A new anjiang model regionalization method based on historical parameter migration performance

Abstract

This invention discloses a regionalization method for the Xin'anjiang model based on historical parameter migration performance. It utilizes meteorological driving forces and runoff observations from the developing watershed to calibrate 15-dimensional Xin'anjiang model parameters, screens donors, and establishes a parameter library. The donor parameters are applied to each developing and receiving watershed without recalibration, constructing a directed historical parameter migration performance matrix. Donor migration characteristics are obtained through standardization and principal component analysis. Based on seven static attributes of the target watershed and six hydrological characteristics formed by finite runoff, ridge regression is used to estimate the target migration characteristic coordinates. Continuous donor weights are calculated according to characteristic distances, forming 15-dimensional prior parameters. These are then locally corrected using a bounded differentiable Xin'anjiang model. The final parameters and meteorological driving data are input into a fixed-structure Xin'anjiang model to obtain simulated runoff in the target watershed. This method preserves the original hydrological process structure and makes the source and contribution of parameters traceable.

Description

Technical Field

[0001] This invention belongs to the field of hydrological model parameter regionalization and runoff simulation technology, specifically involving a Xin'anjiang model regionalization method based on historical parameter migration performance under limited runoff data conditions. Background Technology

[0002] Runoff processes are the combined result of precipitation input, evapotranspiration, soil moisture changes, watershed water storage status, and runoff generation and confluence mechanisms. Their formation is influenced by a variety of factors, including climate conditions, topographic features, soil properties, and the moderating effect of groundwater. Therefore, even with similar precipitation inputs, different watersheds may exhibit significantly different runoff responses. This heterogeneity in response, caused by differences in hydrological mechanisms within the watershed, necessitates that runoff simulation not only characterize the statistical relationship between input and output but also consider the reasonable representation of hydrological processes within the watershed. Particularly in applications such as flood risk assessment, water resource allocation, drought monitoring, and ecological flow management, the model's ability to reliably describe runoff changes at different time scales and under different flow conditions directly impacts the effectiveness of related decisions.

[0003] To describe the complex processes of watershed runoff formation, researchers have developed various rainfall-runoff simulation methods, including data-driven models based on statistical relationships and conceptual hydrological models with well-defined process structures. In recent years, the development of large-sample hydrological data and machine learning methods has significantly improved cross-basin runoff prediction capabilities, enabling models to learn the potential relationships between meteorological inputs and runoff responses from large amounts of watershed data. However, conceptual rainfall-runoff models remain valuable in applications requiring adherence to water balance constraints, process interpretability, and parameter analyzability. These models conceptually describe evapotranspiration, water storage changes, runoff generation mechanisms, and runoff confluence processes, transforming intra-basin hydrological processes into meaningful model structures. Therefore, conceptual models not only serve for runoff prediction but also provide important tools for understanding watershed hydrological response mechanisms.

[0004] The regionalization of conceptual rainfall-runoff models depends on obtaining applicable model parameters for the target watershed. However, under limited runoff data, target watersheds often lack sufficient observational information to support stable parameter identification, making parameter regionalization a key challenge for cross-watershed applications of conceptual models. Existing methods typically infer parameter applicability based on geographical proximity, static watershed attributes, or attribute-parameter relationships. Their implicit assumption is that watershed similarity represents parameter portability, but this indirect relationship cannot explain the actual effectiveness of a parameter set in other watersheds. Summary of the Invention

[0005] This invention provides a regionalization method for the Xin'anjiang model based on historical parameter migration performance, in order to solve the technical problem that it is difficult to directly determine the cross-basin applicability of parameters based solely on geographical proximity or static watershed attributes.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A regionalization method for the Xin'anjiang model based on historical parameter migration performance includes the following steps: Step 1: Establish a donor parameter library First, obtain the Xin'anjiang model parameters for multiple development basins, and then select development basins that meet the performance requirements as donor basins to form a donor basin set; Step 2: Constructing the historical migration feature space Each donor watershed in the donor watershed set is applied to each development watershed to calculate the corresponding historical parameter migration performance, construct a historical parameter migration performance matrix, and then perform principal component analysis on the historical parameter migration performance matrix to obtain the historical migration feature coordinates of each donor watershed, forming a historical migration feature coordinate matrix. Step 3: Determine the regionalized prior parameters of the target watershed First, the static attributes and hydrological characteristics represented by the limited runoff data of the target watershed are obtained to form the target watershed description vector. Then, the historical migration characteristic coordinates of the target watershed are estimated by using the multi-output ridge regression model trained by the donor watershed. Then, the continuous weights are calculated according to the distance between the target watershed and each donor watershed, and all donor watersheds are weighted and combined to obtain the regionalized prior parameter vector of the target watershed. Step 4: Perform bounded local correction Based on the regionalized prior parameter vector of the target watershed, combined with its target watershed description vector, bounded local correction is performed by dXAJ under preset parameter boundaries and joint constraints to obtain the final parameter vector of the target watershed. Then, the final parameter vector and meteorological driving parameters are input into the Xin'anjiang model to complete the runoff simulation of the target watershed.

[0007] Furthermore, in step two, the historical parameter migration performance from donor watershed i to development watershed j is calculated based on the overall runoff simulation efficiency KGE2009, the overall runoff simulation efficiency logKGE of logarithmically transformed runoff, and the overall water volume deviation PBIAS. This process is repeated to complete the historical parameter migration performance of each donor watershed relative to all development watersheds, thus constructing a historical parameter migration performance matrix with donor watersheds as rows and development watersheds as columns. The historical parameter migration performance matrix is ​​then standardized according to the development watershed column. Principal component analysis is then performed on the standardized historical parameter migration performance matrix. The first few principal components whose cumulative explained variance reaches a preset threshold are retained as the historical migration feature coordinates of each donor watershed, and a historical migration feature coordinate matrix is ​​constructed.

[0008] Furthermore, for the donor basin i and the development basin j, the Xin'anjiang model parameters corresponding to the donor basin i, the meteorological driving data of the development basin j, and the initial state of the model are input into the Xin'anjiang model to obtain the simulated runoff sequence corresponding to the development basin j. At the same time, combined with the measured runoff of the development basin j during the same period as the observed runoff sequence, the donor basin is calculated using the following formula. To develop the watershed Historical parameter migration performance , First, transform the simulated runoff and observed runoff by log(1+Q) respectively. Then, use the same calculation method as KGE2009 to calculate the transformed simulated runoff sequence and observed runoff sequence to obtain logKGE. Where r is the Pearson correlation coefficient between the simulated runoff series and the observed runoff series, α is the ratio of the standard deviation of the simulated runoff series to the standard deviation of the observed runoff series, and β is the ratio of the mean of the simulated runoff series to the mean of the observed runoff series. and Let be the simulated runoff sequence and the observed runoff sequence for day t, respectively, and summation be performed on the date when both are valid.

[0009] Furthermore, in step three, the static attributes of each donor basin and the hydrological characteristics represented by limited runoff data are first obtained to form a donor basin description vector. Then, the donor basin description vector of each donor basin is used as input and the corresponding historical migration feature coordinates are used as output to train the multi-output ridge regression model. Then, the trained multi-output ridge regression model is used to estimate the historical migration feature coordinates of the target basin by using the target basin description vector formed by the static attributes of the target basin and the hydrological characteristics represented by limited runoff data as input.

[0010] Furthermore, the distance between the historical migration feature coordinates of donor watershed i and target watershed b is calculated using the following formula. in, The coordinates represent the historical migration characteristics of the target watershed. Coordinates representing the historical migration characteristics of the donor watershed; Then, using the following formula, the distance is transformed into continuous weights through exponential decay. : Where τ represents the distance decay parameter, and the continuous weights satisfy... , , Finally, the regionalized prior parameter vector of the target watershed It is obtained by continuously weighting all available donor parameters: ,in, This represents the parameter vector of the i-th donor watershed, which consists of multiple parameters from the Xin'anjiang model. This represents the set of donor parameter vector indices available for the target watershed b.

