Wind Field Modeling over Hilly Terrain: A Review of Methods, Challenges, Limitations, and Future Directions

Abstract

Accurate wind field modeling over hilly terrain is critical for wind energy, infrastructure safety, and environmental assessment, yet its inherent complexity poses significant simulation challenges. This paper systematically reviews this field’s major advances by analyzing 610 key publications from 2015 to 2024, selected from core databases (e.g., Web of Science and Scopus) through targeted keyword searches (e.g., ‘wind flow’, ‘complex terrain’, ‘CFD’, ‘hilly’) and subsequent rigorous relevance screening. We critique four primary modeling paradigms—field measurements, wind tunnel experiments, Computational Fluid Dynamics (CFD), and data-driven methods—across three key application areas, filling a gap left by previous single-focus reviews. The analysis confirms CFD’s dominance (75% of studies), with a clear shift from idealized 2D to real 3D terrain. Key findings indicate that high-fidelity coupled models (e.g., LES), validated against benchmark field experiments such as Perdigão, can reduce mean wind speed prediction bias to below 0.1 m/s; and optimized engineering designs for mountainous infrastructure can mitigate local wind speed amplification effects by 15–20%. Data-driven surrogate models, represented by FuXi-CFD, show revolutionary potential, reducing the inference time for high-resolution wind fields from hours to seconds, though they currently lack standardized validation. Finally, this review summarizes persistent challenges and outlines future directions, advocating for physics-informed neural networks, high-fidelity multi-scale models, and the establishment of open-access benchmark datasets.

1. Introduction

According to statistics, mountainous regions account for approximately 24% of the Earth’s surface, including 33% of Eurasia, 19% of South America, 24% of North America, and 14% of Africa [1]. As shown in Figure 1, the map illustrates the world’s major mountain ranges. Over the past decade, with the ongoing development of mountainous areas, an increasing number of infrastructures such as long-span bridges, transmission lines, and wind farms have been constructed. The design life and safety of these structures are largely dependent on the precise assessment of local wind fields. However, the accuracy of wind field modeling over hilly terrain represents a significant and persistent challenge, and inaccurate modeling carries severe real-world consequences: underestimation of wind loads can lead to catastrophic structural failure; erroneous assessment of wind resources can result in substantial economic losses for wind farms; and inaccurate prediction of pollutant dispersion can endanger public health and ecological safety during industrial accidents. Therefore, high-fidelity modeling of wind fields over hilly terrain has become a critical frontier of scientific inquiry.

In wind engineering and atmospheric science, the connotation of relevant terminology has evolved. In its former, narrow sense, the term “hilly terrain” primarily referred to idealized landforms composed of relatively regular two-dimensional (2D) ridges or three-dimensional (3D) isolated hills, often used for mechanistic analysis and model validation [2]. However, in the current, broader perspective, its meaning has expanded significantly to encompass both these regular topographies and the “complex terrain” found in the real world, which consists of irregular landforms such as multiple mountain ranges, valleys, and steep slopes [3]. When near-surface wind flows over these topographies, its physical properties undergo drastic changes. For an ideal 2D ridge, the airflow decelerates on the windward slope, accelerates significantly over the crest, and then decelerates again on the leeward side [4], as shown in Figure 2. For a 3D hill, the situation becomes substantially more complex, with the airflow separating behind the crest to form large-scale recirculation zones and intricate vortex structures [5]. This transition from 2D to 3D marks an exponential increase in wind field complexity and poses a fundamental challenge to traditional modeling methods. This review will adopt a broader perspective, encompassing studies on various terrains from idealized hills to real complex topographies.

Two primary approaches are commonly employed: experimental methods (full-scale on-site monitoring and reduced-scale wind tunnel testing) and numerical methods. Notably, this review focuses on the period after 2015, as the last decade has been a critical phase of a fundamental “paradigm shift” in the field. This shift is driven by four key factors: first, the leap in High-Performance Computing (HPC) capabilities has transformed high-fidelity Large Eddy Simulation (LES) from an exploratory technique into a viable research tool; second, the explosive growth of Artificial Intelligence (AI) and data-driven algorithms has introduced revolutionary efficiency and new perspectives to wind field modeling [6,7]; third, the research focus has massively shifted from simulating idealized 2D terrains to modeling real 3D complex terrains, which are more aligned with practical engineering needs; finally, there is a growing academic consensus on the necessity of considering the integrated effects of multi-physics coupling, such as thermal, vegetation, and precipitation effects, on the wind field.

