Method for constructing tank water storage increment lag response model in ice flood frost-up period in alpine region

Abstract

The invention discloses an alpine region ice flood frost-up period tank water storage increment lag response model construction method. Comprising the following steps: S1, for rivers in an alpine region, collecting ice flood freezing date and river opening date, and day-by-day temperature, flow and tank water storage increment data in the freezing period; s2, constructing a lagging response model of the tank water storage increment in the river ice flood frost-up period in the alpine region; s3, constructing a calculation mode of the tank water storage increment lag response model in the river ice flood frost-up period in the alpine region; s4, establishing a calibration method for parameters of the tank water storage increment lag response model in the river ice flood frost-up period in the alpine region; s5, analyzing the lagging response rule of the tank water storage increment in the river ice flood freezing-up period in the alpine region and applying the model; and S6, evaluating the effect of the tank water storage increment lag response model in the river ice flood frost-up period in the alpine region. According to the method, the influence of water-ice phase state transformation in the ice flood freezing period is considered, the river system lag response model is deepened and developed, and the calculation method is relatively simple.

Description

Technical Field

[0001] The present invention provides a method for constructing a delayed response model of trough water storage increment during the ice flood and freezing period in high-altitude areas, which belongs to the field of water conservancy technology. It is mainly based on the Muskingum method, considers the influence of water-ice phase transformation during the ice flood and freezing period, and proposes to construct a delayed response model of trough water storage increment, thereby providing a scientific and practical method for simulating the change process of trough water storage increment in ice flood and freezing areas of rivers in high-altitude areas. Background Art

[0002] Rivers in alpine regions, flowing from low to high latitudes, are prone to freezing and ice-covered floods during the winter due to factors such as low temperatures and prolonged periods of freezing. This is known as ice floods. Examples include the Neva, Yenisei, and Lena Rivers in Russia, the Red River in the United States, the lower Elbe River in Hamburg, Germany, the Saint Lawrence River in Canada, the Ergun River (a tributary of the Heilongjiang River), the Jiamusi River section of the Songhua River, and the upper Ningxia Hui Autonomous Region and Mengmeng (Inner Mongolia Autonomous Region) sections of the Yellow River and the lower Shandong section. During the ice flood period, increased water storage in these rivers is a significant direct cause of rising water levels, potentially leading to dike breaches and flooding. The complex patterns of these rivers' fluctuations have attracted the attention of water conservancy professionals.

[0003] Existing research on the increase in trough water storage during the ice-flood and freezing periods in high-altitude and cold-weather rivers primarily involves: 1) analysis of measured data. For example, for the Yellow River section in Inner Mongolia Autonomous Region, this study analyzes measured data on trough water storage increases during ice-flood and freezing periods, along with factors influencing these changes, such as temperature, upstream flow, and riverbed boundary conditions. However, quantitative simulation and prediction of the changes in trough water storage increases cannot be achieved solely through analysis of measured data. 2) simulation of ice-water dynamics. Related models include RICE, RIVJAM, HEC-RAS, and RIVER2D, but these often suffer from numerous equations and parameters, leading to complex calculations.

[0004] It is well known that in river hydrological systems, river flood evolution often exhibits a "memory hysteresis" effect, also known as a delayed response. This is often described using the Muskingum method (named after its initial application to the Muskingum River). The Muskingum method's basic principle is to simplify the continuity equation and the equation of motion in the hydrodynamic equation into a water balance equation and a channel storage equation, respectively, and then solve them jointly. This method boasts the advantages of simplicity and practicality, and has been used to simulate flow evolution during the ice-frozen and frozen-opening periods, as well as the open flow period, in high-altitude regions, such as the Ningxia Hui Autonomous Region and Inner Mongolia Autonomous Region sections of the Yellow River, with good results. However, the delayed response of channel storage increments during the ice-frozen period in high-altitude regions remains limited, as this involves a complex multiphase system involving water, ice, sediment, and bedrock. Summary of the Invention

[0005] In response to the above problems, the purpose of the present invention is to provide a scientific and practical method for simulating the incremental change process of trough water storage in ice-flood and frozen areas of rivers in high-altitude areas. It is mainly based on the Muskingum method, considering the influence of water-ice phase transformation during ice-flood and frozen periods, and proposes to construct a hysteresis response model for trough water storage increment.

[0006] The technical solution adopted by the present invention is as follows: a method for constructing a delayed response model of trough water storage increment during ice flood and freezing period in high-altitude cold areas, comprising the following steps:

[0007] Step S1: For rivers in high-altitude cold regions, data on ice flood freezing dates and river opening dates, daily temperature, flow, and water storage increment during the freezing period are collected;

[0008] For data on freezing and river opening dates during the ice flood season in high-altitude and cold regions, as well as daily temperature and flow data during the freezing period, data can be obtained through on-site monitoring or by consulting relevant hydrological and meteorological statistical data. For data on incremental water storage during the freezing period, the incremental water storage process is calculated period by period based on the freezing and river opening dates and daily flow data, according to the principle of conservation of mass:

[0009]

[0010] Where: ΔS n is the water storage increment on the nth day, m 3 ;Q i,in , Q i,out are the inlet and outlet cross-sectional flow rates of the river section on day i, m 3 / s; Δt is the calculation period, which is taken as 1d.

