Distributed Xinanjiang model water storage capacity calculation method under unsteady state evaporation condition

Abstract

The invention discloses a distributed Xinanjiang model water storage capacity calculation method under an unsteady state evaporation condition, and relates to the technical field of water conservancy projects. It is assumed that the evaporation flux and the matric potential absolute value are in a power exponential function relation, a one-dimensional vertical Richards difference equation is adopted, analytical solutions of the water storage capacity, the evaporation capacity and the underground water burial depth about the matric potential absolute value are deduced, firstly, the surface matric potential absolute value is deduced according to the underground water burial depth, and then according to the phreatic evaporation capacity and the evaporation capacity, the ground surface matric potential absolute value is calculated. Calculating to obtain parameters M and x of the power exponential function relationship between the evaporation flux and the matrix potential absolute value, further calculating the water storage capacity, and then obtaining the spatial distribution of the water storage capacity according to the relationship between the terrain index and the burial depth and the spatial distribution of the terrain index, thereby obtaining a new water storage capacity curve. The method effectively improves the precision of the distributed Xinanjiang model for simulating the spatial and temporal variation of the hydrological variables of the watershed.

Description

Technical Field

[0001] The invention relates to the technical field of water conservancy engineering, and in particular to a method for calculating the water storage capacity of a distributed Xin'anjiang model under non-steady-state evaporation conditions. Background Art

[0002] Distributed hydrological models have the ability to describe the spatiotemporal distribution of hydrological variables in a watershed, and are widely used in hydrological and water resources simulation, hydrological effect assessment of the ecological environment, and hydrological prediction in areas with insufficient data. There are two main types of general distributed hydrological models. One is a distributed hydrological model based on the numerical solution of micro-unit hydrological physics equations, such as the SHE model and the DHSVM model. However, this type of model is complex to calculate and requires many parameters to be calibrated. The uncertainty of the model parameters determined only based on limited observation data such as flow is large, and the huge amount of calculation required when calculating the calibration parameters grid by grid also limits the use of this type of distributed hydrological model.

[0003] The distributed Xin'anjiang model is a conceptual watershed hydrological model independently developed by Hohai University and proposed by the team of Professor Zhao Renjun, a famous hydrological expert. The model was originally centered on the measured rainfall station and used Thiessen polygons to divide the calculation units, mainly to consider the uneven spatial distribution of rainfall. With the continuous development of science and technology, especially the development of 3S technology, the calculation units are basically divided by natural watershed watersheds, which effectively promotes the distributed simulation based on the Xin'anjiang model, especially through scientific and technological means to obtain information such as the topography, soil, and vegetation of the underlying surface of the watershed, which greatly improves the distributed simulation capabilities of the Xin'anjiang model.

[0004] In recent years, establishing a functional relationship between topography, soil, vegetation and other information that is easily obtained from the underlying surface of the watershed and hydrological variables has become a new idea for the development of distributed hydrological models. For example, the distributed Xin'anjiang model proposed by some scholars derives an analytical solution of water storage capacity with respect to the terrain index, thereby obtaining the spatial distribution of water storage capacity to give the Xin'anjiang model a distributed function. Some scholars assume that the water storage capacity and the terrain index present a logarithmic Weibull relationship, while others assume that the soil moisture content in the unsaturated zone is the wilting moisture content, and some others assume that the soil is in a vertical equilibrium state. They all obtained expressions for water storage capacity with respect to the terrain index, thereby obtaining the spatial distribution of water storage capacity and the distributed Xin'anjiang model.

[0005] The distributed Xin'anjiang model proposed above simplifies the hydrodynamic characteristics of the unsaturated zone to a certain extent, such as assuming that the water storage capacity and the terrain index are logarithmic Weibull empirical relations, assuming that the soil moisture content in the unsaturated zone is the wilting moisture content, or ignoring the effect of evaporation on the soil water potential in the unsaturated zone (i.e., the soil is in a vertical equilibrium state). These simplifications weaken the physical mechanism of the model to a certain extent, resulting in certain distortions in the calculation. Some scholars have considered the effect of evaporation when calculating soil water deficit and derived an analytical solution of water deficit with respect to matrix potential. However, these scholars assume that the soil is in a vertical steady state and still simplify the vertical distribution of evaporation flux to a certain extent. In fact, the soil is in a non-steady state vertically, and the soil vertical evaporation flux is changing. The simplification of the above method will cause a certain error between the calculated soil vertical profile and the actual situation.

