Model parameter estimation method of distributed hydrological physical model in watershed lacking data

Abstract

The invention relates to the technical field of hydrogeology. Aiming at the problem of inaccurate parameter estimation in the prior art, the invention discloses a distributed hydrological physical model parameter estimation method suitable for a watershed lacking data, and the model parameters of the watershed lacking data are estimated by establishing the relationship between the model parameters and watershed characteristics. The technical scheme of the invention is a model parameter estimation method of a distributed hydrological physical model in a watershed lacking data. The method comprises the following steps: a, selecting characteristic factors; b, calculating characteristic factors; c, optimizing model parameters; d, establishing a correlation between the model optimization parameters and the characteristic factors; e, constructing a parameter transfer function; and f, estimating data-lacking watershed model parameters according to the parameter transfer function. According to the method, the characteristics of the drainage basin lacking data are better considered, the quantitative relation between the model parameter values and the physical characteristics such as the soil type, the land utilization, the vegetation and the terrain of the underlying surface of the drainage basin is revealed, and the model parameter transfer function is established.

Description

Technical Field

[0001] The present application relates to the field of hydrogeological technology, and in particular to a method for calibrating parameters of a hydrological physics model, and more specifically, to a method for estimating model parameters of a distributed hydrological physics model in a data-deficient basin. Background Art

[0002] With the development of society and the increasing impact of human activities, water-related problems are becoming more and more serious, and runoff simulation and hydrological forecasting in data-deficient basins are also facing greater challenges. Mountain floods are most typical in small and medium-sized basins with an area of ​​less than hundreds of square kilometers. Most of them are "data-deficient basins" where there is a serious lack of measured data on surface precipitation and river cross-sectional flow. The changeable weather in the basin and the rapid flow generation due to heavy rains make it very difficult to forecast floods in mountainous areas. At the 23rd International Geophysical and Geodetic Conference held in Sapporo, Japan in July 2003, the International Association of Hydrological Sciences officially launched an international hydrological program called PUB (Predication in Ungauged Basin). The conference defined PUB as: in basins with no observations or poor observations, using meteorological inputs (including observations, predictions and other methods of inference), but unable to use past observations (i.e., it is impossible or not allowed to debug and calibrate model parameters), to predict or forecast various hydrological responses (such as runoff, water quality and sediment, etc.). Although decades of research have been done, many problems (hydrological forecasting, scientificity and reliability of runoff simulation) have not been fully and effectively solved. In this context, how to reasonably assign values ​​to hydrological model parameters in data-deficient basins and improve the adaptability and accuracy of hydrological models are still hot and difficult issues in the current hydrological science community.

[0003] The distributed hydrological physics model BTOPMC (Block-wise use of the TOPMODEL), sometimes referred to as a hydrological model or model, is a distributed hydrological physics model for large-scale watersheds developed by Kuniyoshi Takeuchi, Tianqi Ao and others from Yamanashi University in Japan based on the TOPMODEL model. The model consists of three parts: terrain sub-model, flow generation sub-model and flow confluence sub-model. It can reliably simulate the flow generation and confluence process, soil moisture changes and flow size in the watershed. The model has a strong physical basis and has been widely used in more than 2,000 watersheds around the world, involving water resources management, flood forecasting, water environment simulation and other fields.

[0004] Strictly speaking, the parameters in the distributed hydrological physical model have physical meanings, which can respectively reflect the influence of basin physical characteristics such as basin topography, soil characteristics, vegetation and land use types on the basin hydrological response process. The parameter values ​​should be respectively corresponding to or comprehensively determined quantitatively using these physical characteristics. However, this quantitative correspondence between the model parameter values ​​and the basin physical characteristics has not yet been scientifically and systematically established. Therefore, although this type of model has its unique advantages, it is difficult to play a role in basins lacking measured data at this stage because its parameter values ​​are difficult to determine reasonably and reliably.