[0011] Furthermore, both the donor watershed description vector and the target watershed description vector consist of seven static attributes and six hydrological features. The seven static attributes are watershed area, average elevation, average slope, soil depth, soil porosity, forest cover ratio, and drought index. The six hydrological features are runoff coefficient, baseflow index, slope of flow duration curve, recession constant, high flow frequency, and low flow index.

[0012] Furthermore, in step four, a multilayer perceptron is used to process the target watershed description vector. The 15-dimensional parameter correction was obtained. : For each parameter First, calculate the symmetric margins from the regional priors to the upper and lower bounds: Then use the donor sampling standard deviation The smaller of the boundary margin and the effective correction scale is used: The final parameter vector is: ; Among them, the donor sampling standard deviation of each parameter The calculation follows the aforementioned weighted resampling with replacement process, which involves calculating the sample standard deviation from the mean of the corresponding parameters obtained from multiple resamplings.

[0013] Furthermore, daily precipitation, basin latitude, daily maximum temperature, daily minimum temperature, and daily runoff observation data for each development basin are obtained. Potential evapotranspiration is calculated using daily maximum temperature, daily minimum temperature, and basin latitude. A 15-dimensional candidate parameter vector is generated within a preset parameter value range using the SCE-UA algorithm. Daily precipitation, potential evapotranspiration, candidate parameter vector, and the initial state of the model are input into a fixed-structure Xin'anjiang model to obtain simulated runoff data. Based on the unified calibration target between simulated runoff data and observed runoff data, the candidate parameter vector is iteratively updated using the SCE-UA algorithm to obtain a set of 15-dimensional Xin'anjiang model parameter vectors corresponding to each development basin. Development watersheds that meet the preset screening criteria are selected as donor watersheds, and their corresponding 15-dimensional Xin'anjiang model parameter vectors are used as qualified donor parameters, thereby forming a donor watershed set and a donor parameter library. The preset screening conditions are: KGE ≥ 0.5, NSE ≥ 0, and |PBIAS| ≤ 15%. Where KGE represents the Kling–Gupta efficiency coefficient, NSE represents the Nash–Sutcliffe efficiency coefficient, and PBIAS represents the total water volume deviation.

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention no longer determines the applicability of a set of parameters to another watershed solely based on geographical proximity or similar static watershed properties. Instead, it directly applies the calibrated donor parameter vector to different developing and receiving watersheds, performs runoff simulations without recalibrating the parameters, and records the past cross-watershed applicability of the parameter vector based on the actual difference between simulated and observed runoff. Therefore, donor selection is no longer based solely on the similarity of external watershed characteristics, but also includes historical performance information of the parameters after actual use in other watersheds.

[0015] 2. This invention utilizes seven static attributes of the target watershed and six hydrological features calculated from limited runoff data to estimate the target watershed's position in the historical migration feature space. Continuous weights are then determined based on the distance between this position and each donor parameter. The 15-dimensional regionalized prior parameters of the target watershed are formed by weighting multiple donor parameters, rather than directly replicating the parameters of a single donor. Therefore, each parameter can be traced back to its corresponding donor weight and parameter contribution, while reducing the impact of slight changes in the ranking of a single donor that could lead to sudden changes in parameter results.

[0016] 3. Based on the 15-dimensional regionalized prior parameters obtained through continuous donor weighting, this invention generates local corrections corresponding to the 15 XAJ parameters using the 13-dimensional description vector of the target watershed. The correction magnitude is limited by parameter-by-parameter upper and lower bounds, donor sampling variation, and joint constraints of KI and KG. After correction, the final parameter vector is obtained. The final runoff is still calculated using the evapotranspiration, water storage, runoff generation, runoff component classification, and confluence equations of the Xin'anjiang model with the same structure as in step one. This ensures that the limited target runoff data is primarily used for local parameter adaptation, rather than replacing the original XAJ hydrological process structure. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall technical process of regionalization of the Xin'anjiang model based on historical parameter migration performance in this invention. In the diagram, ① represents the calibration of watershed parameters and donor selection, ② represents the cross-watershed simulation without recalibration of donor parameters and the construction of the historical parameter migration performance matrix, ③ represents matrix standardization, principal component analysis and formation of historical migration feature coordinates, ④ represents the estimation of historical migration features of the target watershed, the calculation of continuous donor weights and the formation of regionalized prior parameters, and ⑤ represents the bounded local correction of dXAJ and the Xin'anjiang model runoff simulation. The timeline of data usage in this embodiment is shown below the diagram.

[0018] Figure 2 The diagram illustrates the target watershed input availability under different limited runoff data conditions and the pairing effect of the present invention relative to the static kNN parameter transfer. In this diagram, (a) represents the number of watersheds that can form a complete 13-dimensional target watershed description vector under FS30, FS90 and FS365 conditions, and (b) represents the KGE pairing difference and 95% confidence interval of TU-dXAJ relative to the static kNN parameter transfer in the validation set and independent test set.

[0019] Figure 3 A schematic diagram of the contribution of continuous donor weighting and bounded local correction of dXAJ for historical migration, where (a) represents the watershed pairing KGE difference of the complete method A4 relative to A1, A2 and A3, and (b) represents the normalized parameter correction root mean square of the validation set and independent test set as a function of FS30, FS90 and FS365 data conditions.

[0020] In the figure, XAJ represents the Xin'anjiang model, dXAJ represents the differentiable Xin'anjiang model, kNN represents the k-nearest neighbor method, KGE represents the Kling–Gupta efficiency coefficient, and FS30, FS90, and FS365 represent finite runoff data scenarios of 30 days, 90 days, and 365 days, respectively. Detailed Implementation

[0021] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the Xin'anjiang model regionalization method based on historical parameter migration performance of this invention. It should be noted that the description of these embodiments is for the purpose of helping to understand this invention, but does not constitute a limitation of this invention.

[0022] Under conditions of limited runoff data, the key to regionalization of conceptual models is not merely finding donors with external characteristics similar to the target watershed, but rather determining whether existing parameters remain effective within the target watershed. This addresses the problem that traditional regionalization primarily relies on geographical proximity or static attributes to indirectly infer parameter applicability, such as... Figure 1 As shown, this invention proposes a regionalization method for the Xin'anjiang model based on historical parameter migration performance. This method uses the actual simulation results of donor parameters in different development basins in the past to characterize their cross-basin applicability mode, and combines the static attributes of the target basin and finite runoff records to estimate its position in the historical migration feature space. Then, XAJ regionalization parameters are formed by continuous multi-donor weighting. At the same time, dXAJ is used to make bounded local corrections only near the prior of the XAJ regionalization parameters, without changing the original evapotranspiration, water storage, runoff generation, runoff division and confluence structure of the Xin'anjiang model.

[0023] Specifically as follows: First, 15-dimensional donor parameter vectors are obtained and screened in the development watershed. Then, each donor parameter vector is applied to each development and receiving watershed without recalibration. A historical parameter migration performance matrix is ​​constructed based on simulated runoff and concurrently observed runoff. The historical migration feature coordinates of the donor parameter vectors are formed through column standardization and principal component analysis. The historical migration feature coordinates of the target watershed are estimated using a 13-dimensional descriptive vector of the target watershed and multi-output ridge regression. The continuous donor weights are determined according to the distance between the target and donor coordinates. Multiple sets of 15-dimensional donor parameter vectors are weighted to form a 15-dimensional regionalized prior parameter vector. Finally, a 15-dimensional parameter correction amount is generated from the 13-dimensional target watershed descriptive vector through a dXAJ multilayer perceptron. The prior is locally corrected under preset parameter boundaries, donor sampling variation, and joint constraints to obtain a 15-dimensional final parameter vector. The final parameter vector, meteorological driving data of the target watershed, and the initial state of the model are input into the fixed-structure Xin'anjiang model to output simulated runoff.

