A flash flood dynamic critical rainfall probability early warning method

Abstract

The present application belongs to the technical field of mountain torrent disaster early warning, and discloses a mountain torrent disaster dynamic critical rainfall probability early warning method, which comprises the following steps: determining a 24h hourly rainfall type distribution ratio according to annual maximum 6-hour and 24-hour rainfall; dividing a previous soil humidity state to obtain a corresponding initial soil water content; determining a plurality of hydrological model input parameter groups; performing a trial calculation on the hydrological model according to the 24h hourly rainfall type distribution ratio, the previous soil humidity state and different input parameter groups to obtain critical rainfall values of each early warning period corresponding to different previous soil humidity states or / and different input parameter groups; determining early warning probabilities corresponding to the cumulative rainfall of each early warning period under a confidence level, and evaluating the mountain torrent disaster according to the early warning probabilities. The present application can realize effective dynamic early warning of the mountain torrent disaster.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology, and relates to flash flood disaster early warning technology, and in particular to a dynamic critical rainfall probability early warning method for flash flood disasters. Background Technology

[0002] Floods are among the most severe natural disasters in my country and even the world. They not only have a significant impact on economic and social development but also pose a serious threat to the lives and property of the people. Flash floods, a typical type of flood disaster, generally refer to a type of flood triggered by rainfall in hilly areas that is extremely destructive and characterized by seasonality, suddenness, difficulty in prediction, high destructive power, and rapid onset. The occurrence and destructive extent of flash floods are mainly influenced by a combination of factors, including climatic and hydrological conditions, watershed underlying surface conditions, vegetation cover, and human activities.

[0003] Timely and effective disaster early warning is crucial to the success or failure of flash flood prevention and control. Currently, deterministic early warning based primarily on critical rainfall indicators is a commonly used method for flash flood early warning. However, conventional methods only provide one (or a set of) definite critical rainfall thresholds to determine whether a flash flood will occur, i.e., a probability of 0% or 100%, lacking consideration for the uncertainty of the warning results. This often leads to missed warnings and false alarms, indicating that the early warning results contain errors and significant uncertainties, making it difficult to truly meet the actual needs of flash flood prevention and control.

[0004] Gao Liangmin et al. studied the determination and analysis of rainfall warning indicators for flash floods in small watersheds of Zhejiang Province, and proposed a method for estimating rainfall warning indicators based on the principle of back-calculating rainfall from water level and considering the characteristics of soil moisture content in the watershed in the early stages. This method uses an empirical floating-point approach based on critical rainfall to determine the immediate and prepared-for-transfer rainfall warning indicators (see Gao Liangmin, Du Huimin, Analysis and Determination of Rainfall Warning Indicators for Flash Floods in Small Watersheds of Zhejiang Province, Standardization and Quality Supervision, 2020, No. 2). The warning indicators of this method are essentially deterministic indicators under different anterior soil moisture conditions, and do not consider the significant influence of the hydrological model on the warning indicators in the hydrological model method. The influence of watershed hydrophysical mechanisms is often reflected in model parameters; therefore, the forecast and warning results are greatly affected by factors such as model parameters. In addition, the influence of different parameters having the same effect means that traditional methods lack consideration of the uncertainty of model parameters, resulting in low reliability of the warning results. Furthermore, in reality, there are often situations where rainfall is below the threshold but still causes flooding, or rainfall is above the threshold but no flooding occurs. This reflects complex situations such as "light rain causing disaster" and "heavy rain causing little (or no) disaster," indicating that early warning results may contain missed or false alarms. This suggests that the probability of flooding corresponding to a certain critical rainfall level is not 100%, but rather exists within a certain range. The main reason for this is that current hydrological models cannot fully and accurately characterize the influencing factors of flood disasters and accurately describe the physical mechanisms of flood occurrence; therefore, disaster early warnings often involve uncertainty.

[0005] Therefore, addressing the challenges of complex runoff generation and confluence mechanisms and significant uncertainties in multiple parameters in determining flash flood disaster warning indicators, providing a rainfall warning method with higher accuracy and reliability is a key technical challenge in this field. Summary of the Invention

[0006] This invention aims to address the significant uncertainties and high false alarm rates inherent in traditional flash flood warning methods. By considering the inherent relationship between precipitation events and flash flood disasters, as well as the uncertainties of model parameters and prior soil moisture conditions, this invention provides a dynamic critical rainfall probability warning method for flash flood disasters. This method takes into account the uncertainties of warning indicator parameters and prior soil moisture conditions, and can reasonably and effectively deduce the warning indicator range for flash flood disasters. It has higher accuracy and reliability and is suitable for early warning and forecasting of flash flood disasters.

[0007] Conventional deterministic critical rainfall estimation methods primarily determine whether a flash flood will occur based on a fixed rainfall threshold, i.e., a probability of 0% or 100%. However, considering the unavoidable uncertainty in flash flood warnings, a more reasonable and effective approach to overcome the shortcomings of conventional deterministic warnings is to fully explore the rich information implicit in rainstorm and flood sample data. This invention quantitatively describes the possibility and probability of a flash flood occurring based on critical rainfall, i.e., "probabilistic warning." Addressing the sources of uncertainty in flash flood warnings, this invention considers the impact of uncertainties in previous soil moisture conditions and model parameters, and then uses the GLUE method to classify the critical rainfall threshold.

