Introduction

Wind speed is a vital aspect of atmospheric airflow and plays a crucial role in understanding weather systems, atmospheric circulation, pollution dispersion, and related phenomena1. Wind is fluctuating and difficult to predict, causing substantial temporal changes with complex implications2. When wind speeds increase, surface soil can be removed, resulting in soil infertility and land degradation. Wind erosion is a prominent form of land degradation in arid and semi-arid areas and has adverse effects on agricultural production and the ecological environment3,4. Strong winds can transport dust particulate matter from the surface to the atmosphere, contributing to the emergence of dust storms, which can cause widespread damage5. In addition to their devastating impacts on localized areas, strong winds can also affect regions far from their sources through atmospheric transport and deposition. This poses a considerable threat to human health, air quality, and ecosystems6. Therefore, it is critical to implement measures to reduce their occurrence and mitigate their adverse effects.

Wind erosion and dust emissions are major problems in the inland Pacific North-west (iPNW) owing to poor soil aggregation, low vegetation protection, and high winds7. Land management practices such as shelter forests and conservation tillage have been used to mitigate wind erosion in this region. To ensure environmental protection and ecological security, land management practices have been adopted in other regions8, including returning farmland to forests, afforestation, the Three–North Shelter Forest Program, and the Great Plains Shelterbelt, to reduce dust emissions and mitigate poor air quality and atmospheric visibility in areas eroded by wind9,10 Assessing protective forest stands and their characteristics is a major concern in many countries, owing to desertification and wind erosion11.

The simulation and analysis of wind speed in the near-surface layer are crucial research tasks in meteorology and aerodynamics and play a major role in meteorological forecasting, preventing and controlling meteorological disasters, predicting atmospheric pollution, using renewable energy source12. The importance of wind speed modeling is immense because it helps us to understand atmospheric motion, assess wind energy resources, and design wind-resistant structures and buildings. Among meteorological disasters, wind damage is a dangerous natural phenomenon characterized by its frequent occurrence and wide-ranging destruction13. Extreme wind events have a strong impact on urban high-rise buildings, electric facilities, transportation, and human lives14. Air pollution is affected by wind speed, which influences the diffusion and transmission of pollutants15. The speed of atmospheric pollutants in the air column is determined by wind speed, whereas wind shear affects the strength and character of atmospheric turbulence, indirectly influencing the diffusion of pollutants16. Therefore, accurately simulating wind speed is crucial, but challenging. From the microscopic surface to the field, the wind speed is influenced by a significant scale effect, and wind factors vary based on the scale of the study. Wind speed is influenced by numerous complex factors, including topographic features, such as forests, mountains, valleys, and oceans, which alter wind flow and intensity. In addition, a larger air pressure differential can result in higher wind speeds. In the atmospheric boundary layer, that is, the layer closest to the Earth’s surface, wind speeds can vary substantially owing to surface friction and turbulence17.

Traditional surface-level wind-speed simulation methods mostly depend on observational data and empirical formulas. However, these methods have considerable limitations that can result in inaccurate wind field information18,19,20. The development of computer technology and improvement in numerical simulation methods have contributed to substantial progress in simulating and analyzing near-surface wind speeds. Wind speed modeling is a vital tool for precise wind speed prediction and reducing the risk of related meteorological disasters21. Numerous wind speed prediction methods have been proposed in the academic literature. These methods can be broadly categorized into two types, that is, physical methods, including those of Yang et al.5 and Wang et al.22, and traditional statistical methods, including those of Erdem23 and Ren24. Physical models can explain wind speed generation by constructing intricate mathematical and physical models. These models predict the wind speed by simulating the entire wind formation process, necessitating data collection, including relative humidity, air temperature, barometric pressure, wind speed, wind direction, and terrain data. Examples of such models include numerical weather prediction (NWP) models25 and Weather Research and Forecasting (WRF) models26. These methods offer high interpretability and high prediction accuracy. However, data collection is more difficult, the modeling is highly intricate, and reaching the solution is time-consuming27. Meanwhile, the simulation accuracy is relatively poor owing to the limited resolution of the input parameters26. Wind-speed prediction using traditional statistical methods relies on historical wind-speed data, such as time-series models. Time series models primarily consist of moving average (MA), autoregressive (AR), and autoregressive moving average (ARMA) models, and their variations23. Statistical methods do not consider the physical processes of wind-speed fluctuation. Instead, they use statistical analysis to extract patterns from substantial amounts of historical wind measurement data obtained from wind farms. By selecting appropriate mathematical models, relationships are established between past and future wind speed data27. Therefore, statistical techniques can predict future wind speeds for wind farms. Various statistical models have been used to depict wind speed distributions28,29,30. Seven wind probability density functions are commonly used to estimate actual wind speed values. To estimate the wind probability density, each statistical model has distinctive merits and demerits. The Weibull, Rayleigh, Lognormal, Gamma, Inverse Gaussian, Pearson type V, Burr, and histogram models have varying strengths and weaknesses in forecasting wind probability density. Different wind speed distribution functions have differing effects on the fitting of the actual wind speed values in various study areas. Each method also has advantages and disadvantages related to their temporal and spatial resolution18,19, although the statistical approach remains the benchmark method20.