[0024] Step 1: Establish the donor watershed set and obtain the donor parameter library. First, obtain the Xin'anjiang model parameters for multiple development basins, and then select development basins that meet the performance requirements as donor basins to form a donor basin set.

[0025] S11. Establish a comparable set of candidate parameters for subsequent donor selection and cross-basin migration of historical parameters.

[0026] Specifically, daily precipitation, basin latitude, daily maximum temperature, daily minimum temperature, and daily runoff observation data are acquired for each development basin. Potential evapotranspiration is calculated using the daily maximum temperature, daily minimum temperature, and basin latitude. A 15-dimensional candidate parameter vector is generated within a preset parameter value range using the SCE-UA algorithm. Daily precipitation, potential evapotranspiration, candidate parameter vectors, and the initial state of the model are input into a fixed-structure Xin'anjiang model to obtain simulated runoff data. Based on the unified calibration target between simulated runoff data and observed runoff data, the candidate parameter vector is iteratively updated using the SCE-UA algorithm to obtain a set of 15-dimensional Xin'anjiang model parameter vectors corresponding to each development basin. The above parameter vectors constitute a candidate parameter set, which is further filtered in S12 according to preset performance conditions to form a donor parameter library.

[0027] A. Data Source The study employed the CAMELS-US large-sample watershed dataset. This dataset contains meteorological drivers, daily runoff, and watershed attributes for 671 watersheds in the continental United States, providing a foundation for unified comparison of regionalized methods under different climatic and underlying surface conditions.

[0028] Meteorological driving data include daily precipitation, daily maximum temperature, and daily minimum temperature, while daily runoff is derived from observations at U.S. Geological Survey hydrological stations. Potential evapotranspiration is calculated using the Hargreaves–Samani method based on daily maximum temperature, daily minimum temperature, and watershed latitude. Precipitation, potential evapotranspiration, and runoff are all standardized to a daily scale for driving and evaluating the Xin'anjiang model.

[0029] Watershed attributes are used to describe relatively stable climate, topography, soil, and vegetation conditions. Seven static attributes are ultimately used: watershed area, mean elevation, mean slope, soil depth, soil porosity, forest cover percentage, and drought index. The watershed area is transformed using the natural logarithm before analysis to reduce skewness caused by different area sizes. The latitude and longitude of hydrological stations are used only for spatial stratification, watershed location visualization, and map creation; they are not used as model input and are not included in the calculation of donor similarity or historical migration weights.

[0030] Within their respective limited data windows, both the development and target watersheds are characterized by six hydrological features representing runoff information: runoff coefficient, baseflow index, slope of the flow duration curve, recession constant, high-flow frequency, and low-flow index. These features respectively summarize the overall water distribution, contribution of slow-velocity water sources, flow distribution, water storage and release, and high- and low-flow states. These features of the development watershed, along with seven static attributes, are used to fit the target location mapping relationship, while these features of the target watershed are used to estimate its historical migration characteristic coordinates.

[0031] B. Watershed Selection and Spatial Delineation Watershed selection criteria are determined before model development and results evaluation. Candidate watersheds must simultaneously meet the following conditions: daily runoff integrity rates must be no less than 95% during the parameter rate period (1981–1994), the historical migration analysis period (1995–1999), the limited data support period (2000), and the evaluation period (2001–2004); the meteorological variables, seven static attributes, and hydrological station coordinates required by the model must all be finite values. Missing runoff values ​​are not imputed, nor are they replaced using data from adjacent watersheds or other years.

[0032] After screening, 582 out of 671 candidate watersheds were selected for the formal experiment. To reduce regional distribution bias caused by adjacent watersheds being included in both the development and test sets, the 582 watersheds were fixedly divided into 407 development watersheds, 87 validation watersheds, and 88 independent test watersheds, based on the HUC-02 hydrological zoning. This division was completed before method development and will not be readjusted subsequently due to model performance or pairing effects.

[0033] The development set is used to establish all the cross-basin relationships required for the regionalization method, including XAJ donor parameter acquisition, historical parameter migration performance analysis, data standardization, migration feature extraction, target location mapping, and dXAJ training. The validation set is used to check the performance and stability of the established method in watersheds not involved in the development, but does not participate in the construction of historical migration relationships. The independent test set is uniformly evaluated after the model structure, comparison methods, parameter settings, and statistical rules are determined, and does not participate in any form of training, parameter selection, or threshold adjustment.

[0034] C. Time-based application and finite runoff data scenario The study period spans from 1980 to 2004, with each year serving an independent experimental purpose. 1980 served as a model warm-up period, aimed at mitigating the impact of initial water storage conditions on subsequent simulations; 1981–1994 were used for calibrating XAJ parameters in the development basins; and 1995–1999 were used to evaluate the historical parameter migration performance between the development basins. These periods solely served method development and do not overlap with the limited data support period or the final evaluation period for the target basins.

[0035] The above periodization does not require all applications to use the same year. Its necessity is to isolate the data used for parameter calibration, historical migration relationship construction, target limited data support, and final effect evaluation. Other time periods that meet the information isolation requirements can be used in other embodiments, but the historical migration feature space should be reconstructed after changing the historical period.

[0036] Limited runoff data for the target watershed were collected starting from January 1, 2000, and three progressively expanding consecutive windows were set: FS30: January 1, 2000 – January 30, 2000 FS90: January 1, 2000 – March 30, 2000 FS365: January 1, 2000 – December 30, 2000 The three support windows share the same starting point: FS30 is contained within FS90, and FS90 is contained within FS365. Precipitation, potential evapotranspiration, and runoff observations are provided for the target watershed within the corresponding support window, with runoff used to calculate six hydrological characteristics or for small-sample parameter fitting. The period from January 1, 2001, to December 31, 2004, following the support period, is uniformly designated as the evaluation period; no method may use runoff from this period for training, parameter correction, or donor selection.

[0037] Because the three support windows, while increasing in length, also alter seasonal coverage, the number of precipitation events, and the composition of high- and low-current states, FS30, FS90, and FS365 represent three predetermined information conditions, rather than gradients determined solely by sample size. Therefore, the relevant results are reported separately for each support scenario, and 365 days is not interpreted as a universal threshold for regionalizing limited data.

[0038] The current experiment requires the target watershed to have at least short-term runoff observations that can be used to calculate hydrological characteristics. Therefore, the research object belongs to a watershed with limited runoff data, rather than a strictly data-free watershed that completely lacks target runoff observations. For watersheds where complete hydrological characteristics cannot be obtained from the corresponding support window, static attributes or other watershed statistics are not used as substitutes.

[0039] D. 15 parameters of the Xin'anjiang model The Xin'anjiang model, based on the theory of runoff generation upon saturation, describes the transformation of precipitation into runoff through processes such as evapotranspiration, tension water storage, runoff generation upon saturation, free water storage, runoff component classification, and confluence. The model used in this invention contains 15 parameters, divided into four groups according to their hydrological effects: • Evapotranspiration parameters: KC; • Water storage and runoff parameters: IM, WUM, WLM, WDM, C, and B; • Runoff component classification parameters: SM, EX, KI, and KG; where KI is the soil outflow coefficient and KG is the groundwater outflow coefficient, both of which are dimensionless parameters. In this embodiment, the preset ranges for KI and KG are both 0.01–0.70. In addition to satisfying the upper and lower bounds of each parameter, they also satisfy the joint constraint KI + KG ≤ 0.90, which is part of the feasible domain of the preset parameters in this embodiment.

[0040] •Channel parameters: CI, CG, N, and NK.

[0041] The specific meanings, units, and value ranges of each parameter are shown in Table A1. The TU-dXAJ regionalization targets these 15 process parameters, rather than directly applying empirical corrections to the final runoff sequence. Regardless of how the parameters are obtained, the final runoff is calculated using the evapotranspiration, water storage, runoff generation, water source distribution, and confluence equations from the original Xin'anjiang model.