[0011] Step S2, constructing a hysteresis response model for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0012] The construction of a hysteresis response model for the increment of water storage in the flume during the ice flood and freezing period in high-altitude cold regions mainly includes the hysteresis response equation for the increment of water storage in the flume and the equation for the change of solid ice volume. The main steps include:

[0013] Step S21, constructing a hysteresis response equation for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0014] Based on the basic equations of the Muskingum method, including the liquid water balance equation and the tank storage equation:

[0015]

[0016] S′=k[xQ in +(1-x)Q out ]

[0017] Where: S' is the amount of liquid water stored in the tank, m 3 ;Q in is the flow rate at the river inlet section, m 3 / s;Q out is the discharge at the river outlet, m 3 / s; k is the flow routing coefficient, which is generally considered to be the average propagation time of flood waves in the river section, s; x is the flow routing distribution coefficient, which is the weight to measure the comprehensive impact of the inflow and outflow of the river section on the liquid water volume in the channel; t is time, s.

[0018] When the flow rate at the inlet section of the river is constant, when the flow rate at the outlet section is equal to the flow rate at the inlet section, the water flow in the river section reaches a balanced state, and the corresponding balance equation of the liquid water volume in the tank can be obtained:

[0019] S′ e =kQ in

[0020] Where: S′ e is the balance value of liquid water storage in the tank, m 3 .

[0021] Combining the above formulas and deducing them together, we can obtain the hysteresis response model of liquid water storage in the river channel. The corresponding basic differential equation is:

[0022]

[0023] Where: β is the adjustment rate parameter, β = 1 / [k(1-x)]

[0024] Solve the above differential equation, ignoring the change of β value for the time being, and taking into account that the flow process of the inlet section of the actual river section is often constantly changing, for each given finite time period Δt, the corresponding analytical solution can be expressed as the following iterative relationship:

[0025] S′i =(1-e -β△t )S′ e,i +e -β△t S′ i-1

[0026] Where: S′ i is the liquid water storage capacity of the river channel in the i-th period, m 3 ; S′ e,i is the balance value of liquid water stored in the tank in period i, m 3 ; S′ i-1 is the liquid water storage capacity of the river channel in the i-1 period, m 3 ; i is the time period number; Δt is the time period length.

[0027] For rivers in the ice flood and freezing period, the impact of the trough water storage-ice phase transition needs to be considered. The existence of solid ice before the period is considered, and the amount of ice melted in this period is concentrated at the end of the period to correct the solid ice in the next period. The iterative equation of the lag response model of the trough water storage during the ice flood and freezing period can be established as follows:

[0028] S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )=(1-e -β△t )S e,i +e -β△t S i-1

[0029] Where: S i is the water storage capacity of the tank in the i-th period of the ice flood and freezing period, including liquid water and solid ice, m 3 ;S i-1 ″ is the volume of solid ice in the tank water storage in the i-1 period during the ice flood and freezing period, m 3 ;S i-1 is the water storage capacity at the end of the i-1 period during the ice flood and freezing period, including liquid water and solid ice, m 3 .

[0030] Based on the hysteresis response model of the tank water storage during the ice flood and freezing period, the hysteresis response equation of the tank water storage increment can be obtained by further deduction:

[0031] △S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )-S0=(1-e -β△t)△S e,i +e -β△t △S i-1 Where: ΔS i is the increment of water storage in the trough in the i-th period during the ice flood and freezing period, m 3 ; S0 is the initial value of the tank water storage during the ice flood and freezing period, m 3 ;ΔS e,i is the incremental balance value of the tank water storage in the i-th period during the ice flood and freezing period, ΔS e,i =S′ e,i +S i-1 ″-S0,m 3 ;ΔS i-1 is the increment of water storage in the tank in the i-1 period during the ice flood and freezing period, ΔS i-1 =S′ i-1 +S i-1 ″-S0,m 3 .

[0032] Step S22, constructing an equation for the change of solid ice volume during the ice flood and freezing period of rivers in high-altitude cold regions;

[0033] In the delayed response equation for the increase in trough water storage during the ice flood and freezing period, the volume change of solid ice is complex, with dimensions including length, width, and thickness, which are comprehensively affected by thermal, hydraulic, and river boundary conditions. Among them, thermal conditions have a significant impact on the thickening of solid ice (ice cover), and the freezing degree-day method of the thermal growth model is often used for calculation. The specific formula is:

[0034] δ=C1I 0.5

[0035] Where: δ is the thickness of solid ice (ice cover), cm; C1 is the empirical coefficient; I is the freezing degree, that is, the absolute value of the daily accumulated negative temperature after solid ice formation, °C·d.