[0005] At present, researchers have proposed a series of parameter transfer function methods, including statistical analysis, data mining and machine learning, which can infer the parameters of the hydrological model from limited observational data and other relevant indicators, and can be used to estimate the parameters of the hydrological model in data-deficient basins. However, there are still some challenges and issues that need further research, such as data uncertainty, model adaptability and the generalizability of parameter transfer functions.

[0006] In order to solve the problem that the key data (precipitation and runoff) required by the model cannot be assigned reasonable parameter values ​​to the distributed hydrological physical model through the parameter optimization process in the data-deficient basin, the commonly used method is the parameter transplantation method, which is the technology of applying the parameters of the existing hydrological model to the new basin or region. Its basic idea is to reduce the workload of parameter estimation or improve the accuracy of parameter estimation by transferring parameters from a basin with data to another basin with insufficient data. The following are common types of parameter transplantation methods:

[0007] (1) Direct parameter transplantation: The direct parameter transplantation method directly applies the parameters of the basin with data to the new basin. This method is simple and direct, does not require parameter estimation, and can save time and workload. However, direct parameter transplantation may ignore the climate and underlying surface characteristics of the new basin, resulting in poor model adaptability and inaccurate results.

[0008] (2) Parameter linear scaling: The parameter linear scaling method adapts the parameters of the data basin to the new basin by linearly scaling the parameters of the data basin according to the characteristics of the new basin. This method can take into account some characteristics of the new basin, but it still lacks flexibility. Linear scaling may not capture the nonlinear relationship between different basins, resulting in inaccurate parameter estimation.

[0009] Both of the above parameter transplantation methods have certain limitations in terms of model adaptability. If the new basin has significant differences in climate and underlying surface characteristics from the basin with data, parameter transplantation may result in the simulation performance of the hydrological model being unable to meet actual needs. Summary of the invention

[0010] The main purpose of this application is to provide a distributed hydrological physical model parameter estimation method suitable for data-deficient basins. By establishing the relationship between model parameters and basin characteristics, model parameters of data-deficient basins are estimated to solve the problem of inaccurate parameter estimation in the prior art.

[0011] In order to achieve the above object, according to one aspect of the specific implementation of the present application, a method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin is provided, comprising the following steps:

[0012] a. Select characteristic factors, which include climate characteristic factors, underlying surface characteristic factors and watershed characteristic factors;

[0013] b. Calculation of characteristic factors;

[0014] c. Model parameter optimization;

[0015] d. Establish the correlation between model optimization parameters and characteristic factors;

[0016] e. Select characteristic factors with linear correlation coefficients greater than or equal to a specific value with respect to the model optimization parameters as independent variables, and construct parameter transfer functions;

[0017] f. Estimate the model parameters of the data-deficient watershed based on the parameter transfer function.

[0018] In certain embodiments, the linear correlation coefficient is obtained by the following formula:

[0019]

[0020] In the formula, CC is the linear correlation coefficient, and They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding distributed hydrological physical model parameter. is the mean of the characteristic factors, is the mean value of the model parameters.

[0021] In certain embodiments, the specific value refers to CC ≥ 0.4.

[0022] In some embodiments, the steps are further included:

[0023] g. Evaluate the fitting effect of the parameter transfer function.

[0024] In certain embodiments, the following formula is used to evaluate the fitting effect in step g:

[0025]

[0026] In the formula, R 2 is the goodness of fit, and They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding distributed hydrological physical model parameter. is the mean of the characteristic factors, is the mean of the model parameters; R 2 ≥0.50, the fitting effect is considered to meet the requirements.

[0027] In certain embodiments, the climate characteristic factors include precipitation P, potential evapotranspiration ET0, and potential intercepted evaporation PET0.

[0028] In some embodiments, the underlying surface characteristic factors include average elevation DEM, average slope S, average terrain index TI, average leaf area index LAI, average soil particle size Φ and average root depth T.

