A cressman ground wind speed interpolation method based on terrain mean square deviation

Abstract

This invention discloses a Cressman surface wind speed interpolation method based on topographic root mean square error, comprising: acquiring meteorological observation station data and digital elevation model (DEM) data; extracting the elevation values ​​of DEM pixels within a preset topographic analysis range, centered on each observation station, and calculating the topographic root mean square error at the station; for the grid points to be interpolated, calculating the original Cressman distance weights based on the spatial distance between each observation station and the grid points; constructing a topographic correction index based on the ratio of the topographic root mean square error at each observation station to the mean of the topographic root mean square errors at all stations; exponentiating the original Cressman distance weights with the topographic correction index as the exponent to obtain new weights after topographic root mean square error correction; using the new weights to perform a weighted average of the station observation increments within the search radius, correcting the background values ​​of the grid points, and obtaining the interpolated grid wind speed values; the technical effect of this invention is reliable and consistent.

Description

Technical Field

[0001] This invention relates to the field of meteorological data processing technology, specifically to a Cressman surface wind speed interpolation method based on topographic mean square error. Background Technology

[0002] The topographic root mean square (or topographic standard deviation), as a second-order topographic statistic describing the degree of local elevation dispersion, is mainly used in the field of subgrid topographic parameterization of numerical weather prediction models in the study of near-surface wind fields in complex terrain.

[0003] Existing techniques for improving Cressman interpolation have, to some extent, enhanced the simulation accuracy of Cressman interpolation in complex terrain regions, but the following prominent problems still exist:

[0004] (1) Insufficient representation ability of topographic factors. Existing topographic correction schemes generally use topographic relief (i.e., the difference between the maximum and minimum elevations within a statistical window) as the topographic correction variable. This indicator is a first-order statistic and can only reflect the overall undulation of the topography, but cannot characterize the degree of discrete variation of elevation within the neighborhood of the interpolation point. Under the condition of similar relief values, the friction and flow effects on near-surface wind speeds differ significantly between gentle continuous slopes and broken steep slopes, and existing methods are unable to effectively distinguish the above-mentioned geomorphic structures.

[0005] (2) Insufficient attention has been paid to second-order topographic statistics. As a second-order statistic characterizing the local elevation dispersion, topographic mean square error can sensitively reflect the fragmentation and complexity of the terrain and has important indicative significance for judging the characteristics of local wind speed variation. In areas with large topographic mean square errors, airflow is strongly disturbed by the terrain, and the wind speed recorded by observation stations often contains key topographic forcing information such as uphill acceleration and canyon flow. However, existing studies have not yet systematically introduced topographic mean square error as an influencing factor into the weighting function of Cressman interpolation.

[0006] (3) The response mechanism of the weighting function to the terrain effect needs to be optimized. Most existing improvement schemes construct joint weights by simply multiplying or linearly adding the terrain factor and the distance factor. This kind of treatment implies the assumption that the contribution of terrain and distance to the weight is independent of each other. However, in the actual near-surface wind field, the modulation of wind speed by terrain has highly nonlinear characteristics, and the above-mentioned linear superposition mechanism is difficult to accurately reflect the real spatial distribution law of wind speed under complex terrain conditions. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide a Cressman ground wind speed interpolation method based on topographic mean square error, thereby solving the problems existing in the background technology.

[0008] Technical solution: The Cressman surface wind speed interpolation method based on topographic mean square error described in this invention includes the following steps:

[0009] Step 1: Obtain data from ground meteorological observation stations and digital elevation model data within the study area;

[0010] Step 2: Taking each observation station as the center, extract the elevation values ​​of digital elevation model pixels within the preset terrain analysis range, and calculate the terrain root mean square error at the station.