[0036] Based on the freezing degree-day method, the influence of hydraulic conditions, ice flower (layer) transport and other factors are further considered, the ice thickness calculation is corrected, and the ice length and ice width are comprehensively considered. The formula for calculating the solid ice volume can be simplified as follows:

[0037] S″=BLδ=CI 0.5

[0038] Where: S″ is the volume of solid ice during the ice flood and freezing period, m 3 ; B is the average width of solid ice during the ice flood freezing period, m; L is the length of solid ice during the ice flood freezing period, m; C is the comprehensive coefficient, which comprehensively reflects the influence of factors such as ice width and ice flower (layer) thickness, m 3 ℃ -1 / 2 ·d -1 / 2 .

[0039] Step S3, constructing a calculation model for a delayed response model of trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0040] The delayed response model for the trough water storage increment during the ice flood and freezing period in high-altitude and cold regions can be divided into the following two calculation modes, depending on how the initial value is selected during the calculation process: ① Single-step analytical mode. This mode uses the measured trough water storage increment of the previous period as the initial value for the calculation of the next period. ② Multi-step recursive mode. This mode uses the calculated trough water storage increment of the previous period as the initial value for the calculation of the next period.

[0041] Step S4, establishing a calibration method for the parameters of a delayed response model for the increment of water storage during the ice flood and freezing period of rivers in high-altitude cold regions;

[0042] The main steps for calibrating the parameters of the model for the delayed response of the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions include:

[0043] Step S41, constructing a multi-step recursive calculation expression for the delayed response of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0044] Based on the hysteresis response model of the tank water storage increment during the ice flood and freezing period, a multi-step recursive calculation expression for the tank water storage increment can be established through derivation:

[0045]

[0046] Where: Q in,i is the flow rate at the inlet section of the river section in the i-th period, m 3 / s;;I i-1 is the freezing degree on day i-1, ℃·d.

[0047] Step S42, simplifying and establishing a sliding average calculation expression for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0048] In the multi-step recursive calculation expression of the delayed response of the trough water storage increment during the ice flood and freezing period, the calculation period Δt is 1d, and the function term (1-e -βΔt )e -(n-i)βΔt Essentially, it is a weighted average coefficient that reflects the impact of previous daily flow and freezing degrees. If we further simplify and use a sliding average method instead of a weighted average to approximately reflect the impact of previous flow and freezing degrees on the tank water increment, we can establish a sliding average calculation expression for the tank water increment:

[0049]

[0050] Where: Q in,mf is the daily sliding average of the flow rate at the river inlet section, m 3 / s;I 0.5 mfThe sliding average value of freezing degree to the power of 0.5 for m days, ℃ 0.5 ·d 0.5 .

[0051] Step S43, determining the parameters of the hysteresis response model of the trough water storage increment during the ice flood and freezing period of the river in the high-altitude cold region by multiple linear regression;

[0052] Based on the sliding average calculation expression for the calculation of the trough water storage increment during the ice flood and freezing period, combined with the daily measured trough water storage increment, flow rate and temperature data, different sliding average days were taken respectively, and the relationship between the trough water storage increment and the sliding average flow rate and freezing degree was analyzed. The one with the best relevant effect was selected, and the parameters k, C and the initial trough water storage capacity S0 value were determined through multivariate linear regression. These were then substituted into the calibration parameter β of the lag response model of the trough water storage increment during the ice flood and freezing period, and optimized and adjusted to finally determine the model parameters β, k, C and the initial trough water storage capacity S0 value.

[0053] Step S5, analysis and model application of the hysteresis response law of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0054] Based on the delayed response model of trough water storage increment during the ice flood and freezing period of rivers in high-altitude areas, combined with the daily temperature, daily flow and trough water storage increment data during the ice flood and freezing period, different sliding average days were taken respectively, and the relationship between the trough water storage increment and the sliding average flow and freezing degree was analyzed to determine the optimal sliding average day. The model parameters were determined through multivariate linear regression and substituted into the delayed response model of trough water storage increment during the ice flood and freezing period to simulate the changing process of the trough water storage increment.

[0055] Step S6, evaluating the effect of the delayed response model for the increment of trough water storage during the ice flood and freezing period of rivers in high-altitude cold regions.

[0056] The coefficient of certainty R 2 and Nash-Sutcliffe efficiency coefficient E NS Quantitative evaluation of the model effect. Among them, the coefficient of certainty R 2 It is the most basic quantitative indicator for evaluating simulation effects. 2 The value is between 0 and 1.0, R 2 The closer the value is to 1.0, the better the fit between the simulated value and the measured value. 2 The value can be obtained by simply performing linear regression between the simulated value and the measured value using Excel software. Nash-Sutcliffe efficiency coefficient E NS It is a standardized statistical value that determines the relative amount of variance between the residual and the measured data. NS The value is generally between -∞~1.0. NS =1.0, indicating that the calculated value is completely consistent with the measured value. NSWhen E > 0.5, it indicates that the simulation results are within an acceptable level. NS >0, indicating that the simulation results are valid. NS When ≤0, it means that there is a large deviation between the calculated value and the measured value. NS The value can be calculated using the following formula:

[0057]

[0058] Where: E NS is the Nash-Sutcliffe efficiency coefficient; ΔS o i is the measured value of the tank water storage increment on day i, m 3 ;ΔS c i is the calculated value of the tank water storage increment on day i, m 3 ; n and i are calculation numbers.