[0029] In certain embodiments, the average particle size of the soil Among them, r i refers to the proportion of the i-th soil component, Φ i It refers to the average particle size of the i-th soil component, and n is the number of soil types;

[0030] The average root depth Among them, r i refers to the i-th land use type, T i is the root depth corresponding to the i-th land use type, and m is the number of grids in the study basin.

[0031] In some embodiments, the watershed characteristic factor is a morphological factor F.

[0032] In some embodiments, the parameter transfer function expression is as follows:

[0033] D0_bk=-4.38e-03+1.16e-02×ET0-2.59e-02×PET0-2.48e-04×Φ+7.47e-07×DEM-

[0034] 2.023e-02×S-1.83e-04×TI;

[0035] m=-0.43+1.22×ET0-0.09×Φ+0.03×TI;

[0036] n0=-6.94e-02-1.47e-01×P+2.33e-01×ET0-2.47e-05×DEM+1.33e+00×S;

[0037] α=-2.65e+01+2.55e+01×PET0+1.57e-03×A+9.31e+01×F.

[0038] According to the technical solution of the present application and the further improved technical solution in some embodiments thereof, the present application has the following beneficial effects:

[0039] This application takes better account of the characteristics of data-deficient basins, reveals the quantitative relationship between model parameter values ​​and physical characteristics such as soil type, land use, vegetation, and topography of the basin's underlying surface, and establishes a model parameter transfer function, thereby realizing the automatic calculation and assignment of parameter values ​​for each block in the basin. The model parameter estimation method of this application has low uncertainty and strong applicability, breaking through the technical bottleneck that it is difficult or even impossible to determine model parameters for flood forecasting in data-deficient areas, and provides a new method for determining model parameters with good applicability for flood forecasting in mountainous basins with insufficient data that is widely present in high-altitude and cold regions. It has high academic and practical value and is widely replicable and extensible.

[0040] The present application is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present application will be partially given in the following description, partially become apparent from the following description, or be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings constituting a part of this application are used to provide a further understanding of this application. The specific implementation modes, illustrative embodiments and their descriptions of this application are used to explain this application and do not constitute an improper limitation on this application. In the drawings:

[0042] Figure 1 It is a flow chart of a method for estimating parameters of a watershed model with insufficient data according to a specific implementation method of the present application;

[0043] Figure 2 It is a schematic diagram of the distribution of L model watershed and N model watershed blocks according to a specific implementation of the present application, wherein Figure a is the L model watershed and Figure b is the N model watershed;

[0044] Figure 3 Schematic diagram of parameter fitting of parameter transfer function at rate period according to a specific implementation mode of the present application, wherein FIG a is a watershed constructed by parameter transfer function; FIG b is a watershed verified by parameter transfer function; the upper horizontal coordinates of FIG a and FIG b indicate the numbers of the watershed blocks involved; the lower horizontal coordinates indicate the three soil compositions in different watersheds; the left side of the black vertical dotted line in FIG a corresponds to the L model watershed, and the right side corresponds to the N model watershed DETAILED DESCRIPTION

[0045] It should be noted that, in the absence of conflict, the specific implementation modes, exemplary embodiments and features thereof in this application can be combined with each other. The present application will now be described in detail with reference to the accompanying drawings and in combination with the following content.

[0046] In order to enable those skilled in the art to better understand the solution of this application, the following will be combined with the drawings in the specific implementation methods and exemplary embodiments of this application to clearly and completely describe the technical solutions in the specific implementation methods and exemplary embodiments of this application. Obviously, the described exemplary embodiments are only part of the embodiments of this application, not all of them. Based on the specific implementation methods and exemplary embodiments in this application, all other implementation methods and embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of this application.

[0047] In the BTOPMC model, five parameters with clear physical meanings need to be calibrated, namely, the groundwater discharge capacity D0, the average value of the saturated water shortage in the unsaturated layer SD bar , runoff attenuation coefficient m, average Manning roughness coefficient n0 and drying parameter α. The information on the relevant variables and value ranges of each parameter is shown in Table 1. Among them, the parameter SD bar , m, n0 and α need to be calibrated on each "block", that is, different "blocks" correspond to different parameter values; parameter D0 needs to be calibrated according to different soil types in the entire basin, using D 0clay , D 0sand and D 0silt Represents the groundwater discharge capacity of clay, sand and silt respectively.