[0006] How to find a method to calculate water storage capacity that takes into account physical mechanism, calculation accuracy and calculation efficiency has become a new idea for the development of the distributed Xin'anjiang model. In the process of calculating water storage capacity of the distributed Xin'anjiang model, in order to improve the calculation efficiency, the model will inevitably be simplified, the physical mechanism will be weakened, and the calculation accuracy will be reduced. In order to enhance the physical mechanism and increase the calculation accuracy, the calculation of the model will inevitably become very complicated, thereby reducing the calculation efficiency. If a simplified method is used to process the hydrodynamic characteristics of the unsaturated zone, the calculation efficiency will be improved, but such processing will inevitably weaken the physical mechanism, thereby causing unnecessary calculation errors. If the general numerical difference method is used to calculate the soil moisture content, in order to prevent the simulation data from diverging, the time step must be very small. Although the physical mechanism and calculation accuracy are guaranteed, doing so will bring a huge amount of calculation, thereby limiting its use. In order to solve the above problems, the present invention proposes a method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions. Summary of the invention

[0007] The purpose of the present invention is to propose a distributed Xin'anjiang model water storage capacity calculation method under non-steady-state evaporation conditions that takes into account physical mechanism, calculation accuracy and calculation efficiency to solve the problem that the prior art simplifies the hydrodynamic characteristics of the unsaturated zone in order to ensure calculation efficiency, which affects the calculation accuracy and physical mechanism. The present invention effectively improves the accuracy of the distributed Xin'anjiang model in simulating the spatiotemporal changes of basin hydrological variables.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions: The calculation method of water storage capacity of distributed Xin'anjiang model under non-steady-state evaporation conditions includes the following steps: S1. Assuming that the evaporation flux and the absolute value of the matrix potential are in a power exponential function relationship, the specific function is expressed as: (1) in,E represents the evaporation flux; M , x Represents the power exponential function parameter; represents the absolute value of matrix potential; The Monte Carlo method is used to randomly generate several of the above power exponential functions. M The value of S2, calculated based on the diving evaporation formula and the power exponential function relationship in S1, M Corresponding power exponential function parameters x ; S3. Based on the one-dimensional Richards difference equation, the analytical solution of groundwater depth and evaporation capacity with respect to the absolute value of surface matrix potential is derived; among them, under the condition of known actual groundwater depth and evaporation capacity, several sets of parameters M , x The corresponding evaporation capacity at the groundwater depth is obtained by back calculation; S4. Select the parameter group with the smallest error between the inverse evaporation capacity and the actual evaporation capacity as the best M , x Parameters, derive the analytical solution of water storage capacity with respect to the absolute value of surface matrix potential; S5. Based on the relationship between groundwater depth and terrain index, the spatial distribution of terrain index, and the analytical solution of groundwater depth and water storage capacity with respect to the absolute value of surface matrix potential, the water storage capacity curve considering non-steady-state evaporation is obtained to achieve accurate calculation of water storage capacity. S6. Combined with the obtained water storage capacity curve considering non-steady-state evaporation, the runoff calculation of the distributed Xin'anjiang model is carried out to obtain the spatiotemporal changes of the basin's hydrological variables.

[0009] Preferably, the diving evaporation formula in S2 specifically refers to: (2) in, E g For diving evaporation, d The depth of groundwater, d max is the evaporation limit burial depth, nn is the evaporation parameter; The evaporation flux when the absolute value of the matrix potential calculated according to formula (2) is the phreatic evaporation E g ,but: (3) in, Indicates the momentum of the incoming air; Evaporating the diving E g And the momentum Substituting into formula (3) we can get M Corresponding power exponential function parameters x .

[0010] Preferably, the derivation process of the analytical solution of the groundwater depth in S3 with respect to the absolute value of the surface matrix potential is as follows: Based on the one-dimensional Richards difference equation, equation (1) is rewritten as: (4) in, Ks represents the saturated hydraulic conductivity; Indicates the momentum of the incoming air; p The coefficient representing the relationship between hydraulic conductivity and matrix potential; definition , simplify formula (4) to get: (5) definition , simplify the function on the left side of equation (5) to the sum of geometric progression, and then integrate to obtain hour, , (6) when hour, , (7) if , (8) (9) if , (10) Combining equations (8)-(10), we can calculate the groundwater depth The corresponding absolute value of the surface matrix potential .