[0059] Compared with the existing simulation technology of the incremental change process of trough water storage during the ice flood and freezing period of rivers in high-altitude cold regions, the advantages of the present invention are mainly reflected in the following aspects:

[0060] (1) The present invention is based on the Muskingum method for hydrological flood routing for rivers in alpine regions, and further considers the impact of water-ice phase transformation during the ice flood and freezing period, which has a solid theoretical basis;

[0061] (2) The calculation method of the present invention is relatively simple and is convenient for simulating the change process of trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0062] (3) This invention deepens and expands the theory and method of the hysteresis response model of complex river systems, and realizes its organic integration with the river ice model. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is the technical roadmap of the method of the present invention;

[0064] Figure 2 A schematic diagram of a river section to which the method of the present invention is applied;

[0065] Figure 3 This is a diagram of daily temperature changes during the ice flood and freezing period of the river section in which the method of the present invention was applied from 1987 to 1988;

[0066] Figure 4 This is a graph showing the changes in daily flow and trough water storage increment during the ice flood and freezing period of the river section in which the method of the present invention was applied from 1987 to 1988;

[0067] Figure 5This is a diagram of daily temperature changes during the ice flood and freezing period of the river section in which the method of the present invention was applied from 2003 to 2004;

[0068] Figure 6 This is a graph showing changes in daily flow and trough water storage increment during the ice flood and freezing period of the river section in which the method of the present invention was applied from 2003 to 2004;

[0069] Figure 7 This is a simulation result diagram of the embodiment of the method of the present invention from 1987 to 1988;

[0070] Figure 8 This is a simulation result diagram of the embodiment of the method of the present invention from 2003 to 2004. DETAILED DESCRIPTION

[0071] The following will describe in detail the specific implementation methods of the present invention in conjunction with the embodiments of the present invention and the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0072] Example: Taking the simulation of the change process of the trough water storage increment during the ice flood and freezing period in 1987-1988 and 2003-2004 in the Sanhuhekou to Toudaoguai section of the Yellow River in Inner Mongolia Autonomous Region as an example, the specific implementation method of the method for constructing the hysteresis response model of the trough water storage increment during the ice flood and freezing period in the high-altitude cold region of the present invention is further explained. The technical process is as follows: Figure 1 As shown, the following steps are included:

[0073] Step S1: For rivers in high-altitude cold regions, data on ice flood freezing dates and river opening dates, daily temperature, flow, and water storage increment during the freezing period are collected;

[0074] In this embodiment, the simulation of the change process of the trough water storage increment in the section from Sanhuhekou to Toudaoguai in the Yellow River in Inner Mongolia Autonomous Region during the ice flood and freezing period in 1987-1988 and 2003-2004 is taken as an example. Figure 2As shown. The freezing date and river opening date of the river section during the ice flood period, as well as the daily flow data during the freezing period were obtained by consulting the relevant hydrological yearbooks of the Yellow River Basin. The daily temperature change data during the ice flood period were mainly obtained from the National Key Basic Research Program Project (973) of the National Glacier, Permafrost and Desert Science Data Center, "Wind and Sediment Processes and Regulation Mechanisms in the Wide Valley of the Upper Yellow River Desert", Topic 6 "Prediction of Erosion and Sedimentation Evolution Trends and Regulation Countermeasures in the Wide Valley of the Upper Yellow River Desert" - Comprehensive Data Platform of the Ningxia-Inner Mongolia Section of the Upper Yellow River, http: / / westdc.westgis.ac.cn / yrnmr, with the daily temperature change data of Tuoketuo Station as a reference. The data on the incremental water storage during the ice flood and freezing period were mainly based on the freezing date, river opening date and daily flow data. According to the principle of conservation of mass, the incremental water storage change process was calculated for each period:

[0075]

[0076] Where: ΔS n is the water storage increment on the nth day, m 3 ;Q i,in , Q i,out are the inlet and outlet cross-sectional flow rates of the river section on day i, m 3 / s; Δt is the calculation period, which is taken as 1d.

[0077] For the Yellow River section from Sanhukou to Toudaoguai in Inner Mongolia Autonomous Region, the data on daily temperature, daily flow and trough water storage increment during the ice flood and freezing period in 1987-1988 and 2003-2004 are as follows: Figures 3 to 6 shown.

[0078] Step S2, constructing a hysteresis response model for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0079] The construction of a hysteresis response model for the increment of water storage in the flume during the ice flood and freezing period in high-altitude cold regions mainly includes the hysteresis response equation for the increment of water storage in the flume and the equation for the change of solid ice volume. The main steps include:

[0080] Step S21, constructing a hysteresis response equation for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0081] Based on the basic equations of the Muskingum method, including the liquid water balance equation and the tank storage equation:

[0082]

[0083] S′=k[xQ in +(1-x)Q out ]

[0084] Where: S' is the amount of liquid water stored in the tank, m 3 ;Q inis the flow rate at the river inlet section, m 3 / s;Q out is the discharge at the river outlet, m 3 / s; k is the flow routing coefficient, which is generally considered to be the average propagation time of flood waves in the river section, s; x is the flow routing distribution coefficient, which is the weight to measure the comprehensive impact of the inflow and outflow of the river section on the liquid water volume in the channel; t is time, s.