Wind speed and direction can be influenced by rough terrain or intricate surfaces with more obstructions. Despite the use of advanced technology such as advanced numerical models and supercomputers, typical weather forecasts only offer alterations in meteorological factors over the next few days31. The Wind Erosion Prediction System (WEPS) was conceived by the U. S. Agricultural Research Service (ARS) and features seven submodels, that is, Soil, Crop, Hydrology, Residue Decomposition, Management, Weather, and Erosion. Among these, the WEPS weather sub-model can be used to simulate hourly changes in wind speed near the surface, which aids in predicting wind erosion with accuracy. The WEPS is an objective, continuous model that simulates the physical mechanisms responsible for daily dynamic changes in various factors including but not limited to weather, field conditions, hydrology, management, and wind erosion conditions32. This model is one of the few wind models that operates on an hourly process-based scale. The capability of the WEPS weather sub-model to forecast hourly wind speeds and directions across the United States in response to current and future climates relies heavily on a large weather database compiled over the last few decades33. This database was constructed by continuously monitoring hourly wind data from 1304 weather stations located at a 10 m altitude. Earlier versions of WEPS (version 1.0) used a Weibull model to fit the wind speed distribution34. Van Donk et al.35 tested the WEPS (1.0) weather sub-model’s ability to simulate hourly wind data. They discovered that the two-parameter Weibull model did not adequately fit the wind speed distribution. Hourly wind speeds that exceeded 100 m s−1 in specific instances made the model questionable for wind erosion modeling. The hourly wind speed and direction histogram appeared to conform better to the wind speed distribution than the Weibull model, prompting the current WEPS (2.0) the adoption of histograms in the simulation of wind speed and direction to predict wind erosion, as per van Donk et al.35.

Given that wind is the main contributor to wind erosion, knowledge of wind patterns is essential. Models for stochastic wind power prediction that are effective in other contexts may not be appropriate for predicting wind erosion. Wind power businesses seek to identify wind speed thresholds at which wind turbines may provide the highest possible output36,37. The highest wind speed that a structure is anticipated to experience over its service life is the primary focus of the construction industry38,39. Although accurate modeling of high wind speeds is not necessary, researchers require data on wind speeds over the full spectrum to anticipate evaporation and transpiration. Wind deserves an in-depth study owing to its crucial role in forecasting electricity generation40, its impacts on vegetation41,42, and its effects on society43. Various techniques have been used to investigate wind in challenging terrains, with positive outcomes. A well-known issue is the creation of short-term wind speed forecast models for intricate subsurface environments. However, wind erosion studies require accurate simulation and forecasting of short-term wind speeds in intricate subsurface environments.

The precise estimation of wind occurrence and the distribution of wind erosion for different wind speeds are significantly affected by different evaluation factors. There is little information available on the effectiveness of the WEPS in simulating wind speeds, indicating the need for an in-depth study on the effectiveness of WEPS in wind forecasting. Therefore, the objective of this study was to evaluate the ability of the WEPS (2.0) in simulating temporal and geographical distribution features of the hour-by-hour near-surface wind speed in the iPNW of the US. To the best of our knowledge, no studies have tested this model in this region. By offering a scientific foundation for planning and decision-making in relevant domains (e.g., shelter forest and agricultural land management practices), this study seeks to advance sustainable development and environmental preservation.

Materials and methods

Study area

The iPNW is located in the western United States and covers an area of 75,000 km2 across Oregon, Washington, and Idaho (Fig. 1). Annual precipitation is unevenly distributed in the region and ranges from 150 to 600 mm. The region is characterized by a pronounced eolian sedimentary landscape with aeolian deposits that are up to 76 m deep44. The Pacific Northwest region of the conterminous United States is surrounded by a series of tall mountain ranges that block humid air from the Pacific Ocean, thereby creating a semi-arid climatic environment in the region45. Westerly winds are prevalent in the region and are usually the strongest in spring or fall, with peak gusts exceeding 20 m s−1 every two years or 30 m s−1 every 10 years46. Wheat has been the main cash crop in the region with a history of 130 years47. More than 1.5 million hectares have been planted, and winter wheat–summer recreation is the main crop rotation in the region, which aids in soil moisture retention and wind erosion prevention48. Agriculture is one of the dominant industries in the region. However, tillage leads to soil structure destruction. Dust emissions generated by wind erosion during the windy season can severely affect the regional air quality49. Land degradation caused by wind erosion hinders the sustainable development of agriculture50, therefore various agricultural land management practices are used to mitigate soil wind erosion.

Fig. 1
Fig. 1
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Site location distribution in the iPNW of the United States (Generated by ArcGIS 10.8, https://www.esri.com/zh-cn/home). Circles represent the sites of Data set 1, which was also known as the first wind data set and was derived from WSU AgWeatherNet. The representative of this serial number can be found in Table 1. Symbol × represents the sites of Data set 2, which was also known as the second wind data set and was derived from DCDC (Table 2). The WEPS weather sub-model was developed from substantial amounts of historical wind measurement data obtained from DCDC.