[0008] Based on the above analysis, the dynamic critical rainfall probability early warning method for flash flood disasters provided by this invention includes the following steps:

[0009] S1 determines the 24-hour hourly rainfall pattern allocation ratio based on the annual maximum 6-hour and 24-hour rainfall;

[0010] S2 is used to determine the soil moisture state in the early stage and obtain the corresponding initial soil moisture content;

[0011] S3 determines several sets of input parameters for the hydrological model;

[0012] S4 performs trial calculations on the hydrological model based on the 24-hour hourly rainfall pattern allocation ratio, the previous soil moisture status, and different input parameter groups to obtain the critical rainfall values ​​for each warning period corresponding to different previous soil moisture status and / or different input parameter groups.

[0013] S5 determines the warning probability corresponding to the cumulative rainfall for each warning period at the given confidence level using the following formula, and assesses the flash flood disaster based on the warning probability:

[0014]

[0015] In the formula, RT 上限 RT 下限 RT P These represent the upper and lower limits of the critical rainfall range and the cumulative rainfall (mm) of the actual rainfall event, respectively; Probability 上限 Probability 下限 These represent the confidence level probabilities of the upper and lower limits of the threshold confidence interval, respectively.

[0016] Step S1 above includes the following sub-steps:

[0017] S11 determines the annual maximum 6h and 24h average rainfall and coefficient of variation for the current region at a specified frequency;

[0018] S12 determines the design point rainfall amounts for 6 hours and 24 hours;

[0019] S13 determines the 6-hour and 24-hour average rainfall over the watershed;

[0020] S14 multiplies the ratio of the 6-hour average rainfall in the basin area to the 24-hour average rainfall in the basin area by the 6-hour allocation ratio in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio within 6 hours. Then, it multiplies (the ratio of the 1-6-hour average rainfall in the basin area to the 24-hour average rainfall in the basin area) by the remaining 18-hour allocation ratio in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio for 18 hours. This gives the 24-hour hourly rainfall pattern allocation ratio for the specified frequency in the basin.

[0021] In step S2 above, WM represents the soil saturation moisture content. The critical values ​​of Pa = 0.5WM and Pa = 0.8WM are used to classify the soil moisture content under three conditions: low, moderate, and high rainfall. These represent three typical conditions within the watershed: relatively dry (Pa ≤ 0.5WM), moderate (0.5WM ≤ Pa ≤ 0.8WM), and relatively moist (Pa > 0.8WM). Therefore, 0.5WM, 0.75WM, and 0.9WM are selected as the initial soil moisture content for the corresponding watershed. For watersheds lacking watershed-scale soil saturation moisture content, the maximum rainfall loss of 1m is first determined and used as the soil saturation moisture content WM.

[0022] The hydrological models and parameters given in steps S3 and S4 above are conventional models already disclosed in this field, and can be determined according to different watersheds, and are not limited here.

[0023] In step S3 above, a multi-objective GLUE method is used to determine multiple sets of input parameters that satisfy the threshold range of the objective function. The basic principle of the multi-objective GLUE method is to first randomly sample within the initial range of model parameters, and then input the sampled parameters into the model for simulation; then, a likelihood objective function is selected to judge the quality of the simulation results. This is based on the certainty coefficient (DC) and the absolute value of the peak flow error (ΔQ). pk The objective function value DC ranges from (-∞, 1), with values ​​closer to 1 indicating better results; ΔQ pk The value range is [0, 100%], where 0 indicates the optimal model result. Finally, effective parameter sets are selected based on the thresholds of the objective functions. Referring to the Hydrological Information Standard (GB / T22482-2008), the thresholds for the two objective functions are DC ≥ 0.6 and ΔQ, respectively. pk ≤20%. The expressions for each likelihood function are:

[0024]

[0025]

[0026] In the formula, Q c (i) represents the predicted flow rate for the i-th time period, m 3 / s, calculated by the following formula (34); Q0(i) is the measured flow rate value of the i-th time period, m 3 / s; n is the given flood sequence length; Q cmax Indicates the predicted peak traffic volume, m 3 / s;Q 0max Indicates the measured peak flow rate, m 3 / s; This represents the average measured flow rate, m. 3 / s.

[0027] Based on the determined input parameters of several sets of hydrological models, several sets of hydrological models can be determined.

[0028] In step S4 above, under different soil moisture conditions, within a given rainfall range, the cumulative rainfall for each warning period is determined according to the 24-hour hourly rainfall pattern distribution ratio at a specified frequency in the watershed. Then, by inputting several sets of hydrological models, the rainfall calculation process can be carried out to obtain the critical rainfall value under the corresponding soil moisture conditions and the corresponding input parameter set.

[0029] The rainfall calculation process involves repeatedly performing flood runoff simulations under the given initial soil moisture content and model parameters until the simulated peak flow rate is closest to the critical disaster-causing flow rate, i.e., satisfying the equation:

[0030]

[0031] In the formula, Q c Q represents the peak flow rate simulated during the trial calculation process; 灾 This represents the disaster-causing flow rate under the corresponding return period (i.e., frequency). When the trial calculation results satisfy the above formula, the assumed rainfall for that period is the critical rainfall under the initial soil moisture content state for that period. By continuously repeating this process and making repeated adjustments and trial calculations, the critical rainfall value for each case is finally determined.