[0085] When the flow rate at the inlet section of the river is constant, when the flow rate at the outlet section is equal to the flow rate at the inlet section, the water flow in the river section reaches a balanced state, and the corresponding balance equation of the liquid water volume in the tank can be obtained:

[0086] S′ e =kQ in

[0087] Where: S′ e is the balance value of liquid water storage in the tank, m 3 .

[0088] Combining the above formulas and deducing them together, we can obtain the hysteresis response model of liquid water storage in the river channel. The corresponding basic differential equation is:

[0089]

[0090] Where: β is the adjustment rate parameter, β = 1 / [k(1-x)]

[0091] Solve the above differential equation, ignoring the change of β value for the time being, and taking into account that the flow process of the inlet section of the actual river section is often constantly changing, for each given finite time period Δt, the corresponding analytical solution can be expressed as the following iterative relationship:

[0092] S′ i =(1-e -β△t )S′ e,i +e -β△t S′ i-1

[0093] Where: S′ i is the liquid water storage capacity of the river channel in the i-th period, m 3 ; S′ e,i is the balance value of liquid water stored in the tank in period i, m 3 ; S′ i-1 is the liquid water storage capacity of the river channel in the i-1 period, m 3 ; i is the time period number; Δt is the time period length.

[0094] For rivers in the ice flood and freezing period, the impact of the trough water storage-ice phase transition needs to be considered. The existence of solid ice before the period is considered, and the amount of ice melted in this period is concentrated at the end of the period to correct the solid ice in the next period. The iterative equation of the lag response model of the trough water storage during the ice flood and freezing period can be established as follows:

[0095] S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )=(1-e -β△t )S e,i +e -β△t S i-1

[0096] Where: S i is the water storage capacity of the tank in the i-th period of the ice flood and freezing period, including liquid water and solid ice, m 3 ;S i-1 ″ is the volume of solid ice in the tank water storage in the i-1 period during the ice flood and freezing period, m 3 ;S i-1 is the water storage capacity at the end of the i-1 period during the ice flood and freezing period, including liquid water and solid ice, m 3 .

[0097] Based on the hysteresis response model of the tank water storage during the ice flood and freezing period, the hysteresis response equation of the tank water storage increment can be obtained by further deduction:

[0098] △S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )-S0=(1-e -β△t )△S e,i +e -β△t △S i-1 Where: ΔS i is the increment of water storage in the trough in the i-th period during the ice flood and freezing period, m 3 ; S0 is the initial value of the tank water storage during the ice flood and freezing period, m 3 ;ΔS e,i is the incremental balance value of the tank water storage in the i-th period during the ice flood and freezing period, ΔS e,i =S′ e,i +S i-1 ″-S0,m 3 ;ΔS i-1 is the increment of water storage in the tank in the i-1 period during the ice flood and freezing period, ΔS i-1 =S′i-1 +S i-1 ″-S0,m 3 .

[0099] Step S22, constructing an equation for the change of solid ice volume during the ice flood and freezing period of rivers in high-altitude cold regions;

[0100] In the delayed response equation of the trough water storage increment during the ice flood and freezing period, the change pattern of solid ice volume is complex, with dimensions including length, width, and thickness, which are comprehensively affected by thermal, hydraulic, river boundary and other conditions. Among them, thermal conditions have a significant impact on the thickening of solid ice (ice sheet), and the freezing degree-day method of the thermal growth model is often used for calculation. The specific formula is: δ = C1I 0.5

[0101] Where: δ is the thickness of solid ice (ice cover), cm; C1 is the empirical coefficient; I is the freezing degree, that is, the absolute value of the daily accumulated negative temperature after solid ice formation, °C·d.

[0102] Based on the freezing degree-day method, the influence of hydraulic conditions, ice flower (layer) transport and other factors are further considered, the ice thickness calculation is corrected, and the ice length and ice width are comprehensively considered. The formula for calculating the solid ice volume can be simplified as follows:

[0103] S″=BLδ=CI 0.5

[0104] Where: S″ is the volume of solid ice during the ice flood and freezing period, m 3 ; B is the average width of solid ice during the ice flood freezing period, m; L is the length of solid ice during the ice flood freezing period, m; C is the comprehensive coefficient, which comprehensively reflects the influence of factors such as ice width and ice flower (layer) thickness, m 3 ℃ -1 / 2 ·d -1 / 2 .

[0105] Step S3, constructing a calculation model for a delayed response model of trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0106] The delayed response model for the trough water storage increment during the ice flood and freezing period in high-altitude and cold regions can be divided into the following two calculation modes, depending on how the initial value is selected during the calculation process: ① Single-step analytical mode. This mode uses the measured trough water storage increment of the previous period as the initial value for the calculation of the next period. ② Multi-step recursive mode. This mode uses the calculated trough water storage increment of the previous period as the initial value for the calculation of the next period.

