Method for calculating monthly ecological base flow of frozen river in semi-arid region

Abstract

The application discloses a kind of semi-arid region frozen river monthly ecological base flow calculation method, with river section geometry and wet week response as basis, coupling typical aquatic organism habitat water depth constraint in different periods, and combining long-term hydrological sequence and monthly rating curve back propagation flow, form monthly output, explainable, reproducible ecological base flow sequence, especially for frozen period water level-flow relationship distorted problem gives independent processing scheme;The application relates to the field of ecological hydrology and river ecological restoration technology.Semi-arid region frozen river monthly ecological base flow calculation method, biological water requirement is upgraded from single threshold to stage-month threshold H2 (m) throughout the year, avoid unreasonable constraints on non-resident months for migratory species, improve ecological suitability;Non-frozen period uses monthly rating curve back propagation flow, reduce the system deviation that month difference is regarded as water level difference, improve back propagation accuracy and month scale availability.

Description

Technical Field

[0001] This invention relates to the field of ecohydrology and river ecological restoration technology, specifically a method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions. Background Technology

[0002] In arid and semi-arid regions, seasonal river flow interruptions or droughts are common, leading to insufficient water inflow and resulting in degradation of river wetland ecosystems, decreased biodiversity, and loss of aquatic ecological functions. Existing methods for calculating ecological baseflow, such as the minimum monthly average flow method, the Tennant method, and the IFIM model, struggle to take into account river morphology, biological water requirement depth, and riparian habitat characteristics, thus failing to accurately reflect the water requirement characteristics of river ecosystems at different times.

[0003] Therefore, there is an urgent need for a calculation method that comprehensively considers the water level-wet perimeter relationship, the characteristics of abrupt changes in the beach, and the biological water requirement depth in different seasons or months. Summary of the Invention

[0004] To solve the above-mentioned technical problems, the present invention is implemented through the following technical solutions.

[0005] This method is based on the geometry of the river cross section and the wetted perimeter response, coupled with the water depth constraints for the habitat of typical aquatic organisms at different stages, and combines long-term hydrological series and monthly rating curves to back-calculate the flow, forming an ecological base flow sequence that can be output monthly, explained, and reproduced. In particular, it provides an independent treatment scheme for the problem of distorted water level-flow relationship during the freezing period.

[0006] A method for calculating monthly ecological baseflow in glaciers in semi-arid regions includes the following steps:

[0007] Step 1: Based on the measured hydrological cross-sectional data (distance from the starting point to the riverbed elevation), calculate the corresponding wetted perimeter value within the preset water level range, establish the water level-wetted perimeter relationship, and fit the water level-wetted perimeter relationship curve.

[0008] Step 2: Identify abrupt change points in the water level-wet perimeter relationship curve, and take the water level corresponding to the abrupt change point as the protection threshold water level H1 of the beach.

[0009] Step 3: Based on the suitable average water depth requirements of typical aquatic organisms in the target river during key ecological periods, construct monthly ecological constraint water levels. The ecological periods are divided into spawning / reproduction period (spawn), pre-wintering sensitive period (winter_pre), and base maintenance period (base), and each ecological period is mapped to a month. Using the riverbed baseline elevation Z0 or historical reference water level H0 as a benchmark, and establishing a baseline value, calculate the monthly ecological water level H for each species. 2i (m) = baseline value + d i (m), and according to the strictest principle, H2(m) = maxi {H 2i (m)};

[0010] Step 4: Using daily water level-flow paired data during the non-freezing period, group by month to establish a monthly water level-flow rating curve Q=f m (H), and by inversely deriving Q1(m)=f from the rating curve. m (H1) and Q2(m) = f m (H2(m));

[0011] Step 5: Calculate the statistical baseline P10 (m) for low flow in each month based on the multi-year runoff series;

[0012] Step 6: Determine the ecological base flow on a monthly basis: In the months with freezing conditions, take Qe(m) = P10(m); in the months without freezing conditions, take Qe(m) = max{Q1(m),Q2(m),P10(m)}, thus obtaining the monthly ecological base flow sequence.

[0013] Preferably, the wet perimeter is obtained by accumulating the lengths of the riverbed segments below the water level H in the discrete broken line of the river cross section, and the intersection point is determined by linear interpolation at the intersection of the riverbed segment and the water level line.

[0014] Preferably, the identification method for the beach protection threshold water level H1 is as follows: performing derivative analysis on P(H) and determining the abrupt change position of dP / dH; or using piecewise regression to search for the inflection point with the smallest sum of squared residuals among the candidate water levels as the abrupt change point.

[0015] Preferably, when the reference value is Z0, Z0 is determined by any of the following methods: the average elevation of the bottom channel section after the main channel is identified, the lowest elevation of the cross section, the average elevation of the entire cross section, or manual designation; the appropriate water depth and monthly mapping for the stage of typical aquatic organisms can be corrected based on the results of habitat surveys or the regional ecological water demand database.

[0016] Preferably, the freezing period can be preset to December to March of the following year, or determined based on water temperature, ice condition observations, and data screening rules; a monthly rating curve Q=f is established. m (H) Remove water level-flow paired samples that are frozen or affected by ice cap backwater.