[0011] Step 3: For the grid points to be interpolated, calculate the original Cressman distance weights based on the spatial distance between each observation station and the grid points;

[0012] Step 4: Construct the topographic correction index based on the ratio of the root mean square error of the topography at each observation station to the mean root mean square error of the topography at all stations;

[0013] Step 5: Power the original Cressman distance weights with the terrain correction exponent to obtain the new weights after terrain root mean square error correction;

[0014] Step 6: Use the new weights to perform a weighted average of the station observation increments within the search radius, correct the background values ​​of the grid points, and obtain the interpolated grid wind speed values.

[0015] Furthermore, in step 2, the calculation of the terrain mean square error specifically involves: within the terrain analysis scope, the standard deviation of the elevation values ​​of all digital elevation model pixels, which is used to characterize the degree of discrete variation of the terrain in the neighborhood of the observation station.

[0016] Furthermore, in step 2, the preset terrain analysis range is equal to the spatial search radius of Cressman interpolation, so that the calculation range of the terrain mean square error is consistent with the spatial influence range of the station observations.

[0017] Furthermore, in step 4, the terrain correction index is always positive. When the mean square error of the terrain at the observation station is greater than 0, the new weight is greater than the original Cressman distance weight; when the mean square error of the terrain at the observation station approaches 0, the new weight approaches the original Cressman distance weight.

[0018] Furthermore, in step 6, interpolation calculation is performed using a zero initial background field, that is, the initial wind speed value of all grid points is set to 0, so that the interpolation result is completely determined by the station observation value and the new weight.

[0019] Furthermore, in step 6, interpolation calculation is performed using either a single-iteration mode or a multi-iteration mode; the multi-iteration mode uses a sequence of progressively smaller spatial search radii, with each iteration using the interpolation result of the previous iteration as the new background field, until the last iteration is completed.

[0020] Furthermore, in step 1, the ground wind speed is the wind speed at a height of 10 meters above the ground.

[0021] Furthermore, in step 1, the digital elevation model data is derived from SRTM data and is resampled to a spatial resolution of 250 meters.

[0022] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0023] (1) Systematic improvement of interpolation accuracy under all terrain conditions. By introducing a terrain mean square error correction factor into the original Cressman distance weight function, the weight allocation can be adaptively adjusted according to the degree of terrain dispersion variation at the location of the station, avoiding the limitations of a single distance weight under complex terrain, and achieving better interpolation accuracy across the entire region.

[0024] (2) The accuracy improvement is more significant in areas with strong topographic variations. The core of the method of the present invention lies in the reasonable enhancement of the weight of observation stations in areas with high topographic mean square error. As the topographic mean square error increases, the accuracy improvement of the method of the present invention compared with the original method becomes more prominent, especially under complex topographic conditions, it shows stronger robustness and stability.

[0025] (3) It has stable applicability under different weather conditions. The improvement of wind speed interpolation accuracy by the method of the present invention does not depend on specific atmospheric circulation patterns or weather types. It can stably improve the interpolation accuracy under a variety of typical weather cases, indicating that the introduced terrain mean square error correction mechanism has strong universality and reliability.

[0026] (4) Low computational complexity, easy to deploy in operations. The method of this invention only adds the calculation of the mean square error of terrain and the operation of the weight correction factor on the basis of the original Cressman interpolation framework. The mean square error of terrain can be pre-calculated and stored as a lookup table. The overall calculation process is consistent with the standard method, which is convenient for rapid integration and application in existing meteorological business systems. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the process of the present invention;

[0028] Figure 2 This is a weight function distribution diagram of the present invention (scanning radius R = 10 km); Figure 3This illustrates the variation of each index with the mean square error of terrain in a single iteration of the present invention; wherein... Figure 3 (a) in the text represents the verification date 20250504. Figure 3 (b) in the text represents the verification date 20250625. Figure 3 (c) in the text refers to the verification date 20260129; Figure 4 This shows the variation of each index with the mean square error of terrain during the three iterations of this invention; wherein... Figure 4 (a) in the text refers to the verification date 20250504. Figure 4 (b) in the text refers to the verification date 20250625. Figure 4 (c) in the text refers to the verification date 20260129; Figure 5 This is a comparison of the distribution of errors in different weather cases under three iterations of the present invention with the mean square error level of the terrain. Figure 5 (a) in the text refers to the verification date 20250504. Figure 5 (b) in the text refers to the verification date 20250625. Figure 5 (c) in the text refers to the verification date 20260129. Detailed Implementation