[0032] In step S5 above, the upper and lower limits of the critical rainfall value interval are obtained as follows: First, the cumulative frequency distribution map of critical rainfall is determined. For a given confidence level, interpolation is used to find the predicted values ​​corresponding to the (1-α) / 2×100% and (1+α) / 2×100% quantiles on the cumulative frequency distribution map. These two points are the lower and upper limits of the model uncertainty prediction range at a confidence level of α, respectively. The specific method for obtaining the cumulative frequency distribution map of critical rainfall is as follows: Weights are assigned to each critical rainfall value obtained in step S4 to obtain corrected critical rainfall values. The corrected critical rainfall values ​​are arranged in ascending order, and their cumulative frequency distribution map is calculated, which is the cumulative distribution map of critical rainfall. The weight of each critical rainfall value is (1 - absolute value of peak flow error).

[0033] Compared with existing technologies, the dynamic critical rainfall probability early warning method for flash flood disasters provided by this invention has the following beneficial effects:

[0034] (1) This invention incorporates the uncertainty of hydrological model parameters into the consideration of flash flood early warning. First, the critical rainfall corresponding to different hydrological model parameters is determined, then the critical rainfall early warning interval is determined, and then the actual early warning probability is obtained by combining the cumulative rainfall value of actual rainfall events, which can realize effective dynamic early warning of flash flood disasters.

[0035] (2) The present invention also takes into account different soil moisture conditions to improve the accuracy of early warning. Attached Figure Description

[0036] Figure 1 A watershed water storage capacity-area distribution curve;

[0037] Figure 2 This is a structural diagram of a free reservoir.

[0038] Figure 3 This is a curve showing the free water storage capacity versus area distribution.

[0039] Figure 4 A flowchart illustrating the dynamic critical rainfall probability early warning method for flash flood disasters provided in this embodiment of the invention;

[0040] Figure 5 This is a schematic diagram of the dynamic critical rainfall probability early warning results for flash flood disasters provided in an embodiment of the present invention. Detailed Implementation

[0041] The technical solutions of various embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] The hydrological model used in the following embodiments is the Xin'anjiang hydrological model.

[0043] The Xin'anjiang hydrological model includes evapotranspiration calculation, runoff generation calculation, water source division, and confluence calculation.

[0044] (I) Evapotranspiration calculation

[0045] Basin evapotranspiration is mainly used for vegetation interception, surface depression filling, and the recession of soil water storage, which is an important part of the basin water balance calculation. A three-layer evapotranspiration model is used to calculate the evapotranspiration of the basin, and the calculation formulas (Equations (4) to (7)) are as follows:

[0046] WM = UM + LM + DM (4)

[0047] W = WU + WL + WD (5)

[0048] E = EU + EL + ED (6)

[0049] EP = KC·E (7)

[0050] In the formulas, WM is the average water storage capacity of the whole basin, in mm; UM, LM, and DM are the water storage capacities of the upper, lower, and deep layers of the soil, respectively, in mm; W is the total soil water content of the basin, in mm; WU, WL, and WD are the water contents of the upper, lower, and deep layers of the soil, respectively, in mm; E is the total evapotranspiration, in mm; EU, EL, and ED are the evapotranspirations of the upper, lower, and deep layers of the soil, respectively, in mm; EP is the basin evaporation capacity, in mm; and KC is the evapotranspiration conversion coefficient.

[0051] The specific calculation is as follows:

[0052] If P + WU ≥ EP, then EU = EP, EL = 0, ED = 0; P represents the rainfall;

[0053] If P + WU < EP and WL > C·LM, then EU = P + WU, ED = 0; C is the deep evapotranspiration conversion coefficient;

[0054] If P + WU < EP and C(EP - EU) ≤ WL < C·LM, then EU = P + WU, EL = C(EP - EU), ED = 0;

[0055] If P + WU < EP and WL < C(EP - EU), then EU = P + WU, EL = WL, ED = C(EP - EU) - WL.

[0056] (II) Runoff generation calculation

[0057] The Xin'anjiang model follows the runoff generation mechanism based on water storage capacity: during rainfall, when the soil water storage in the vadose zone is below field capacity, all rainfall is absorbed by the soil without generating runoff; once the soil moisture content reaches maximum field capacity, all effective rainfall is converted into runoff. Addressing the spatial heterogeneity of soil moisture shortage within the watershed, the water storage capacity-area distribution curve is used to determine the corresponding total runoff under uneven rainfall conditions, such as... Figure 1 As shown.

[0058] Its line type is:

[0059]

[0060] In the formula, f is the runoff generation area, km² 2 F represents the total drainage area, in km². 2 W′ represents the water storage capacity at a single point in the basin, in mm; WMM represents the maximum water storage capacity at a single point in the basin, in mm; B represents the index of the water storage capacity-area distribution curve; IM represents the proportion of impermeable area to the total basin area.

