A flood runoff simulation method based on time-varying outflow coefficient

Abstract

This invention belongs to the field of hydrological modeling and flood forecasting technology, and discloses a flood runoff simulation method based on time-varying outflow coefficients. The method includes the following steps: determining the existence of interflows, modeling hydrological connectivity mechanisms, constructing a time-varying outflow coefficient model, and parameter calibration and verification. The method described in this invention accurately describes the behavior of interflows, can precisely simulate the inflection point of flood recession, significantly improves the accuracy of flood forecasting in semi-arid and semi-humid regions, and provides reliable technical support for flood prevention and disaster reduction.

Description

Technical Field

[0001] This invention belongs to the field of hydrological modeling and flood forecasting technology, specifically relating to a flood runoff simulation method based on time-varying outflow coefficients. Background Technology

[0002] Flood forecasting is one of the core technical means of flood control and disaster reduction, and its accuracy directly affects the timeliness and reliability of early warnings. Currently, operational hydrological models perform well in humid regions, but in semi-arid and semi-humid regions, their simulation accuracy, especially in simulating flood recession processes, is often unstable and fails to meet the requirements of engineering practice. The main reason for this problem is that the runoff generation and confluence processes in semi-arid and semi-humid regions have extremely strong nonlinear characteristics, which existing models fail to adequately characterize.

[0003] Interflow is one of the key runoff mechanisms for torrential floods in the aforementioned regions. It occurs in the transient saturated zone above a relatively impermeable soil layer, and its flow velocity is much faster than that of groundwater runoff, having a decisive influence on flood peak formation and the inflection point of receding water levels. Currently, methods for simulating interflow in hydrological models mainly have the following limitations:

[0004] First, while mechanistic models based on physical processes such as the Richards equation are theoretically rigorous, they require numerous parameters, are computationally complex, and have extremely high requirements for soil spatial heterogeneity data, making it difficult to implement them in operational applications at the watershed scale.

[0005] Second, existing conceptual models (such as the Xin'anjiang Three-Source Model and its derivatives) often employ simplified methods with linear or fixed thresholds to handle interflow, such as using a fixed outflow coefficient. These methods cannot effectively reflect the dynamic impact of soil moisture content changes on hydrological connectivity and runoff paths, resulting in the models' inability to simulate significant differences in receding rates between different flood events, and in particular, difficulty in capturing inflection points on the receding curve.

[0006] Third, while existing studies have shown a correlation between soil moisture content and hydrological connectivity, they have failed to translate this correlation into a clear, quantifiable, and easily embeddable dynamic computational mechanism within the existing model framework. Current models generally lack a mechanism to adjust runoff generation parameters in real time based on soil moisture conditions, thus limiting their simulation capabilities in strongly nonlinear watersheds.

[0007] Therefore, existing technologies have significant shortcomings in flood simulation in semi-arid and semi-humid regions, especially in the detailed characterization of the receding process. There is an urgent need for a dynamic runoff generation model that can both reflect the physical process and be easy to apply in business operations to solve the above problems. Summary of the Invention

[0008] To overcome the problems of existing technologies, this invention proposes a flood runoff simulation method based on time-varying outflow coefficients. This method uses historical data to simulate strongly nonlinear flood processes in arid and semi-arid regions, providing reliable technical support for flood prevention and disaster reduction.

[0009] The objective of this invention is achieved as follows:

[0010] This invention provides a flood runoff simulation method based on time-varying outflow coefficients, comprising the following steps:

[0011] Step 1, Determining the Existence of Interflow

[0012] Design a criterion for determining the existence of interflow based on soil moisture content, the criterion including:

[0013] (1) The soil moisture in the rising section is replenished from bottom to top, and some soil layers reach full capacity or field water holding capacity.

[0014] (2) The soil moisture content in the receding water section drops sharply;

[0015] (3) The sudden drop in soil moisture content occurs earlier than the inflection point of the flow process line in the receding section, and is 1 to 2 times earlier than the average confluence time of the watershed.