Previously, several excellent reviews have explored this field, as summarized in Table 1. However, an analysis of these works reveals a clear “silo effect,” where research perspectives are fragmented within distinct disciplinary domains, thereby leaving specific knowledge gaps. These reviews generally fall into two categories: The first focuses on a single methodology, such as Wani et al. [2] analyzing wind tunnel techniques or Bradley et al. on remote sensing wind measurement technologies. The second centers on specific physical phenomena or application scenarios, such as the work by Serafin et al. [8] on mountain atmospheric exchange processes and Giovannini et al. [9] on pollutant dispersion issues. This specialized fragmentation leads to two key limitations. First, while method-centric reviews are insightful, they fail to provide a critical comparative assessment across different methods. For instance, they do not elucidate the key trade-offs (e.g., cost, accuracy, feasibility, and scalability) that decision-makers require when choosing between wind tunnel experiments, high-precision Computational Fluid Dynamics (CFD), or data-driven models in an engineering context, which is vital for practical guidance. Second, application-oriented reviews fail to systematically evaluate the combined potential and constraints of the entire modern modeling toolbox (especially the tools emerging after 2015) in addressing these challenges within a unified framework. Consequently, there is a pressing need for a comprehensive review that systematically integrates physical methods (field measurements, wind tunnel experiments), numerical methods (CFD), and emerging data-driven approaches, and critically evaluates their progress, challenges, and limitations across the three core application areas: wind resource assessment, infrastructure design, and pollutant dispersion. This paper aims to fill this gap.

To this end, this review sets the following specific objectives:

• To critically and comprehensively review the key technical advancements, inherent advantages, and core limitations of the four main paradigms in hilly terrain wind field modeling since 2015: field measurements, wind tunnel experiments, CFD simulations, and data-driven methods.
• To systematically evaluate the applicability, validation challenges, and existing knowledge gaps of these modeling methods in the three major engineering applications: wind resource development, wind-resistant design of infrastructure, and pollutant dispersion.
• To identify and analyze the deep-seated, systemic challenges currently facing the field (e.g., the contradiction between high-fidelity models and sparse validation data, the inherent complexity of multi-physics coupling), and to propose a clear and actionable roadmap for future research directions.

Table 1. Previous review articles related to wind field over hilly terrain.

Review	Detail	Year	Key Findings
Bradley et al. [10]	Remote sensing winds	2015	Under the recirculating detached flow, the linear model may be inaccurate.
Serafin et al. [8]	Airflow exchange	2018	Studying diurnal boundary layer variation aids analysis of exchange processes over mountains.
Giovannini et al. [9]	Pollutant dispersion	2020	Pollutant dispersion modeling is more complicated over complex terrain.
Finnigan et al. [11]	Gravity-driven flow	2020	The study of gravity-driven flow on hillsides and valley slopes faces challenges.
Wani et al. [2]	Wind tunnel test	2021	More experimental studies on the cliff are needed.
Farina et al. [12]	Heat-driven wind	2023	Future efforts should focus on field studies over near-ideal slopes.

Table 1. Previous review articles related to wind field over hilly terrain.

Review	Detail	Year	Key Findings
Bradley et al. [10]	Remote sensing winds	2015	Under the recirculating detached flow, the linear model may be inaccurate.
Serafin et al. [8]	Airflow exchange	2018	Studying diurnal boundary layer variation aids analysis of exchange processes over mountains.
Giovannini et al. [9]	Pollutant dispersion	2020	Pollutant dispersion modeling is more complicated over complex terrain.
Finnigan et al. [11]	Gravity-driven flow	2020	The study of gravity-driven flow on hillsides and valley slopes faces challenges.
Wani et al. [2]	Wind tunnel test	2021	More experimental studies on the cliff are needed.
Farina et al. [12]	Heat-driven wind	2023	Future efforts should focus on field studies over near-ideal slopes.