Data sources

Hourly wind speed data were obtained from Washington State University’s AgWeatherNet (http://weather.WSU.edu/), which records hourly wind speed measurements from 175 weather stations in the iPNW region (Fig. 1 and Table 1). These stations have been in operation since 1950, most of which are located in agricultural zones of the iPNW area. Weather and climate data collected from 13 AgWeatherNet weather stations from 2009 to 2018 were selected to ensure consistent data throughout the decade. The WEPS weather sub-model uses monthly parameters derived from historical hourly measurements to generate wind, thereby providing the hourly wind speeds and daily wind directions required for the WEPS daily simulation. Given that the WEPS weather submodel is based on historical wind statistics, it reflects the wind history at a given location. Table 1 shows that of the 1304 weather stations in the WEPS database, the 17 stations selected for model validation do not overlap geographically with the locations of measurement. Therefore, the WEPS used spatial interpolation to calculate the hourly near-surface layer wind speeds at the 13 observation sites. The data derived from the WSU AgWeatherNet is hereafter referred to as the first wind data set (Data set 1, or WSU wind data set). Interpolation has previously been proven to affect the simulation of weather parameters51,52. Therefore, we tried to avoid the impact of spatial interpolation on the WEPS simulation performance. In the WEPS weather database, weather data from 1304 stations were extracted from the National Climatic Data Center (NCDC, https://www.ncei.noaa.gov/) (Tables 1 and 2) and assumed to accurately reflect the past wind histories at 1304 locations. From 2009 to 2018, in situ observations from 13 NCDC-selected stations were gathered, and hourly observations of near-surface wind speeds were obtained (https://www.ncdc.noaa.gov/cdo-web/datatools/lcd). The data derived from the NCDC is hereafter referred to as the second wind data set (Data set 2, or the NCDC wind data set). The WEPS model yielded hourly near-surface wind speed data based on the second wind data set, which removed the impact of spatial interpolation on the simulation.

Table 1 Locations of WSU AgWeatherNet wind data observations and weights and locations of each station used in the WEPS simulations.
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Table 2 Locations of the stations used in the NCDC wind data set (Dataset 2).
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WEPS weather submodel

The WEPS weather sub-model interacts with six other WEPS sub-models to simulate changes in the soil, soil surface conditions, plants, and atmosphere32. There are two steps in the WEPS weather sub-model generation of wind data for a given site. First, the distributions of the measured daily wind direction and hourly speed were calculated from historical records to generate monthly statistics (Tables 3 and 4). The wind was divided into 16 cardinal directions. The maximum and minimum wind speeds were assumed to be 45.5 and 0.5 m s−1 respectively. Wind speeds equal to or less than 0.5 m s−1 were categorized as “static winds”. Wind speeds that ranged from 0.5 to 45.5 m s−1 were divided into 25 segments (0.5–1.5, 1.5–2.5, 2.5–3.5, 3.5–4.5, 4.5–5.5, 5.5–6.5,6.5–7.5, 7.5–8.5, 8.5–9.5, 9.5–10.5,10.5–11.5, 11.5–12.5, 12.5–13.5, 13.5–14.5, 14.5–15.5, 15.5–16.5, 16.5–17.5, 17.5–18.5, 18.5–19.5, 19.5–20.5, 20.5–25.5, 25.5–30.5, 30.5–35.5, and 35.5–40.5, and 40.5–45.5 m s−1). The measured daily wind direction and hourly speed were calculated to generate statistical descriptions of the 16 cardinal wind directions and 25 segments for each month. This step was performed daily, resulting in cumulative wind speed distributions for 12 months and 16 wind directions. This process resulted in 192 aggregates at the given site, comprising 16 cardinal wind directions × 12 months. In each aggregate, for example, south–southeast wind in June, the fraction of hourly wind speeds fitting the 25 segments was calculated to elucidate the wind characteristics for the given site. Second, the wind data were stochastically generated from this statistical description by a stochastic generation. The first step was performed only once, whereas the second step was performed in every WEPS simulation.

Table 3 An example of a WEPS hourly wind speed probability histogram for ELLENSBURG2 NARR, WA. The table represents wind direction frequency (%) by month (12 columns) for various wind directions (16 rows).
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Table 4 An example of a WEPS hourly wind speed probability histogram for ELLENSBURG2 NARR, WA. The table represents cumulative hourly wind speed distributions for 12 months and 16 wind directions.
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When the WEPS simulation was run at a selected location, one of the 16 cardinal wind directions (or calm) was selected from Tables 3 and 4 using a random number generator with a distribution for the current month. The 192 aggregates gathered at each station comprised the daily wind direction distribution (16 directions) and frequency over 12 months. Subsequently, using the selected wind direction, the WEPS yields the wind speed for the entire day. By using the cumulative wind speed profiles for the month and the wind direction already chosen, the generator interpolates the data. The WEPS then uses its random number generator to provide figures for wind speeds over 24 h, that is, 24 hourly wind speeds. Although natural wind occurrences sometimes last for several hours or days in a row, the generated wind speed data are not sequential. Therefore, the generated wind speeds need to be rearranged to approximate this pattern. Based on the duration of the wind event, hourly wind speeds were created over a default period of five days in the WEPS. These wind speeds and wind direction were maintained in a data pool that was produced more than once per month. Six of the highest wind-speeds from each of these pools were provided each day for a total of 24 wind-speed readings collected over five consecutive days. The WEPS weather sub-model has been shown to successfully reproduce both wind speeds and directions across consecutive years for several states in the U.S.53. The accuracy of the generated wind speeds is increased by using histograms to depict the measured wind speed distribution35. Consequently, the United States Department of Agriculture’s Agricultural Service (USDA-ARS) regularly uses the WEPS model to simulate wind erosion of agricultural soils across the country.