[0042] Table A1 lists the parameter order, value range, unit, and calculation function consistent with the experimental code, categorized by evapotranspiration, water storage and runoff generation, water source distribution, and runoff confluence. The same range is used for SCE-UA search and dXAJ parameter correction, but does not mean that the parameter can be uniquely identified by field observation. Table A1. XAJ parameters, preset ranges, units, and calculation functions. In addition to the parameter ranges, KI and KG also satisfy... .

[0043] S12. Select the candidate parameter set obtained in S11 according to the preset performance conditions to form the donor watershed set and the donor parameter library.

[0044] Specifically, using data from 1981 to 1994, the simulation results of candidate parameter vectors for each development basin obtained from S11 in their source basins were evaluated. Only candidate parameter vectors that simultaneously met the predetermined KGE, NSE, and PBIAS conditions were retained. The development basins whose parameter vectors met the screening conditions were called donor basins, and their corresponding 15-dimensional Xin'anjiang model parameter vectors were called donor parameter vectors, thus forming a donor basin set and a donor parameter library.

[0045] The above screening criteria are determined in advance before parameter calibration and are applied consistently to all development watersheds, as detailed below: KGE ≥0.5, NSE ≥0, and |PBIAS| ≤15% Where KGE represents the Kling-Gupta efficiency coefficient, NSE represents the Nash-Sutcliffe efficiency coefficient, and PBIAS represents the total water volume deviation.

[0046] Of the 407 developing watersheds, 316 watersheds had parameter vectors that met the preset screening criteria, resulting in 316 sets of 15-dimensional donor parameter vectors, thus yielding a total of 316 donor watersheds. The i-th set of donor parameter vectors is denoted as... The purpose of donor watershed selection is not to use local calibration performance as a regional conclusion, but to avoid subsequent cross-watershed results being dominated by parameters that are clearly unqualified in the source watershed. After obtaining the donor parameters, the next step is no longer to select parameters based on whether the donor watershed is "like the target watershed", but to directly examine the actual performance of each set of parameters after leaving the original calibration watershed.

[0047] Step 2: Constructing the historical migration feature space Each donor watershed in the donor watershed set is applied to each development watershed to calculate the corresponding historical parameter migration performance, construct a historical parameter migration performance matrix, and then perform principal component analysis on the historical parameter migration performance matrix to obtain the historical migration feature coordinates of each donor watershed, forming a historical migration feature coordinate matrix.

[0048] The historical parameter migration performance matrix is ​​structured with donor parameter vectors as rows and development / receiving watersheds as columns. Matrix elements represent the historical parameter migration performance of the i-th donor watershed in the j-th development watershed. For a fixed j-th development watershed, the mean and standard deviation of all historical parameter migration performance in that column are calculated at donor watershed index i, and the column is standardized accordingly. Principal component analysis is performed on the standardized historical parameter migration performance matrix. The principal components are arranged in order of their contribution to the explained variance, and the top few principal components that cause the cumulative explained variance to reach a preset threshold are retained. The scores of each donor parameter vector on the retained principal components are standardized according to the principal component dimensions to form the historical migration feature coordinates of the corresponding donor parameter vector.

[0049] S21, Historical Parameter Migration Performance The i-th group of donor parameter vectors The simulation was applied to the j-th developing receiving basin without recalibration, and the simulation results were evaluated using data from 1995–1999.

[0050] Specifically, for donor watershed i and development watershed j, the 15-dimensional donor parameter vector corresponding to donor watershed i is... Meteorological driving data and initial state of the model for watershed j are input into the Xin'anjiang model to obtain the simulated runoff sequence corresponding to watershed j. At the same time, the measured runoff of watershed j during the same period is combined as the observed runoff sequence. These simulated runoff sequences and observed runoff sequences are used together to calculate three evaluation indicators: KGE2009, Kling-Gupta efficiency coefficient logKGE for logarithmic transformed runoff, and PBIAS.

[0051] The overall runoff simulation capability was evaluated using the Kling–Gupta efficiency coefficient: In the formula, To simulate the Pearson correlation coefficient between runoff sequences and observed runoff sequences, This is the ratio of the standard deviation of the simulated runoff series to the standard deviation of the observed runoff series. This is the ratio of the simulated runoff sequence mean to the observed runoff sequence mean.

[0052] logKGE does not take the logarithm of the KGE values. Instead, it first transforms the simulated and observed runoff by log(1+Q) respectively, and then calculates the transformed simulated and observed runoff sequences using the same calculation method as KGE2009. KGE2009 is used to evaluate overall runoff processes, while logKGE improves the sensitivity to changes in medium and low flow rates by compressing the range of high-flow values.

[0053] Total water volume deviation is defined as In the formula, and Let be the simulated runoff and the observed runoff on day t, respectively, and summation be performed on dates when both are valid.

[0054] Considering that a single indicator cannot simultaneously represent the overall process, the low-flow process, and the water volume deviation, the historical parameter migration performance of the i-th group of donor parameter vectors in the j-th development basin is defined as follows: The coefficients in equation (3) are set using the freezing experiment settings. Higher... This indicates that the set of parameters simultaneously demonstrates good overall runoff performance, logarithmic flow performance, and water balance performance within the receiving watershed.

[0055] The migration results of the i-th group of donor parameter vectors in all 407 developed receiving water domains collectively constitute its historical migration performance profile: Arrange the historical migration profiles of the 316 donor parameter vectors by row to obtain the historical parameter migration matrix. (5) One row of the matrix describes the performance changes of the same set of donor parameters when applied to different development basins, while the other column compares the differences when different donor parameters are applied to the same development basin. It records the actual cross-basin application results of the parameter combination, rather than another expression of the static properties of the donor basin.

[0056] Parameter migration is directional, generally having (6) This is because the parameter vectors and receiving basins used in the two migrations are different. Therefore, the historical migration performance is not a symmetrical physical distance between the two basins, but rather an empirical record determined by the specific Xin'anjiang model structure, calibration objectives, meteorological conditions, and migration analysis period. Neither the validation basin nor the independent test basin participated in the matrix construction.

[0057] S2.2 Extraction of Historical Migration Features The original historical parameter migration performance matrix contains 407 receiving watershed dimensions. This reflects both differences in the applicability of donor parameters and the overall simulation difficulty of different receiving watersheds. For example, some watersheds may be easily simulated for most donor parameters, while others perform poorly for all parameters. Directly using the original values ​​to calculate donor distances could lead to an overemphasis on results from receiving watersheds with higher overall difficulty or larger variations. Therefore, the historical parameter migration performance matrix is ​​first standardized by receiving watershed column. This process preserves the relative performance of different donor parameters within the same receiving watershed while mitigating the impact of absolute simulation difficulty across different receiving watersheds. All standardized statistics were calculated from development data.

[0058] make =U(i→j), standardized by development basin as follows: For a fixed j-th developing receiving basin, the mean and sample standard deviation of the historical parameter migration performance of this column are calculated using the following formulas: (7) The mean and standard deviation mentioned above are calculated along the donor index direction after fixing the j-th development basin, based on the historical parameter migration performance corresponding to all donor parameter vectors in this column. This represents the total number of donor parameter vectors. The migration performance of an individual historical parameter is a scalar, and its mean and standard deviation are not calculated separately. This standardization preserves the relative merits of different donor parameters within the same receiving basin and reduces the impact of the overall simulation difficulty across different receiving basins.

[0059] Subsequently, principal component analysis was performed on the standardized historical parameter migration performance matrix. The principal components were arranged in order of their contribution to the explained variance, and the top few principal components that caused the cumulative explained variance to reach a preset threshold were retained. In this embodiment, the preset cumulative explained variance threshold was 95%, and the top 6 principal components were retained. The scores of each donor parameter vector on the retained principal components were standardized again according to the dimensions of each principal component to form the historical migration feature coordinates of the corresponding donor parameter vector, i.e., donor watershed i. : (8) Here, it is necessary to distinguish between the two concepts of historical parameter migration performance and historical migration characteristics. The former is the actual cross-basin simulation result defined by equations (3) and (4); the latter is the compact representation obtained after standardizing and reducing the dimensionality of these results. Historical migration characteristics are used to compare the overall migration patterns of different donor parameters, but do not constitute a universal hydrological distance.