[0017] This invention provides a method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions. It offers the following advantages:

[0018] The method for calculating monthly ecological baseflow in frozen rivers in this semi-arid region identifies the protection threshold of the riverbank based on abrupt changes in the wetted perimeter of the river cross-section; it upgrades biological water demand from a single annual threshold to a phased-monthly threshold H2(m) to avoid unreasonable constraints imposed by migratory species on non-resident months and improve ecological suitability; during the non-frozen period, it uses monthly rating curves to back-calculate the flow, reducing the systematic bias of treating monthly differences as water level differences and improving the accuracy and usability of the back-calculation at the monthly scale; it uses P10(m) as the monthly statistical baseline and adopts ecological baseflow Qe(m)=P10(m) during the frozen period to avoid the impact of the distortion of the H–Q relationship during the frozen period on the back-calculation results, thereby enhancing seasonal applicability and robustness. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process for calculating the monthly ecological baseflow of frozen rivers in semi-arid regions according to the present invention;

[0020] Figure 2 This is a schematic diagram of a typical river water level-wetted perimeter relationship curve according to the present invention;

[0021] Figure 3 This is a schematic diagram of the wetted perimeter variation characteristic curve based on abrupt change point identification according to the present invention;

[0022] Figure 4 This is a schematic diagram of the river channel cross-section and wetted perimeter under the threshold water level for beach protection (H1=149.172m) of this invention;

[0023] Figure 5 This is a schematic diagram of the river cross-section and wetted perimeter morphology under the ecological water level of each month during the non-freezing period according to the present invention.

[0024] Figure 6 This is a schematic diagram of the reverse curve of water level-discharge relationship in April during the non-freezing period of this invention;

[0025] Figure 7 This is a schematic diagram of the reverse curve of water level-discharge relationship in May during the non-freezing period of this invention;

[0026] Figure 8 This is a schematic diagram of the inverse curve of the water level-discharge relationship in June during the non-freezing period of this invention;

[0027] Figure 9 This is a schematic diagram of the back-calculation curve of the water level-discharge relationship in July during the non-freezing period of this invention;

[0028] Figure 10 This is a schematic diagram of the reverse calculation curve of water level-discharge relationship in August during the non-freezing period of this invention;

[0029] Figure 11 This is a schematic diagram of the reverse calculation curve of water level-discharge relationship in September during the non-freezing period of this invention;

[0030] Figure 12This is a schematic diagram of the reverse calculation curve of water level-discharge relationship in October during the non-freezing period of this invention;

[0031] Figure 13 This is a schematic diagram of the reverse curve of water level-flow relationship in November during the non-freezing period of this invention. Detailed Implementation

[0032] The technical solutions of the 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.

[0033] The freezing period is set as December, January, February and March of each year. The main input data are the hydrological cross-sectional data of a certain hydrological station at the river section (data corresponding to the distance from the starting point to the riverbed elevation) and the daily water level and flow data of the station over many years (at least 10 years of daily water level and flow data are required).

[0034] Step 1: Investigate hydrological cross-sections, measure wetted perimeter at different water levels, and fit a water level-wetted perimeter relationship curve;

[0035] (1) Theoretical basis:

[0036] Within a certain river section, when the geometry of the riverbed and banks remains relatively stable, changes in water level H continuously alter the length of the water-receiving boundary, i.e., the wetted perimeter P(H). During the in-channel flow stage, the water level mainly fluctuates within the main channel, and the newly added water-receiving boundaries are mostly steep banks or riverbeds. The increase in wetted perimeter per unit water level rise is relatively small, so P(H) increases relatively gradually with H. When the water level rises to the point where the sidebanks / floodplains begin to be submerged, the water surface expands to relatively gentle floodplains or even floodplains. A small increase in water level corresponds to a long newly added water-receiving boundary, resulting in a significantly increased sensitivity of P(H) to H. Therefore, the water level-wetted perimeter curve P(H) not only reflects the cross-sectional geometric characteristics but also implicitly contains the transition information between the two hydraulic geometric stages of "in-channel" and "floodplain," providing a geometric-hydraulic basis for identifying the protection threshold water level of the sidebanks.

[0037] (2) Construction of mathematical methods:

[0038] Cross-sectional geometry discretization:

[0039] Control sections were established for the target river section, and the lateral distance – riverbed elevation was measured using a level or RTK instrument. Points are sequentially placed from the left bank to the right bank to form a polygonal "riverbed profile" cross-sectional geometry. For hydrological stations (river channels) with actual measured large-section results, the polygonal "riverbed profile" cross-sectional geometry can be constructed using the starting point distance and riverbed elevation from the cross-sectional data. The formula for constructing the discretized cross-sectional geometry is as follows:

[0040] ;

[0041] Calculation of wetted perimeter at a given water level:

[0042] For any water level The wetted perimeter P(H) is defined as the total length of the broken line connecting the riverbed profile to the water body below the water level, where... Let the effective length of the j-th polyline segment below the water surface be:

[0043] ;

[0044] In discrete polylines In this case, each line segment – There are three possibilities:

[0045] Possibility 1: If both endpoints are underwater: The entire segment is then included in the wetted perimeter:

[0046] ;

[0047] Possibility 2: If one end is underwater and the other end is above water: By comparing the line segment with the horizontal line... Perform linear interpolation to find the intersection points. Only the length of the "underwater portion" is included:

[0048]

[0049] Possibility 3: If both endpoints are on the water surface: this line segment is not included in the wetted perimeter. .

[0050] In summary, we obtain a strictly geometrical... Calculation formula:

[0051] ;

[0052] Construct the water level-wetted perimeter relationship curve:

[0053] Within a given water level range Inside, with step length Generate a series of discrete water levels:

[0054] ;

[0055] For each Calculate the wetted perimeter using the geometric cutting method described above. This yields a set of scatter points:

[0056] ;

[0057] Connecting these scattered points on a plane forms the water level-wetness curve. The numerical approximation is as follows. In practice, interpolation or smoothing methods can be used to further fit it into a continuous curve, but the subsequent threshold identification can be based directly on the scattered data.