[0048] Table 1 Parameters that need to be calibrated in the BTOPMC model

[0049]

[0050] How to determine the optimal parameters of the hydrological model for a data-deficient basin is one of the key issues in the study of hydrological simulation and prediction in data-deficient basins. At present, the parameter regionalization method is more commonly used, that is, through different methods, a mapping relationship between parameters between the data-deficient basin and the basin with measured data (data-based basin) is established, and the calibrated hydrological parameters are applied to the data-deficient basin. Commonly used regionalization methods include parameter transplantation, parameter regression, interpolation and averaging. Among them, the parameter transplantation method includes the distance proximity method and the attribute similarity method, which respectively refer to finding data-based basins that are geographically adjacent to the research object and similar to the research object in attributes (such as catchment area, river density, topography, vegetation cover, soil type and climatic conditions, etc.), and directly transferring the parameter values ​​optimized in these basins to the data-deficient basins. However, proximity and attribute similarity do not mean exactly the same, which makes the parameter transplantation method have obvious limitations. This application breaks through the limitations of distance proximity and attribute similarity by constructing the correlation between basin characteristics and model parameters in the data-based basin. For example Figure 1 As shown, the model parameter estimation method of the present application includes the steps of:

[0051] S1. Select characteristic factors

[0052] The selection of characteristic factors requires comprehensive consideration of various factors, including meteorological, underlying surface and watershed characteristics, and a variety of characteristic factors that can be obtained through existing technologies or data.

[0053] 1. Climate characteristic factors

[0054] Climate factors include precipitation, evaporation, temperature, humidity, air pressure and wind speed. Precipitation and evaporation are important components of water balance, and their size and distribution have an important impact on runoff. Temperature, air pressure, wind speed and humidity have an indirect impact on runoff mainly by affecting rainfall and evaporation.

[0055] This application only considers precipitation and evapotranspiration, two direct influencing factors. Among them, due to the great difficulty in collecting measured evapotranspiration data, this application uses potential evapotranspiration (ET0) and potential intercepted evaporation (PET0) in the hydrological model input as related factors of evapotranspiration factors. Therefore, this application selects three climate factors for the construction of parameter transfer function, namely precipitation (P), evapotranspiration (ET0) and potential intercepted evaporation (PET0). Taking precipitation as an example, with the joint development of multiple technologies such as satellite inversion, data fusion and numerical simulation, a number of high-resolution satellite precipitation products have emerged, such as GSMaP (Global Satellite Mapping of Precipitation), TMPA (TRMM Multi-satellite Precipitation Analysis), CMORPH (Climate Prediction Center Morphing technique), GPM (Global Precipitation Measurement project), PERSIANN (Precipitation from Remote Sensed Imagery Using Artificial Neural Network), etc. Potential evapotranspiration (ET0) and potential trapped evaporation (PET0) can be obtained through reanalysis data such as ERA5 (ECMWF Reanalysis v5).

[0056] 2. Underlying surface characteristic factors

[0057] The underlying surface conditions of a watershed include the topography, soil structure, land use and vegetation coverage of the watershed. The elevation of the watershed mainly affects the precipitation form and temperature, which in turn affects the change in water volume in the watershed. The surface slope of the watershed affects the slope runoff process. The spatial pattern of the terrain index in the watershed is used to determine the spatial distribution of the saturated water deficit in the watershed and the spatial location and range of the runoff-generating area. Therefore, this application selected three terrain factors, namely the mean elevation (DEM) of the watershed, the mean slope (S) and the mean terrain index (TI), and all of them can be calculated based on the DEM distribution (available) of the study area.