[0029] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this embodiment of the invention provides a Cressman surface wind speed interpolation method based on topographic mean square error, including the following steps:

[0031] Step S1: Basic Data Acquisition and Preprocessing; Acquire basic data within the study area, including:

[0032] Geographic coordinates (longitude and latitude) of ground meteorological observation stations and hourly 10 m wind speed observations;

[0033] The digital elevation model data for the study area, which is derived from SRTM data and resampled to a spatial resolution of 250 m, is used to calculate the mean square error of the terrain at each station and grid point.

[0034] Step S2: Calculation of Topographic Root Mean Square: For each observation station, a topographic analysis range equal to the spatial search radius is set with that point as the center. For example, if the spatial search radius is 0.5°, the elevation values ​​of all DEM pixels within a 0.5° radius centered on the station are extracted, and the root mean square of these elevation values ​​is calculated as the topographic root mean square value for that point. The formula for calculating the topographic root mean square is:

[0035] (1);

[0036] In the formula, Within the spatial search radius, the first i Elevation values ​​of individual DEM pixels This is the average elevation of all pixels within the window. N This represents the total number of pixels within the window. The radius of the terrain analysis range is equal to the spatial search radius of the Cressman interpolation to ensure that the terrain mean square error accurately reflects the degree of terrain dispersion variation within the neighborhood of the interpolation point.

[0037] Step S3: Initial Field Setup and Iteration Preparation: This invention constructs the initial background field by uniformly setting the entire field to zero, meaning that the initial value is 0 for all interpolation grid points. The rationale for this setting is that a zero initial field ensures that the interpolation calculation results are entirely determined by the wind speed values ​​at the observation stations and the weighting function, avoiding interference from prior assumptions about the initial field on the interpolation results, thus more directly reflecting the contribution of the improved weighting function of this invention to the interpolation accuracy.

[0038] The spatial search radius sequence and number of iterations for Cressman interpolation are defined. This invention sets up two modes: single iteration and multiple iterations. The single iteration mode uses only one spatial search radius and the corresponding terrain mean square error analysis range for one interpolation calculation; the multiple iteration mode uses a progressively smaller spatial search radius R1>R2>R3>…> R n Interpolation calculations are performed sequentially on the same range of topographic mean square error analysis.

[0039] Step S4: Constructing the weight function for Cressman interpolation based on terrain mean square error

[0040] For a given grid point requiring interpolation calculation, the original Cressman interpolation weight function... Depends solely on the spatial distance between the observation station and the interpolation grid point:

[0041] (2);

[0042] In the formula, R is the spatial search radius of the current iteration. This represents the distance between the observation station and the grid points used for interpolation calculation.

[0043] This invention introduces a terrain root mean square error correction factor based on the standard distance weight. This yields a Cressman surface wind speed interpolation scheme based on terrain mean square error, and a new weighting function. Calculated by the following formula:

[0044] (3);

[0045] (4);

[0046] (5);

[0047] The mean squared error of the topography at the observation station is calculated using equation (1). It is the average of the standard deviation of the terrain at all stations; in most cases, The value range is [0, 100], because The value range is [0,1]. After correction by the terrain mean square error factor, The value range is still [0,1].