[0060] At this point, all 316 sets of donor parameters have historical migration characteristic coordinates. Since the target watershed did not participate in the cross-watershed migration analysis during the development phase, similar coordinates cannot be directly obtained. Therefore, it is necessary to estimate its position in this characteristic space using the information actually available in the target watershed.

[0061] Step 3: Determine the regionalized prior parameters of the target watershed First, the static attributes and hydrological characteristics represented by limited runoff data of the target watershed are obtained to form a target watershed description vector. Then, the historical migration characteristic coordinates of the target watershed are estimated using the multi-output ridge regression model trained by the donor watershed. Then, the continuous weights are calculated based on the characteristic distances between the target watershed and each donor watershed, and the donor parameters are weighted and combined to obtain the regionalized prior parameter vector of the target watershed.

[0062] S3.1 Estimation of Historical Migration Characteristics of the Target Watershed Directly applying the donor parameters to the target watershed and then selecting the best-performing parameters based on the runoff during the evaluation period would lead to leakage of target information. Therefore, the location of the validation watershed and the independent test watershed in the historical migration feature space can only be estimated based on the static attributes and limited runoff data available at the time of application.

[0063] Specifically as follows: A multi-output ridge regression model with intercept is fitted using a ridge regression penalty coefficient fixed at 1. The input is a 13-dimensional watershed description vector consisting of 7 static attributes and 6 hydrological features, and the output is its corresponding historical migration feature coordinates. The donor watershed description vector with historical migration feature coordinates during the development phase is used as the training input, and the historical migration feature coordinates of the corresponding donor parameter vector are used as the training output to fit the multi-output ridge regression model. Then, the 13-dimensional description vector of the target watershed is input into the fitted multi-output ridge regression model to estimate the historical migration feature coordinates of the target watershed.

[0064] Target watershed The description vector is denoted as The data consists of seven static watershed attributes and six short-term hydrological features. These two types of information are complementary: static attributes are relatively stable but cannot directly reflect the current runoff behavior of the target watershed; hydrological features are closer to the actual response, but their reliability is affected by record length, seasonal coverage, and the number of events. Therefore, the location of the target watershed is estimated by both types of information, rather than by replacing static attributes with hydrological features.

[0065] Specifically as follows: The seven static attributes include watershed area, average elevation, average slope, soil depth, soil porosity, forest cover percentage, and drought index, which are used to describe the long-term stable climate, topography, and underlying surface background of the target watershed.

[0066] The six hydrological characteristics include runoff coefficient, baseflow index, slope of flow duration curve, recession constant, high flow frequency, and low flow index, which are used to summarize water distribution, slow water source contribution, flow distribution, and water storage and release characteristics in short-term records.

[0067] The donor watershed description vector is constructed using the same method, and the normalized description matrix of the donor watershed is set as follows. The corresponding historical migration feature coordinate matrix is The multi-output ridge regression model with intercept is trained using the input and output as the input and output, respectively, to obtain the estimated regression coefficients. and intercept estimate Obtained through the following formula: (9) in, The Frobenius norm is represented by the ridge regression penalty coefficient, which is fixed at 1. , This represents the regression coefficient matrix, where 1 represents a matrix of length 1. A column vector of all 1s This represents the intercept vector.

[0068] In the FS30, FS90, and FS365 scenarios, there are 309, 314, and 316 donor watersheds with complete input features, respectively. For each of the three support scenarios, a multi-output ridge regression model from a 13-dimensional descriptive vector to a 6-dimensional historical migration feature coordinate is fitted, because the stability and information coverage of hydrological features are not the same under different record lengths.

[0069] Substituting the description vector of the target watershed into the fitted multi-output ridge regression relationship under the corresponding support scenario, the 6-dimensional historical migration feature coordinates of the target watershed are estimated: (10) S3.2, Continuous Donor Weighted and Regionalized Parameters Historical migration feature coordinates of the target watershed Once obtained, the matching relationship between the data and the donor's historical migration characteristics needs to be transformed into specific parameters. If only the most recent donor is selected, the parameter results may be too sensitive to subtle changes in the donor ranking, and information from other donors with similar historical applicable patterns will be discarded. Therefore, TU-dXAJ uses continuous multi-donor weighting instead of single-donor replication.

[0070] The set of donor watersheds available for target watershed b is denoted as All 316 qualified donors were used for the validation and independent test watersheds; when developing watersheds as internal targets, donors with the same number as the target watershed were excluded to avoid directly transferring the calibration parameters back to the watershed itself.

[0071] The distance between donor watershed i and target watershed b in the historical migration feature space is defined as the Euclidean distance between their historical migration feature coordinates: The smaller the distance, the closer the historical migration pattern of the donor parameters is to the estimated location of the target watershed. The distance is converted into continuous weights through exponential decay: The distance attenuation parameter is fixed at τ = 0.1; The continuous weight satisfies , , The 15-dimensional regionalized prior parameter vector of the target watershed is obtained by continuously weighting all available donor parameters: In the formula, The prior parameter vector of the 15-dimensional Xin'anjiang model before dXAJ correction is given, where the p-th parameter can be further written as: , Therefore, each regionalization parameter can be traced back to the corresponding donor weight and donor parameter contribution.

[0072] The purpose of continuous weighting is to transform historical migration patterns into prior parameters for the target watershed, rather than to prove that the weighted result represents the true parameters of the target watershed. The relationship between parameters and runoff in the Xin'anjiang model is nonlinear, and linear weighting of the parameter vector is not equivalent to a linear combination of simulated runoff. The effectiveness of regionalized parameters needs to be determined through subsequent independent testing and ablation experiments.

[0073] To provide a scale corresponding to the donor combination sensitivity for local corrections in dXAJ, after fixing the weights of consecutive donors, sampling with replacement is performed on the donors according to their respective weights. For the k-th resampling, M donors are selected from the donor set, and the mean parameters are recalculated from the 15-dimensional parameter vectors of the selected donors. After repeating B times, the sample standard deviation is calculated for each mean parameter obtained from the B times. In this embodiment, B = 500 and M = 54. The calculation relationship is as follows: (14) Each donor index is independently extracted according to the category probability corresponding to the continuous donor weights; the donor sampling standard deviation only represents the degree of regional parameter dispersion caused by the change of the extracted donor combination when the continuous donor weights are fixed, and does not represent runoff observation error, meteorological driving error, target coordinate estimation error or Xin'anjiang model structure error.

[0074] Step 4: Perform bounded local correction Based on the regionalized prior parameter vector of the target watershed, combined with the target watershed description vector, the final parameter vector of the target watershed is obtained by local correction under preset parameter boundaries and joint constraints through dXAJ. Then, the final parameter vector, meteorological driving data and the initial state of the model are input into the original Xin'anjiang model to complete the runoff simulation of the target watershed.

[0075] S41. Input the 13-dimensional target watershed description vector into a multilayer perceptron to obtain a 15-dimensional parameter correction. Sampling with replacement is performed on the donors according to the continuous donor weights of the target watershed. Each time, the corresponding parameters of the sampled donors form a resampled parameter mean. The sample standard deviation of the donor sampling standard deviation is determined by the sample standard deviation of the resampled parameter mean. The smaller of the donor sampling standard deviation and the margin of the regionalized prior parameter vector to the upper and lower bounds of each parameter is used as the effective correction scale. The parameter correction is constrained by hyperbolic tangent to obtain the final parameter vector.

[0076] Note: The final parameter vector satisfies the parameter-by-parameter boundary and the joint constraints of KI and KG.

