaking through the dependence of traditional methods on long-term historical data and being applicable to the estimation of hydrological parameters in areas with no or few gauging stations. The GIS technology is used to finely extract the basin environmental variables, making the data input more refined and providing high-quality support for subsequent modeling.

[0079] (2) The present application introduces machine learning methods to achieve a high-precision mapping from environmental variables to hydrological parameters. Support vector regression (SVR) is used to construct a non-linear mapping relationship between environmental variables and key hydrological parameters, replacing traditional empirical formulas and improving the generalization ability of parameter estimation.

[0080] (3) The present application combines parameter mapping, spatial interpolation, local correction, and hydrological model integration to improve the accuracy and applicability of hydrological forecasting. The method of combining Kriging interpolation and inverse distance weighting interpolation is used to optimize the spatial distribution of parameters, enabling the parameter field to maintain the overall trend and locally adaptively adjust. A residual correction method is introduced to correct the interpolation error using a small amount of observed data to ensure that the parameter estimation is more in line with the actual situation of the target basin. A complete process of parameter estimation - model application - result verification is proposed to make the transplantation of hydrological parameters more applicable and popularizable. The optimized parameter field is applied to a distributed hydrological model and verified by combining runoff generation and concentration simulation to improve the reliability and accuracy of hydrological forecasting.

[0081] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal, and its internal structure diagram can be as Figure 2As shown in the figure. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. When the computer program is executed by the processor, it implements a method for transplanting hydrological parameters or a method for flood forecasting in a small watershed.

[0082] Those skilled in the art can understand that Figure 2 the structure shown in the figure is only a block diagram of some structures related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0083] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0084] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0085] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or fully authorized by all parties.

[0086] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0087] The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0088] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0089] Specific examples are used in this article to elaborate on the principles and implementation manners of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for transplanting hydrological parameters, characterized in that, including: Dividing the research area into spatial units and obtaining the environmental variables of each spatial unit; According to the environmental variables of each spatial unit, determining the similar areas of each spatial unit, and taking the spatial units with the number of similar areas greater than a preset threshold as the first type of spatial units, and taking the spatial units with the number of similar areas not greater than the preset threshold as the second type of spatial units; According to the environmental variables of each first-type spatial unit, the environmental variables of the similar areas of each first-type spatial unit, and the hydrological parameters, using the parameter mapping method to determine the hydrological parameter mapping values of each first-type spatial unit; According to the hydrological parameter mapping values of each first-type spatial unit, using the spatial interpolation method to determine the hydrological parameter mapping values of each second-type spatial unit.

2. The hydrological parameter transplantation method according to claim 1, wherein The step of determining the hydrological parameter mapping values of each first-type spatial unit by using the parameter mapping method according to the environmental variables of each first-type spatial unit, the environmental variables of the similar areas of each first-type spatial unit, and the hydrological parameters specifically includes: Constructing a training sample set according to the environmental variables and hydrological parameters of the similar areas of the first-type spatial unit m; the training sample set includes multiple training samples, the input feature of the training sample is the environmental variable of the similar area, and the label of the training sample is the hydrological parameter of the similar area; m = 1, 2,..., M, and M is the number of the first-type spatial units; Training a support vector machine regression model according to the training sample set, and taking the trained support vector machine regression model as the mapping model of the first-type spatial unit m; Inputting the environmental variables of the first-type spatial unit m into the mapping model of the first-type spatial unit j to obtain the hydrological parameter mapping value of the first-type spatial unit m.

3. The hydrological parameter transplantation method according to claim 2, characterized in that The objective function adopted in the process of training the support vector machine regression model is: The constraint conditions adopted in the process of training the support vector machine regression model are: where ω is the weight vector in the high-dimensional feature space of the support vector machine regression model, b is the bias term of the support vector machine regression model, and ξ k and are the two slack variables of the k-th training sample respectively, K is the number of training samples, C is the regularization parameter, ∈ is the error tolerance, Y k is the label of the k-th training sample, is the non-linear mapping function that maps the input feature X k of the k-th training sample to the high-dimensional feature space, and the superscript T represents the transpose.

4. The hydrological parameter transplantation method according to claim 1, characterized in that The formula for spatial interpolation is: Among them, Z n is the mapped value of the hydrological parameter of the second type of spatial unit n, Z j is the mapped value of the hydrological parameter of the first type of spatial unit j corresponding to the second type of spatial unit n, J n is the number of the first type of spatial units adjacent to the second type of spatial unit n, λ j is the interpolation weight coefficient of the first type of spatial unit j adjacent to the second type of spatial unit n; n = 1, 2,..., N, where N is the number of the second type of spatial units.

5. The hydrological parameter transplantation method according to claim 1, characterized in that, After determining the hydrological parameter mapping values of each second-type spatial unit by using the spatial interpolation method according to the hydrological parameter mapping values of each first-type spatial unit, it further includes: Performing local correction on the hydrological parameter mapping values of each spatial unit; The formula for local correction is: Among them, Z' i is the corrected value of the hydrological parameter of spatial unit i, Z i is the mapped value of the hydrological parameter of spatial unit i, e f is the residual of the f-th measured point for local correction, e f = S(x f ) - Z(x f ), S(x f ) and Z(x f ) are respectively the measured value and the mapped value of the hydrological parameter of the f-th measured point x f for local correction, d i,f is the spatial distance between the center of spatial unit i and the f-th measured point, p is the power exponent of the distance, and F is the total number of measured points for local correction.

6. A small watershed flood forecasting method, characterized in that, including: Taking the small watershed as the research area and using the hydrological parameter transplantation method described in any one of claims 1-5 to obtain the hydrological parameters of the small watershed; Inputting the hydrological parameters of the small watershed into a distributed hydrological model to perform runoff and confluence simulation of the small watershed; Determining the flood risk of the small watershed based on the runoff and confluence simulation results.

7. The small watershed flood forecasting method according to claim 6, characterized in that, The distributed hydrological model includes: a cumulative infiltration amount simulation model, an instantaneous infiltration amount simulation model, a runoff generation simulation model, and a confluence simulation model; The cumulative infiltration amount simulation model is: Among them, K s is the saturated hydraulic conductivity of the soil, ψ is the capillary pressure head at the wetting front, Δθ is the difference between the saturated water content and the initial water content, and I i (t) is the cumulative infiltration amount of the spatial unit i in the small watershed at time t; The instantaneous infiltration amount simulation model is: where f i (t) is the instantaneous infiltration rate of the spatial unit i in the small watershed at time t; The runoff generation simulation model is: R i (t) = max{0, P i (t) - f i (t)}; Among them, P i (t) is the rainfall intensity of the spatial unit i of the small watershed at time t, and R i (t) is the instantaneous runoff generation rate of the spatial unit i of the small watershed at time t; The confluence simulation model is: Among them, q i (t - T i ) is the runoff generation of the spatial unit i in the small watershed at time t - T i , A i is the area of the spatial unit i in the small watershed, R i (t - T i ) is the instantaneous runoff generation rate of the spatial unit i in the small watershed at time t - T i , Q out (t) is the flow rate at the watershed outlet at time t, I is the number of spatial units in the small watershed, and T i is the time delay for the runoff of the i-th unit to reach the watershed outlet.

8. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the hydrological parameter transplantation method described in any one of claims 1-5 or the small watershed flood forecasting method described in any one of claims 6-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the hydrological parameter transplantation method described in any one of claims 1-5 or the small watershed flood forecasting method described in any one of claims 6-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the hydrological parameter transplantation method described in any one of claims 1-5 or the small watershed flood forecasting method described in any one of claims 6-7.

Images