[0016] If the soil moisture content monitoring value at any point in the watershed meets the above three judgment criteria, then the interflow phenomenon in the watershed cannot be ignored.

[0017] Step 2, Modeling of Hydrological Connectivity Mechanisms

[0018] By proposing the assumptions of gradual connectivity and independent runoff generation, a p-order distribution curve is used to describe the hydrological connectivity mechanism, that is, a p-order parabola is used to depict the spatial non-uniformity of the maximum subsurface outflow coefficient in the watershed:

[0019] α = 1 - (1 - KIM') p

[0020] In the formula, α is the area ratio, and KIM′ is the maximum value of the soil outflow coefficient at each point in the watershed.

[0021] Step 3, Construction of Time-Varying Outflow Coefficient Model

[0022] The functional relationship between the outflow coefficient and soil wetness is derived, and a time-varying outflow coefficient model is constructed, wherein the functional relationship includes:

[0023] (1) Functional relationship between the average soil outflow coefficient KI of the watershed and the soil moisture state and underlying surface characteristics of the watershed;

[0024] (2) Indirect functional relationship between groundwater outflow coefficient KG and soil moisture.

[0025] Step 4, Parameter Calibration and Verification

[0026] The parameters in the time-varying outflow coefficient model obtained in step 3 were calibrated, and the simulation effect of the model was verified using measured hydrological data.

[0027] Furthermore, in step 1, a sudden drop index is used to identify whether there is a sudden drop in soil moisture content in the receding water section. The formula for calculating the sudden drop index is:

[0028] SR = max(|a t |)

[0029] a t =(θ t+1 -2θ t +θ t-1 ) / Δt 2

[0030] In the formula, SR is the precipitate exponent, a t Let θ be the second derivative of the soil moisture content at time t. t Let θ be the soil moisture content at the beginning of time period t. t+1 Let θ be the soil moisture content at the beginning of time period t+1. t-1 Let t be the soil moisture content at the beginning of time period t-1, and Δt be the time step of the soil moisture content sequence.

[0031] When SR>1, it is determined that there is a sudden drop in soil moisture content.

[0032] Furthermore, in step 2, the gradual connectivity assumption states that hydrological connectivity at the watershed scale is gradual, and its degree of connectivity is uniquely determined by the watershed's mean free water content.

[0033] KI = KI(S / SM)

[0034] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, and SM is the average free water storage capacity of the watershed.

[0035] Furthermore, in step 2, the assumption of independent runoff generation means that the runoff generation at each point in the watershed is independent, and each point has its own maximum interflow coefficient KIM'. If the underlying surface is discretized into n grids, it is assumed that the maximum interflow coefficients of each grid have the following relationship: KIM'1 <KIM'2<…<KIM' n As rainfall progresses, the average free water content in the watershed gradually increases. The soil outflow coefficient KI'1 of grid 1 reaches KIM'1 first and remains stable, followed by grid 2, and finally grid n.

[0036] Furthermore, in step 3, the functional relationship between the watershed average soil outflow coefficient KI and the watershed soil moisture state and underlying surface characteristics is specifically expressed as follows:

[0037]

[0038] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, SM is the average free water storage capacity of the watershed, and KIM is the maximum value of the average outflow coefficient of the watershed.

[0039] Furthermore, in areas with abundant interflow (KIM→1), the calculation of the watershed average interflow outflow coefficient simplifies to:

[0040]

[0041] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, and SM is the average free water storage capacity of the watershed.

[0042] Furthermore, in step 3, the indirect functional relationship between the groundwater runoff outflow coefficient KG and soil moisture is specifically expressed as follows:

[0043] KG = (1-KI)·KGX

[0044] In the formula, KG is the average groundwater outflow coefficient, KI is the average soil outflow coefficient, and KGX is the groundwater outflow factor.

[0045] Furthermore, in step 4, the gradient descent algorithm is used to jointly calibrate the generation, confluence, and evapotranspiration parameters of the model.

