Prediction of wind speed in complex topography is integral to the design and operation of civil infrastructure (e.g., Baker et al., 1985; Huang and Xu, 2013; Ngo and Letchford, 2009), siting and optimization of wind energy resources (Barthelmie et al., 2009; Badger et al., 2014; Wilczak et al., 2015; Brahimi, 2019; Haupt et al., 2019; Olson et al., 2019; Santoni et al., 2020), forest management (e.g., Quill et al., 2020), and meteorological forecasting (e.g., Finnigan et al., 2020; Donadio et al., 2021). Within the context of wind loads on structures, surface gusts occurring in a flat expanse can double in magnitude upslope (Kondo et al., 2002), quadrupling the loads occurring on low-rise buildings. Therefore, modern wind load provisions (e.g., ASCE 7–16) account for the presence of hills, escarpments, and other topographic features through provisioning of rational engineering analysis for simple landforms or special wind region maps for areas that have complex topography. Additional methods to account for complex terrain in structural design include wind tunnel testing and computational fluid dynamics (CFD) simulation. While over time CFD will likely become the dominant method to predict speedup, these methods are still computationally expensive, time intensive, and occasionally prone to not resolving flows in complex terrain well. Thus, this study explores the use of shallow neural networks, which are excellent universal function approximators when trained properly (Hornik et al., 1989).

Flow over isolated topographic features has been studied for decades (e.g., Taylor and Teunissen, 1987; Salmon et al., 1998), later extending to the study of complex landforms (e.g., Chock and Cochran, 2005; Rasouli et al., 2009; Kikuchi and Ishihara, 2012; McAuliffe and Larose, 2012; Lange, 2016). The present research adds to the body of work that uses data-driven methods to predict speedup, using six mountainous regions in mainland Puerto Rico and the municipal islands of Vieques and Culebra as the study testbed (Figure 1). Multiple shallow neural network configurations are applied to surface velocity measurements obtained from boundary layer wind tunnel (BLWT) modeling of complex terrain, including coastal-to-mountain transitions and inner mountain ranges. The results support the efficacy of this approach for rapid and computationally inexpensive prediction of wind speedup in complex topography using digital elevation model (DEM) data. We conclude that BLWT topographic modeling data obtained from different facilities should be warehoused in a single, openly accessible data atlas to validate, improve, and cross-compare the results of predictive models for a wide range of terrain and land cover types.

Motivating the study is the impact of Hurricane Maria (2017), which struck the island as a Saffir Simpson Hurricane Wind Scale Category 4 storm that caused more than 4,000 deaths (Kishore et al., 2018), $90B in economic loss (Pasch et al., 2019), and widespread power outages that occurred for more than 6 months (Kwasinski et al., 2019). The National Hurricane Center (Pasch et al., 2019) speculated that “winds of category 5 intensity were almost certainly felt at some elevated locations on the island,” which was further evidenced by post-storm damage assessments led by the FEMA Mitigation Assessment Team (Bass et al., 2018) and Prevatt et al. (2018). The testbed encompasses many of the most heavily impacted areas, as data were collected at the request of the FEMA Building Science Branch for the development of a special wind region map that was later adopted by the 2018 Puerto Rico Construction Code. The selection of these six regions during this study considered Hurricane Maria’s path, location of urban areas, and terrain complexity parameters (i.e., elevation, slope, curvature, and rugosity) calculated using ArcGIS and DEM Surface Tools for ArcGIS (Jenness, 2013). Table 1 lists the corresponding range of values for elevation, slope, curvature, and rugosity. Data collected for this project are available for download at the National Science Foundation Natural Hazards Engineering Research Infrastructure (NHERI) DesignSafe site (www.designsafe-ci.org). ¹

Sensitivity analyses were conducted on multiple configurations of shallow neural networks. Figures 9, 10 present results for single and double hidden layer network configurations, respectively. The number of neurons was parametrically increased from 10 to 150 neurons for the single hidden layers and 10 to 80 neurons for the double hidden layers, in steps of 20 neurons. Fine (10 m) and coarse (100 m) horizontal DEM input resolutions were evaluated separately for each network. Results are stratified by the upwind terrain (smooth-to-rough transition, rough) and horizontal fetch resolution. The box and whisker markers characterize coefficients of determination (R ² ) based on 10 training sets, comparing predicted to measured values of M _zt . Complementary values for root-mean-square-error (RMSE) are also given.

In all model configurations, R ² and RMSE vary little for the lower neuron counts, ranging from approximately 0.65–0.75. Larger neuron counts produce a slight improvement for the rough terrain cases but reduce the accuracy of the model for three of four smooth-to-rough transition cases. This degradation in the model is the worst for the double hidden layer case (Figure 10A). The only model that shows improvement as the number of neurons increases is the rough terrain case using 100 m horizontal fetch resolution (Figure 9D), however the marginal improvement is far outweighed by the increased computational expense. For example, training a 150 neuron model takes approximately 30 times longer than training the 10 neuron model. Similarly, the use of a fine (10 m) resolution DEM input data slowed down the training process and did not improve the performance when compared to the use of a coarse (100 m) DEM.

Figures 11, 12 present the testing, training, and validation results for two cases of the smooth-to-rough transition and rough terrain models using 30 and 150 neuron single hidden layer architectures, respectively. Data are stratified by the magnitude of the speedup value. Testing the neural network on data yields R ² values of 0.67 and 0.74 (and RMSE values of 0.11 for both cases), exceeding the observed R ² value of 0.5 by Chock and Cochran (2005). The neural network performance was compared to the linear regression method, using the same data for the training, and testing of the neural network. The linear model performance on the stratified data resulted in R ² of 0.65 and 0.61. Notably, the neural network models exhibit less variability between runs as the speedup value increases.