[0048] like Figure 2 As shown in the figure, the weight function is plotted when the scanning radius is R = 10 km. It can be seen from the figure that the weight function constructed in this invention... Simultaneously affected by the distance between the station and the grid point The weighting is controlled by both the mean squared error of the terrain. During weight allocation, if two stations have the same mean squared error of terrain, their weights are determined entirely by distance. The decision follows the basic principle that the greater the distance, the smaller the weight; if the distance between two stations and the grid point... When the distances to the grid points are equal, stations with larger topographic mean squared errors receive higher weights in the weighting calculation. This implies an important physical meaning: there is a fundamental difference between the spatial representativeness and the importance of a station. Specifically, a large topographic mean squared error means that the station is located in a complex terrain area (such as a ridge or valley), and its observations often include significant topographic effects (such as cold pools in valleys or enhanced precipitation on windward slopes), making its spatial representativeness more "local," but more important. On the other hand, stations with small topographic mean squared errors are located in flat areas, and the spatial representativeness of their observations is more "regional." When the distances to the grid points are equal for both types of stations, the observations from stations with complex topography are prioritized. This enhances the interpolation field's ability to characterize topographic details, avoids being masked by smooth signals from flat areas, and thus generates a spatial distribution that more accurately reflects the actual influence of topography.

[0049] Specifically, when the local mean squared error approaches 0, it reverts to the original Cressman method; if the local mean squared error approaches infinity, the weight is 1, which still has physical meaning in extreme cases.

[0050] Step S4: Interpolation Calculation

[0051] Aside from the aforementioned improvements to the weighting function, the new scheme remains unchanged, continuing to use the original Cressman interpolation calculation method.

[0052] (6);

[0053] (7);

[0054] These are the interpolated grid point values. Represents the station observation value. It is the grid background value. Indicates the observation increment. This represents the weight of the observation increment.

[0055] Step S5: Iterate multiple times and output results

[0056] For the single-iteration mode, the interpolation calculation in step S4 is performed only once using a preset single spatial search radius, and the interpolated grid wind field is directly output.

[0057] For the multiple iteration mode, R1, R2, R3…R are used sequentially. n The spatial search radius is reduced successively, and the interpolation calculation in step S4 is performed. In each iteration, the interpolation result of the previous iteration is used as the new background field to participate in the interpolation calculation. Finally, the grid wind speed field after the iteration is completed is output.

[0058] This embodiment focuses on the southwestern region of my country (99°–110°E, 22°–33°N). This region exhibits significant topographic relief, encompassing diverse landforms including the Yunnan-Guizhou Plateau, the Hengduan Mountains, the Sichuan Basin, and the southeastern edge of the Qinghai-Tibet Plateau. The highest elevation in the region exceeds 7000 m, while the lowest is less than 100 m, resulting in extremely complex terrain. Approximately 9000 surface meteorological observation stations are located within the study area. However, due to topographical and economic constraints, the spatial distribution of these stations is highly uneven. Stations are relatively densely distributed in river valleys and basins, while they are sparsely distributed in high mountain and canyon areas, with some high-altitude areas exhibiting severely insufficient station density. This embodiment utilizes hourly 10 m height wind speed observation data from these stations to interpolate the wind speeds of discrete stations to a regular grid with a spatial resolution of 0.1° × 0.1°.

[0059] This embodiment uses the 10 m wind speed gridded product of ERA5-Land as the benchmark reference data to verify the accuracy of the interpolated wind field. ERA5-Land is a high-resolution reanalysis dataset of the global land surface released by the European Centre for Medium-Range Weather Forecasts (ECMWF) under the Copernicus Climate Change Service (C3S) framework. Compared with the original ERA5's resolution of approximately 31 km and the previous generation ERA-Interim's resolution of approximately 80 km, ERA5-Land's spatial resolution is improved to approximately 9 km (i.e., 0.1° × 0.1°), while maintaining the hourly temporal resolution, and the data coverage extends from 1950 to the present. Its data generation is based on ECMWF's advanced H-TESSEL land surface model, using the ERA5 atmospheric field as meteorological forcing for offline simulation, and elevation corrections were made to the input temperature, humidity, and pressure to correct for elevation differences between the ERA5 forcing field and the ERA5-Land high-resolution grid. Although ERA5-Land does not directly assimilate observational data, ERA5 itself employs a four-dimensional variational data assimilation system, integrating global multi-source observational data. ERA5-Land indirectly inherits this data assimilation advantage through ERA5 atmospheric forcing, resulting in wind field data with high consistency and reliability in terms of physical laws and statistical characteristics. In its applicability assessment over land areas, the average annual wind speed deviation of ERA5-Land is only -0.06 m / s. -1 The correlation coefficient for monthly average wind speed reached 0.99, and the average root mean square error was 0.14 m / s. -1 It outperforms ERA5; other studies have shown that ERA5-Land is the best product for wind energy resource assessment, and can relatively accurately characterize wind speed and its fluctuations.