[0058] Step 2: Identify abrupt changes in the water level-wet perimeter curve and determine the threshold water level for beach protection.

[0059] (1) Theoretical basis:

[0060] From a geometric perspective, the first derivative This indicates the increase in wetted perimeter caused by a unit rise in water level, i.e., the "sensitivity of the newly added water-receiving boundary length to water level":

[0061] ;

[0062] During the in-channel flow phase, the water surface only undulates within the main channel, and the newly added water-receiving boundaries mainly originate from the relatively steep river walls and riverbed. The value is small and changes slowly; when the water level rises to the point where it begins to submerge the side beaches / shoals, the newly added water-receiving boundary rapidly expands to wide and gentle beaches, and the increase in wetted perimeter per unit water level rise increases significantly. A sudden jump or significant increase occurs; after continuing to rise to a high water level, the already submerged beaches gradually increase in size. The water level may stabilize or change again, but the location of the first significant jump can usually be considered the "shoal protection threshold level". It is close to the traditional flat-shore water level.

[0063] Therefore, theoretically, it can be analyzed The change in the first derivative or slope can be used to identify abrupt change points on the beach.

[0064] (2) Construction of mathematical methods:

[0065] The method uses two segments of linear least squares (broken-stick piecewise regression) to identify abrupt change points in the curve:

[0066] ;

[0067] in and These correspond to the average slope (average derivative) of the "in-trough stage" and the "beach stage," respectively, and typically have... .

[0068] The specific steps are as follows:

[0069] Imagine the inflection point is located at a candidate water level index. (Corresponding water level) Divide all data into two segments, "left" and "right", as follows: Left segment: Right section: .

[0070] Perform linear least squares regression on both the left and right segments respectively, and obtain:

[0071] ;

[0072] Calculate the total sum of squared residuals (SSE) under this segmentation method:

[0073]

[0074] In all cases that satisfy the condition that "both the left and right segments have at least a certain number of points" In the middle, searching The smallest one Its corresponding water level This is the optimal inflection point water level:

[0075] ;

[0076] The processes described above, namely "1. Investigating hydrological cross-sections, measuring wetted perimeter at different water levels, and fitting water level-wetted perimeter relationship curves" and "2. Identifying abrupt change points in the curve through differentiation to obtain the shoreline protection threshold water level H1," are implemented in practice using a Python program. The program reads the cross-sectional coordinates from Excel, rigorously calculates the wetted perimeter at each water level using geometric clipping and the Pythagorean theorem, and then... The data is processed using a broken-stick piecewise regression model to automatically find the breakpoint water level that minimizes the sum of squared residuals. This process generates water level-wet cycle curves and result files. This ensures both the physical and mathematical rigor of the method and facilitates batch application under multiple cross-sections and operating conditions.

[0077] Step 3: Introduce the key ecological period constraints for aquatic organisms to obtain the monthly ecological constraint water level. ;

[0078] (1) The proposal and overall approach of phased constraints;

[0079] In an eco-hydrological sense, key fish species in river ecosystems often exhibit relatively stable suitable ranges for water depth, flow velocity, and substrate conditions. Different fish species inhabit different depths. For example, large benthic fish such as sturgeon prefer deeper, slower-flowing main channels or riverbed depressions, while migratory cold-water fish such as salmon require moderate depths and certain flow velocities in general river sections or shallow areas during spawning and migration. Common small fish and omnivorous fish can inhabit shallower shoals and areas with aquatic plants. Based on actual literature and watershed survey results, a "suitable average water depth" range can be assigned to each representative aquatic organism; for example, approximately 2-4 m for sturgeon, 0.4-0.6 m for salmon, and 0.2-0.4 m for most fish. An ecological water level is determined based on the "suitable average water depth" as one of the constraints on ecological baseflow. However, this "suitable average water depth" is not constant throughout the year: during key stages such as breeding, migration, and before and after winter, fish are more sensitive to their habitat and available water depth. Therefore, biological constraints are shifted from a single ecological water level. Expanded to phased ecological water levels In this implementation, the year is divided into at least three ecological periods: the spawning / migration period, the pre-wintering sensitive period (winter_pre), and the general maintenance period (base), and corresponding ecological threshold water levels are established for each period. , , Ultimately forming a lunar scale constraint.

[0080] (2) Ecological period - monthly division and determination of appropriate average water depth for each period;

[0081] First, determine the representative aquatic organism types and their suitable average water depth ranges. Following existing implementation methods, the controlled organisms can be divided into three categories: sturgeon, salmon, and general fish. Based on literature and watershed surveys, suitable average water depth ranges can be provided; for example, sturgeon is approximately 2-4m, salmon is approximately 0.4-0.6m, and general fish is approximately 0.2-0.4m. To ensure the ecological thresholds are "strict rather than lenient," a slightly stricter representative value can be selected within the range as the basic parameter (e.g., sturgeon 4.0m, salmon 0.5m, and general fish 0.3m). Based on this, a "critical ecological period segmentation" is introduced, which is at least divided into the spawning / migration period, the pre-wintering sensitive period, and the general maintenance period. These ecological periods are mapped to months: April and November are preferably classified as the pre-wintering sensitive period (corresponding to the critical stages after thawing and before freezing); May–June are designated as the spawning sensitive period for sturgeon and other fish species; July–September are designated as the migration-spawning window for salmon; July–October is designated as the general maintenance period; and December to March of the following year is the freezing period. In the overall framework of this invention, this stage directly uses the historical flow rate of the dry year (90% frequency) as the ecological base flow control, and is not considered as... The constraints are derived through reverse deduction. The above-mentioned monthly division can be incorporated into the implementation as a preferred scheme, or it can be used as a user-configurable parameter in engineering applications. Correspondingly, the appropriate average water depth for each period can be set according to the principle of "stricter for critical periods and moderate for general periods": for example, for sturgeon, the depth is 3.5-4.0m (preferably 4.0m) during spawn and winter_pre, and 3.0-3.5m during the base period; for general fish, the depth is 0.35m (within the range of 0.2-0.4m and more conservative) during spawn and winter_pre, and 0.30m during the base period; for salmon, the depth is only constrained in its spawn month set (preferably July-September), and is set to 0.5m. The above-mentioned method of determining the period values ​​is consistent with the parameterization idea of ​​"giving the interval first, then taking the representative value", and avoids unreasonable constraints on the annual threshold by migratory fish in non-resident months.