The wind speeds at a height of 10 m were simulated using WEPS. AgWeatherNet weather stations detect hourly wind speeds and daily wind directions at a height of 2 m above ground level. Wind-speed profiles were used to determine the wind speed at a height of 10 m as follows:

$$U_{Z} = \frac{{u^{*} }}{k} \ln \frac{Z}{{Z_{0} }}$$
(1)

where k is the von Karman constant (k = 0.4), u* is the friction velocity (m s−1), and Z0 is the aerodynamic roughness of the surface (m), Uz (m s−1) is the wind speed at a height of Z (m), according to Stull52. Using the wind speed 2 m above the surface (U2) as a starting point, the wind speed 10 m above the surface (U10 in m s−1) can be calculated as:

$$U_{10} = U_{2} \frac{{\ln \frac{10}{{Z_{0} }}}}{{\ln \frac{4}{{Z_{0} }}}}$$
(2)

According to Stull54, farmland typically has an aerodynamic roughness length (Z0) of 5–100.0 mm. Cropland roughness is affected by several variables, including the size of aggregates on the soil surface, plant poking through the soil, and tool marks left by tillage techniques55. The aerodynamic roughness lengths for crop management techniques that are common in nature are provided by the WEPS Crop and Management Database. According to the USDA (2016), the Z0of a winter wheat crop after tillage is approximately 7.6 mm. In the winter wheat–summer fallow rotation, this value is close to the reported Z0of 7 mm56. To determine the Uz on farms for different crops, Z0 values from the WEPS crop and management databases were used.

Spatial interpolation of wind data

Over wind-erosion regions in the United States, the WEPS has proven successful in estimating hourly wind speeds and directions for several consecutive years57,58. However, the locations of the WSU AgWeatherNet stations are not geographically consistent with those of the weather stations used to create the WEPS database. Therefore, the WEPS used a specific spatial interpolation technique. The hourly wind speeds at the simulated locations were calculated directly from adjacent weather stations in the WEPS database or extrapolated from several nearby weather stations (Table 1). Consequently, simulated hourly wind speed data at the sites were interpolated from many adjacent weather stations or directly approximated from nearby weather stations in the WEPS database (Table 1). Delaunay triangulated weights and WINDGEN station locations were used for spatial interpolation, where three stations were weighted and added to one. The interpolation technique applies INTERPOLATE to normalize the provided non-normalized centroid (or face) coordinates, enabling the selection of nearby stations and the development of weights depending on distance.

Statistical analysis

Correlation coefficients and coefficients of determination have been widely used to evaluate the goodness of fit of wind erosion models59. Legates60 have indicated that these statistics are oversensitive to extreme values (outliers) and insensitive to additive and proportional differences between model predictions and observations. Given these limitations, we used a combination of the following statistical indices to evaluate the WEPS performance, including R2, the Will-mott61d-index, modeling efficiency (EF), root-mean-square error (RMSE), difference of mean (DOM), and regression analysis model fit index. Willmott sought to address the insensitivity of correlation-based statistics to variations in the means and variances of observations and model simulations using Eq. (3).

$$d = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {\left| {P_{i} - O_{m} } \right| + |O_{i} - O_{m} } \right)^{2} }}$$
(3)

where Oi is the actual measurement, Pi is the model’s prediction, Om is the average of the actual measurement, n is the number of comparisons, and d (unitless) is the number between 0 and 1, which indicates how well the model’s predictions match the observations. The higher the value, the greater the consistency. The d values of 0.5 are regarded as an acceptable criterion62. The d value is susceptible to extreme values. Loague and Green63 used EF to assess the efficacy of solute transport models as follows:

$$EF = \frac{{\mathop \sum \nolimits_{i = 1}^{n} (O_{i} - \overline{O})^{2} - \mathop \sum \nolimits_{i = 1}^{n} (P_{i} - O_{i} )^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - \overline{O}} \right)^{2} }}$$
(4)

Here, EF (unitless), which has a range of − ∞ to 1, stands in for the efficiency factor while \(\overline{O }\) represents the average observed value. Positive values indicated that the simulated value was more accurate than the average measured value. Higher values indicate greater alignment between the simulated and measured values. The RMSEprovides an evaluation of variable unit errors, should be included in a thorough evaluation of model performance60. As defined by RMSE:

$$RMSE = \left[ {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{n}} \right]^{\frac{1}{2}}$$
(5)
$$DOM = \overline{P} - \overline{O}$$
(6)

where RMSE ranges from zero (when the estimates and observations are the same) to infinity and explains the discrepancy between the model estimates and observations. Values closer to zero indicate that the model functions more accurately. Legates60 has provided the necessary information to evaluate the model performance. In addition, \(\overline{P }\) represents the average predicted value.