[0060] Step 1: Basic Data Acquisition and Preprocessing

[0061] (1) Station wind speed data. Hourly 10 m altitude wind speed observation data were collected from 8126 ground meteorological observation stations in the study area for three typical weather events: 20250504 (severe convection), 20250625 (heavy rain), and 20260129 (stationary front). The station data came from the hourly ground observation dataset released by the Guizhou Provincial Big Data Cloud Platform "Tianqing", which includes station number, longitude, latitude, and hourly wind speed and direction values. Wind speed and direction were converted to UV wind using a formula.

[0062] (8);

[0063] (9);

[0064] In the above formula Indicates wind speed. It represents the wind direction.

[0065] (2) Digital Elevation Model Data. SRTM digital elevation model data of the study area was acquired, with an original spatial resolution of 90 m. To match the interpolation scale and control the computational load, the SRTM data was resampled to a spatial resolution of 250 m using the Resample tool in ArcGIS software and the bilinear interpolation method, serving as the basis for calculating the mean square error of the terrain.

[0066] (3) ERA5-Land benchmark validation data. 10 m wind speed gridded products from the ERA5-Land reanalysis data released by the European Centre for Medium-Range Weather Forecasts (ECMWF) were obtained, covering three typical weather events: May 4, 2025; June 25, 2025; and January 29, 2026, with a spatial resolution of 0.1° × 0.1°. Longitude, latitude, and UV wind speed values ​​for each grid point were extracted as benchmark reference data to validate the interpolation accuracy.

[0067] Step 2: Interpolation Mesh Construction

[0068] A regular interpolation grid covering the study area was constructed, with a longitude range of 99°E to 110°E and a latitude range of 22°N to 33°N. The grid spatial resolution was set to 0.1° × 0.1°, maintaining complete consistency with the ERA5-Land data grid for grid-by-grid comparison and verification. There are 111 grid points in both the longitude and latitude directions, for a total of 12,321 grid points. The initial wind speed value for each grid point is set to 0. The rationale for using a zero initial field is that the interpolation results are entirely determined by the station observations and the weighting function constructed in this invention, avoiding the interference of prior assumptions about the initial field on the interpolation accuracy, thus more directly reflecting the technical contribution of the improved weighting function of this invention.

[0069] Step 3: Calculation of the mean square error of the terrain

[0070] For each valid observation station, square terrain analysis windows with side lengths of 1°, 0.5°, and 0.25° are set with each point as the center. The elevation values ​​of all DEM pixels in the window are extracted, and the terrain root mean square error at the point is calculated according to formula (1) for later use.

[0071] After the calculation is completed, the mean squared error of the terrain corresponding to each observation station is obtained. For example... Figure 3 As shown in the figure, statistics show that the high-value areas of the topographic mean square error at each resolution are mainly distributed in the high mountain and canyon areas of the Hengduan Mountains and the southeastern edge of the Qinghai-Tibet Plateau, while the low-value areas are mainly distributed in the Sichuan Basin and flat river valley areas, which is in good agreement with the actual degree of topographic fragmentation in the region.

[0072] For ease of verification later, such as Figure 4 As shown, the mean square error of the terrain at the grid points is calculated using the same method with the grid points as the center and R=0.1° for later use.

[0073] Step 4: Setting Iteration Parameters

[0074] This embodiment tests both single-iteration and three-iteration modes to verify the performance of the method of the present invention under different iteration strategies:

[0075] Single iteration mode: Scan radius R = 0.25°.

[0076] Three-step iteration mode: The scanning radius sequence is set to R1=1°, R2=0.5°, R3=0.25°, and iterated in descending order.