[0082] (3) Water depth to water level conversion and monthly calculation ;

[0083] After obtaining the suitable average water depth for various fish species at different ecological stages, it is necessary to convert the "minimum water depth relative to the riverbed" into "absolute water level elevation" by combining the measured cross-sectional topography. The core issue is selecting a benchmark elevation for the riverbed. It should represent the overall elevation level of the bottom of the main channel, rather than the lowest point in any individual locality; The selection of elevation abrupt change thresholds can be based on scanning from the geometric center of the cross-section to both sides to identify the main channel section and calculate the average elevation. Alternatively, the lowest elevation can be taken when the bottom channel is relatively flat, or the average elevation of the entire cross-section can be used as a reference. It can also be directly specified by the user. Mathematically, for any given month... (Non-freezing period) First determine its ecological period. And determine the set of species participating in the constraint that month. (For example, salmon only enter the collection from July to September), so the minimum controlled depth for that month can be the maximum value according to the "strictest principle":

[0084] ;

[0085] Further, the monthly ecological constraint water level was obtained:

[0086] ;

[0087] The meaning of this "strictest principle" is: when the water level is not lower than... At that time, all selected control species must meet their respective suitable average water depth requirements in the central area of ​​the main channel for the month; otherwise, at least one control species will have a habitat that is difficult to maintain, which is an unacceptably low water level from an ecological protection perspective.

[0088] The entire process described above is automated using a Python script. The program reads the cross-section Excel file and calculates according to the selected rules. It reads the user-configured "suitable average water depth for each species / species group in each ecological period" and "month-ecological period mapping relationship", and automatically calculates the monthly data. It outputs a structured table (containing species name, stage water depth parameters, etc.). Type and value, correspondence (and control markers, etc.), making the process of deriving the monthly ecological constraint water level from the measured cross section and fish demand reproducible and transferable, and can be directly connected to the subsequent monthly ecological baseflow calculation process.

[0089] Step 4: Establish water level-discharge relationship curves for each month during the non-freezing period. And by reverse calculation on a monthly basis , ;

[0090] (1) Theoretical basis;

[0091] Under conditions where the river cross-sectional morphology is relatively stable and not significantly disturbed by abnormal conditions such as ice cover uplift and backflow, water level and flow rate typically exhibit a relatively stable one-to-one correspondence, which can be characterized using a "rating curve" and used to infer control flow. During the freezing period, factors such as ice cover raising the water level and backflow significantly alter the water level-flow rate relationship. Therefore, samples from the freezing period are excluded, and only daily-scale samples from the non-freezing period are retained for fitting. To avoid back-calculation bias caused by abnormal operating conditions, this invention addresses the issue of significant seasonal differences within the non-freezing period (such as intra-month variations in aquatic plant resistance, channel roughness, backwater boundary conditions, and local scheduling). Fitting different months together to a single curve can easily misinterpret "monthly differences" as "water level differences," leading to a systematic overestimation or underestimation of flow rates for certain months. Therefore, this invention divides the non-freezing period into natural months... Grouping, establishing separate groups So that the reverse calculation for each month can be performed. It better aligns with the hydraulic correspondence of that month.

[0092] (2) Data screening and monthly sample construction: forming a fitable sample for each month. Sample set

[0093] The basic data required to establish a monthly-scale rating curve is water level from multi-year, daily paired observations. With traffic The sequence and data tables can be organized by date, average daily flow, and average daily water level for easy reading. For sample selection, the months of the freezing period are first divided according to the ice conditions at each station and then excluded to avoid issues caused by ice cover backflow and water ingress. The relationships are distorted. Subsequently, the remaining non-freezing period diurnal samples are grouped by month: for each month... (Except for months with freezing temperatures), compile the data for that month from all years. Pairing points form monthly sample sets This approach of merging data from the same month over multiple years can expand the sample size and improve the statistical stability of the monthly curve while maintaining relatively consistent hydraulic conditions within the month. If the sample size for a particular month is insufficient, a minimum sample size threshold can be specified in the implementation examples, and merging adjacent months or months of the same ecological period can be used as alternative solutions to ensure the reliability of the fit.

[0094] (3) Mathematical method construction: Fit log_poly3 relationship by month and obtain

[0095] Specifically, for any non-freezing month Collecting water level observations from the same month over many years With traffic As sample points, a cubic polynomial model (log_poly3) with the logarithm of traffic as the dependent variable is constructed, that is, in each month sample set Upper fitting:

[0096] ;

[0097] in The average water level for the month is used. Centering the independent variable improves the correlation between polynomial terms and enhances the numerical stability of parameter estimation. The least squares method is then used to estimate the parameters of the above model. After fitting, the flow prediction formula can be written as:

[0098] ;

[0099] This form naturally guarantees It is defined within the observed water level range of that month and is applicable to appropriate interpolation and extrapolation within the water level range of the same month.