[0077] dXAJ is used to locally correct regionalized prior parameters. A 13-dimensional target watershed description vector is input into a multilayer perceptron to obtain 15-dimensional parameter corrections. This 15-dimensional regionalized prior parameter vector serves as the baseline parameters to be corrected. The network output, constrained by a hyperbolic tangent function and scaled according to an effective correction scale, is added to the baseline parameters to obtain the final 15-dimensional parameter vector. Subsequently, the final parameter vector, the meteorological driving data of the target watershed, and the initial state of the model are input into the Xin'anjiang model with the same fixed structure used in step one to complete the runoff simulation.

[0078] Continuous donor weighting has formed a regionalized parameter prior vector for the target watershed. However, regionalization is mainly based on shared experience from the developed watersheds, which may still not fully describe the local differences in the target watershed. Therefore, dXAJ utilizes limited data from the target watershed to optimize the prior vector of regionalization parameters. Make minor adjustments.

[0079] The role of dXAJ is to locally correct the regionalized prior parameters, rather than regenerating a new set of parameters independent of the regionalized prior. The input to the multilayer perceptron is a 13-dimensional description vector of the target watershed, and the output is a 15-dimensional parameter correction. The 15-dimensional regionalized prior parameter vector is only used as the baseline parameters to be corrected and is not used as the ordinary input to the multilayer perceptron. This 15-dimensional parameter correction is expressed as: (15) After the network output is constrained by the hyperbolic tangent function, the final parameter vector is expressed as follows: (16) in, Represents element-wise product. This indicates the effective correction scale allowed for each parameter.

[0080] For the p-th parameter, the symmetric margin from the regionalization parameter to the preset upper and lower bounds is defined as... (17) Effective correction scales are constrained by both donor sampling variation and parameter boundary margins. (18) Among them, the donor sampling standard deviation The weighted resampling process with replacement described above is used to calculate the sample standard deviation of the mean of the corresponding parameters obtained from multiple resamplings; in this embodiment, the process is repeated 500 times, with 54 donors selected each time.

[0081] Equations (9) to (11) ensure that the parameter-by-parameter correction does not exceed the preset upper and lower bounds shown in Table A1; the final parameter vector must also satisfy the joint constraint that KI + KG ≤ 0.90, which belongs to the feasible domain of the preset parameters in this embodiment. Wherein, KI: soil outflow coefficient, dimensionless, the value range of this embodiment is 0.01–0.70; KG: groundwater outflow coefficient, dimensionless, the value range of this embodiment is 0.01–0.70.

[0082] For KI and KG, the effective correction scale is also constrained by the residual margin of the sum of their prior values ​​being 0.90, and the joint constraint is checked again after obtaining the final parameters: KI + KG ≤ 0.90.

[0083] S42. Input the final parameter vector, along with meteorological driving data such as daily precipitation and potential evapotranspiration of the target watershed and the initial state of the model, into the Xin'anjiang model with the same fixed structure used in step one. Calculate evapotranspiration, water storage, runoff generation, surface runoff, interflow, groundwater runoff and confluence, and output the simulated daily runoff of the target watershed.

[0084] The target loss function during the development phase consists of runoff simulation error, water balance error, and parameter offset constraints: (19) Among them, L Q L is the runoff loss term used to constrain the efficiency of runoff simulation. W The loss term is used to constrain water balance; the parameter offset regularization term is defined as follows: (20) Suppressing large parameter changes that are not supported by target watershed data allows dXAJ to preferentially retain parameter priors formed by historical migration weighting.

[0085] Each data scenario uses only precipitation, potential evapotranspiration, and runoff from the corresponding support period of the development watershed to train the dXAJ. Runoff from the evaluation period (2001–2004) in the validation and independent test sets is not included in the training. Final parameter vectors The original Xin'anjiang model equations are still input, and dXAJ does not change the evapotranspiration, water storage, runoff generation, runoff division, and confluence processes.

[0086] To verify the feasibility of the technical solution of this invention and its parameter regionalization effect, a comparative experiment was conducted using a fixed spatial division, a limited runoff data window, and a unified evaluation period. All six comparison methods used the same independent test period from 2001 to 2004; historical parameter migration performance matrix, standardized statistics, principal component analysis, multi-output ridge regression, and dXAJ training all used only the development set, while the validation set and independent test set were not involved in the above fitting; runoff during the evaluation period was not used for donor selection, target location estimation, parameter correction, or model training.

[0087] All six comparative methods and four ablation experiments used the same spatial partitioning, support window, and evaluation period of 2001–2004. The information available to different methods was determined by their method definitions, but could not exceed the limits allowed by the corresponding support scenario. XAJ-SCEUA used only the target watershed support period runoff for local calibration; Regionalized XAJ and static kNN did not use target runoff, therefore their regionalization parameters remained unchanged across the three support scenarios; LSTM, dXAJ, and TU-dXAJ utilized development watershed information and target support period data according to their respective established methods. All methods were computed within the same target watershed and the same evaluation period to ensure a consistent data basis for cross-method comparisons and intra-watershed paired analyses.

[0088] Historical parameter migration performance was established solely from cross-basin simulation results of the developing watershed from 1995 to 1999. Support period data for the target watershed in 2000 were used only to form target information under the corresponding scenario, while evaluation runoff from 2001 to 2004 remained isolated. Validation and independent test sets were not included in the construction of historical migration performance, nor were they involved in variable standardization, migration feature extraction, or fitting of target location mapping relationships.

[0089] All indicators are calculated using dates when both observed and simulated values ​​are valid, and missing values ​​are not imputed. Watersheds for which valid simulations or evaluation indicators cannot be generated are left as unevaluable, and the denominator is divided into reporting coverage using fixed data. This process avoids the bias caused by retaining only successful watersheds and allows for the simultaneous evaluation of performance and method availability under short-record conditions.

[0090] 1. Spatial Division The 582 qualified watersheds were stratified according to the HUC-02 hydrological zoning: 407 constituted the development set, 87 constituted the validation set, and 88 constituted the independent test set. The development set was used for parameter calibration, donor selection, historical migration feature space construction, and model training; the validation set was used for testing the established methods; and the independent test set was evaluated only once after the methods, hyperparameters, comparison methods, and statistical rules were fixed.

[0091] 2. Time Purpose and Limited Data Scenario In terms of time, this study used 1980 to adjust the initial state of the XAJ, 1981–1994 for developing watershed parameter calibration, and 1995–1999 for developing historical parameter migration analysis between watersheds. Limited data for the target watershed were collected from January 1, 2000, and three scenarios (FS30, FS90, and FS365) were set up; the unified evaluation period was from January 1, 2001 to December 31, 2004.

[0092] The three finite data windows share the same starting point and are nested sequentially, recording changes in seasonal coverage, the number of rainfall events, and the composition of hydrological conditions as the data grows. Therefore, they represent three given information conditions and cannot be used to determine a universally applicable threshold for the number of days.

[0093] 3. Examples of the method of the present invention The XAJ implementation in this study includes p=15 parameters and a target watershed description dimension q=13, comprising 7 static attributes and 6 hydrological features. Historical migration features retain 95% of the cumulative explained variance, resulting in an actual r=6. Among the 407 developing watersheds, n_s=316 sets of parameters satisfy the donor conditions. The ridge regression penalty coefficient is fixed at 1, and the distance decay parameter τ=0.1 for continuous weights is used. Donor parameter uncertainty is addressed through B=500 weighted sampling iterations, with M=54 donors sampled each time.

[0094] dXAJ uses a predetermined network width [13, 128, 64, 15], ReLU activation, and five preset random seeds; the loss weights in equation (12) are fixed at [1.0, 0.2, 0.1]. The range and function of XAJ parameters are shown in Table A1. The six hydrological features, comparison methods, and optimization and training configurations are all executed according to the fixed settings described above in this embodiment.