[0046] Furthermore, in step 4, after completing the runoff calculation in step 3, the runoff is connected to the confluence module for calculation to obtain the flow process at the watershed outlet section; among which, surface runoff adopts Nash unit hydrograph confluence, and interflow and groundwater runoff adopt linear reservoir method confluence.

[0047] The advantages and beneficial effects of this invention are:

[0048] 1. This invention achieves the physicalization and dynamization of runoff generation parameters, effectively improving simulation accuracy: It abandons the traditional approach of fixing the outflow coefficient in conceptual models and creatively establishes a dynamic functional relationship between the outflow coefficient and the average free water content of the watershed. This allows runoff generation parameters to be adjusted in real time according to soil moisture conditions, fundamentally enhancing the model's ability to describe the nonlinear response of hydrological processes. In particular, this mechanism can accurately capture the inflection point of flood discharge during the receding phase, a key breakthrough that is difficult to achieve with existing fixed-parameter models, thus significantly improving the simulation accuracy of flood peaks and volumes in semi-arid and semi-humid regions.

[0049] 2. The physical foundation of the model is strengthened while ensuring practicality and stability: Based on the assumptions of "gradual hydrological connectivity" and "independent runoff generation," this invention cleverly describes the spatial heterogeneity of inter-soil runoff capacity through statistical methods. All parameters have clear physical meanings (e.g., SM, KIM) and can be obtained through experiments or optimization. The model structure is rigorous, with a total number of parameters comparable to the traditional Xin'anjiang model. In areas with abundant inter-soil runoff, one parameter can even be reduced, effectively lowering the risk of "different parameters having the same effect" during parameter calibration and enhancing the model's robustness and portability.

[0050] 3. Enhanced adaptability to "sudden rise and fall" type floods: The "time-varying soil outflow coefficient - time-varying groundwater runoff outflow coefficient" linkage mechanism constructed in this invention incorporates more nonlinear factors compared to traditional models, enabling the model to respond more sensitively to changes in rainfall and underlying surface conditions. This characteristic makes it particularly suitable for simulating "sudden rise and fall" type floods in semi-arid and semi-humid regions characterized by strong infiltration capacity, short runoff time, and rapid receding water, providing a more reliable technical tool for disaster prevention and mitigation in such areas. Attached Figure Description

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] Figure 1 This is a flowchart illustrating the flood runoff simulation method based on time-varying outflow coefficient described in this application.

[0053] Figure 2 This is a schematic diagram of the spatial distribution curve of the maximum interflow coefficient (KIM′) in the watershed.

[0054] Figure 3 Map of the Liulin experimental watershed;

[0055] Figure 4 The results of the determination of the existence of interflow in the soil are shown;

[0056] Figure 5 This is a simulation diagram of a typical flood event. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed herein will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0058] Example:

[0059] like Figure 1 As shown, this embodiment provides a flood runoff simulation method based on time-varying outflow coefficients, including the following steps:

[0060] Step 1, Determining the Existence of Interflow

[0061] Three criteria for determining the existence of interflow based on soil moisture content are proposed, and the criteria include:

[0062] (1) One is that the soil moisture in the flooded section is replenished from bottom to top, and some soil layers reach full capacity or field water holding capacity.

[0063] (2) Secondly, the soil moisture content in the receding water section drops sharply.

[0064] The sudden drop index is used to identify whether there is a sudden drop in soil moisture content in the receding water section. The formula for calculating the sudden drop index is as follows:

[0065] SR = max(|a t |)

[0066] a t =(θ t+1 -2θ t +θ t-1 ) / Δt 2

[0067] In the formula, SR is the precipitate exponent, a t Let θ be the second derivative of the soil moisture content at time t. t Let be the soil moisture content at the beginning of time period t, % θ t+1 The soil moisture content at the beginning of time period t+1 is %, θ t-1 Let be the soil moisture content at the beginning of time period t-1, %; Δt is the time step of the soil moisture content sequence.

[0068] When SR>1, it is determined that there is a sudden drop in soil moisture content.

[0069] (3) Thirdly, the sudden drop in soil moisture content occurs earlier than the inflection point of the flow process line in the receding section, which is 1 to 2 times earlier than the average confluence time of the basin.