[0100] To avoid instability of the curve due to sample dispersion or insufficient sample size in certain months, this invention calculates the coefficient of determination for the fitting results of each month. The root mean square error (RMSE) and mean absolute error (MAE) are used to evaluate the ability of the monthly curve to fit the "monthly flow range". At the same time, 5-fold cross-validation can be used to perform multiple training-validation combination tests on the monthly sample. The average cross-validation index is used to measure the robustness of the model, avoiding the judgment of the inverse conclusion based on only one fitting result.

[0101] (4) Monthly reverse calculation Convert water level control to flow rate control.

[0102] In receiving each month Then, the control water level determined in the aforementioned steps can be substituted into the calculation to reverse the process. (Shorebank protection threshold water level) Due to cross-sectional morphology – hydraulic geometry constraints, the water level can remain at a fixed value throughout the year; ecological constraints. The monthly threshold is obtained from the "critical ecological period segmentation". Therefore, for any non-freezing month... Calculate separately

[0103] ;

[0104] This completes the monthly-scale conversion from "minimum ecologically significant control water level" to "minimum ecologically significant control flow rate." Simultaneously, to ensure the physical rationality of the reverse calculation, the embodiment may specify that: when... or When the water level exceeds the range of the sample for that month, only moderate extrapolation is allowed within a small range, and an "extrapolation flag" is output. If the range is too large, it is recommended to revert to the curve of the adjacent month / season or use statistical methods to supplement it, so as to avoid introducing uncertainty by extrapolation.

[0105] The entire process described above is automated using Python code: the script reads daily data from Excel over many years. The data was processed by removing samples based on the month of freezing and grouping them by month. A log_poly3 function was then fitted to each month. Output the fitting parameters and accuracy index for that month, and... and Substitute into the calculation to obtain This ultimately led to the formation of "monthly" The result table and the corresponding The graph serves as a basis for directly implementing the "non-glacial period monthly data collection" strategy. Ice Age The ecological base flow is aggregated and calculated.

[0106] Step 5: Calculate P10(m) for each month as the statistical baseline, and determine the ecological baseflow for each month during the freezing period.

[0107] (1) Theoretical basis and setting principles;

[0108] In rivers in arid and semi-arid regions, the spatial and temporal distribution of annual water inflow is uneven, and the transition between dry and wet seasons is dramatic. Simply relying on cross-sectional geometric thresholds to infer control flow may result in situations where ecological needs cannot be fully met in extremely dry years. To ensure the operability and sustainability of ecological baseflow results, this invention introduces a statistical baseline based on multi-year runoff statistical characteristics, using the low quantile of the multi-year daily flow series for each month as the minimum water volume guarantee for that month. Refers to the first The 10th percentile of daily flow samples over multiple years indicates that approximately 10% of daily flows are below this value and 90% are above it in the long-term series. This reflects a water level that is "low but still sufficient to maintain basic system operation," while avoiding the problem of using extreme minimum values ​​that result in excessively low base flow and unrepresentativeness. As a statistical baseline for monthly ecological baseflow calculations, it can better balance ecological protection and water supply realities in areas with significant hydrological fluctuations, ensuring that subsequent monthly ecological baseflow results have both ecological significance and statistical traceability.

[0109] (2) Data construction and computation methods;

[0110] In terms of data organization, this invention is based on multi-year daily flow observation sequences and constructs statistical samples in a month-to-multi-year merging manner: for each month It aggregates the daily traffic flow for that month across all years. Forming a sample set After removing missing data and obvious outliers, and ensuring consistent units (e.g., m³ / s), the quantile algorithm is used to calculate the 10th percentile of the sample set, thus obtaining the monthly quantile. In mathematical terms, it can be written as

[0111] ;

[0112] To ensure robustness of the results, the implementation example may specify that: when the effective sample size for a certain month is insufficient, the sample period can be expanded or adjacent months can be merged to enhance the sample size; when there are abnormal mutations caused by human scheduling, outlier identification rules (such as box plot thresholds or experience-based upper and lower limits) can be used to remove or mark them, thereby ensuring robustness. This represents a "lower flow level under natural or normal scheduling conditions." The final result is... A sequence list is formed in 12-month units to provide a unified and verifiable statistical lower limit for subsequent monthly ecological baseflow values.

[0113] (3) Determination of ecological base flow during the freezing period;

[0114] During the freezing period, river hydraulic processes are significantly affected by ice sheet formation and melting, often resulting in phenomena such as ice sheet backwater raising water levels, changes in cross-sectional flow capacity, and increased backwater, leading to significant differences in the water level-discharge relationship compared to the non-freezing period. If the data established during the non-freezing period continues to be used in this situation... Or based on the water level threshold to infer This can easily introduce systematic errors, reducing the engineering reliability of the calculation results. Based on this understanding, this invention defines the ecological baseflow of the freezing month as the statistically significant lower limit for low flow guarantee, that is, for months belonging to the freezing period... Take directly

[0115] ;

[0116] This approach has two significant implications: First, it avoids forcibly introducing unstable water level-flow back-calculation during periods of complex ice conditions, ensuring the method's feasibility. Second, aquatic biological activity and habitat requirements typically decrease seasonally during the freezing period (e.g., entering the overwintering stage). Using a conservative and sustainable statistical baseline as the ecological baseflow aligns better with the management logic of "maintaining basic habitat and water body continuity during the freezing period." Therefore, this invention achieves "maximizing multiple constraints during non-freezing periods and using a more conservative and sustainable statistical baseline during freezing periods." The unified framework of "as the bottom line" lays the foundation for the subsequent formation of a complete monthly ecological base flow sequence.