Results and discussion

Observed hourly near-surface wind speed over the iPNW

This study investigated the near-surface hourly wind speed characteristics of 13 weather stations within the iPNW. The critical erosion wind speed, also known as the threshold wind speed (TWS), which normally varies between 6.4 and 10 m s−1, is influenced by vegetation and soil surface characteristics64. The TWS value in this study was defined as the wind speed at a height of 10 m, which exceeded 8 m s−165. Six different wind speed characteristic indices, including the annual mean wind speed, the annual mean of speeds calculated by hourly wind speed greater than 8 m s−1 (annual mean of speeds > 8, hereafter), the monthly mean of speeds calculated by hourly wind speed greater than 8 m s−1 (monthly mean of speeds > 8, hereafter), the annual total numbers of days with hourly wind speeds greater than 8 m s−1 for at least one hour (annual days > 8, hereafter), the monthly total number of hours with speeds greater than 8 m s−1 (monthly hours > 8, hereafter), and the annual total number of hours with speeds greater than 8 m s−1 (annual hours > 8, hereafter), were selected to analyze the hourly near-surface wind speed characteristics in the region. These indices were selected because the average, maximum, and minimum wind speeds may not accurately represent the wind speed in wind erosion modeling63.

Interannual variations in hourly wind speed

The inter-annual fluctuations of annual hours > 8 at the 13 iPNW locations are depicted in Fig. 2. Compared to the peak value of 890 h in 2012, the annual hours > 8 fell to the lowest value of 476 h in 2017. The annual total number of hours with speeds greater than 8 m s−1 (annual hours > 8) was gradually rising from 2009 to 2012. These hours progressively declined from 2013 to 2018. From 2009 to 2018, the change in the annual hours > 8 decreased at a rate of 24.74 h per year (y =  − 24.74x + 801.28, R2= 0.28, p = 0.12), although the trend was not statistically significant. Similar to annual hours > 8, the annual mean wind speed, annual mean of speeds > 8, and annual days > 8 have similar declining trends to that of annual hours > 8.

Fig. 2
Fig. 2
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Characteristics of inter-annual variations in the annual total number of hours with speeds greater than 8 m s−1 (annual hours > 8) across stations in the iPNW.

Wind speeds are strongly influenced by climate change66. Liu and Zhang67 reported that wind speeds decreased as the air temperature increased in Northwest China68. Although the area’s temperature has increased over the last century (0.7 °C)69, this increase is not large in comparison to those at other places in the world70. Global temperatures have increased, on average, by 0.34 °C/10 years from 1989 to 202171. Therefore, the decline in wind speed in this region appears to correspond to increasing air temperatures. However, the trends for wind speed and temperature were not significant72.

Characteristics of monthly hourly wind speed > 8

Figure 3 shows the trend of the monthly mean of speeds > 8 across the sites. The greatest monthly mean of speeds > 8 occurred in January with a value of 9.96 m s−1, and the lowest value, is 9.02 m s−1 in July. After January, the monthly mean wind speed steadily decreased until July, during which the monthly mean of speeds > 8 decreased to its minimum value, and then gradually increased from August to December. Given the considerable wind speed and warm and dry weather in the iPNW, wind erosion is more severe in late summer or early fall than in other periods48,55. The trend analysis (y =  − 0.02x + 9.74, R2= 0.07, p = 0.42) suggested that the monthly rate was 0.02 m s−1. Seasonally, the wind speed increased in fall and winter, but declined in spring and summer with higher average wind speeds in the fall and winter.

Fig. 3
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Characteristics of intra-annual variations in the monthly mean of speeds > 8 calculated from hourly wind speeds greater than 8 m s−1 across stations in the iPNW.

The means of speeds > 8 and hours > 8 in the spring generally had consistent patterns (Fig. 4a). For the seasonal mean speeds > 8, the lowest value of > 8 m s−1 (9.52 m s−1) occurred in spring 2017, and the highest value (10.30 m s−1) occurred in spring 2013. For hours > 8, the lowest value of > 8 m s−1 (170 h) occurred in spring 2017, whereas the highest value (364 h) occurred in spring 2012. However, the patterns of the seasonal mean of speeds > 8 and hours > 8 are similar in summer, fall, and winter, thereby indicating that the mean of speeds > 8 is closely connected with hours > 8. However, the lowest values of the seasonal mean of speeds > 8 occurred in the summer and fall of 2017 (9.10 m s−1 and 9.70 m s−1, respectively). Meanwhile, the highest values were in the summer and fall of 2010 (9.61 m s−1) and 2013 (Fig. 4b,c), respectively (10.65 m s−1). In 2017, the seasonal hours > 8 were 76 h in summer and 145 h in fall, whereas the seasonal hours > 8 were 151 h in summer, 2010 and 264 h in fall 2013. When compared to those in spring, summer, and fall, the mean of speeds > 8 h and hours > 8 h varied over the winter. However, the patterns for the mean of speeds > 8 and hours > 8 were mostly stable in winter (Fig. 4d). The lowest seasonally mean of speeds > 8 (9.49 m s−1) occurred in 2010, while the highest (11.10 m s−1) occurred in 2014. Seasonal hours > 8 reached their maximum point in winter 2014 (439 h) and their lowest point in winter 2010 (121 h). These findings have shown a large seasonal fluctuation in wind, which can be explained by the influence of various weather systems on the wind in different seasons. The intensity of the seasonal monsoon also affects the wind direction and speed. In addition, there are other scales at which wind fluctuations can be observed, including seasonal, interannual, and interdecadal variations22. From 2009 to 2018, there was a tendency toward a progressive decline in the mean of speeds > 8 and hours > 8, with 2017 being the lowest point. The winds were more intense in spring and winter than in summer and fall. The trend of hours > 8 and seasonal variance of mean speed > 8 remained constant.