[0011] Preferably, the back-calculation derivation process of the analytical solution of the evaporation capacity in S3 with respect to the absolute value of the surface matrix potential is as follows: According to the correlation between actual evapotranspiration and soil moisture content, we can get: (11) ,

[0012] Combined with formula (1), the evaporation capacity can be calculated: (12) In formula (11)-(12), E represents actual evapotranspiration; E p Indicates evaporation capacity; Indicates soil moisture content; represents the evaporation relationship coefficient; They represent wilting water content, field holding capacity and saturated water content respectively; It represents the relationship coefficient between soil water content and matrix potential; definition , substituting into formula (11) we get: (13) definition ,when hour, , (14) when hour, , (15) if , (16) if , (17) (18) Combining equations (16)-(18), we can calculate the inverse evaporation capacity On the absolute value of ground potential Analytical solution of .

[0013] Preferably, the derivation process of the analytical solution of the water storage capacity with respect to the absolute value of the surface matrix potential in S4 is as follows: Based on formula (5) and definition , calculate soil moisture content at field capacity The specific formula for the above water content is: (19) The water storage capacity at this depth is the field water holding capacity. Subtract water content: (20) In the above formula, Whan Indicates water content above field capacity; W Indicates water storage capacity; when hour, , (twenty one) when hour, , (twenty two) if , (twenty three) if ,

[0014] (twenty four) ,

[0015] (25)

[0016] The combined equations (23)-(25) can be used to calculate the water storage capacity at a certain groundwater depth. On the absolute value of ground potential Analytical solution of .

[0017] Preferably, the S5 specifically includes the following contents: Select the one with the smallest error between the inversely calculated evaporation capacity and the actual evaporation capacity. M , x The parameter group is the power exponential function parameter group of the optimal evaporation flux and the absolute value of the matrix potential. It is substituted into the analytical solution of the water storage capacity with respect to the absolute value of the surface matrix potential. Then, the spatial distribution of the water storage capacity is obtained by combining the analytical solution of the groundwater depth and the surface matrix potential, the linear relationship between the groundwater depth and the terrain index, and the spatial distribution of the terrain index, thereby obtaining the water storage capacity curve. Among them, the linear relationship between groundwater depth and terrain index is expressed as follows:

[0018] in, t pi Represents the terrain index of the grid points; sz Represents model parameters.

[0019] Preferably, the runoff calculation of the distributed Xin'anjiang model in S6 includes evapotranspiration calculation, full storage runoff calculation, water source division calculation and runoff calculation, and the specific contents are as follows: S6.1. Based on the rainfall in period t, evaporation capacity and soil storage at the beginning of period t, a three-layer evaporation model is used to calculate the evaporation of the basin and obtain the net rainfall in period t; S6.2. Based on the net rainfall in period t, the soil storage at the beginning of period t and the distributed water storage capacity curve, the soil storage at the end of period t and the flow production in period t are obtained, and then the spatial distribution of water shortage and flow production is obtained; S6.3, the runoff generated in period t enters the free water reservoir, and the surface runoff, soil runoff and underground runoff in period t are obtained; S6.4. Surface runoff is collected by unit line confluence, subsurface flow and underground runoff are collected by linear reservoir confluence, and the Muskingum method is used to collect the three types of runoff after they enter the river channel and converge at the outlet section of the basin.

[0020] Compared with the prior art, the present invention provides a method for calculating the water storage capacity of a distributed Xin'anjiang model under non-steady-state evaporation conditions, which has the following beneficial effects: The present invention takes into account the influence of non-steady-state evaporation when calculating water storage capacity, and obtains an analytical solution to water storage capacity by applying the one-dimensional vertical Richards differential equation, so that the calculation result is more accurate; and compared with the prior art, the calculation method proposed by the present invention has high efficiency and small amount of calculation. Since the vertical hydrodynamic characteristics of the unsaturated zone are not simplified, the physical mechanism of the present invention is stronger; at the same time, the present invention takes into account the calculation accuracy, calculation efficiency and physical mechanism, and realizes the organic unity of the three. When the water storage capacity curve that takes into account the calculation accuracy, calculation efficiency and physical mechanism is used to calculate the runoff of the basin, the temporal and spatial changes of the basin hydrological variables calculated by the distributed Xin'anjiang model under the condition of non-steady-state evaporation are more accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is an overall flow chart of the method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions proposed by the present invention; Figure 2 This is a structural diagram of the distributed Xin'anjiang model mentioned in Example 1 of the present invention; Figure 3 The watershed storage capacity curve mentioned in Example 1 of the present invention; Figure 4 is the basin free water capacity curve mentioned in Example 1 of the present invention; Figure 5 This is a schematic diagram of the simulated and measured 0-60 cm soil water deficit change process of the observation point 2 mentioned in Example 2 of the present invention; Figure 6-8 A diagram showing the vertical distribution of soil moisture content at a certain burial depth and evaporation capacity calculated by the method of the present invention and other methods mentioned in Example 3 of the present invention; Figure 9-11 This is a correlation diagram of the method of the present invention mentioned in Example 3 of the present invention and the actual evaporation flux and the absolute value of the matrix potential. DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0023] The present invention aims to construct a new method for calculating water storage capacity that takes into account physical mechanism, calculation accuracy and calculation efficiency, and solves the problem that the original method simplifies the hydrodynamic characteristics of the unsaturated zone in order to ensure calculation efficiency, which affects the calculation accuracy and physical mechanism, thereby improving the accuracy of the distributed Xin'anjiang model in simulating the spatiotemporal changes of basin hydrological variables.