[0077] In this invention, the selection of the scanning radius is based on the target spatial scale of the analysis field, the distribution density of observation stations, and the convergence characteristics of the successive correction algorithm. For the single-iteration mode, a fixed radius of 0.25° is selected to achieve a balance between computational efficiency and preservation of local details, suitable for local analysis fields with complete observations that need to be generated quickly. For the three-iteration mode, a radius sequence from large to small is used: R1=1°, R2=0.5°, R3=0.25°. The first large-radius iteration corrects the large-scale background field and fills in the coarse grid values ​​of unobserved areas; the second iteration introduces mesoscale observation information; and the final small-radius iteration refines the local gradient. This sequence avoids the interpolation ill-conditioned problems caused by excessive smoothing of a single radius or data sparsity, achieving an optimal trade-off between spatial continuity and observation constraints in the interpolation results.

[0078] Step 5: Construction of the Cressman interpolation weight function

[0079] The original Cressman interpolation weight function only depends on the spatial distance between the observation station and the interpolation grid point: in this embodiment, the distance is directly calculated using latitude and longitude, that is, the distance between the interpolation grid point g and the observation station s. Defined as:

[0080] (10);

[0081] In the formula, and These are the longitude and latitude (in degrees) of the grid points, respectively. and These are the longitude and latitude of the station (in degrees).

[0082] The original Cressman interpolation distance weight function is:

[0083] (11);

[0084] R is the current scan radius;

[0085] This invention introduces a terrain mean square error influence factor into the original distance weighting function to construct a new weighting function:

[0086] (12);

[0087] (13);

[0088] σ is the mean square error of the topography centered at the observation station. It is the average of the mean squared deviation of the terrain for all 8126 stations;

[0089] Step 6: Interpolation Calculation

[0090] This embodiment uses the following two interpolation schemes for comparison:

[0091] Option 1 (original Cressman surface wind speed interpolation scheme): The weighting function only uses standard distance weights. No terrain correction factor is introduced. Single-iteration and three-iteration modes are performed respectively.

[0092] Option 2 (Cressman surface wind speed interpolation method based on terrain mean square error): Employs the new weighting function proposed in this invention. Perform single-iteration and three-iteration modes respectively.

[0093] The specific interpolation calculation process is as follows:

[0094] (1) Original Cressman interpolation scheme (single iteration): Using a scanning radius R=0.25°, calculate the UV wind at each grid point according to the following formula. The UV wind calculation formula and method are the same. Here, we take the V wind as an example:

[0095] (14);

[0096] (15);

[0097] In the formula Use the original Cressman weights , This represents the observed wind V at the i-th station. This represents the initial V-wind value of the grid point, which is 0. The above calculation needs to be performed for each grid point.

[0098] In the first iteration of the three iterations, R=1°. The initial value is 0; in the second iteration, R = 0.5°. This is the value after the first iteration; in the third iteration, R = 0.25°. This is the value after the second iteration.

[0099] (3) The Cressman interpolation method based on terrain mean square error uses a scanning radius of R=0.25° in a single iteration. The grid point values ​​are calculated in the same way as the original scheme, except that the formula is changed to R=0.25°. Replace with The same method was used to complete the iterative calculations in the third iteration, only the... Replace with .

[0100] Step 7: Interpolation accuracy verification

[0101] The grid wind fields generated by the two schemes above were compared and verified grid by grid with the ERA5-Land benchmark wind field. The specific verification steps are as follows:

[0102] (1) Extract the hourly UV wind from the 12321 grid points corresponding to the interpolation grid in the ERA5-Land data as the baseline true value. The formula for UV wind verification calculation is the same. Here, we take the V wind as an example and denote the V wind in ERA5-Land as The V-wind in the grid field generated by interpolation is .