[0095] 4. Information isolation In this embodiment, the historical parameter migration performance matrix, standardized statistics, principal component analysis, multi-output ridge regression, and dXAJ training all use only the development set. The validation set and independent test set neither provide donor parameters nor participate in any of the above fitting. The limited data for the target watershed in 2000 are only used to calculate the permissible hydrological characteristics for each scenario or to complete the comparative method adaptation; the runoff during the evaluation period from 2001 to 2004 is not involved in donor selection, target coordinate estimation, parameter correction, or model training.

[0096] 5. Comparison Methods and Ablation Tests Six predetermined comparison methods cover local calibration, regionalization, data-driven modeling, differentiable process modeling, and parameter transfer: • XAJ-SCEUA: Direct calibration of XAJ using the corresponding limited records of the target watershed, representing local calibration of short records.

[0097] • Regionalized XAJ: Uses the parameter-wise median of qualified development donors within the target HUC-02; if no regional donors are available, uses the median of all donors.

[0098] • Regional LSTM: Learns regional rainfall-runoff relationships from watershed meteorological, attribute, and runoff sequences.

[0099] • dXAJ: Initializes all donor parameters with an equal-weighted mean and applies the same bounded correction as the full method.

[0100] • Static kNN parameter migration: Select the 5 nearest donors based on 7 static attributes and weight them by the inverse of the distance.

[0101] • TU-dXAJ: Employs historical migration feature localization, continuous donor weighting, and bounded local correction.

[0102] The four ablation schemes serve to differentiate between donor-weighted and subsequent correction methods: • A1: Corrected by dXAJ after equal-weighted averaging of donor parameters; • A2: Static kNN weighting followed by dXAJ correction; • A3: Uses continuously weighted parameters with TU, without dXAJ correction; • A4: Complete TU-dXAJ.

[0103] A4 A1 examines the effect of historical migration weighting relative to donor equal weighting, A4 A2 examines the effect of historical migration information relative to static similarity, A4 A3 quantization adds the additional effect of dXAJ to the same TU regionalization parameters.

[0104] 5. Evaluation Indicators and Statistical Methods The primary metric is KGE2009, and NSE, RMSE, PBIAS, high flow volumetric deviation, low flow volumetric deviation, peak flow deviation, and logKGE are also reported. High flow and low flow diagnostics are explained separately and not combined into a single ranking. Each metric uses only finite and non-negative dates for both observations and simulations; missing values ​​are not imputed.

[0105] Models with stochastic elements first aggregate pre-set seeds within the same watershed, then perform cross-watershed statistical analysis. The main effect size is the paired KGE difference of TU-dXAJ relative to the static kNN under the same watershed and data scenario: In equation (14), b represents the watershed and s represents the data scenario. The 95% confidence interval was obtained by 2,000 bootstraps per watershed. According to predetermined thresholds, ΔKGE ≥ 0.02 is defined as a positive effect, |ΔKGE| < 0.02 as a near-neutral effect, and ΔKGE ≤ A negative effect of 0.02 is considered. Watersheds that cannot form a common effective indicator are retained as unevaluable, and the effective coverage and fixed data are reported to divide the denominator.

[0106] 6 Results The results compare the overall performance of the six methods, the pairing effect and donor selection differences of TU-dXAJ relative to static parameter migration, the relative contributions of continuous donor weighting and dXAJ correction, and the applicability boundaries in different flow states and watersheds. All statistics retain a fixed denominator and unevaluable watersheds.

[0107] 6.1 Overall runoff simulation results Six methods were evaluated within the same independent test period. The median KGE and effective coverage are shown in Table 1. In the independent test set, the median KGE of TU-dXAJ was 0.464, 0.517, and 0.524 under FS30, FS90, and FS365 conditions, respectively; the median KGE of static kNN parameter migration was 0.504 in all three scenarios. Therefore, TU-dXAJ is lower than static kNN under FS30 conditions, but higher than static kNN under FS90 and FS365 conditions. The median KGE of XAJ-SCE-UA under FS365 conditions was 0.552, higher than TU-dXAJ's 0.524, so this result does not indicate that TU-dXAJ is the best among all compared methods. The key point supported by the experiment is that, compared to the traditional static similarity parameter migration targeted by this invention, historical parameter migration information can form a favorable overall pairing effect under conditions of sufficient limited runoff data.

[0108] Short records also affected the effective coverage of some methods. In the FS30 independent test, XAJ-SCE-UA, dXAJ, and TU-dXAJ achieved effective KGE in 79, 86, and 86 watersheds, respectively; by FS365, all six methods covered all 88 independently tested watersheds.

[0109] Table 1. KGE Median and Effective Coverage for Six Methods under Different Limited Runoff Data Conditions Note: The cell format is "KGE median (number of effective watersheds / fixed denominator)".

[0110] 6.2 Pairing effect and differences in donor selection To directly evaluate the effect of historical migration information relative to static similarity parameter migration, the KGE pairing difference of TU-dXAJ minus static kNN parameter migration is calculated within the same watershed and data scenario. Figure 2 (Table 2). The number of qualified watersheds capable of forming complete 13-dimensional target watershed description vectors increased from 563 in FS30 to 578 in FS90 and 582 in FS365, as shown in Table 2. Figure 2 As shown in (a) of the validation set, the median paired KGE difference under FS30, FS90, and FS365 conditions are respectively... 0.004, +0.011, and +0.042; respectively in the independent test set. 0.010, +0.025, and +0.032. Under FS30 and FS90 conditions, the 95% confidence intervals of both the validation set and the independent test set include zero; under FS365 conditions, the 95% confidence intervals of the validation set are [+0.011, +0.093], and those of the independent test set are [+0.011, +0.072], both above zero. Figure 2 As shown in (b) of this embodiment. Thus, under the FS365 condition, the historical parameter migration performance-driven regionalization method achieves a stable positive overall pairing effect compared to parameter migration based solely on static attributes; this result does not indicate an improvement in all watersheds, nor does it interpret 365 d as a universal threshold in other regions or other models.

[0111] Table 2. Paired KGE difference of TU-dXAJ relative to static kNN parameter transfer 6.3 Contributions to Core Technology Modules Ablation results indicate that the main increments of the complete method come from the continuous donor weighting driven by historical migration information and the resulting regionalized prior parameters. Figure 3 (Table 3). For example... Figure 3 As shown in (a), under FS365 conditions, the median paired KGE difference of A4 relative to A1 after equal weighting of the donor and applying the same dXAJ correction is +0.050 and +0.046 in the validation set and independent test set, respectively; and the median paired KGE difference of A4 relative to A2 after static kNN weighting and applying the same dXAJ correction is +0.022 and +0.026, respectively. In contrast, after adding local dXAJ correction to the same TU regionalized prior parameters, the median paired KGE difference of A4 relative to A3 is only +0.0005 in the validation set and +0.0010 in the independent test set.

[0112] Table 3. Pairing effect of intact TU-dXAJ relative to ablation protocol under FS365 conditions. The parameter correction range is consistent with the above ablation results. Figure 3 ).like Figure 3 As shown in (b), the normalized root mean square median of the validation set is 0.01971, 0.01219, and 0.00765 under FS30, FS90, and FS365 conditions, respectively, and 0.01854, 0.01146, and 0.00674 under independent test sets, respectively. This result indicates that the main performance difference in this embodiment arises when the historical migration continuous donor weighting forms the regionalized prior parameters, and dXAJ plays a small, boundary-constrained local adaptation role; this result does not mean that dXAJ can be generally omitted in other applications.

[0113] In summary, this embodiment demonstrates that historical parameter migration performance can supplement donor relationships formed solely by static watershed attributes, and forms traceable 15-dimensional regionalized prior parameters through continuous multi-donor weighting. Under FS365 conditions, the paired KGE difference confidence intervals of the parameter migration relative to the static kNN on both the validation set and the independent test set are above zero.