[0058] Soil structure affects the water supply, water retention and permeability of the watershed. Vegetation type, distribution, coverage and growth conditions mainly affect its ability to conserve water sources and regulate runoff. This application selects the average leaf area index (LAI) to characterize the vegetation coverage of the watershed. As for soil type and land use, this application defines two new characteristic factors: average soil particle size Φ and average root depth T. The Food and Agriculture Organization of the United Nations FAO forms different soil types based on the composition of clay, silt and sand. The soil average particle size index introduces soil particle size information based on the proportion information of each component of the soil type, and its formula is:

[0059]

[0060] Among them, r i refers to the proportion of the i-th soil component, Φ i It refers to the average particle size of the i-th soil component {clay: 0.001mm; silt: 0.026mm; sand: 1.025mm)}, and n is the number of soil types.

[0061] The land use type input required by the BTOPMC model is based on the International Geosphere-Biosphere Program (IGBP) global vegetation classification scheme, which is divided into 17 categories. The average root depth comprehensively considers the land use type and root depth information of each grid in the basin, and its formula is:

[0062]

[0063] Among them, r i refers to the i-th land use type, T i is the root depth corresponding to the i-th land use type, and m is the number of grids in the study basin.

[0064] 3. Basin characteristic factors

[0065] The basin area (A), also known as the catchment area, is one of the important characteristics of a basin. Generally speaking, in areas with similar natural conditions, the larger the basin area, the greater the water volume, and the greater the basin's role in regulating runoff. The basin shape is often expressed by the basin area and basin length (L b ) squared, which is called the morphological factor (F) of the basin. The larger the shape factor coefficient, the shorter and fatter the basin is, and the shorter the confluence time is; the smaller the shape factor coefficient, the thinner and longer the basin is, and the slower the confluence is. Through the analysis of many small basin data, it is found that the basin length (L b ) and the drainage area (A) have the following relationship:

[0066] L b =1.4A 0.568 (3)

[0067] Therefore, the morphological factor of the watershed can be expressed as:

[0068]

[0069] In summary, this application selects a total of 11 climate characteristic factors, underlying surface characteristic factors and watershed characteristic factors.

[0070] S2. Characteristic factor calculation

[0071] This application can obtain the values ​​of the above 11 characteristic factors by calculating the characteristic factors of the basin with data.

[0072] As a specific implementation of the present application, the L model watershed and the N model watershed are taken as examples for detailed description.

[0073] According to the characteristics of the parameter block values ​​of the BTOPMC model, the two basins are divided into 18 blocks (numbered 0 to 17) and 16 blocks (numbered 0 to 15), respectively. Figure 2 It should be noted that the parameter D0 (groundwater discharge capacity) is calibrated for different soil components, that is, the D0 value of the same soil component in the same basin is the same, and the drainage capacity of grid i is calculated using the following formula:

[0074] D i =U clay D 0clay +U sand D 0sand +U silt D 0silt (5)

[0075] Where: U clay , U sand and U silt Refers to the proportion of clay, sand and silt in grid i respectively; D 0clay, D 0sand and D 0silt They refer to the groundwater discharge capacity of clay, sand and silt respectively.

[0076] In order to obtain a certain number of parameter samples, this application calculates the groundwater discharge capacity of each grid according to formula (5), and takes the mean of the groundwater discharge capacity of all grids in each block as the groundwater discharge capacity of the corresponding block (denoted as D0_bk) to establish the correlation between it and each characteristic factor.

[0077] Among the 11 characteristic factors selected, the climate factor is a dynamic factor. First, the spatial distribution of the multi-year average value must be obtained by averaging on the time scale, and then the factors of the grids contained in each block are spatially averaged to obtain the size of the climate factor corresponding to the block. The characteristic factors related to the underlying surface conditions are static factors, and only spatial averaging is required. The basin area is obtained by counting the number of grids in the block and multiplying it by the area of ​​a single grid. The morphological factor of the basin is directly obtained according to formula (4). After calculation, the size of the characteristic factors of each block in the L model basin and the N model basin during the rate period and the verification period are shown in Table 2 and Table 3 respectively.