[0117] The above The calculation process is automatically implemented by a Python program: the script reads daily flow data over many years, groups the data by month to construct a sample set, calculates the 10th percentile values ​​for 12 months and outputs them as a monthly-scale statistical table; simultaneously, based on a preset set of freezing month months, the monthly ecological baseflow for the freezing period is directly assigned as... The results table will then be marked with the months of freezing period (e.g., "Freezing Period = TRUE"). The table serves not only as a direct source of monthly ecological baseflow during the freezing period but also as a "statistical baseline" item for calculating monthly ecological baseflow during the non-freezing period. In the next step, it will be used in conjunction with... We will jointly participate in the final determination of the non-freezing period ecological baseflow, thereby ensuring that the monthly ecological baseflow sequence has both ecological constraints and statistical traceability.

[0118] Step Six: Determine the monthly ecological baseflow sequence based on three types of constraints during the non-freezing period. ;

[0119] (1) Theoretical basis and determination of approach;

[0120] This invention uses the "strictest principle" as the comprehensive rule for the monthly scale: for each non-freezing month Meanwhile, the control flow required for beach / habitat protection should also be considered. Control flow rates corresponding to the critical ecological period constraints of aquatic organisms And the low flow baseline in the sense of hydrological statistics over many years .in and These represent the protection threshold and ecological threshold for the beach area, respectively. This represents the statistical baseline for multi-year runoff. Incorporating all three factors and taking the maximum value ensures that the determined monthly ecological baseflow meets the minimum requirements of ecological processes while avoiding unrepresentatively low values ​​under extreme drought conditions, thus achieving a balance between ecological goals and water resource realities.

[0121] (2) Mathematical expression of monthly ecological base currents during non-freezing periods;

[0122] Based on the above theoretical framework, the ecological base current in non-freezing months... The following unified calculation formula shall be adopted:

[0123] ;

[0124] in, This is a collection of months that are not in the freezing period. To set the protection threshold water level for the riverbank Substitute into the monthly water level-discharge curve The control flow obtained afterwards, i.e. ; To adjust the monthly ecological constraint water level The control flow rate obtained by substituting it into the curve for the same month is... .in This reflects the differences in water level constraints caused by changes in ecological demand across different months. Meanwhile, It is obtained from the 10th percentile of the flow samples of the same month over many years, reflecting the lowest inflow level of the month that is "partially dry but statistically representative". Taking the maximum value of the three means that when the ecological or hydraulic constraints are higher than the statistical bottom line, the ecological constraints shall prevail, and when the ecological constraints are lower than the statistical bottom line, the statistical bottom line shall be used as a fallback, so as to ensure that the formed monthly ecological baseflow sequence is both ecologically meaningful and has long-term feasibility.

[0125] (3) Connection and output with the results of the freezing period;

[0126] To achieve continuous monthly-scale ecological baseflow scheduling throughout the year, this invention integrates the comprehensive results of the non-freezing period with the rules for determining the freezing period: the ecological baseflow for the freezing month is directly taken according to the aforementioned provisions. For non-freezing months, the maximum value is taken according to the three constraints. This yields an ecological baseflow sequence covering all 12 months of the year. The results table will synchronously record the source composition for each month, including whether it is marked as a freezing period and the corresponding... , , And the source of the final value (e.g., "from") "Control" or "by" reveal all the details").

[0127] The above-mentioned process of comprehensively determining monthly ecological base flows can be automated using a Python program: the program reads and organizes data at multi-year monthly scales. The table can simultaneously read or calculate the data for each month during the non-freezing period. , Implemented each month The calculation yields the final result. The program automatically determines the control term (i.e., the constraint source corresponding to the largest of the three) and provides information such as monthly baseflow values, control sources, and key parameters in the output file. In addition to numerical results, the program can also output monthly scale comparison charts or statistical summaries to verify the rationality of the seasonal variation of ecological baseflow in each month during the non-freezing period, ensuring that the final results not only conform to the theoretical logic of the patented method but also have transparency and traceability in engineering applications.

[0128] This method is applicable to river, lake and wetland systems in arid and semi-arid regions and can provide a scientific basis for ecological scheduling and restoration projects.

[0129] Usage examples;

[0130] The calculation of ecological baseflow for each month was carried out, with December, January, February, and March of each year designated as the freezing period. The study was conducted using the following methods:

[0131] (1) Investigate hydrological cross sections, measure wetted perimeter at different water levels, and fit water level-wetted perimeter relationship curves;

[0132] During the hydrological cross-section survey and data collection process, the "2010 13-Measured Cross-Section Results Table" was obtained. This table details the year and date of the cross-section measurement, station code, measured water level, vertical line number, starting point distance, riverbed elevation, and unit and dimension information. After processing, a worksheet easy to read by code was created, with the first column representing the starting point distance and the second column representing the riverbed elevation. The processed "2010 13-Measured Cross-Section Results Table" is shown in Table 1.