[0114] The ablation results further indicate that the main performance differences in this embodiment arise during the continuous donor weighting stage driven by historical migration information, with dXAJ only implementing small, constrained local corrections near the regionalized prior. The above results are used to demonstrate the feasibility of the technical solution and the role of the core modules, and do not imply that this method achieves optimal results in all watersheds, all finite data lengths, or all comparison methods.

[0115] Importantly, the CAMELS-US dataset, time division, specific parameter values, network width, and experimental configuration given in the exemplary implementation are only for illustrating the implementation of the present invention and do not constitute a limitation on the scope of protection of the present invention. Without changing the synergistic relationship between the historical migration performance construction, target location estimation, continuous donor weighting, and bounded local correction as defined in the claims, those skilled in the art can adjust the specific configuration according to other regions, process models, and data conditions; when changing the process model, calibration target, meteorological drive, or historical period, the donor should be recalibrated and the historical migration feature space reconstructed.

[0116] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the best mode of carrying out the invention as currently considered, or those features that are not relevant to implementing the invention) may be omitted.

[0117] It should be understood that in actual engineering implementation, the data processing and model calculation process can be specifically configured according to the data scale, computing resources and deployment environment; these implementations do not change the aforementioned method steps and their data dependencies.

[0118] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A regionalization method for the Xin'anjiang model based on historical parameter migration performance, characterized in that... Includes the following steps: Step 1: Establish a donor parameter library First, obtain the Xin'anjiang model parameters for multiple development basins, and then select development basins that meet the performance requirements as donor basins to form a donor basin set; Step 2: Constructing the historical migration feature space Each donor watershed in the donor watershed set is applied to each development watershed to calculate the corresponding historical parameter migration performance, construct a historical parameter migration performance matrix, and then perform principal component analysis on the historical parameter migration performance matrix to obtain the historical migration feature coordinates of each donor watershed, forming a historical migration feature coordinate matrix. Step 3: Determine the regionalized prior parameters of the target watershed First, the static attributes and hydrological characteristics represented by the limited runoff data of the target watershed are obtained to form the target watershed description vector. Then, the historical migration characteristic coordinates of the target watershed are estimated by using the multi-output ridge regression model trained by the donor watershed. Then, the continuous weights are calculated according to the distance between the target watershed and each donor watershed, and all donor watersheds are weighted and combined to obtain the regionalized prior parameter vector of the target watershed. Step 4: Perform bounded local correction Based on the regionalized prior parameter vector of the target watershed, combined with its target watershed description vector, bounded local correction is performed by dXAJ under preset parameter boundaries and joint constraints to obtain the final parameter vector of the target watershed. Then, the final parameter vector and meteorological driving parameters are input into the Xin'anjiang model to complete the runoff simulation of the target watershed.

2. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 1, characterized in that: In step two, the historical parameter migration performance from donor watershed i to development watershed j is calculated based on the overall runoff simulation efficiency KGE2009, the overall runoff simulation efficiency logKGE of logarithmically transformed runoff, and the overall water volume deviation PBIAS. This process is repeated to complete the historical parameter migration performance of each donor watershed relative to all development watersheds, and a historical parameter migration performance matrix is ​​constructed with donor watersheds as rows and development watersheds as columns. The historical parameter migration performance matrix is ​​then standardized according to the development watershed column. Principal component analysis is then performed on the standardized historical parameter migration performance matrix. The first few principal components whose cumulative explained variance reaches a preset threshold are retained as the historical migration feature coordinates of each donor watershed, and a historical migration feature coordinate matrix is ​​constructed.

3. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 2, characterized in that: For the donor basin i and the developing basin j, the Xin'anjiang model parameters corresponding to the donor basin i, the meteorological driving data of the developing basin j, and the initial state of the model are input into the Xin'anjiang model to obtain the simulated runoff sequence corresponding to the developing basin j. Simultaneously, the measured runoff of the developing basin j during the same period is combined as the observed runoff sequence. The donor basin is then calculated using the following formula. To develop the watershed Historical parameter migration performance , First, transform the simulated runoff and observed runoff by log(1+Q) respectively. Then, use the same calculation method as KGE2009 to calculate the transformed simulated runoff sequence and observed runoff sequence to obtain logKGE. Where r is the Pearson correlation coefficient between the simulated runoff series and the observed runoff series, α is the ratio of the standard deviation of the simulated runoff series to the standard deviation of the observed runoff series, and β is the ratio of the mean of the simulated runoff series to the mean of the observed runoff series. and Let be the simulated runoff sequence and the observed runoff sequence for day t, respectively, and summation be performed on the date when both are valid.

4. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 1, characterized in that: In step three, the static attributes of each donor basin and the hydrological characteristics represented by limited runoff data are first obtained to form a donor basin description vector. Then, the multi-output ridge regression model is trained using the donor basin description vector as input and the corresponding historical migration feature coordinates as output. Finally, the trained multi-output ridge regression model is used to estimate the historical migration feature coordinates of the target basin by taking the static attributes of the target basin and the hydrological characteristics represented by limited runoff data to form the target basin description vector as input.

5. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 4, characterized in that: The distance between the historical migration feature coordinates of donor watershed i and target watershed b is calculated using the following formula. in, The coordinates represent the historical migration characteristics of the target watershed. Coordinates representing the historical migration characteristics of the donor watershed; Then, using the following formula, the distance is transformed into continuous weights through exponential decay. : Where τ represents the distance decay parameter, and the continuous weights satisfy... , , Finally, the regionalized prior parameter vector of the target watershed It is obtained by continuously weighting all available donor parameters: ,in, This represents the parameter vector of the i-th donor watershed, which consists of multiple parameters from the Xin'anjiang model. This represents the set of donor parameter vector indices available for the target watershed b.

6. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 5, characterized in that: Both the donor watershed description vector and the target watershed description vector consist of seven static attributes and six hydrological features. The seven static attributes are watershed area, average elevation, average slope, soil depth, soil porosity, forest cover ratio, and drought index. The six hydrological features are runoff coefficient, baseflow index, slope of flow duration curve, recession constant, high flow frequency, and low flow index.

7. The Xin'anjiang model regionalization method based on historical parameter migration performance according to claim 5, characterized in that: In step four, the target watershed description vector is processed using a multilayer perceptron. The 15-dimensional parameter correction was obtained. : For each parameter First, calculate the symmetric margins from the regional priors to the upper and lower bounds: Then use the donor sampling standard deviation The smaller of the boundary margin and the effective correction scale is used: The final parameter vector is: ; Among them, the donor sampling standard deviation of each parameter The calculation follows the aforementioned weighted resampling with replacement process, which involves calculating the sample standard deviation from the mean of the corresponding parameters obtained from multiple resamplings.

8. The regionalization method of the Xin'anjiang model based on historical parameter migration performance according to claim 1, characterized in that: Daily precipitation, basin latitude, daily maximum temperature, daily minimum temperature, and daily runoff observation data were obtained for each development basin. Potential evapotranspiration was calculated using daily maximum temperature, daily minimum temperature, and basin latitude. A 15-dimensional candidate parameter vector was generated within a preset parameter range using the SCE-UA algorithm. Daily precipitation, potential evapotranspiration, candidate parameter vector, and the initial state of the model were input into a fixed-structure Xin'anjiang model to obtain simulated runoff data. Based on the unified calibration target between simulated runoff data and observed runoff data, the candidate parameter vector was iteratively updated using the SCE-UA algorithm to obtain a set of 15-dimensional Xin'anjiang model parameter vectors for each development basin. Development watersheds that meet the preset screening criteria are selected as donor watersheds, and their corresponding 15-dimensional Xin'anjiang model parameter vectors are used as qualified donor parameters, thereby forming a donor watershed set and a donor parameter library. The preset screening conditions are: KGE ≥ 0.5, NSE ≥ 0, and |PBIAS| ≤ 15%. Where KGE represents the Kling–Gupta efficiency coefficient, NSE represents the Nash–Sutcliffe efficiency coefficient, and PBIAS represents the total water volume deviation.

Images