[0107] Step S4, establishing a calibration method for the parameters of a delayed response model for the increment of water storage during the ice flood and freezing period of rivers in high-altitude cold regions;

[0108] The main steps for calibrating the parameters of the model for the delayed response of the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions include:

[0109] Step S41, constructing a multi-step recursive calculation expression for the delayed response of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0110] Based on the hysteresis response model of the tank water storage increment during the ice flood and freezing period, a multi-step recursive calculation expression for the tank water storage increment can be established through derivation:

[0111]

[0112] Where: Q in,i is the flow rate at the inlet section of the river section in the i-th period, m 3 / s;;I i-1 is the freezing degree on day i-1, ℃·d.

[0113] Step S42, simplifying and establishing a sliding average calculation expression for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0114] In the multi-step recursive calculation expression of the delayed response of the trough water storage increment during the ice flood and freezing period, the calculation period Δt is 1d, and the function term (1-e -βΔt )e -(n-i)βΔt Essentially, it is a weighted average coefficient that reflects the impact of previous daily flow and freezing degrees. If we further simplify and use a sliding average method instead of a weighted average to approximately reflect the impact of previous flow and freezing degrees on the tank water increment, we can establish a sliding average calculation expression for the tank water increment:

[0115]

[0116] Where: Q in,mf is the daily sliding average of the flow rate at the river inlet section, m 3 / s;I 0.5 mf The sliding average value of freezing degree to the power of 0.5 for m days, ℃ 0.5 ·d 0.5 .

[0117] Step S43, determining the parameters of the hysteresis response model of the trough water storage increment during the ice flood and freezing period of the river in the high-altitude cold region by multiple linear regression;

[0118] Based on the sliding average calculation expression for the calculation of the trough water storage increment during the ice flood and freezing period, combined with the daily measured trough water storage increment, flow rate and temperature data, different sliding average days were taken respectively, and the relationship between the trough water storage increment and the sliding average flow rate and freezing degree was analyzed. The one with the best relevant effect was selected, and the parameters k, C and the initial trough water storage capacity S0 value were determined through multivariate linear regression. These were then substituted into the calibration parameter β of the lag response model of the trough water storage increment during the ice flood and freezing period, and optimized and adjusted to finally determine the model parameters β, k, C and the initial trough water storage capacity S0 value.

[0119] Step S5, analysis and model application of the hysteresis response law of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions;

[0120] Based on the delayed response model of trough water storage increment during the ice flood and freezing period of rivers in high-altitude areas, combined with the daily temperature, daily flow and trough water storage increment data during the ice flood and freezing period, different sliding average days were taken respectively, and the relationship between the trough water storage increment and the sliding average flow and freezing degree was analyzed to determine the optimal sliding average day. The model parameters were determined through multivariate linear regression and substituted into the delayed response model of trough water storage increment during the ice flood and freezing period to simulate the changing process of the trough water storage increment.

[0121] In this embodiment, for the section of the Yellow River from Sanhukou to Toudaoguai in Inner Mongolia Autonomous Region, based on the hysteresis response model of the tank water storage increment during the ice flood and freezing period and its simplified sliding average calculation expression, combined with the data on the change process of daily temperature, daily flow, and tank water storage increment during the ice flood and freezing period in 1987-1988 and 2003-2004, different sliding average days were taken respectively, and the relationship between the tank water storage increment and the sliding average flow and freezing degree was analyzed. The optimal sliding average days were determined to be 10 days and 14 days, respectively. The parameters k, C and the initial tank water storage capacity S0 value were determined by multivariate linear regression, and then substituted into the hysteresis response model of the tank water storage increment during the ice flood and freezing period to calibrate the parameter β, and optimized and adjusted. Finally, the model parameters β, k, C and the initial tank water storage capacity S0 value were determined, as shown in Table 1. The calibrated model parameters β, k, C and the initial tank water storage capacity S0 are substituted into the lag response model of tank water storage increment during the ice flood and freezing period. The single-step analytical and multi-step recursive calculation modes are used to simulate the change process of tank water storage increment during the ice flood and freezing period in different years. The results are as follows: Figure 7 and Figure 8 shown.

[0122] Table 1 Model parameters and effect evaluation table

[0123]

[0124]

[0125] Step S6, evaluating the effect of the delayed response model for the increment of trough water storage during the ice flood and freezing period of rivers in high-altitude cold regions.