[0061] W0 is calculated using the following formula:

[0062]

[0063] When A = WMM and W0 = WM, substituting them into equation (9) yields the formula for calculating WM:

[0064]

[0065] The ordinate value A corresponding to the W0 value is calculated using the following formula:

[0066]

[0067] Let PE be the precipitation after deducting evaporation, then the formula for total runoff is:

[0068]

[0069] If PE+A <WMM,

[0070] That is, the localized flow is calculated using the following formula:

[0071]

[0072] If PE + A ≥ WMM, then the total flow rate is calculated according to the formula:

[0073] R = PE - (WM - W0) (14)

[0074] In the formula, W0 is the initial soil water storage of the watershed, mm; R is the total runoff, mm.

[0075] The soil moisture content for the next period will be calculated using the following process:

[0076] WU(t)=WU(t-1)+P(t-1)-EU(t-1)-R(t-1);

[0077] WL(t) = WL(t-1) - EL(t-1);

[0078] WD(t) = WD(t-1) - ED(t-1);

[0079] If WU(t) > UM, then

[0080] WL(t)=WL(t-1)-EL(t-1)+WU(t)-UM;

[0081] WU(t) = UM;

[0082] If WL(t) > LM, then

[0083] WD(t)=WD(t-1)-ED(t-1)+WL(t)-LM;

[0084] WL(t) = LM;

[0085] If WD(t) > DM, then

[0086] WD(t) = DM;

[0087] Soil moisture content for the next period: W(t) = WU(t) + WL(t) + WD(t).

[0088] (III) Water Source Division

[0089] The problem of dividing different water sources was effectively solved by adopting a three-source water allocation model based on free-storage reservoirs. For example... Figure 2 As shown, the overall calculation process is as follows: R, calculated according to the aforementioned full-capacity runoff model, first enters the reservoir for regulation and storage, and then is divided into different water sources. In the diagram, there is an outlet next to the free-water reservoir, forming a channel for interflow RS; it also forms a channel for groundwater runoff RG, formed by a downward drainage outlet at the bottom of the reservoir area. The bottom width FR of the free-water reservoir changes with the runoff area, resulting in corresponding changes in runoff formation over the runoff area. To address the watershed's strong regulation capacity for interflow, an interflow reservoir is specifically included in the diagram for further regulation and storage when needed. However, this reservoir is generally unnecessary and is therefore marked with a dashed line in the diagram.

[0090] Before the soil moisture storage in the watershed's vadose zone reaches saturation, the runoff generation area of saturated overland flow keeps changing, resulting in uneven distribution of free water storage capacity over the runoff generation area. Therefore, the free water storage capacity-area distribution curve of the watershed (as shown in Figure 3 ) is used to divide the three water sources to show the cumulative frequency of the runoff generation area changing with the free water storage capacity.

[0091] The linear formula of this curve is:

[0092]

[0093] In the formula, S′ is the free water storage capacity of a single point in the watershed, in mm; MS is the maximum free water storage capacity of a point in the watershed, in mm; EX is the exponent of the free water storage capacity-area distribution curve of the watershed.

[0094] S0 is calculated according to the following formula:

[0095]

[0096] Integrating Equation (16) gives:

[0097]

[0098] When AU = MS and S0 = SM, substituting them into Equation (17) gives:

[0099]

[0100] The calculation formula for MS can be obtained from Equation (18) as:

[0101] MS = SM(1 + EX) (19)

[0102] The ordinate value AU corresponding to S0 is calculated according to the following formula:

[0103]

[0104] The runoff generation area FR is calculated according to the following formula:

[0105]

[0106] Considering the change in AU caused by the difference in the runoff generation area between this period and the previous period, through the following conversion formula:

[0107]

[0108] When PE + AU < MS, the surface runoff RS is calculated according to Equation (20):

[0109]

[0110] The free water storage capacity for this period is calculated using the following formula:

[0111]

[0112] The corresponding interflow and groundwater runoff are calculated according to equations (25) and (26), respectively:

[0113] RI=KI·S·FR (25)

[0114] RG = KG·S·FR (26)

[0115] The free water storage at the end of this period and the beginning of the next period is calculated according to formula (27):

[0116] S1=S(1-KI-KG) (27)

[0117] In the formula, S0 is the free water storage capacity at the beginning of the time period; S is the free water storage capacity in the current time period; S1 is the free water storage capacity at the end of the current time period and the beginning of the next time period; SM is the average free water storage capacity of the watershed; KI is the outflow coefficient of the watershed free water storage capacity to the midstream flow; KG is the outflow coefficient of the watershed free water storage capacity to the groundwater runoff; FR0 and FR are the proportions of the runoff-producing area in the previous time period and the current time period, respectively.

[0118] (iv) Convergence Calculation

[0119] (1) Surface runoff confluence

[0120] The unit hydrograph or linear reservoir formula can be used. For example, the unit hydrograph formula is:

[0121] QS(t)=RS(t)·U (28)

[0122]

[0123] In the formula, QS represents surface runoff, in meters. 3 / s; RS is surface runoff, mm; U is unit conversion factor.

[0124] (2) Confluence of streams in the soil

[0125] The calculation can be performed using a linear reservoir or a time-delay algorithm. For example, the formula for a linear reservoir is:

[0126] QI(t)=CI·QI(t-1)+(1-CI)·RI(t)·U (30)

[0127] In the formula, QI represents the interflow, m 3 / s; CI is the interflow recession coefficient; RI is the interflow runoff, mm.