Fig. 4
Fig. 4
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Seasonal variation in the mean of speeds calculated according to hourly wind speed greater than 8 m s−1 and the total number of seasonal hours with speeds greater than 8 m s−1 across stations in the iPNW.

Figure 5 shows the monthly hours > 8 recorded for each month at 13 local meteorological stations, which varied from 0 to 375 h. Three sites encountered wind speeds of > 8 m s−1 between 0 and 400 h, whereas five stations experienced > 8 m s−1 wind speeds between 0 and 250 h. The St. John, Broadview, and Anatone stations (Fig. 8h,m,g) were hit by high winds (> 8 m s−1) over 372, 372, and 375 h, respectively. The wind speeds in the area were relatively stable from 2009 to 2018, except for a few stations that experienced extremely high wind conditions. The high > 8 m s−1 wind speeds recorded at St. John and Broadview stations indicate that nearby areas experienced stronger winds for longer periods. A few monthly hours > 8 h were recorded at the Ringold, Badger Canyon, and Konnowac Pass stations, indicating that the wind was relatively weak and short-lived in these areas. Given that annual hours > 8 were closely related to the annual mean wind speed based on the regression analysis, the longer the sustained wind speed, the greater the mean wind speed (y = 0.01x + 9.17, R2 = 0.88). There were substantial wind pattern variations among the different sites and landforms.

Fig. 5
Fig. 5
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The observed and simulated monthly total number of hours with speeds greater than 8 m s−1. Dashed lines represent 1:1 line.

Hourly simulations of near-surface wind speeds over the iPNW

Hourly near-surface wind speeds at the 13 meteorological stations in the iPNW from 2009 to 2018 were simulated using the WEPS. The WEPS successfully recreated hourly wind speeds and directions for many consecutive years in the most significant wind-erosion zones in the United States73. WEPS (2.0) simulates the near-surface wind characteristics of a particular location using a histogram of hourly wind speed/direction probability tables. For locations outside the weather stations in the WEPS database, the hourly wind speed data were simulated using the spatial interpolation approach and a histogram of hourly wind speed/direction probability. The simulated monthly hours of > 8 h at the 13 meteorological stations are shown in Fig. 5. Monthly hours > 8 for the 13 stations ranged from 0 to 330 h. Nine stations had hours between 0 and 120 h, three stations had hours between 0 and 250 h, one station had hours between 0 and 400 h, the Triple-S and Badger Canyon stations had hours between 136 and 150 h, and the Broadview station had hours between 136 and 150 h. By comparing the observed wind data, the simulated wind speed values tended to be smoother than the observed values. For instance, the maximum and minimum simulated monthly hours > 8 were found to be at the Broadview and Anatone sites, with values of 330 and 75 h, respectively. The maximum and minimum observed monthly hours > 8 was 375 and 15 h at the Anatone and Konnowac Pass sites, respectively. The simulated wind speeds had fewer fluctuations, smaller amplitudes, and longer periods than the actual wind speeds, which fluctuated more frequently with higher amplitudes and shorter periods (Fig. 6). This suggests that the observed values were more susceptible to extremes.

Fig. 6
Fig. 6
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The observed and simulated monthly mean of speeds calculated by hourly wind speed greater than 8 m s−1 (a) and the monthly total number of hours with speeds greater than 8 m s−1 (b) at the Triple-S site.

Performance of the WEPS in simulating hourly wind speed within the iPNW

In this study, six wind speed characteristics at the 13 stations (Fig. 7), along with the spatial interpolation method, were used to verify the performance of the WEPS model in simulating the hourly near-surface wind speed. Initial WEPS adequately simulated monthly hours > 8 (d > 0.5) at 7 of 13 stations and the d values are 0.56, 0.52, 0.50, 0.60, 0.50, 0.50 and 0.60 at Triple-S, Pullman, St. John, Wheeler, Mae, K2H, Mae respectively. However, the model was not suitable for simulating wind speeds at other six sites. The observed annual mean wind speed, annual mean of speeds > 8, annual hours > 8, annual days > 8, monthly mean of speeds > 8, and monthly hours > 8 were not consistent with those simulated by WEPS at the McClure site. The d values are less than 0.5, and RMSE error only smaller annual mean wind speed, annual mean of speeds > 8, and monthly mean of speeds > 8. Figure 7 shows an example (McClure site) of the observed and simulated values of the six wind speed characteristics. Lower d values of the index of agreement (d > 0.43) suggest that the performance of the model was relatively poor for the McClure site. Table 5 shows the model’s performance in simulating monthly hours > 8 at all 13 sites. Figure 7 also illustrates the regression relationships between model estimates and observations for the six metrics at the McClure site, showing that the WEPS underestimated the annual mean wind speed (y =  − 0.87x + 6.76), annual mean of speeds > 8 (y =  − 0.07x + 10.30), annual hours > 8 (y =  − 0.13x + 568.19), annual days > 8 (y =  − 0.03x + 119.24) and monthly hours > 8 (y =  − 0.11x + 46.69). The initial WEPS did not appear to perform well in simulating the hourly wind speed within the iPNW.

Fig. 7
Fig. 7
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An example of observed and simulated values of annual mean wind speed, annual mean of speeds > 8, annual hours > 8, annual days > 8, monthly mean of speeds > 8, and monthly hours > 8 at the McClure site. Dashed lines represent 1:1 line.