[0133] Table 1. Compiled Results of Measured Cross-Sections (December 13, 2010)

[0134]

[0135]

[0136]

[0137] (2) Identify abrupt change points in the water level-wet perimeter curve and determine the threshold water level for beach protection. ;

[0138] The prepared Excel worksheet is input into the written Python program. After adjusting the configuration parameters, the program is run, and the results folder is generated. The main output results are as follows:

[0139] 1. Schematic diagram of typical river channel water level-wetted perimeter relationship curve (with appendix) Figure 2 );

[0140] 2. Characteristic curves of wetted perimeter variation based on mutation point identification (attached) Figure 3 );

[0141] 3. Schematic diagram of river channel cross-section and wetted perimeter-water level (attached) Figure 4 ).

[0142] The output results clearly show the threshold water level for beach protection. It is 149.172m.

[0143] (3) Introducing the phased constraints of key ecological periods for aquatic organisms to obtain monthly ecological constraint water levels. ;

[0144] Based on common fish species, primarily sturgeon and salmon, and supplemented by other fish species, the ecological water level is determined. The suitable average water depth for sturgeon is approximately 2-4m, for salmon approximately 0.4-0.6m, and for most fish approximately 0.2-0.4m. Based on the suitable average water depth, key ecological periods are further constrained: for sturgeon, the water depth requirement is set at 4.0m during the pre-wintering period (April and November) and the spawning period (May-June), and 3.0m during the non-critical period (July-October); for salmon, the constraint is only applied during the migration-spawning window (July-September), with a water depth of 0.5m; for most fish, the corresponding values ​​are 0.35m for winter-pre and spawn, and 0.30m for base, representing the water depth requirements for each species at different ecological periods. After setting the relevant parameters and data in the Python code, for each non-freezing month... Calculate the ecological water level each month. The maximum value for that month will be used as the monthly ecological constraint water level, following the strictest principle. It also automatically records the controlled species and controlled ecological period for that month. December to March is excluded from the calculation as it falls within the freezing period. Complete output will be available from April to November. After the program runs, it automatically generates the following main result files: 1. Monthly ecological water level result table; 2. PNG diagram of wetted weekly water level for a specified month.

[0145] In this case study, the ecological water level for each month during the non-freezing period was... As shown in Table 2, the ecological water level diagrams for each month during the non-freezing period are attached. Figure 5 .

[0146] Table 2. Ecological water levels in each month during the non-freezing period

[0147] month Ecological water level_H2(m) Species control Controlling ecological periods 4 150.352 sturgeon winter_pre 5 150.352 sturgeon spawn 6 150.352 sturgeon spawn 7 149.352 sturgeon base 8 149.352 sturgeon base 9 149.352 sturgeon base 10 149.352 sturgeon base 11 150.352 sturgeon winter_pre

[0148] (4) Establish water level-discharge relationship curves for each month during the non-freezing period. And by reverse calculation on a monthly basis , ;

[0149] Establishing a water level-discharge relationship curve requires several years of discharge and water level data for the station. In this case study, the daily average runoff (m³) from 2006 to 2022 obtained through the application was used. 3The data on daily average water level (m) and daily average runoff (m) were compiled into an Excel worksheet, "06-22 Water Level and Runoff Data.xlsx", for easy reading by the code "Runoff-Water Level Relationship and Verification.py". This worksheet includes the date, daily average runoff volume, and daily average water level. Based on the 17 years of paired daily water level and runoff observation data, the non-freezing and freezing periods were divided according to the ice conditions at each station: April to November was designated as the non-freezing period, and December to March of the following year as the freezing period. The non-freezing period was further divided into natural months. Grouping, establishing separate groups So that the reverse calculation for each month can be performed. Enter H1 and ... in the code After parameter adjustment and execution, the main results are as follows: 1. QH relationship curves for each non-freezing month.png; 2. Monthly QH curve parameter indices and back-calculation results.xlsx. The results show H1 and... corresponding and , It is 149.1855m 3 / s, The results are shown in Table 3. The monthly statistical indicators used by the log_poly3 model to fit the data are shown in Table 4. A schematic diagram of the inverse curves of the water level-discharge relationship for each month during the non-freezing period is attached. Figures 6-13 The results show that the model performs well.

[0150] Table 3. Monthly QH curves established based on non-freezing months The result was deduced by reverse reasoning;

[0151] month H1(m) <![CDATA[Q1(m 3 / s)]]> H2(m) <![CDATA[Q2(m 3 / s)]]> 4 149.172 145.807 150.352 454.150 5 149.172 171.043 150.352 484.135 6 149.172 155.786 150.352 481.392 7 149.172 156.283 149.352 188.285 8 149.172 158.972 149.352 191.426 9 149.172 150.504 149.352 180.132 10 149.172 174.950 149.352 193.325 11 149.172 125.075 150.352 409.707

[0152] Table 4. Fitting ability index of QH curve established for each non-freezing month;

[0153] month R2 RMSE MAE CV_R2_mean CV_RMSE_mean CV_MAE_mean 4 0.786 91.064 65.844 0.770 92.568 66.694 5 0.931 64.137 49.378 0.928 64.638 49.812 6 0.974 65.769 53.560 0.973 66.149 54.063 7 0.985 67.842 53.010 0.984 68.311 53.787 8 0.990 73.093 50.604 0.989 72.716 51.330 9 0.986 56.472 43.004 0.986 56.959 43.295 10 0.921 51.454 40.136 0.912 51.804 40.442 11 0.693 86.986 64.865 0.684 87.830 65.408

[0154] (5) Calculate P10(m) for each month as the statistical baseline and determine the ecological base flow for the months of freezing;