[0078] Table 2 Corresponding characteristic factors and values ​​of each block rate in the basin (2010-2013)

[0079]

[0080]

[0081]

[0082] Table 3 Corresponding characteristic factors and values ​​of each block in the basin during the verification period (2014-2015)

[0083]

[0084]

[0085]

[0086] S3. Model parameter optimization

[0087] The SCE-UA algorithm was used to optimize the BTOPMC models constructed in the L model basin and the N model basin to obtain the optimal parameter combination for each block, as shown in Table 4.

[0088] Table 4 Optimal parameters corresponding to each block

[0089]

[0090]

[0091] It can be seen from Table 4 that the D0_bk values ​​corresponding to each block in different watersheds are very close, and five significant digits need to be retained to see the difference.

[0092] S4. Establish the correlation between model optimization parameters and characteristic factors

[0093] Before constructing the parameter transfer function, it is necessary to first conduct a quantitative analysis of the correlation between the model parameters and characteristic factors obtained by calibration in the study basin. The most common correlation coefficient between variables is the Pearson correlation coefficient, also known as the linear correlation coefficient, which is defined as:

[0094]

[0095] In the formula, and They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding BTOPMC model parameter. is the mean of the characteristic factors, is the mean value of the model parameters.

[0096] The absolute value of the linear correlation coefficient CC is between 0 and 1. Generally speaking, the closer the value is to 1, the stronger the correlation between the variables. Conversely, the closer the value is to 0, the weaker the correlation between the variables. It is generally believed that when the absolute value of the correlation coefficient between two variables is higher than 0.40, the correlation between the variables can be considered to be moderately correlated.

[0097] After calculation, the linear correlation coefficients between the parameters obtained by the BTOPMC model in the periodic optimization and the characteristic factors of the corresponding blocks are shown in Table 5.

[0098] Table 5 Correlation coefficients between optimal model parameters and watershed characteristic factors

[0099]

[0100] In Table 5, the absolute values ​​of the correlation coefficients corresponding to the bold words are all ≥ 0.40, indicating that there is a moderate correlation between the corresponding characteristic factors and the parameters, and they can be used to construct the parameter transfer function.

[0101] The above results show that, except for SD barIn addition, all other parameters in the BTOPMC model have basin characteristic factors with correlation coefficients higher than 0.40 (moderate correlation). Among them, groundwater discharge capacity D0 and runoff attenuation coefficient m reflect the influence of basin soil type on model output, and both have a certain relationship with soil saturated permeability T0. Therefore, the correlation coefficients between the two and the average soil particle size index Φ are higher than 0.60, which has a strong correlation. As the only parameter that needs to be calibrated in the confluence submodel of the BTOPMC model, the average Manning roughness coefficient n0 reflects the friction resistance of the water channel to the water flow. This parameter is affected by many factors at the same time, such as riverbed characteristics and riverbed materials, river channel structure and riverbank roughness. The basin slope affects the riverbed to a certain extent, so its correlation coefficient with n0 is the highest, which is 0.65. As for the dryness parameter α, if and only if the water storage in the root zone does not reach the maximum water storage capacity, this parameter will participate in the dryness function related to the surface soil moisture required for the calculation of root zone evapotranspiration. Therefore, there is a certain correlation between the drying parameter α and the size of the entire study area and the interception evaporation variables within the basin, especially the basin area, with a correlation coefficient of 0.81.

[0102] S5. Construct parameter transfer function

[0103] Based on the correlation analysis results between the optimized values ​​of the rate-based BTOPMC model parameters and the basin characteristic factors, this application selects the characteristic factors with a correlation coefficient greater than 0.4 with the model parameters as independent variables, and uses the Python programming language to construct the parameter transfer function between the model parameters D0_bk, m, n0 and α and the corresponding basin characteristic factors with higher correlation, as shown in Table 6. Among them, the construction of the parameter transfer function uses the parameters and basin characteristic factor data of the blocks contained in the L model basin and the N model basin. Part of the data of the N model basin is used to verify the transferability of the constructed parameter transfer function in space. In addition, the goodness of fit R is selected 2 As an evaluation index of the parameter transfer function fitting effect, the calculation formula is:

[0104]

[0105] In the formula, and They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding BTOPMC model parameter. is the mean of the characteristic factors, is the mean value of the model parameters.