Table 5 Statistical relationships between the observed and simulated monthly hours > 8 at 13 selected meteorological stations in the iPNW.
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Figure 5 shows the regression relationships between the model estimates and observations for the 13 stations. Regression lines above the 1:1 line indicate that the model overestimated hourly wind speeds at three stations, whereas regression lines below the 1:1 line indicate that the hourly wind speeds were underestimated at three stations. Regression lines that intersect the 1:1 line indicate that the model overestimated smaller hourly wind speeds, but underestimated larger hourly wind speeds at seven stations. There was no evidence that the model consistently overestimated or underestimated the hourly wind speed at all stations. Thus, the model appears to perform differently at different stations, suggesting that the poor model performance may be related to the characteristics of each individual station.

The iPNW was surrounded by several high mountains, and traversed by the Columbia river and Snake rivers74. Most spatial interpolation techniques rely on spatial distances and surface complexity51,52. The complex topography and geomorphology of the iPNW may be one of the reasons why the WEPS model was unable to adequately describe the wind speed in the region. Fred Fox, the creator of WEPS, created a particular interpolation method in which WEPS operates in “NRCS mode”. In this WEPS wind speed interpolation, the WEPS weather sub-model uses site records associated with the selected site if it is inside the selection polygon. Otherwise, the sub-model performs interpolation to create a temporary interpolated site if it is outside the selection polygon but inside the interpolation region polygon. The granularity of the interpolation in the WEPS was set to the county boundary level such that the same interpolated WINDGEN station would be used for all simulations within a single county. Discrepancies are caused by the interpolation method used to simulate the wind speed75. Wind speeds are affected by a wide range of factors such as different subsurface characteristics, elevations, topographies, latitudes, air temperatures, and precipitation76,77,78, although the WEPS interpolation minimizes the uncertainty associated with the interpolation method32. Interpolation can be used to estimate temperature79, precipitation80, and other meteorological parameters, but still demonstrates uncertainty when used for wind speed. Reinhardt and Samimi78 assessed the performance of 12 different interpolation methods for winds over the mountainous regions of Central Asia to determine whether an optimal interpolation method exists and found that the explanatory variables improved the interpolation results. Luo77 compared seven spatial interpolation methods, but none adequately simulated the wind speed variations in southwest England and Wales. To determine which set of variograms, and nonlinear kriging techniques is optimal for describing and interpolating wind data, ten sets were analyzed by Asa80, who indicated that the study should be expanded to additional kriging models to evaluate their performance. Owing to variations in geographical breadth and time scales, the spatial and temporal variability of data is defined by the variable spatial and temporal variabilities, thereby leading to diverse spatial and temporal interpolation approaches76. Therefore, the inverse distance weights used by the WEPS for spatial interpolation may be a reason for the inadequate simulation. Instead of using observations away from the WEPS database site, that is, WSU wind-speed data, real-time data observed in situ at the WEPS database site were used to validate the model. The impact of spatial interpolation was removed to improve the accuracy of WEPS.

Performance of the WEPS in simulating hourly wind speed in absence of interpolation

Six wind speed characteristics, namely, annual mean wind speed, annual mean of speeds > 8, annual hours > 8, annual days > 8, monthly mean of speeds > 8, and monthly hours > 8 (Figs. 8 and 9), were chosen to test the effectiveness of the WEPS model in simulating hourly near-surface wind speeds. In the absence of interpolation, the WEPS model exhibited strong alignment for simulating wind speeds, and the model’s simulated monthly hours > 8 values were accurate (d > 0.5) at nine stations (Fig. 8), for example, El-lensburg2 Narr Station: 0.69 (Fig. 8a), Pendleton Municipal Station:0.59 (Fig. 8c), La Grande (awos) Sta-tion:0.84 (Fig. 8d), Yakima Air Terminal Station:0.66 (Fig. 8e), Lewiston (Amos) Station:0.65 (Fig. 8h), Walla Walla Rgnl Station:0.61 (Fig. 8j), Fairchild Afb Station:0.57 (Fig. 8k), Pullman/Moscow Rgnl Station:0.65 (Fig. 8l), and Wenatchee/Pangborn Station:0.91 (Fig. 8f). The greater number of regression lines intersecting the 1:1 line (11 of 13 sites) is encouraging because intersection suggests that model doesn’t consistently overestimate or underestimate hourly wind speed, that is, regression lines that intersect the 1:1 line are likely to indicate good model performance (Fig. 8). In contrast, when spatial interpolation was included, the WEPS model performed well (d > 0.5) at only seven locations (Fig. 5). Compared with the simulations that used spatial interpolation with the 1st set of wind speed data, the simulation performance improved by 16% ((9 − 7)/13 × 100%). The d-values based on the NCDC wind data set, that is, the second set of wind speed data, were significantly higher than those based on the WSU wind data set, that is, the first set of wind speed data. The d-values between the simulated and observed monthly mean of speeds > 8 according to the NCDC wind data set were greater than those based on the WSU wind data set (Table 6) for all six characteristics at all 13 selected sites. The performance of WEPS in simulating the annual mean wind speed, annual mean of speeds > 8, and annual days > 8 based on the NCDC wind data set was better than that based on the WSU wind data set at nine sites based on greater d-values. The performance of WEPS in simulating the annual hours > 8 at 11 sites and in simulating the monthly hours > 8 at 13 sites was improved by using the NCDC wind data set based on greater d-values than those using the WSU data set. The performance of the WEPS in simulating the hourly wind speed was improved by avoiding interpolation.