[0070] If the soil moisture content monitoring value at any point in the watershed meets the above three criteria, then the interflow phenomenon in the watershed cannot be ignored, and a hydrological model that takes into account interflow in detail should be adopted.

[0071] Step 2, Modeling of Hydrological Connectivity Mechanisms

[0072] By proposing the assumptions of gradual connectivity and independent runoff generation, a p-order distribution curve is used to describe the hydrological connectivity mechanism, that is, a p-order parabola is used to depict the spatial non-uniformity of the maximum subsurface outflow coefficient in the watershed:

[0073] α = 1 - (1 - KIM') p

[0074] In the formula, α is the area ratio, and KIM′ is the maximum value of the soil outflow coefficient at each point in the watershed.

[0075] like Figure 2 As shown, the point (0.4, 0.7) indicates that 40% of the area in the watershed has a maximum outflow coefficient of no more than 0.7.

[0076] The connectivity gradualism hypothesis assumes that hydrological connectivity at the watershed scale is gradual, and its degree of connectivity is uniquely determined by the watershed's average free water content; more free water means a higher proportion of interflow.

[0077] KI = KI(S / SM)

[0078] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed (mm), and SM is the average free water storage capacity of the watershed (mm).

[0079] The assumption of independent runoff generation means that the runoff generation at each point in the watershed is independent, and each point has its own maximum interflow coefficient KIM′. If the underlying surface is discretized into n grids, it is assumed that the maximum interflow coefficients of each grid have the following relationship: KIM′1 <KIM'2<…<KIM' n As rainfall progresses, the average free water content in the watershed gradually increases. The soil outflow coefficient KI′1 of grid 1 reaches KIM′1 first and remains stable, followed by grid 2, and finally grid n.

[0080] Step 3, Construction of Time-Varying Outflow Coefficient Model

[0081] The functional relationship between the outflow coefficient and soil wetness is derived, and a time-varying outflow coefficient model is constructed, wherein the functional relationship includes:

[0082] (1) The functional relationship between the average soil outflow coefficient KI and the soil moisture state and underlying surface characteristics of the watershed is expressed as follows:

[0083]

[0084] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, SM is the average free water storage capacity of the watershed, and KIM is the maximum value of the average outflow coefficient of the watershed.

[0085] In areas with abundant interflow, KIM→1, the calculation of the average interflow outflow coefficient of the watershed is simplified as follows:

[0086]

[0087] In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, and SM is the average free water storage capacity of the watershed.

[0088] (2) The indirect functional relationship between the groundwater runoff outflow coefficient KG and soil moisture is expressed as follows:

[0089] KG = (1-KI)·KGX

[0090] In the formula, KG is the average groundwater runoff outflow coefficient of the watershed, KI is the average soil runoff outflow coefficient of the watershed, and KGX is the groundwater runoff outflow factor, with a value between 0 and 1.

[0091] Step 4, Parameter Calibration and Verification

[0092] The parameters in the time-varying outflow coefficient model obtained in step 3 were calibrated, and the simulation effect of the model was verified using measured hydrological data.

[0093] In this embodiment, surface runoff in the runoff confluence module adopts Nash unitline confluence, while interflow and groundwater runoff adopt linear reservoir method confluence. After the model is built, the gradient descent algorithm should be used to jointly calibrate the runoff generation, confluence, and evapotranspiration parameters. This is because the model contains multiple series nonlinear factors, and the parameters may have strong correlations. Therefore, the gradient descent algorithm, which is good at finding the best results, should be selected.

[0094] Application examples:

[0095] In this application example, the Liulin small watershed in Neiqiu County, Xingtai City, located in a semi-arid and semi-humid region, is utilized. Figure 3 Based on measured rainfall-runoff data from 1982 to 2024, a time-varying outflow coefficient model was established using the method described in the above embodiments. The surface runoff confluence was represented by the Nash unit hydrograph, while the confluence of interflow and groundwater runoff was represented by the linear reservoir method. Due to the lack of measured evapotranspiration data, the evapotranspiration module was omitted from the model. Twenty-four floods were selected for the study, with a time step of 1 hour, of which 20 were for calibration and 4 were for validation.