[0106] Table 6 Multivariate linear regression equations between optimal model parameters and watershed characteristic factors

[0107]

[0108] According to the parameter transfer function between the model parameters and the basin characteristic factors listed in Table 6, the parameter values ​​of the basin blocks involved in the equation construction (i.e., the blocks involved in the L model basin and the N model basin and the corresponding sub-basins, a total of 27 blocks) and the blocks involved in the corresponding sub-basins of the N model basin used for equation verification (a total of 7 blocks) in the rate period and the verification period were obtained respectively. Figure 3 The fitting of the parameter values ​​obtained by the parameter transfer function and the optimized parameter values ​​at the rate period is shown. It should be noted that the parameter D0 obtained by the parameter transfer function is the parameter mean of the corresponding block, that is, D0_bk. According to formula (5), this application randomly selects three blocks from the involved blocks and uses the corresponding D0_bk values ​​of the blocks to solve D 0clay , D 0sand and D 0silt . Repeat the above calculation task ten times to obtain ten different sets of D 0clay , D 0sand and D 0silt The combinations that do not meet the parameter D0 value range are screened out, and the remaining combinations are averaged as the D0 values ​​of the three soil components in the corresponding sub-basins of the N model basin.

[0109] S6. Estimating the parameters of the watershed model with insufficient data according to the parameter transfer function

[0110] Depend on Figure 3 It can be seen that the goodness of fit R between the parameters n0 and α of each block obtained by using the parameter transfer function and the optimized parameter value 2 All are higher than 0.50, and the fitting effect is good. Among them, n0 performs even better in the validation block than in the block participating in the construction of the parameter transfer function, which may be related to the small number of validation blocks. Although the goodness of fit between the parameter m obtained by the parameter transfer function and the optimized value is not as good as the above two parameters, they are all higher than 0.40, which is acceptable in practical applications. The parameter transfer function obtained according to this application is feasible for estimating the parameters of the watershed model with insufficient data.

[0111] As for parameter D0, since this parameter is assigned to different soil types, the differences in D0 between the three soil types in different basins obtained through parameter optimization are small. However, since the parameter transfer function is based on the meteorological and underlying surface characteristics of the study area, the values ​​of D0 between different study basins have relatively obvious differences, which is the cause Figure 3 In (a), D0 corresponds to R 2 The possible reason is that the parameter D0 is only 0.37. 2 They are 0.55 and 0.63 respectively, which shows that the above analysis reasons are reasonable.

[0112] In order to further evaluate the applicability of the parameter transfer function, the present invention also uses the parameter transfer function to obtain the D0, m, n0 and α values ​​of each block in the L model basin and the N model basin during the verification period (Table 7). bar The default parameter values ​​are taken and assigned to the model together with the parameter transfer function to simulate the flow. The simulated runoff obtained is compared with the simulated runoff corresponding to the optimized parameters and the measured runoff to evaluate the effectiveness and applicability of the parameter transfer function.

[0113] Table 7 Model parameter values ​​of each block in the L model basin and the N model basin during the validation period obtained using the parameter transfer function.