Fig. 8
Fig. 8
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Observed and simulated by WEPS in absence of interpolation monthly total number of hours with speeds greater than 8 m s−1 at 13 meteorological stations across iPNW. Dashed lines represent 1:1 line.

Fig. 9
Fig. 9
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Comparative analysis of observed and simulated by WEPS in absence of interpolation values of annual mean wind speed, annual mean of speeds > 8, annual hours > 8, annual days > 8, monthly mean of speeds > 8, monthly hours > 8 at the Wenatchee Pangborn site. Dashed lines represent 1:1 line.

Table 6 Comparison of d-values of two sets of wind speed data for six wind speed characterization metrics, that is, annual mean wind speed, annual mean of speeds > 8, annual hours > 8, annual days > 8, monthly mean of speeds > 8, monthly hours > 8 for the 13 selected sites on the iPNW.
Full size table

The WEPS adequately simulated the hourly wind speed at the Wenatchee Pangborn site based on a high d (> 0.5) for four metrics (Fig. 9). For example, d values of 0.50 for the annual mean wind speed, 0.64 for annual hours > 8, 0.59 for annual mean of speeds > 8, 0.91 and monthly hours > 8. In contrast, the WEPS inadequately simulated the hourly wind speed at the site for all wind characteristic wind speed metrics except for monthly hours > 8 when the simulated hourly wind was generated using spatial interpolation (Table 6). All the d values were less than 0.5, and the root mean square error (RMSE) was smaller except for the annual hours > 8, and monthly hours > 8. The results demonstrate that the performance of the WEPS in simulating the hourly wind speed was improved by avoiding interpolation (Table 6). Van Donk53 previously indicated that the WEPS accurately yielded simulations of annual mean soil loss and wind speeds in La Junta, Colorado, Sidney, Nebraska, and Pendleton, Oregon. The findings of the present study demonstrate that the WEPS weather sub-model can adequately simulate wind speed for potential wind erosion hazard assessment when avoiding the use of its spatial interpolation module but may produce uncertainties when invoking its spatial interpolation.

Earlier versions of WEPS (version 1.0) used the two-parameter Weibull model to fit wind speed distributions and then to predict hourly wind speed. However, the Weibull model predicted unreasonable hourly wind speeds, even speeds exceeding 100 m s-1, when modeling was based on high hourly wind data (van Donk et al., 2005), which may result in considerable overestimation off wind erosion risk. Although the hourly wind speed simulation performance of the current version of WEPS (version 2.0, using histogram) was acceptable in the iPNW, points falling below the 1:1 line, relatively small slopes (< 1) of regression, and negative DOM (Fig. 8) suggest that the model may have a tendency to underestimate observed hourly wind speeds. Pragmatically, this suggests that model users should consider the possibility that WEPS may underestimate wind erosion risk in the iPNW and plan implementation of conservation practices accordingly.

Using WEPS to optimize shelter practices and land management decisions for wind erosion control

In this study, we validated the ability of the WEPS to simulate hourly wind speeds in the iPNW and found that WEPS could accurately simulate wind speeds when its spatial interpolation was disabled. When protective practices are constructed to ease wind erosion in the iPNW, the wind speed and direction should be considered to achieve the best protective effect and make adaptive land management decisions. WEPS requires “barriers” (e.g., shelter forests and fences) to set the eroded boundary. The parameters of these barriers include their heights, densities, widths, and locations; however, different tree species have differing effects on wind erosion. Future research should therefore test the WEPS barrier module’s performance on the impacts of wind erosion processes. The WEPS barrier module should also be expanded to include more protective forest schemes to optimize shelter forests for wind erosion control. In general, the WEPS can be a useful tool for yielding hourly wind speed, particularly when highly precise wind speed data are required to interpret farmland biophysical processes related to mass and energy exchanges among the biosphere, hydrosphere, and atmosphere81.

Conclusions

Hourly near-surface wind speed observations from the WSU and NCDC wind speed data sets from iPNW, USA, were compared and analyzed with the results simulated by the WEPS to test the accuracy of the WEPS weather sub-model in simulating wind speed in the iPNW. The WEPS model was ineffective at some stations, particularly those where the model applied its spatial interpolation module. We assumed that this may have been related to the complex topography and geomorphology of the iPNW, making accurate wind forecasts challenging when the model used spatial interpolation approach. The performance of the WEPS in simulating hourly wind speeds was improved by removing the impact of spatial interpolation. Strong wind causes a series of environmental and agricultural problems such as wind erosion, dust emissions, drought, soil organic carbon loss, and disasters due to windstorms in the rainfed area of the iPNW. Therefore, planting trees would increase forest coverage and aerodynamic roughness, while decreasing dust emission rates. Future work should evaluate the effects of wind on these environmental problems and agricultural concerns by incorporating the WEPS weather sub-model into regional environmental and agricultural models, as well as determining the effects of shelter forests on wind erosion and quantifying the impact of wind on ecosystems in response to future climates. Model accuracy when simulating near-surface wind speeds must be clearly reported to allow for the appropriate selection of shelter forest and agricultural land management practices to control wind erosion, which could result in the over or under protection of soil resources.