[0024] The present invention assumes that the evaporation flux and the absolute value of the matrix potential are in a power exponential function relationship. The one-dimensional vertical Richards difference equation is used to derive the analytical solution of the water storage capacity, evaporation capacity and groundwater depth with respect to the absolute value of the matrix potential. First, the absolute value of the surface matrix potential is deduced according to the groundwater depth. Then, according to the phreatic evaporation and evaporation capacity, the parameters of the power exponential function relationship between the evaporation flux and the absolute value of the matrix potential are calculated. M , x , and then the water storage capacity is deduced, and then the spatial distribution of the water storage capacity is obtained according to the relationship between the terrain index and the burial depth and the spatial distribution of the terrain index, thereby obtaining a new water storage capacity curve. Because the method of the present invention obtains an analytical solution to the water storage capacity and does not simplify the one-dimensional vertical hydrodynamic equation, the method takes into account the physical mechanism, calculation accuracy and calculation efficiency, and solves the calculation error problem caused by the simplified unsaturated zone hydrodynamic characteristics in the distributed Xin'anjiang model proposed by some scholars before. The method proposed in the patent of the present invention has a faster calculation speed, higher calculation accuracy, and stronger physical mechanism. It is suitable for calculating the spatial distribution of water storage capacity in the basin in the simulation of runoff generation and confluence in the basin, thereby realizing the distributed calculation of the distributed Xin'anjiang model considering non-steady-state evaporation, and obtaining the spatiotemporal distribution of hydrological variables such as soil moisture content and runoff depth. The following is an explanation of the water storage capacity calculation method of the distributed Xin'anjiang model under non-steady-state evaporation conditions proposed by the present invention in conjunction with relevant drawings and specific examples. The specific content is as follows.

[0025] Embodiment 1: The evapotranspiration calculation of the three-water-source distributed Xin'anjiang model adopts a three-layer evaporation model; the runoff calculation adopts the water storage capacity curve (calculated according to the distribution of terrain index and the functional relationship between water storage capacity and terrain index); the water source division is based on the free water reservoir and is divided into surface runoff, subsoil flow and groundwater runoff; the confluence calculation adopts the unit line (surface runoff) and linear reservoir (subsoil flow and groundwater runoff) to calculate the slope confluence, and the Muskingum method is used to calculate the river confluence.

[0026] Based on the above content, the present invention proposes a method for calculating the water storage capacity of a distributed Xin'anjiang model under non-steady-state evaporation conditions, which specifically includes the following contents: Assume that the evaporation flux and the absolute value of the matrix potential have a power exponential function relationship: (1) In formula (1), E represents the evaporation flux; M , x Represents the power exponential function parameter; Represents the absolute value of matrix potential.

[0027] To calculate the water storage capacity under a certain burial depth and evaporation capacity, it is necessary to obtain an analytical solution of the absolute value of the surface matrix potential for groundwater burial depth, evaporation capacity and water storage capacity. Let’s derive them one by one.

[0028] According to the one-dimensional Richards equation, we can get: (2) In formula (2), Ks represents the saturated hydraulic conductivity; Indicates the momentum of the incoming air; p The coefficient representing the relationship between hydraulic conductivity and matrix potential.

[0029] The vertical distance to the groundwater depth is calculated according to equations (3)-(8): z The absolute value of the matrix potential at this position The analytical solution of D The absolute value of the ground potential under ( ).

[0030] definition , simplifying formula (2) yields: (3) definition , simplify the function on the left side to the sum of a geometric progression, and then integrate it to get hour, , (4) when hour, , (5) if , (6) (7) if , (8) According to equations (6)-(8), the groundwater depth can be calculated: The corresponding absolute value of the surface matrix potential .

[0031] Based on equations (9)-(16), the analytical solution of the inverse evaporation capacity with respect to the surface matrix potential is calculated.