[0155] Using the Python program "Calculate P10(m) for each month.py", this program calculates the runoff data for each month, including the freezing period, from the 2017-year runoff data in the Excel worksheet "06-22 Water Level and Runoff Data.xlsx". It aggregates the daily traffic flow for that month across all years. Forming a sample set The 10th percentile value of the sample set is calculated using the quantile algorithm, thus obtaining the monthly quantile. After parameter adjustment and operation, the main results are stored in an Excel spreadsheet: monthly P10 (m) and ecological base current during the freezing period, which can be directly used to determine the ecological base current sequence during the non-freezing period. Application. Table 5 shows the monthly P10(m) and ecological baseflow results during the freezing period in this case study:

[0156] Table 5. Monthly P10 (m) and ecological base flow during freezing period;

[0157] month P10(m) (m3 / s) Ecological base current during freezing period_Qice(m) 1 174.884 174.884 2 175.943 175.943 3 192.748 192.748 4 272.400 - 5 361.135 - 6 361.040 - 7 374.432 - 8 343.619 - 9 236.453 - 10 215.187 - 11 185.953 - 12 160.219 160.219

[0158] (6) Determine the monthly ecological baseflow sequence based on three types of constraints during the non-freezing period. ;

[0159] The results obtained above: Months of the non-freezing period P10 (m) for each month, and for each month during the non-freezing period. and The results are summarized in the worksheet "Monthly Ecological Baseflow Calculation - Input Data Table.xlsx", which is then input into the Python program "Three Types of Constraints to Determine Monthly Ecological Baseflow.py". After parameter tuning, the program is run to obtain the corresponding monthly ecological baseflow sequences. The results are shown in Table 6.

[0160] Table 6. Monthly Ecological Baseflow Sequence ;

[0161] month Is it a month with freezing temperatures? P10(m) H2(m) H1(m) Q1(m) Q2(m) Qe(m) 1 yes 174.884 149.172 174.884 2 yes 175.943 149.172 175.943 3 yes 192.748 149.172 192.748 4 no 272.400 150.352 149.172 145.807 454.150 454.150 5 no 361.135 150.352 149.172 171.043 484.135 484.135 6 no 361.040 150.352 149.172 155.786 481.392 481.392 7 no 374.432 149.352 149.172 156.283 188.285 374.432 8 no 343.619 149.352 149.172 158.972 191.426 343.619 9 no 236.453 149.352 149.172 150.504 180.132 236.453 10 no 215.187 149.352 149.172 174.950 193.325 215.187 11 no 185.953 150.352 149.172 125.075 409.707 409.707 12 yes 160.219 149.172 160.219

[0162] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0163] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions, characterized in that, Includes the following steps: Step 1: Based on measured hydrological cross-sectional data, calculate the corresponding wetted perimeter value within the preset water level range, establish the water level-wetted perimeter relationship, and fit the water level-wetted perimeter relationship curve. Step 2: Identify abrupt change points in the water level-wet perimeter relationship curve, and take the water level corresponding to the abrupt change point as the threshold water level for the protection of the beach. Step 3: Based on the appropriate average water depth requirements of typical aquatic organisms in the target river during key ecological periods, construct ecological constraint water levels on a monthly basis. The ecological periods are divided into spawning / reproduction period, pre-wintering sensitive period, and basic maintenance period, and each ecological period is mapped to a month. Using the riverbed baseline elevation Z0 or historical reference water level H0 as a benchmark, calculate the monthly ecological water level H for each species. 2i (m), where H 2i (m) = baseline value + d i (m), and according to the strictest principle, H2(m) = max i {H 2i (m)}, where the benchmark value is the riverbed benchmark elevation Z0 or the historical reference water level H0; Step 4: Using daily water level-flow paired data during the non-freezing period, establish monthly water level-flow rating curves by grouping them by month; Step 5: Calculate the statistical baseline P10 (m) for low flow in each month based on the multi-year runoff series; Step Six: Monthly Ecological Baseflow Sequence During the freezing months, Qe(m) = P10(m) is taken; during the non-freezing months, Qe(m) = max{Q1(m),Q2(m),P10(m)} is taken, thus obtaining the monthly ecological base flow sequence. in and These represent the protection threshold and ecological threshold, respectively.

2. The method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions according to claim 1, characterized in that: The wetted perimeter is obtained by accumulating the lengths of the riverbed segments below the water level H in the discrete broken line of the river cross section, and the intersection point is determined by linear interpolation at the intersection of the riverbed segment and the water level line.

3. The method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions according to claim 1, characterized in that, The identification method for the beach protection threshold water level H1 is as follows: The location of the abrupt change in wetted perimeter P(H) is determined by performing derivative analysis on the wetted perimeter increment dP / dH caused by a unit rise in water level; or piecewise regression is used to search for the inflection point with the minimum sum of squared residuals among the candidate water levels as the abrupt change point.

4. The method for calculating monthly ecological baseflow in frozen rivers in semi-arid regions according to claim 1, characterized in that, When the reference value is Z0, Z0 is determined in any of the following ways: After the main channel is identified, the average elevation of the bottom channel section, the lowest elevation of the cross section, the average elevation of the entire cross section, or the manually specified elevation can be used. The appropriate water depth and monthly mapping for the typical aquatic organisms can be corrected based on habitat survey results or regional ecological water demand databases.

5. The method for calculating monthly ecological baseflow of frozen rivers in semi-arid regions according to claim 1, characterized in that: The freezing period can be preset to December to March of the following year, or determined based on water temperature, ice condition observation and data screening rules; Establish a monthly rating curve Q=f m (H) Remove water level-flow paired samples that are frozen or affected by ice cover.

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