[0114]

[0115]

[0116] In order to quantitatively evaluate the difference between the two, CC, NSE and RMSE were used to evaluate the simulation performance of the hydrological model corresponding to different parameter sources. At the rate period, the three evaluation indicators of the simulated flow of the L model basin corresponding to the parameter value obtained by the parameter transfer function reached 0.90, 0.70 and 167.80m respectively. 3 / s, and the flow rate in the N model simulation reached 0.83, 0.66 and 91.74m 3 / s, the simulation effect meets the actual needs. In addition, since the L model basin participates in the construction of the parameter transfer function, the parameters obtained by the parameter transfer function perform slightly better in the L model basin than in the N model basin. The RMSE of the N model basin is low, which is mainly related to the fact that the simulated flow in the L model basin is significantly higher than that in the N model basin. Compared with the simulated flow corresponding to the optimized parameters, the evaluation factors of the two stations only decreased by 0.02, 0.08, and 23.59 m 3 / s and 0.06, 0.12, 17.29m 3 During the validation period, the three evaluation indicators of the simulated flow of the L model basin corresponding to the parameters obtained by using the parameter transfer function were 0.81, 0.63 and 211.02 m 3 / s, and 0.82, 0.60 and 106.27 m / s in the N model basin. 3 / s. Although the simulation performance is not as good as the regular rate, it can still meet the actual needs. Compared with the simulated flow corresponding to the optimized parameters, the evaluation factors of the two stations are reduced by 0.07, 0.11, and 33.91m 3 / s and 0.07, 0.15, 22.77m 3 / s, the gap is still small. In short, the hydrological model simulation effect corresponding to the hydrological model parameter value obtained by using the parameter transfer function is close to the parameter optimization scenario, which is of great significance for the flow prediction of basins with insufficient data.

Claims

1. A method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin, characterized in that: The steps include: a. Select characteristic factors, which include climate characteristic factors, underlying surface characteristic factors and watershed characteristic factors; b. Calculation of characteristic factors; c. Model parameter optimization; d. Establish the correlation between model optimization parameters and characteristic factors; e. Select characteristic factors with linear correlation coefficients greater than or equal to a specific value with respect to the model optimization parameters as independent variables, and construct parameter transfer functions; f. Estimate the parameters of the data-deficient watershed model based on the parameter transfer function.

2. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: The linear correlation coefficient is obtained by the following formula: In the formula, CC is the linear correlation coefficient, X i f and X i p They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding distributed hydrological physical model parameter. is the mean of the characteristic factors, is the mean value of the model parameters.

3. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 2, characterized in that: The specific value refers to CC ≥ 0.

4.

4. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: Also includes the steps: g. Evaluate the fitting effect of the parameter transfer function.

5. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 4, characterized in that: In step g, the following formula is used to evaluate the fitting effect: In the formula, R 2 is the goodness of fit, X i f and X i p They refer to the i-th value of the characteristic factor in the variable relationship and the size of the corresponding distributed hydrological physical model parameter. is the mean of the characteristic factors, is the mean of the model parameters; R 2 ≥0.50, the fitting effect is considered to meet the requirements.

6. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: The climate characteristic factors include precipitation P, potential evapotranspiration ET0 and potential intercepted evaporation PET0.

7. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: The underlying surface characteristic factors include average elevation DEM, average slope S, average terrain index TI, average leaf area index LAI, average soil particle size Φ and average root depth T.

8. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 7, characterized in that: The average soil particle size Among them, r i refers to the proportion of the i-th soil component, Φ i It refers to the average particle size of the i-th soil component, and n is the number of soil types; The average root depth Among them, r i refers to the i-th land use type, T i is the root depth corresponding to the i-th land use type, and m is the number of grids in the study basin.

9. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: The watershed characteristic factor is the morphological factor F.

10. The method for estimating model parameters of a distributed hydrological physical model in a data-deficient basin according to claim 1, characterized in that: The parameter transfer function expression is as follows: D0_bk=-4.38e-03+1.16e-02×ET0-2.59e-02×PET0-2.48e-04×Φ+7.47e-07×DEM-2.023e-02×S-1.83e-04×TI; m=-0.43+1.22×ET0-0.09×Φ+0.03×TI; n0=-6.94e-02-1.47e-01×P+2.33e-01×ET0-2.47e-05×DEM+1.33e+00×S; α=-2.65e+01+2.55e+01×PET0+1.57e-03×A+9.31e+01×F.

Images