[0032] (9) The above formula is the correlation between actual evapotranspiration and soil moisture content. Combined with formula (1), the evaporation capacity can be calculated: (10) In formulas (9) and (10), E represents actual evapotranspiration; E p Indicates evaporation capacity; Indicates soil moisture content; represents the evaporation relationship coefficient; They represent wilting water content, field holding capacity and saturated water content respectively; It represents the relationship coefficient between soil water content and matrix potential; definition , substitute into formula (9): (11) definition ,when (Same principle as above) , (12) when hour, , (13) if , (16) if , (17) (18) According to equations (16)-(18), the evaporation capacity can be calculated: On the absolute value of ground potential Analytical solution of .

[0033] The formula for evaporation from diving is as follows: (19) in, E g For diving evaporation, d The depth of groundwater, d max is the evaporation limit burial depth, nn is the evaporation parameter; According to the formula of phreatic evaporation, the evaporation flux when the absolute value of matrix potential is the air intake potential is phreatic evaporation. ,but: (20) Combined with formula (3), the soil moisture content above the field water holding capacity can be calculated as follows (substitute formula (3) and Substitute into the following formula): (twenty one) The water storage capacity at this depth is the field water holding capacity. Subtract water content: (twenty two) In the above formula, Whan Indicates water content above field capacity; W Indicates water storage capacity; when hour, , (twenty one) when hour, , (twenty two) if , (twenty three) if ,

[0034] (twenty four) ,

[0035] (25)

[0036] (26) According to equations (23)-(25), the water storage capacity at a certain burial depth can be calculated: About Surface Matric Potential Absolute value Analytical solution of .

[0037] The Monte Carlo method is used to randomly generate N sets of values ​​of the power exponential function parameter M of the evaporation flux with respect to the absolute value of the matrix potential. The value of the phreatic evaporation is calculated according to formula (19). The phreatic evaporation and the inlet potential are substituted into formula (20) to calculate the parameter M in the power exponential function. x The value of groundwater depth D is obtained by using formulas (6)-(8). The evaporation capacity is obtained by using formulas (16)-(18). The storage capacity is obtained by using formulas (23)-(25). The absolute value of the surface matrix potential corresponding to the groundwater depth D is calculated by trial and error. The absolute value of the surface matrix potential is substituted into formulas (16)-(18) to obtain the inverse evaporation capacity. The evaporation capacity with the smallest error between the inverse evaporation capacity and the actual evaporation capacity is selected. M , x The parameter group is a power exponential function parameter group of the preferred evaporation flux and the absolute value of the matrix potential, which is substituted into the analytical solution of the water storage capacity with respect to the absolute value of the surface matrix potential. Then, the spatial distribution of the water storage capacity is obtained by combining the analytical solution of the groundwater depth and the surface matrix potential, the linear relationship between the groundwater depth and the terrain index (see formula (26)), and the spatial distribution of the terrain index, thereby obtaining a new water storage capacity curve. It has been verified above that the improved distributed Xin'anjiang model considering non-steady-state evaporation is significantly higher than the original distributed Xin'anjiang model in simulating the spatiotemporal variation of soil moisture content. The present invention takes into account the calculation accuracy, calculation efficiency and physical mechanism, and greatly optimizes the distributed Xin'anjiang model.

[0038] After obtaining the new water storage capacity curve, we can start the distributed Xin'anjiang model (the structure diagram of the distributed Xin'anjiang model is as follows: Figure 2 The calculation of runoff generation and confluence is shown in Figure 1. According to the storage capacity at the beginning of period t, W t and the rainfall during period t P t , Evaporation capacity Ep t , the storage capacity at the end of period t can be calculated W t+1 and t Other hydrological variables in the basin during the period, and then according to W t+1 , P t+1 and Ep t+1 , and we can calculate t+1 hydrological variables in the basin during the period, so as to realize the period-by-period calculation of the basin runoff and obtain the hydrological variables in each period of the basin; it is roughly divided into 4 steps: ① evapotranspiration calculation; ② full storage runoff; ③: water source division calculation; ④ runoff calculation; the specific contents are as follows: 1. Evapotranspiration calculation The Xin'anjiang model uses a three-layer evaporation mode, which is carried out in the order of the upper layer first and the lower layer. When the surface soil has sufficient water content, evaporation mainly occurs in the surface layer of the soil. As the water content of the surface soil zone gradually decreases due to evaporation and cannot meet the evaporation capacity, the lower layer begins to provide the water required for evaporation. When the moisture content of the soil zone further decreases and the water content held by the lower layer cannot provide the water required for the remaining evaporation capacity, water must be evaporated from the third layer of soil. In the model, the soil layer is divided into three virtual layers according to the non-uniformity of the vertical distribution of the soil.