[0103] (2) Calculate the root mean square error (RMSE), mean deviation (MAE), and correlation coefficient (RR) between the interpolation results of each scheme and the benchmark value:

[0104] (16);

[0105] (17);

[0106] (18);

[0107] (3) Sort the results data in ascending order of grid point topographic mean square error and group them into 8 intervals [0,50,100,200,300,400,500,600,inf]. Calculate the above indicators for single iteration and three iterations for three weather cases respectively.

[0108] like Figure 3As shown, the single-iteration verification results demonstrate that the Cressman interpolation scheme based on topographic mean square error used in this invention outperforms the original Cressman interpolation scheme in terms of overall interpolation performance across all three weather processes and the entire topographic mean square error range. Furthermore, the larger the topographic mean square error, the more significant the accuracy advantage. The RMSE of the new scheme is lower than that of the original scheme across the entire topographic mean square error range, with a more significant optimization margin for larger topographic mean square errors. Under highly complex terrain conditions with a topographic mean square error var>=600, the RMSE of the U and V components of the severe convective weather process 250504 is reduced by 9.5% and 14.8%, respectively; the RMSE of the rainstorm process 250625 is reduced by 9.6% and 10.6%, respectively; and the RMSE of the stationary front process 260129 is reduced by 8.1% and 10.2%, respectively, showing a significant improvement in interpolation accuracy under complex terrain. Simultaneously, the new scheme effectively improves the correlation of wind field interpolation results and has a stronger ability to reconstruct the spatial distribution of the wind field under high terrain complexity. The new scheme achieves higher RR (Recordability Scale) across all terrain root mean square deviation ranges compared to the original scheme, effectively mitigating the problem of rapid correlation coefficient decay under complex terrain conditions. Furthermore, the larger the terrain root mean square deviation, the more significant the improvement in RR. When the terrain root mean square deviation var>=600, the RR for the U and V components of strong convection processes increases by 26.0% and 20.2%, respectively; for heavy rainfall processes, by 7.7% and 15.5%, respectively; and for stationary front processes, by 14.0% and 8.6%, respectively, more realistically reflecting the actual wind field distribution characteristics. In addition, this scheme exhibits good error stability and strong applicability across all scenarios. The MAE (Magnitude of Effect) is at the same level as the original scheme, without introducing additional systematic bias.

[0109] like Figure 4As shown, the results of three iterations demonstrate that the proposed Cressman interpolation scheme based on topographic mean square error outperforms the original Cressman interpolation scheme in all three weather processes and across all terrain complexity ranges. This scheme significantly improves interpolation accuracy, with the advantage becoming more pronounced as terrain complexity increases. The RMSE of the new scheme is lower than that of the original scheme across all terrain mean square error ranges, with the optimization becoming more significant as the terrain mean square error increases. Under highly complex terrain conditions with a mean square error var>=600, the RMSE of the U and V components of the severe convective weather process 250504 decreases by 9.3% and 14.7%, respectively; the RMSE of the heavy rain process 250625 decreases by 9.6% and 10.4%, respectively; and the RMSE of the stationary front process 260129 decreases by 8.0% and 10.0%, respectively, demonstrating a significant improvement in interpolation accuracy under complex terrain. Furthermore, this scheme effectively improves the correlation of wind field interpolation results, exhibiting stronger ability to reconstruct the spatial distribution of the wind field under high terrain mean square error conditions. The new scheme achieves higher RR (Restriction of Wind) across all terrain mean square deviation ranges compared to the original scheme, effectively mitigating the problem of rapid correlation coefficient decay under complex terrain conditions. Furthermore, the larger the terrain mean square deviation, the more significant the improvement in RR. When the terrain mean square deviation var>=600, the RR for the U and V components of strong convection processes increases by 24.8% and 19.8%, respectively; for heavy rainfall processes, by 7.6% and 14.8%, respectively; and for stationary front processes, by 13.4% and 8.6%, respectively, more realistically reflecting the actual wind field distribution characteristics. In addition, this scheme exhibits good error stability and strong applicability across all scenarios. The MAE (Magnitude of Effect) is at the same level as the original scheme, without introducing additional systematic bias.