The encouraging results of these sensitivity tests support the use of simple configurations of neural networks for predicting topographic effect multipliers in complex terrain directly from the elevation data. To simplify this approach further, single hidden layer models were trained using data from all terrain types. This modification has the effect of reducing any benefit of stratifying the upwind terrain types but beneficially increases the size of the data available for training, testing, and validation.

Figure 13 presents the R ² and RMSE box and whisker plots based on neuron count for the “all upwind terrain” case. Figure 14 presents the results from training, testing, and validation for a single model. The results yield similar R ² and RMSE values as the terrain stratified model results given in Figures 9–12, indicating that stratifying the data by upwind terrain type did not produce any appreciable improvement in the modeling.

Returning to the primary goal of producing maximum topographic effect multiplier maps, a 30-neuron model with coarse horizontal fetch resolution and no stratification of approach flow condition was trained (R ² = 0.819, RMSE = 0.09) and then applied to the six study regions. To create the maps, data were extracted in a 50 m horizontal resolution grid from a gridded interpolant of the DEM data. The same DEM interpolant was then used to extract the fetch elevation data at 100 m intervals (coarse resolution) ranging from 2 km upwind to 1 km downwind for 16 wind angles. For each grid location and each wind angle, the elevation fetch data were input to the neural network to predict the gust topographic effect multiplier specific to that location and wind angle. Finally, the largest multiplier over all wind angles was determined and plotted in the Figure 15.

Ground truth over the study regions is not available to draw a quantitative comparison to the neural network outputs, but qualitatively it is observed that the gradation of the topographic effect multipliers matches expectations. Values are less than unity in valley regions, approach unity in flat open expanses, and reach 1.6–1.7 for the upper slopes of the mountains. The upper bound compares favorably to previous studies of topographic effect multipliers for surface gusts, e.g., Kondo et al. (2002), Glanville and Kwok (1997), and Bowen and Clucas (1992), which give values of 1.6–1.8. Further, the computational expense of producing these maps, which cover 121 km² at a 50 m resolution, is approximately 5 mins using a single compute core on a laptop. With parallelization, it should be possible to compute a map for the entire island of Puerto Rico within a day or less.

The study provides initial proof-of-concept that shallow neural networks may offer an alternative and computationally inexpensive approach to produce topographic wind speedup maps such as the “special wind regions” in ASCE 7. A shallow neural network was successfully trained using digital elevation data (inputs) and surface velocity measurements taken at 25 m FS over 1:3,100 scale models of regions of Puerto Rico and its municipal islands (outputs). Training a neural network requires voluminous amounts of data, thus data collection was automated to conduct high throughput experimentation, making it possible to collect hundreds of measurements per day. Six 4 m diameter models were tested in BLWT for approximately 2 weeks, producing 5,968 records measured from 373 unique geographic locations in 16 wind directions. Feed forward neural networks were trained varying the number of hidden layers, comparing different horizontal resolutions of the DEM data (input) and by stratifying the approach flow conditions. It was ultimately found that low neuron count, single hidden layer networks are sufficient to train models to predict topographic effect multipliers, which opens the door to applying the model to similar terrain in other parts of Puerto Rico. Sensitivity studies revealed that stratifying the approach flow conditions before training and using as input a finer (10 m) resolution of the DEM data did not cause a significant improvement in the predictive performance of the neural network. Lastly, six topographic wind speedup maps provide predictions over six complex terrain regions, demonstrating the computational advantage of using this methodology.

We conclude that this approach could be extended to other terrain and land-use/land-cover (LULC) types if the BLWT dataset was expanded to other geographical regions, particularly those that possess different gross physical features, taller landforms, and landform elements atypical to the terrain evaluated in this study. Synthetic topography could also be generated from target information about elevation, slope, curvature, and rugosity, with variations in surface roughness introduced to model LULC effects. The results from these studies could be combined to create a shared global topographic wind speedup database that warehouses BLWT experimental data to validate, generalize, and cross-compare predictive modeling and ultimately reduce the need for the extremely laborious physical testing required to collect these data. Alternatively, these data could augment existing field measurement atlases such as the New European Wind Atlas (Mann et al., 2017).

Future research will be required to standardize experimental methods and data processing to achieve this vision. Our experience with this study, a thorough review of the literature, and follow up discussions with other BLWT modelers led us to identify multiple key areas that warrant further investigation. Examples of topics include:

• Revisiting the acceptable range of geometric scales. The accepted upper bounds for geometric scaling (∼1:2,500—1:6,000) appear to originate from early BLWT tests on low hills free of obstructions (e.g., trees). While the Reynolds number requirement u ∗ k s / ν > 70 can be relaxed without loss of simulation accuracy (Taylor and Teunissen, 1987), it is questionable if the relaxation will hold for more complex environments (Bowen, 1983)—particularly for mountainous landforms that are (partially) covered in tree canopies. Further, the effect of geometric scale on the observed power spectra has received scarce discussion in the literature. As McAuliffe and Larose (2012) and the current (1:3,100 scale) study observed, analysis of the power spectra clearly indicate that surface (10–25 m FS) measurements sample the eddy surface layer, not the inertial sublayer.