[0128] (3) Subsurface runoff confluence

[0129] Linear reservoir simulation or lag-based algorithms can be used. For example, the formula for a linear reservoir is:

[0130] QG(t)=CG·QG(t-1)+(1-CG)·RG(t)·U (31)

[0131] In the formula, QG represents groundwater runoff, in meters. 3 / s; CG is the subsurface runoff recession coefficient; RG is the subsurface runoff volume, mm.

[0132] (4) The total runoff of the river network per unit area is the sum of surface runoff, interflow, and groundwater runoff, and is calculated using the following formula:

[0133] QT(t)=QS(t)+QI(t)+QG(t) (32)

[0134] In the formula, QT represents the total runoff, in meters. 3 / s.

[0135] (5) The confluence of river networks in a unit area can be simulated using a lag algorithm and calculated according to the following formula:

[0136] Q(t)=CS·Q(t-1)+(1-CS)·QT(tL) (33)

[0137] In the formula, CS is the river network flow recession coefficient; Q is the total flow of the river network per unit area, in meters. 3 / s; L represents the confluence lag time of the river network, ranging from 0 to 2 hours.

[0138] (6) River confluence below the unit area

[0139] The Muskingan method is used for river confluence calculation. By combining the water balance equation and the channel storage equation, and taking the finite difference form, the flow calculation formula of the Muskingan method is derived as equation (34):

[0140] Q2=C0I2+C1I1+C2Q1 (34)

[0141] in:

[0142]

[0143] as well as:

[0144] C0 + C1 + C2 = 1.0 (36)

[0145] In the formula, Q1 and I1 are the outflow and inflow of the previous period, respectively, and Q2 and I2 are the outflow and inflow of the next period, respectively. I1 and I2 are calculated by formula (33). The initial base flow value of Q1 is a given empirical value. KE is the propagation time of the flood in the river channel. Generally, KE≈Δt is taken for each unit river channel. XE is the flow proportion factor. C0, C1, and C2 are coefficients. Δt is the calculation period.

[0146] The dynamic critical rainfall probability early warning method for flash flood disasters provided in this embodiment is as follows: Figure 4 As shown, it includes the following steps:

[0147] S1 determines the allocation of cumulative rainfall for each warning period based on the annual maximum 6-hour and 24-hour rainfall.

[0148] In this embodiment, the initial rainfall value is given as the 24-hour rainfall. The rainfall force formula is used to determine the total rainfall for each planned warning period, and the cumulative rainfall for each rainfall time step is calculated according to the rainfall pattern distribution. The warning periods consider five time periods: 1 hour, 3 hours, 6 hours, 12 hours, and 24 hours. The algorithm provided in the "Sichuan Province Small and Medium Watershed Rainstorm and Flood Calculation Manual" (hereinafter referred to as the "Manual") is used, and the cumulative rainfall for the corresponding time period is converted from the total 24-hour rainfall.

[0149] This step includes the following sub-steps:

[0150] S11 determines the annual maximum 6-hour and 24-hour average rainfall and coefficient of variation for the current region at a specified frequency.

[0151] First, after determining the design frequency (i.e., return period, such as once every 2 years, 5 years, 10 years, 20 years, and 50 years), the corresponding frequency characteristic values ​​(i.e., the average annual maximum rainfall for each time period under the corresponding frequency) and coefficients of variation are found in the manual to calculate the design point rainfall. The 6-hour and 24-hour rainfall are controlled at the same frequency. Based on the location of the center of gravity of the study watershed, the average annual maximum 6-hour rainfall and coefficient of variation, and the average annual maximum 24-hour rainfall and coefficient of variation are found in the manual, respectively.

[0152] S12 determines the design point rainfall amounts for 6 hours and 24 hours.

[0153] Based on the coefficient of variation and the modulus ratio corresponding to the frequency found in the manual, the point rainfall is then calculated according to equation (37):

[0154]

[0155] In the formula, H P The amount of point rainfall at frequency P; K represents the average rainfall obtained from the survey. PThis is the corresponding modulus ratio obtained from the lookup table. The 6-hour and 24-hour design point rainfall amounts at frequency P are then calculated sequentially.

[0156] S13 determines the average rainfall over the watershed over 6 hours and 24 hours.

[0157] Based on the actual conditions and geographical location of the watershed, appropriate adjustments were made, and the average rainfall at the design surface was calculated. The watershed centroid was located according to the handbook, and the areal-depth relationship zones during heavy rainfall were determined. Based on the area of ​​the watershed under study, corresponding error reduction relationships were applied. The point-area reduction coefficients for various areas during 6-hour and 24-hour periods during heavy rainfall were found in the handbook. Based on the correspondence between area and point-area reduction coefficients, a curve showing the relationship between point-area reduction coefficients and area was plotted. Then, through curve interpolation, the point-area reduction coefficients α6 and α6 corresponding to the watershed area during 6-hour and 24-hour periods were read from the graph. 24 (Table 1 provides the point-area reduction coefficients for 6h and 24h in a region). Then, the corrections are made according to the following formulas (38) and (39):

[0158] α 6修正 =0.94·α6 (38)

[0159] α 24修正 =0.96·α 24 (39)

[0160] The corrected 6-hour and 24-hour rainfall point-area reduction coefficients for each zone are obtained. Multiplying the corrected 6-hour and 24-hour rainfall point-area reduction coefficients for each zone with the previously calculated 6-hour and 24-hour design point rainfall amounts yields the 6-hour and 24-hour watershed average rainfall for each zone.