[0126] The coefficient of certainty R 2 and Nash-Sutcliffe efficiency coefficient E NS Quantitative evaluation of the model effect. Among them, the coefficient of certainty R 2 It is the most basic quantitative indicator for evaluating simulation effects. 2 The value is between 0 and 1.0, R 2 The closer the value is to 1.0, the better the fit between the simulated value and the measured value. 2The value can be obtained by simply performing linear regression between the simulated value and the measured value using Excel software. Nash-Sutcliffe efficiency coefficient E NS It is a standardized statistical value that determines the relative amount of variance between the residual and the measured data. NS The value is generally between -∞~1.0. NS =1.0, indicating that the calculated value is completely consistent with the measured value. NS When E > 0.5, it indicates that the simulation results are within an acceptable level. NS >0, indicating that the simulation results are valid. NS When ≤0, it means that there is a large deviation between the calculated value and the measured value. NS The value can be calculated using the following formula:

[0127]

[0128] Where: E NS is the Nash-Sutcliffe efficiency coefficient; ΔS o i is the measured value of the tank water storage increment on day i, m 3 ;ΔS c i is the calculated value of the tank water storage increment on day i, m 3 ; n and i are calculation numbers.

[0129] In this embodiment, the coefficient of certainty R 2 and Nash-Sutcliffe efficiency coefficient E NS A quantitative evaluation was conducted on the simulation results of the change process of the trough water storage increment in the Sanhuhekou to Toudaoguai section of the Yellow River in Inner Mongolia Autonomous Region during the ice flood and freezing periods in 1987-1988 and 2003-2004. The results are listed in Table 1.

[0130] comprehensive Figure 7 、 Figure 8 As can be seen from Table 1, the simulated values of the change process of the trough water storage increment in the Sanhuhekou to Toudaoguai section of the Yellow River in Inner Mongolia Autonomous Region during the ice flood and freezing period in 1987-1988 and 2003-2004 are in good agreement with the measured values. For the two calculation modes of single-step analysis and multi-step recursion, the deterministic coefficient R 2 With E NS The efficiency coefficient values all reach 0.99, with high simulation accuracy.

Claims

1. A method for constructing a delayed response model for trough water storage increment during ice flood and freezing period in high-altitude cold regions, characterized by: The following steps are involved: Step S1: For rivers in high-altitude cold regions, data on ice flood freezing dates and river opening dates, daily temperature, flow, and water storage increment during the freezing period are collected; Step S2, constructing a hysteresis response model for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; Step S3, constructing a calculation model for a delayed response model of trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; Step S4, establishing a calibration method for the parameters of a delayed response model for the increment of water storage during the ice flood and freezing period of rivers in high-altitude cold regions; Step S5, analysis and model application of the hysteresis response law of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; Step S6, evaluating the effect of the delayed response model for the increment of trough water storage during the ice flood and freezing period of rivers in high-altitude cold regions.

2. The method for constructing a delayed response model for trough water storage increment during ice flood and freezing period in high-altitude cold regions according to claim 1 is characterized in that: In step S2, the lag response model for the increment of water storage in the ice flood and freezing period of the river in the high-altitude cold region includes a lag response equation for the increment of water storage in the ice flood and freezing period, and an equation for the change of the solid ice volume, including the following sub-steps: Step S21, constructing a hysteresis response equation for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; Based on the basic equations of the Muskingum method, including the liquid water balance equation and the tank storage equation: S′=k[xQ in +(1-x)Q out ] Where: S' is the amount of liquid water stored in the tank, m 3 ;Q in is the flow rate at the river inlet section, m 3 / s;Q out is the discharge at the river outlet, m 3 / s; k is the flow routing coefficient, which is considered to be the average propagation time of flood waves in the river section, s; x is the flow routing distribution coefficient, which is the weight of the comprehensive impact of the inflow and outflow of the river section on the liquid water volume in the channel; t is time, s; When the flow rate at the inlet section of the river is stable, when the flow rate at the outlet section is equal to the flow rate at the inlet section, the water flow in the river section reaches a balanced state, and the corresponding balance equation of the liquid water volume in the tank is obtained: S′ e =kQ in Where: S′ e is the balance value of liquid water storage in the tank, m 3 ; Combining the above formulas and deducing them together, we obtain the hysteresis response model of liquid water storage in the river channel. The corresponding basic differential equation is: Where: β is the adjustment rate parameter, β = 1 / [k(1-x)]; Solve the above differential equation, ignoring the change of β value for the time being, and taking into account that the flow process of the inlet section of the actual river section is constantly changing, for each given finite time period Δt, the corresponding analytical solution is expressed as the following iterative relationship: S′ i =(1-e -β△t )S′ e,i +e -β△t S′ i-1 Where: S′ i is the liquid water storage capacity of the river channel in the i-th period, m 3 ; S′ e,i is the balance value of liquid water stored in the tank in period i, m 3 ; S′ i-1 is the liquid water storage capacity of the river channel in the i-1 period, m 3 ; i is the time period number; Δt is the time period length; For rivers in the ice flood and freezing period, the impact of the trough water storage-ice phase transition needs to be considered. The existence of solid ice before the period is considered, and the ice-melting water volume of the current period is concentrated at the end of the period to correct the solid ice in the next period. The iterative equation for the lag response model of trough water storage during the ice flood and freezing period is as follows: S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )=(1-e -β△t )S e,i +e -β△t S i-1 Where: S i is the water storage capacity of the tank in the i-th period of the ice flood and freezing period, including liquid water and solid ice, m 3 ; S i-1 ″ is the volume of solid ice in the tank water storage in the i-1 period during the ice flood and freezing period, m 3 ; S i-1 is the water storage capacity at the end of the i-1 period during the ice flood and freezing period, including liquid water and solid ice, m 3 ; Based on the hysteresis response model of the tank water storage during the ice flood and freezing period, the hysteresis response equation of the tank water storage increment is further derived: △S i =(1-e -β△t )(S′ e,i +S″ i-1 )+e -β△t (S′ i-1 +S″ i-1 )-S0=(1-e -β△t )△S e,i +e -β△t △S i-1 Where: ΔS i is the increment of water storage in the trough in the i-th period during the ice flood and freezing period, m 3 ; S0 is the initial value of the tank water storage during the ice flood and freezing period, m 3 ;ΔS e,i is the incremental balance value of the tank water storage in the i-th period during the ice flood and freezing period, ΔS e,i =S′ e,i +S i-1 ″-S0,m 3 ;ΔS i-1 is the increment of water storage in the tank in the i-1 period during the ice flood and freezing period, ΔS i-1 =S′ i-1 +S i-1 ″-S0,m 3 ; Step S22, constructing an equation for the change of solid ice volume during the ice flood and freezing period of rivers in high-altitude cold regions; In the lag response equation of the trough water storage increment during the ice flood and freezing period, thermal conditions have an important influence on the thickness of solid ice, and the freezing degree-day method of the thermal growth model is often used for calculation. The specific formula is: δ=C1I 0.5 Where: δ is the thickness of solid ice, cm; C1 is the empirical coefficient; I is the freezing degree, that is, the absolute value of the daily accumulated negative temperature after solid ice formation, °C·d; Based on the freezing degree-day method, the ice thickness calculation is modified by further considering the influence of hydraulic conditions and ice flower transport factors. The ice length and ice width are comprehensively considered to simplify the calculation formula of solid ice volume as follows: S″=BLδ=CI 0.5 Where: S″ is the volume of solid ice during the ice flood and freezing period, m 3 ; B is the average width of solid ice during the ice flood freezing period, m; L is the length of solid ice during the ice flood freezing period, m; C is the comprehensive coefficient, which comprehensively reflects the influence of ice width and ice flower thickness factors, m 3 ℃ -1 / 2 ·d -1 / 2 .