[0110] It is evident that, in both single and three iterations, the Cressman surface wind speed interpolation scheme based on terrain mean square error outperforms the original Cressman interpolation scheme in all three weather events: severe convection, heavy rain, and stationary fronts. As the terrain mean square error increases, the advantages of the new scheme in RMSE optimization and RR improvement become increasingly significant, indicating that the accuracy improvement is particularly pronounced under highly complex terrain. Furthermore, the MAE is stable, without additional systematic bias, demonstrating reliable technical performance and good consistency.

[0111] like Figure 5As shown, in the gentle terrain ranges of [0,50) m and [50,100) m, the median error of both the old and new schemes is close to 0. The box height, whisker range, and outlier distribution highly overlap, indicating that both schemes demonstrate comparable modeling accuracy and stability in gentle terrain. As terrain complexity increases ([100,200) m and above), the error dispersion of the original scheme increases significantly, even exhibiting extreme deviations of ±7~15 m / s, and the number of outliers increases significantly. In contrast, the new scheme maintains a more compact error distribution across all terrain ranges, with significantly narrower box and whisker ranges. The number of extreme errors in complex terrain is greatly reduced. Even in extremely complex terrain with a root mean square deviation ≥600m, the error fluctuation amplitude is still significantly lower than that of the old scheme, and no significant deviation expansion is observed.

Claims

1. A Cressman surface wind speed interpolation method based on topographic mean square error, characterized in that, Includes the following steps: Step 1: Obtain data from ground meteorological observation stations and digital elevation model data within the study area; Step 2: Taking each observation station as the center, extract the elevation values ​​of digital elevation model pixels within the preset terrain analysis range, and calculate the terrain root mean square error at the station; the preset terrain analysis range is equal to the spatial search radius of Cressman interpolation, so that the calculation range of terrain root mean square error is consistent with the spatial influence range of the station observation values. Step 3: For the grid points to be interpolated, calculate the original Cressman distance weights based on the spatial distance between each observation station and the grid points; Step 4: Construct the topographic correction index based on the ratio of the root mean square error of the topography at each observation station to the mean root mean square error of the topography at all stations; Step 5: Power the original Cressman distance weights with the terrain correction exponent to obtain the new weights after terrain root mean square error correction; Interpolation calculations are performed using a zero initial background field, meaning that the initial wind speed values ​​of all grid points are set to 0, so that the interpolation results are entirely determined by the station observations and the new weights. Step 6: Use the new weights to perform a weighted average of the station observation increments within the search radius, correct the background values ​​of the grid points, and obtain the interpolated grid wind speed values.

2. The Cressman surface wind speed interpolation method based on topographic mean square error according to claim 1, characterized in that, In step 2, the calculation of the terrain mean square error is specifically: within the terrain analysis range, the standard deviation of the elevation values ​​of all digital elevation model pixels is used to characterize the degree of discrete variation of the terrain in the neighborhood of the observation station.

3. The Cressman surface wind speed interpolation method based on topographic mean square error according to claim 1, characterized in that, In step 4, the terrain correction index is always positive. When the mean square error of the terrain at the observation station is greater than 0, the new weight is greater than the original Cressman distance weight. When the mean squared error of the terrain at the observation station approaches 0, the new weights tend to be similar to the original Cressman distance weights.

4. The Cressman surface wind speed interpolation method based on topographic mean square error according to claim 1, characterized in that, In step 6, interpolation calculation is performed using either a single iteration mode or a multiple iteration mode. The multiple iteration mode uses a sequence of progressively smaller spatial search radii, with each iteration using the interpolation result of the previous iteration as the new background field, until the last iteration is completed.

5. The Cressman surface wind speed interpolation method based on topographic mean square error according to claim 1, characterized in that, In step 1, the ground wind speed is the wind speed at a height of 10 meters above the ground.

6. The Cressman surface wind speed interpolation method based on topographic mean square error according to claim 1, characterized in that, In step 1, the digital elevation model data is derived from SRTM data and is resampled to a spatial resolution of 250 meters.

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