[0039] The calculation process is as follows: if ,but ; if ,but ; if ,but ; if , but ; if , but ; .

[0040] In the above formula, is the rainfall, evaporation capacity and actual evapotranspiration in period t, is the storage of the upper layer, the lower layer and the deep layer in period t, is the evaporation of the upper layer, the lower layer and the deep layer in period t, is the upper water storage capacity, is the water storage capacity of the lower layer, is the deep water storage capacity, is the average water storage capacity of the basin, is the deep scattering coefficient, .

[0041] 2. Full abortion flow like Figure 3The diagram is a schematic diagram of the water storage capacity curve of the watershed. The runoff generation when the watershed is full is a generalization of the runoff generation mechanism. Its basic assumption is that at any point in the watershed, the moisture in the vadose zone will increase with the increase of precipitation, but before the soil moisture content in the vadose zone can reach full storage, precipitation will continue to replenish the soil moisture; as precipitation gradually makes the soil moisture content in the vadose zone reach a critical runoff point, that is, when the vadose zone can no longer store water, the subsequent precipitation will be completely converted into runoff. The water storage capacity of the soil in the vadose zone at each point in a watershed is different under different underlying surface conditions. Therefore, before the soil voids in the entire watershed are fully filled, runoff can also be generated at some points in the watershed. This is because some points have retained some water due to the influence of previous precipitation, or there are differences in water storage capacity at different points.

[0042] The calculation process is as follows: The grid points in the basin are divided into N categories according to the water storage capacity. i The water storage capacity range of the grid point is ( WMM is the maximum water storage capacity of a single point in the basin), and its corresponding source area is (Source Area The meaning is that the water storage capacity is less than The ratio of the area occupied by the grid points to the total area), then the flow rate of the i-th grid point is: ,if ; if The flow calculation process is as follows: if , ; if , ; if , ; if , ; if , , .

[0043] In the above formula, for t Net rainfall during the period, For the basin t The storage volume at the beginning of the period, For the basin t The maximum storage capacity at a single point at the beginning of the period, For the i Grid-like points t The flow rate during the period, It is the average flow depth of the basin.

[0044] 3. Water source division calculation like Figure 4 The diagram is a schematic diagram of the free water capacity curve of the basin; with the increase of accumulated precipitation, the area of ​​saturated surface runoff in the basin is constantly changing, so the distribution of free water storage capacity is also uneven. The free water storage capacity curve used in the model for water source division divides the total runoff calculated by full runoff into three water sources, namely surface runoff RS, soil flow RI and groundwater runoff RG. The free water reservoir takes into account the vertical effect of the vadose zone. Part of the water flow will be stored in the vadose zone, and the rest will be divided into different types of runoff.

[0045] The calculation process is as follows: if ,but

[0046] ; if ,but , .

[0047] In the above formula, is the free water reservoir capacity of the i-th grid point, , It is the largest single-point free water storage capacity in the basin. is the free storage reservoir capacity at the i-th grid point in period t, is the surface runoff depth, subsoil flow depth and underground runoff depth at the i-th grid point in period t, is the outflow coefficient of soil flow and underground runoff 4. Confluence calculation The basin confluence process can be divided into slope confluence and river confluence according to the different ways in which water is collected from the entire basin to the outlet. The process of slope confluence of subsoil flow and groundwater runoff is approximately regarded as a linear reservoir, and the process of slope confluence of surface runoff is approximately regarded as unit line confluence. Different water sources use their own slope confluence methods, enter the river after regulation, and converge to the basin outlet section through the Muskingum method.

[0048] The calculation process is as follows: , , , , , , , .

[0049] In the above formula, is the surface runoff depth, subsoil flow depth and underground runoff depth of the basin during period t, is the unit line parameter, is the drainage coefficient of subsurface flow and groundwater runoff, is the basin area, is the time step, is the surface flow, soil flow, underground flow and total flow entering during period t, is the flow rate at the outlet section of the basin during period t, are Muskingum method parameters, , , , in, is the weight factor, is the storage constant.

[0050] Embodiment 2: Based on Example 1, the hydrological data of a typical basin similar to the Siming Lake Basin in Yuyao, China from December 6, 1995 to November 17, 1997 were selected to simulate the soil water shortage of 17 grid points in the basin using the method of the present invention, the conventional water storage capacity model and the DHSVM model, and the simulation effects of the three methods were compared. The results are as follows: Figure 5 As shown in Table 1.

[0051] Table 1 Comparison of the statistical results of soil water shortage calculated by the model and measured within 0-60 cm

[0052] By comparison, it can be found that the simulation effect of the method of the present invention on simulating soil moisture content is significantly better than that of the unimproved distributed Xin'anjiang model. The method of the present invention greatly improves the simulation effect of the distributed Xin'anjiang model on the spatiotemporal distribution of soil moisture content.