[0161] Table 1. Point-to-area reduction coefficients for 6h and 24h.

[0162]

[0163]

[0164] S14 multiplies the ratio of the 6-hour average rainfall in the basin area to the 24-hour average rainfall in the basin area by the 6-hour allocation ratio in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio within 6 hours. Then, it multiplies (the ratio of the 1-6-hour average rainfall in the basin area to the 24-hour average rainfall in the basin area) by the remaining 18-hour allocation ratio in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio for 18 hours. This gives the 24-hour hourly rainfall pattern allocation ratio for the specified frequency in the basin.

[0165] Referring to the 24-hour design rainfall pattern allocation ratio table for the corresponding zones in Appendix 2, for each zone, multiply the ratio of the 6-hour average rainfall across the watershed to the 24-hour average rainfall across the watershed by the allocation ratio for the 6-hour period in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio within 6 hours. Multiply the ratio of (1-6-hour average rainfall across the watershed to the hourly average rainfall across the watershed) by the allocation ratio for the remaining 18 hours in the current regional rainfall pattern allocation ratio table to obtain the hourly allocation ratio for the 18 hours. Thus, the 24-hour hourly rainfall pattern allocation ratio at the specified frequency of the watershed is obtained.

[0166] Table 2. Hourly (Δt=1 hour) Distribution Ratio of 24-Hour Design Rainfall Patterns in Sichuan Province

[0167]

[0168] Table 2 - Continued

[0169]

[0170] Through the above steps S11-S14, the 24-hour hourly rainfall pattern distribution ratio at a specified frequency in the Qingxi River basin is obtained, as follows: Figure 5 As shown.

[0171] S2 is used to determine the initial soil moisture state and obtain the corresponding initial soil moisture content.

[0172] Soil moisture content significantly affects critical rainfall levels, and considering dynamic changes in soil moisture content can improve early warning accuracy. This scheme adopts the typical classification method specified in the "Technical Requirements for Analysis and Evaluation of Flash Flood Disasters," and discusses the initial soil moisture content of the study watershed in three cases: relatively dry, moderate, and relatively wet.

[0173] WM represents the soil saturation moisture content. Two critical values, Pa = 0.5WM and Pa = 0.8WM, were used to classify the soil moisture content under three conditions: low, moderate, and high rainfall. These represent three typical conditions within the watershed: relatively dry (Pa ≤ 0.5WM), moderate (0.5WM ≤ Pa ≤ 0.8WM), and relatively wet (Pa > 0.8WM). Therefore, 0.5WM, 0.75WM, and 0.9WM were selected as the initial soil moisture contents for these three conditions for the corresponding watershed. For watersheds lacking watershed-scale soil saturation moisture content (WM) data, the location of the watershed within the Sichuan Province rainstorm loss parameter zoning was determined by consulting the "Sichuan Province Small and Medium Watershed Rainstorm and Flood Calculation Handbook." First, the maximum rainstorm loss of 1m in the watershed was determined, and this was used as the soil saturation moisture content (WM). Then, the previous soil moisture content was divided into three typical conditions: relatively dry, moderate, and relatively wet, and the initial soil moisture contents for each of these conditions were determined.

[0174] S3 determines several sets of input parameters for the hydrological model.

[0175] The basic principle of the multi-objective GLUE method is to first randomly sample within the initial range of model parameters, and then input the sampled parameters into the Xin'anjiang hydrological model given earlier for simulation. The input parameters involved in the hydrological model in this embodiment include the water holding capacities UM, LM, and DM of the upper, lower, and deep soil layers, the evapotranspiration conversion factor KC, the deep evapotranspiration conversion factor C, the exponent of the water storage capacity-area distribution curve B, the proportion of impervious area to the total watershed area IM, the power of the watershed free water storage capacity-area distribution curve EX, the average free water storage capacity of the watershed SM, the outflow coefficient of the watershed free water storage capacity to interflow KI, the outflow coefficient of the watershed free water storage capacity to groundwater runoff KG, the interflow recession coefficient CI, the interflow runoff RI, the groundwater runoff recession coefficient CG, the river network flow recession coefficient CS, and coefficients C0, C1, and C2, etc.

[0176] Then, a likelihood objective function is selected to judge the quality of the simulation results. This embodiment uses the certainty coefficient (DC) and the absolute value of the peak flow error (ΔQ). pk The objective function value DC ranges from (-∞, 1), with values ​​closer to 1 indicating better results; ΔQ pk The value range is [0, 100%], where 0 indicates the optimal model result. Finally, effective parameter sets are selected based on the thresholds of the objective functions. Referring to the Hydrological Information Standard (GB / T22482-2008), the thresholds for the two objective functions are DC ≥ 0.6 and ΔQ, respectively. pk ≤20%. The expressions for each likelihood function are shown in formulas (1) to (2) given above.

[0177] Based on historical data, several sets of hydrological model input parameters can be obtained through the above process.