3. The method for constructing a delayed response model for trough water storage increment during ice flood and freezing period in high-altitude cold regions according to claim 2 is characterized in that: In step S3, according to the different ways of selecting the initial values in the model calculation process, there are two calculation modes:

1. Single-step analytical mode; the measured value of the tank water storage increment in the previous period is used as the initial value for calculation in the next period, which is called the single-step analytical mode; 2. Multi-step recursive mode; the calculated value of the tank water storage increment in the previous period is used as the initial value for calculation in the next period, which is called the multi-step recursive mode.

4. The method for constructing a delayed response model for trough water storage increment during ice flood and freezing period in high-altitude cold regions according to claim 2 is characterized in that: In step S4, the method for calibrating the parameters of the hysteresis response model for the trough water storage increment during the ice flood and freezing period of the high-altitude and cold regions river comprises the following sub-steps: Step S41, constructing a multi-step recursive calculation expression for the delayed response of the trough water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; Based on the hysteresis response model of the tank water storage increment during the ice flood and freezing period, a multi-step recursive calculation expression for the tank water storage increment is established through derivation: Where: Q in,i is the flow rate at the inlet section of the river section in the i-th period, m 3 / s;I i-1 is the freezing degree on day i-1, °C·d; Step S42, simplifying and establishing a sliding average calculation expression for the water storage increment during the ice flood and freezing period of rivers in high-altitude cold regions; In the multi-step recursive calculation expression of the delayed response of the trough water storage increment during the ice flood and freezing period, the calculation period Δt is 1d, and the function term (1-e -βΔt )e -(n-i)βΔt The essence of this is a weighted average coefficient that reflects the impact of previous daily flow and freezing degree. The sliding average method is used instead of the weighted average to approximately reflect the impact of previous flow and freezing degree on the tank water storage increment. The sliding average calculation expression for the tank water storage increment is established: Where: Q in,mf is the daily sliding average of the flow rate at the river inlet section, m 3 / s;I 0.5 mf The sliding average value of freezing degree to the power of 0.5 for m days, ℃ 0.5 ·d 0.5 ; Step S43, determining the parameters of the hysteresis response model of the trough water storage increment during the ice flood and freezing period of the river in the high-altitude cold region by multiple linear regression; Based on the sliding average calculation expression for the calculation of the trough water storage increment during the ice flood and freezing period, combined with the daily measured trough water storage increment, flow rate and temperature data, different sliding average days were taken respectively, and the relationship between the trough water storage increment and the sliding average flow rate and freezing degree was analyzed. The one with the best relevant effect was selected, and the parameters k, C and the initial trough water storage capacity S0 value were determined through multivariate linear regression. These were then substituted into the calibration parameter β of the lag response model of the trough water storage increment during the ice flood and freezing period, and optimized and adjusted to finally determine the model parameters β, k, C and the initial trough water storage capacity S0 value.

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