[0053] Embodiment 3: Based on Example 1-2, the difference is that the distributed Xin'anjiang model water storage capacity calculation method under non-steady-state evaporation conditions proposed in the present invention is compared with other similar calculation methods, and the vertical distribution of soil moisture content under a certain burial depth and evaporation capacity is calculated as follows: Figure 6-8As shown in FIG. 1 , the analysis shows that the water storage capacity calculated by the present invention under a certain burial depth and evaporation capacity (assuming that the soil is in a non-steady-state vertical state) is comparable to the general numerical method (when the time step is very small, the calculated value of the general numerical method is very close to the true value, so the calculated value of the general numerical method is selected as the true value to compare the errors of other methods), the equilibrium state method (ignoring evaporation, that is, the method of calculating the water storage capacity of the original distributed Xin'anjiang model) and the steady-state method (assuming that the soil vertical flux is the actual evaporation everywhere). Figure 6-8 It can be found that when the groundwater depth is small, the water storage capacity calculated by the method of the present invention, the equilibrium state method and the steady-state method is not much different. However, when the groundwater depth is large, the errors of the water storage capacity calculated by the equilibrium state method and the steady-state method are very obvious, both exceeding 20%, while the errors of the water storage capacity calculated by the method of the present invention are all within 1%. The calculation accuracy has been greatly improved compared with the original distributed Xin'anjiang model. In addition, the method of the present invention does not simplify the hydrodynamic characteristics of the unsaturated zone, and uses analytical solutions to calculate the water storage capacity. The water storage capacity calculated by the method of the present invention takes into account the calculation accuracy, calculation efficiency and physical mechanism.

[0054] See further Figure 9-11 The correlation between the absolute value of soil vertical evaporation flux and matrix potential calculated by the method of the present invention and the actual certain burial depth and evaporation capacity is as follows: Figure 9-11 As shown, it can be found by observation that the correlation coefficients of the power exponential function trend lines of the real soil vertical evaporation flux and the absolute value of matrix potential are all greater than 0.94, and the power exponential function can better simulate the correlation between the soil vertical evaporation flux and the absolute value of matrix potential, and the relationship curve between the soil vertical evaporation flux and the absolute value of matrix potential calculated by the method of the present invention is very close to the trend line of the real soil. The power exponential correlation between the soil vertical evaporation flux and the absolute value of matrix potential calculated by the method of the present invention has been verified to have high accuracy, and the power exponential function can better simulate the correlation between the soil vertical evaporation flux and the absolute value of matrix potential.

[0055] When the water storage capacity curve that takes into account the calculation accuracy, calculation efficiency and physical mechanism is used for distributed calculation, the spatiotemporal changes of hydrological variables calculated by the distributed Xin'anjiang model under non-steady-state evaporation will be more accurate and reliable.

[0056] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. The calculation method of water storage capacity of distributed Xinanjiang model under non-steady-state evaporation conditions is characterized by: The steps include: S1. Assuming that the evaporation flux and the absolute value of the matrix potential are in a power exponential function relationship, the specific function is expressed as: (1) in, E represents the evaporation flux; M , x Represents the power exponential function parameter; represents the absolute value of matrix potential; The Monte Carlo method is used to randomly generate several of the above power exponential functions. M The value of S2, calculated based on the diving evaporation formula and the power exponential function relationship in S1, M Corresponding power exponential function parameters x ; S3. Based on the one-dimensional Richards difference equation, the analytical solution of groundwater depth and evaporation capacity with respect to the absolute value of surface matrix potential is derived; among them, under the condition of known actual groundwater depth and evaporation capacity, several sets of parameters M , x The corresponding evaporation capacity at the groundwater depth is obtained by back calculation; S4. Select the parameter group with the smallest error between the inverse evaporation capacity and the actual evaporation capacity as the best M , x Parameters, derive the analytical solution of water storage capacity with respect to the absolute value of surface matrix potential; S5. Based on the relationship between groundwater depth and terrain index, the spatial distribution of terrain index, and the analytical solution of groundwater depth and water storage capacity with respect to the absolute value of surface matrix potential, the water storage capacity curve considering non-steady-state evaporation is obtained to achieve accurate calculation of water storage capacity. S6. Combined with the obtained water storage capacity curve considering non-steady-state evaporation, the runoff calculation of the distributed Xin'anjiang model is carried out to obtain the spatiotemporal changes of the basin's hydrological variables.

2. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 1 is characterized in that: The diving evaporation formula described in S2 specifically refers to: (2) in, E g For diving evaporation, d The depth of groundwater, d max is the evaporation limit burial depth, nn is the evaporation parameter; The evaporation flux when the absolute value of the matrix potential calculated according to formula (2) is the phreatic evaporation E g ,but: (3) in, Indicates the momentum of the incoming air; Evaporating the diving E g And the momentum Substituting into formula (3) we can get M Corresponding power exponential function parameters x .

3. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 2 is characterized in that: The derivation process of the analytical solution of the absolute value of the surface matrix potential for the groundwater depth described in S3 is as follows: Based on the one-dimensional Richards difference equation, equation (1) is rewritten as: (4) in, Ks represents the saturated hydraulic conductivity; Indicates the momentum of the incoming air; p The coefficient representing the relationship between hydraulic conductivity and matrix potential; definition , simplify formula (4) to get: (5) definition , simplify the function on the left side of equation (5) to the sum of geometric progression, and then integrate to obtain hour, , (6) when hour, , (7) if , (8) (9) if , (10) Combining equations (8)-(10), we can calculate the groundwater depth The corresponding absolute value of the surface matrix potential .

4. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 3 is characterized in that: The back-calculation derivation process of the analytical solution of the evaporation capacity described in S3 for the absolute value of the surface matrix potential is as follows: According to the correlation between actual evapotranspiration and soil moisture content, we can get: (11) Combined with formula (1), the evaporation capacity can be calculated: (12) In formula (11)-(12), E represents actual evapotranspiration; E p Indicates evaporation capacity; Indicates soil moisture content; represents the evaporation relationship coefficient; They represent wilting water content, field holding capacity and saturated water content respectively; It represents the relationship coefficient between soil water content and matrix potential; definition , substituting into formula (11) we get: (13) definition ,when hour, , (14) when hour, , (15) if , (16) if , (17) (18) Combining equations (16)-(18), we can calculate the inverse evaporation capacity On the absolute value of ground potential Analytical solution of .

5. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 4 is characterized in that: The derivation process of the analytical solution of water storage capacity with respect to the absolute value of surface matrix potential described in S4 is as follows: Based on formula (5) and definition , calculate soil moisture content at field capacity The specific formula for the above water content is: (19) The water storage capacity at this depth is the field water holding capacity. Subtract water content: (20) In the above formula, Whan Indicates water content above field capacity; W Indicates water storage capacity; when hour, , (21) when hour, , (22) if , (23) if , (24) ， (25) The combined equations (23)-(25) can be used to calculate the water storage capacity at a certain groundwater depth. On the absolute value of ground potential Analytical solution of .

6. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 5 is characterized in that: The S5 specifically includes the following contents: Select the one with the smallest error between the inversely calculated evaporation capacity and the actual evaporation capacity. M , x The parameter group is the power exponential function parameter group of the optimal evaporation flux and the absolute value of the matrix potential. It is substituted into the analytical solution of the water storage capacity with respect to the absolute value of the surface matrix potential. Then, the spatial distribution of the water storage capacity is obtained by combining the analytical solution of the groundwater depth and the surface matrix potential, the linear relationship between the groundwater depth and the terrain index, and the spatial distribution of the terrain index, thereby obtaining the water storage capacity curve. Among them, the linear relationship between groundwater depth and terrain index is expressed as follows: (26) in, t pi represents the water permeability coefficient of the i-th layer of soil; sz Represents model parameters.

7. The method for calculating the water storage capacity of the distributed Xin'anjiang model under non-steady-state evaporation conditions according to claim 6 is characterized in that: The runoff calculation of the distributed Xin'anjiang model described in S6 includes evapotranspiration calculation, full storage runoff calculation, water source division calculation and runoff calculation. The specific contents are as follows: S6.

1. Based on the rainfall in period t, evaporation capacity and soil storage at the beginning of period t, a three-layer evaporation model is used to calculate the evaporation of the basin and obtain the net rainfall in period t; S6.

2. Based on the net rainfall in period t, the soil storage at the beginning of period t and the distributed water storage capacity curve, the soil storage at the end of period t and the flow production in period t are obtained, and then the spatial distribution of water shortage and flow production is obtained; S6.3, the runoff generated in period t enters the free water reservoir, and the surface runoff, soil runoff and underground runoff in period t are obtained; S6.

4. Surface runoff is collected by unit line confluence, subsurface flow and underground runoff are collected by linear reservoir confluence, and the Muskingum method is used to collect the three types of runoff after they enter the river channel and converge at the outlet section of the basin.

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