[0178] Based on the 24-hour hourly rainfall pattern allocation ratio, the previous soil moisture status, and different input parameter groups, S4 performs trial calculations on the hydrological model to obtain the critical rainfall values ​​for each warning period corresponding to different previous soil moisture status and / or different input parameter groups.

[0179] After determining the rainfall pattern distribution, warning period, and multiple parameter groups, the dynamic critical rainfall index was calculated using a well-calibrated hydrological model, based on the different soil moisture conditions in the watershed.

[0180] After determining the rainfall threshold RT data corresponding to the warning period and the set time period (taking 24 hours as an example) through the preceding analysis and calculation, the rainfall is distributed temporally according to the hourly rainfall pattern allocation ratio determined in step S1 to obtain the rainstorm process of the watershed, that is, the cumulative rainfall P of each warning period. Since there are cases where the warning period is less than 24 hours, based on the actual situation, for these warning periods, according to the principle of "extending from the point of maximum rainfall to both sides, prioritizing the expansion of the maximum rainfall", the threshold rainfall corresponding to the maximum 1-hour rainstorm ratio is first added, and then the larger value on both sides is taken for allocation until the number of obtained time periods is equal to the number of warning time periods, thus realizing the allocation process of the cumulative rainfall threshold RT.

[0181] Then, by setting multiple sets of optimized model parameters and initial soil moisture content in the model, the allocated rainfall data P can be imported into the hydrological model as model input to perform rainfall calculation.

[0182] The process of rainfall calculation involves setting the model parameters under three different initial soil moisture contents and repeatedly performing flood runoff simulation calculations until the simulated peak flow is closest to the critical disaster flow, which satisfies the formula (3) given above.

[0183] When the trial calculation results satisfy formula (3), the assumed rainfall for that period is the critical rainfall under the initial soil moisture content state for that period. By repeatedly repeating this process and making repeated adjustments and trial calculations, the critical rainfall values ​​under different parameter sets are finally determined.

[0184] S5 determines the warning probability corresponding to the cumulative rainfall for each warning period at the given confidence level using the following formula, and assesses the flash flood disaster based on the warning probability:

[0185]

[0186] In the formula, RT 上限 RT 下限 RT P These represent the upper and lower limits of the critical rainfall range and the cumulative rainfall threshold (mm) for actual rainfall events, respectively; Probability 上限 Probability 下限 These represent the confidence level probabilities of the upper and lower limits of the threshold confidence interval, respectively.

[0187] The upper and lower limits of the critical rainfall range are obtained as follows: First, determine the cumulative frequency distribution map of the critical rainfall. For a given confidence level, use interpolation to find (1-α) / 2×100% (i.e., Probability) from the cumulative frequency distribution map. 下限 ) and (1+α) / 2×100% (i.e., Probability) 上限The predicted values ​​corresponding to the quantiles are the lower bound RT of the model's uncertainty prediction range at a confidence level of α. 下限 and upper limit RT 上限 The specific method for obtaining the critical rainfall cumulative frequency distribution map is as follows: Assign weights to each critical rainfall value obtained in step S4 (i.e., multiply each critical rainfall value by its corresponding weight) to obtain corrected critical rainfall values. Arrange the corrected critical rainfall values ​​in ascending order and calculate their cumulative frequency distribution map, which is the critical rainfall cumulative distribution map. The weight of each critical rainfall value is calculated based on the absolute value of the peak flow error of the corresponding hydrological model input parameter group, specifically (1 - absolute value of peak flow error).

[0188] The dynamic critical rainfall probability early warning results for flash floods in the Qingxi River basin obtained through the above steps S1-S5 are as follows: Figure 5 As shown in the figure, the 24-hour rainfall pattern distribution and the cumulative change trend of critical rainfall at the confidence level can be intuitively presented. Furthermore, the warning probability corresponding to the cumulative rainfall for each warning period can be calculated using the formula given earlier. Based on the warning probability, the flash flood disaster can be assessed, and a flash flood disaster warning is issued when the warning probability exceeds the set warning probability.

[0189] This invention incorporates the uncertainty of hydrological model parameters into flash flood warnings, constructing a dynamic critical rainfall probabilistic early warning method for flash flood disasters. It rationally divides warning intervals and ensures the results are practical, accurate, and reliable. The Xin'anjiang model is applicable to humid and semi-humid regions. Taking 219 precipitation events in the Qingxi River basin of a humid region as an example, the traditional deterministic early warning method resulted in 1 missed event and 21 false alarms, with a false alarm rate as high as 53%. However, using the probabilistic early warning method of this invention, the number of missed events was 0, and the number of false alarms was reduced to 9. Therefore, this invention has better practicality and higher accuracy, effectively improving the reliability of early warnings and the level of flash flood disaster prevention and control.