[0096] First, taking flood event 210721 as an example, the existence of interflow in the soil is analyzed using the criteria for determining the presence of interflow in the soil. For example... Figure 4 As shown, during the rising water phase of flood event 210721, the soil at a depth of 0.8 meters at Shentou Station reached saturation first, followed by the saturation zone extending to the shallower soil layers, with the soil at a depth of 0.2 meters being the last to saturate. During the receding water phase, the soil moisture content at a depth of 0.4 meters at Shentou Station was 43.38%, 43.43%, and 36.22% at 17:00, 18:00, and 19:00 on the 22nd, respectively, with a sudden drop index of:

[0097]

[0098] Therefore, at 18:00 on the 22nd, the soil moisture content at a depth of 0.4 meters at Shentou Station dropped sharply. Comparing the rainfall runoff process line, it can be seen that the inflection point of the receding water curve is close to the time when the soil moisture content at 0.4 meters at Shentou Station dropped sharply. Therefore, the flood simulation of Liulin Watershed should adopt the time-varying outflow coefficient model. The calculation process of the model is as follows.

[0099] Assuming the rainfall at time t is P = 24.8 mm, the average free water content of the watershed is S = 13.0 mm, the runoff at time t is R = 12.8 mm, and the parameters are KIM = 0.99, KGX = 0.41, and SM = 44.7 mm, then the soil outflow coefficient at time t can be calculated:

[0100]

[0101] Since the KIM value in the Liulin watershed is 0.99, interflow is abundant, and a simplified calculation method can be used:

[0102]

[0103] And the groundwater outflow coefficient:

[0104] KG=(1-KI)·KGX=(1-0.29)×0.41=0.29

[0105] The flow rate during that time period:

[0106]

[0107] Assuming the rainfall at time t+1 is P = 12.1 mm, the average free water content of the watershed is S = 9.4 mm, and the runoff at time t+1 is R = 8.0 mm, then the soil outflow coefficient at time t+1 is:

[0108]

[0109] Due to the decrease in free water content, KI decreased by 0.08 compared to time period t. A simplified calculation method can also be used:

[0110]

[0111] And the groundwater outflow coefficient:

[0112] KG=(1-KI)·KGX=(1-0.21)×0.41=0.32

[0113] The flow rate during that time period:

[0114]

[0115] Similarly, after completing the runoff calculations for all time periods, the simulated flow process is obtained by connecting to the confluence model. After comparing it with the measured river flow, the Nash coefficient is calculated as the objective function, and the gradient descent algorithm can be used to optimize the model parameters.

[0116] The parameter optimization results of the model are shown in Table 1, the model accuracy evaluation is shown in Table 2, and the comparison figure of the simulation effect between the time-varying outflow coefficient model and the Xin'anjiang model is shown in the figure. Figure 5 It can be seen that the average Nash coefficient of the time-varying outflow coefficient model is 0.04 higher than that of the Xin'anjiang model, the average flood peak error is reduced by 3%, and the average flood volume error is reduced by 4%.

[0117] Table 1. Model parameter sensitivity and calibration results

[0118]

[0119] Table 2 Accuracy and Error of Flood Simulation

[0120]

[0121] In summary, the runoff generation model proposed in this invention, based on "time-varying soil outflow coefficient - time-varying underground runoff outflow coefficient", can achieve higher simulation accuracy than the lumped-sump runoff generation model used in the Xin'anjiang model.

[0122] This invention significantly improves the simulation effect of floods in experimental watersheds located in semi-arid and semi-humid regions by establishing a time-varying outflow coefficient model and calibrating the model parameters using the gradient descent algorithm. In particular, it is more accurate in simulating the inflection point of the flow during the receding process. This provides accurate and reliable early warning information for the occurrence of floods and is of great significance for flood prevention and disaster reduction.