[0190] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for dynamic critical rainfall probability early warning of flash flood disasters, characterized in that, It includes the following steps: S1 Determine the 24-hour hourly rainfall pattern distribution ratio based on the annual maximum 6-hour and 24-hour rainfall amounts; S2 Divide the initial soil moisture state to obtain the corresponding initial soil water content; S3 Determine several groups of input parameters for the hydrological model; S4 According to the 24-hour hourly rainfall pattern distribution ratio, the initial soil moisture state, and different input parameter groups, conduct trial calculations on the hydrological model to obtain the critical rainfall amounts for each warning period corresponding to different initial soil moisture states or / and different input parameter groups; S5 Determine the warning probabilities corresponding to the cumulative rainfall amounts for each warning period under a confidence level according to the following formula, and evaluate the mountain flood disaster based on the warning probabilities: ； In the formula, , , These represent the upper and lower limits of the critical rainfall range and the cumulative rainfall value of the actual rainfall event, respectively. , These represent the confidence level probabilities of the upper and lower limits of the threshold confidence interval, respectively. The upper and lower limits of the critical rainfall amount interval are obtained as follows: First, determine the critical rainfall cumulative frequency distribution diagram. For a given confidence level, use the interpolation method to find the predicted values corresponding to the (1-α) / 2×100% and (1+α) / 2×100% quantiles from the cumulative frequency distribution diagram. These two points are respectively the lower and upper limits of the prediction range of model uncertainty under a confidence level of α; The specific acquisition method of the critical rainfall cumulative frequency distribution diagram is as follows: Assign weights to each critical rainfall amount obtained in S4 to obtain the corrected critical rainfall amount. Arrange the corrected critical rainfall amounts in ascending order and calculate its cumulative frequency distribution diagram, which is the critical rainfall cumulative distribution diagram; the weight of each critical rainfall amount is (1 - absolute value of peak flow error).

2. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 1, characterized in that, Step S1 includes the following sub-steps: S11 Determine the annual maximum 6-hour and 24-hour rainfall amount means and variation coefficients at a specified frequency in the current area; S12 Determine the 6-hour and 24-hour design point storm rainfall amounts; S13 Determine the basin-averaged rainfall amounts for 6 hours and 24 hours; S14 Multiply the ratio of the 6-hour basin-averaged rainfall amount to the 24-hour basin-averaged rainfall amount by the 6-hour distribution ratio in the current area's rainfall pattern distribution ratio table to obtain the hourly distribution ratio within 6 hours. Multiply (1 - the ratio of the 6-hour basin-averaged rainfall amount to the 24-hour basin-averaged rainfall amount) by the distribution ratio of the remaining 18 hours in the current area's rainfall pattern distribution ratio table to obtain the hourly distribution ratio for 18 hours, thereby obtaining the 24-hour hourly rainfall pattern distribution ratio at the specified frequency of the basin.

3. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 1, characterized in that, In step S2, WM is the soil saturation water content. Two critical values of Pa = 0.5WM and Pa = 0.8WM are selected to divide the initial soil water content states under three conditions of less, medium, and more previous rainfall amounts, which represent three typical conditions of relatively dry soil water content in the basin (Pa ≤ 0.5WM), general (0.5WM < Pa ≤ 0.8WM), and relatively wet (Pa > 0.8WM); therefore, 0.5WM, 0.75WM, and 0.9WM are selected as the initial soil water contents for the corresponding three situations.

4. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 3, characterized in that, For a basin lacking the soil saturation water content at the basin scale, first determine the maximum rainfall loss amount lm of the basin rainfall, and use this as the soil saturation water content WM.

5. The method for dynamic critical rainfall probability early warning of flash floods according to claim 1, characterized in that, In step S3, the multi-objective GLUE method is used to determine multiple groups of input parameter groups that meet the target function threshold range.

6. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 5, characterized in that, Based on the certainty coefficient DC and the absolute value of the peak flow error ΔQ pk As the objective function value, DC takes a range of (-∞, 1), with values ​​closer to 1 indicating better results; ΔQ pk The value range is [0, 100%], where 0 indicates the optimal model result. Finally, effective parameter sets are selected based on the thresholds of the objective functions; the thresholds for the two objective functions are DC ≥ 0.6 and ΔQ. pk ≤20%; the expressions for each likelihood function are: ； ； In the formula, Let m be the predicted flow rate for the i-th time period. 3 / s; Let m be the measured flow rate value for the i-th time period. 3 / s; n is the given flood sequence length; Indicates the predicted peak traffic volume, m 3 / s; Indicates the measured peak flow rate, m 3 / s; This represents the average measured flow rate, m. 3 / s; Determine several hydrological models based on the determined several groups of input parameters for the hydrological model.

7. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 1, characterized in that, In step S4, under different soil moisture conditions, within a given rainfall range, the cumulative rainfall for each warning period is determined according to the 24-hour hourly rainfall pattern distribution ratio at a specified frequency in the watershed. Then, by inputting several sets of hydrological models, the rainfall calculation process can be carried out to obtain the critical rainfall value under the corresponding soil moisture conditions and the corresponding input parameter set.

8. The method for dynamic critical rainfall probability early warning of flash flood disasters according to claim 7, characterized in that, The rainfall calculation process involves repeatedly performing flood runoff simulations under the given initial soil moisture content and model parameters until the simulated peak flow rate is closest to the critical disaster-causing flow rate, i.e., satisfying the equation: ； In the formula, Q c Q represents the peak flow rate simulated during the trial calculation process; 灾 The disaster-causing flow rate is the corresponding return period, i.e. frequency. When the calculation result satisfies the above formula, the assumed rainfall for that period is the critical rainfall under the initial soil moisture content state for that period.

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