[0123] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A flood runoff simulation method based on time-varying outflow coefficient, characterized in that, The method includes the following steps: Step 1, Determining the Existence of Interflow Design a criterion for determining the existence of interflow based on soil moisture content, the criterion including: (1) The soil moisture in the flooded section is replenished from bottom to top, and some soil layers reach full capacity or field water holding capacity. (2) The soil moisture content in the receding water section drops sharply; (3) The sudden drop in soil moisture content occurs earlier than the inflection point of the flow process line in the receding section, and is 1 to 2 times earlier than the average confluence time of the watershed; If the soil moisture content monitoring value at any point in the watershed meets the above three judgment criteria, then the interflow phenomenon in the watershed cannot be ignored. Step 2, Modeling of Hydrological Connectivity Mechanisms By proposing the assumptions of gradual connectivity and independent runoff generation, a p-order distribution curve is used to describe the hydrological connectivity mechanism, that is, a p-order parabola is used to depict the spatial non-uniformity of the maximum subsurface outflow coefficient in the watershed: In the formula, α is the area ratio, and KIM′ is the maximum value of the soil outflow coefficient at each point in the watershed; Step 3, Construction of Time-Varying Outflow Coefficient Model The functional relationship between the outflow coefficient and soil wetness is derived, and a time-varying outflow coefficient model is constructed, wherein the functional relationship includes: (1) The functional relationship between the average outflow coefficient KI in the watershed and the soil moisture state and underlying surface characteristics of the watershed is expressed as follows: In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, SM is the average free water storage capacity of the watershed, and KIM is the maximum value of the average outflow coefficient of the watershed. (2) The indirect functional relationship between the groundwater runoff coefficient KG and soil moisture is expressed as follows: In the formula, KG is the average groundwater runoff outflow coefficient of the watershed, KI is the average soil runoff outflow coefficient of the watershed, and KGX is the groundwater runoff outflow factor. Step 4, Parameter Calibration and Verification The parameters in the time-varying outflow coefficient model obtained in step 3 were calibrated, and the simulation effect of the model was verified using measured hydrological data.

2. The flood runoff simulation method according to claim 1, characterized in that, In step 1, the sudden drop index is used to identify whether there is a sudden drop in soil moisture content in the receding water section. The formula for calculating the sudden drop index is: In the formula, SR is the precipitate exponent, a t Let θ be the second derivative of the soil moisture content at time t. t Let be the soil moisture content at the beginning of time period t. The soil moisture content at the beginning of time period t+1. Let denoted as the soil moisture content at the beginning of time period t-1, and ∆t be the time step of the soil moisture content sequence. When SR > 1, it is determined that there is a sudden drop in soil moisture content.

3. The flood runoff simulation method according to claim 1, characterized in that, In step 2, the runoff independence assumption means that the runoff at each point in the watershed is independent and each point has the largest inter-soil outflow coefficient KIM′. If the underlying surface is discretized into n grids, it is assumed that the largest inter-soil outflow coefficients of each grid have the following relationship: As rainfall continues, the average free water content in the watershed gradually increases, and the outflow coefficient of the soil in grid 1 increases. First to reach And remain stable, followed by grid number 2, and finally grid number n.

4. The flood runoff simulation method according to claim 1, characterized in that, In areas with abundant interflow, KIM→1, the calculation of the average interflow outflow coefficient of the watershed is simplified as follows: In the formula, KI is the average outflow coefficient of the watershed, S is the average free water content of the watershed, and SM is the average free water storage capacity of the watershed.

5. The flood runoff simulation method according to claim 1, characterized in that, In step 4, the gradient descent algorithm is used to jointly calibrate the generation, confluence, and evapotranspiration parameters of the model.

6. The flood runoff simulation method according to claim 1, characterized in that, In step 4, after completing the runoff calculation in step 3, the runoff is connected to the confluence module for calculation to obtain the flow process at the watershed outlet section; among which, surface runoff adopts Nash unitline confluence, and interflow and groundwater runoff adopt linear reservoir method confluence.

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