2. Review Method

This review examined 610 publications, obtained primarily from major academic platforms like Web of Science, Scopus, IEEE Xplore, and ScienceDirect, alongside some peer-reviewed conference proceedings. The core analysis period is 2015 to 2024, as this decade marks a critical phase in which the field has undergone a fundamental ‘paradigm shift.’ Foundational literature before 2015 is cited to introduce historical context, while select, already-published 2025 literature is included to reflect the latest developments.

We employed a combined keyword search strategy. The core search term combinations included (‘wind field’ OR ‘wind flow’) and (‘hilly terrain’ or ‘complex terrain’ or ‘mountainous’), which were combined with keywords related to specific methods (e.g., CFD, LES, wind tunnel, field measurement, data-driven) and applications (e.g., wind energy, bridge, pollutant dispersion).

Figure 3 visually illustrates the four stages of literature screening, ensuring the traceability of the entire process. All retrieved literature underwent a rigorous screening process based on the following criteria:

Inclusion Criteria:

• The document must be a peer-reviewed journal article or a significant conference paper.
• The publication must be in English.
• The research must directly focus on the modeling or validation of wind fields over hilly/complex terrain, or their application in areas like wind energy, infrastructure, and pollutant dispersion.

Exclusion Criteria:

• Studies with low relevance to the main topic.
• Abstracts, short communications, or non-peer-reviewed literature.
• Duplicate publications (for conference papers later extended into journal articles, the more comprehensive journal version was prioritized).

These works cover topics including 2D and 3D hills as well as real-world complex terrain wind fields. Figure 4 presents the frequency and co-occurrence network analysis of keywords from these studies. It not only reveals the core concepts but, more importantly, visually corroborates the ‘paradigm shift’ thesis proposed in this review:

• Shift in Research Objects: “Complex terrain” is the most frequent and central node, far surpassing idealized keywords like “2-D hill.” This indicates a decisive shift in research focus since 2015 from idealized models to more realistic and practical complex terrains.
• Evolution of Research Methods: Methodologically, “numerical simulation,” “CFD,” and “large-eddy simulation” form a prominent cluster. Their node sizes and link densities demonstrate that numerical methods, represented by CFD, have become the dominant research tools. The frequent appearance of “large-eddy simulation,” in particular, aligns with our assessment of HPC advancements driving high-fidelity simulations post-2015. Meanwhile, “wind tunnel” and “field measurement,” as classical physical methods, remain important nodes closely connected to numerical simulation, highlighting their indispensable role in providing validation data.
• Driving Forces of Research Needs: On the application level, keywords such as “wind energy,” “atmospheric boundary layer,” “turbulence,” and “infrastructure design” (e.g., “bridge site”) also hold significant positions. This illustrates that two major engineering demands—wind resource development and infrastructure safety—are the core drivers for research on wind fields over hilly terrain.

The “paradigm shift” is not an isolated academic phenomenon; it has been shaped by a confluence of external forces.

Table 2. Key contextual drivers for research trends in hilly terrain wind field modeling.

Driver Category	Specific Driving Mechanism	Impact on Research Paradigm
Technological	Proliferation of High-Performance Computing (HPC)	Enabled high-fidelity Large Eddy Simulation (LES) to transition from a theoretical tool to a feasible research instrument, addressing the accuracy bottlenecks of RANS models.
	Rise of Artificial Intelligence (AI)/Machine Learning (ML)	Enabled rapid wind field prediction (from hours to seconds), fostering new research directions focused on real-time control and optimization.
Economic	Rapid Growth of the Global Wind Energy Market	The massive market size amplified the impact of model accuracy on economic benefits.
	Financial Impact of Annual Energy Production (AEP) Uncertainty	To secure favorable financing terms (lower cost of capital), project developers must reduce AEP prediction risks, creating strong demand for high-precision models.
Geopolitical & Policy	The Paris Agreement and Nationally Determined Contributions (NDCs)	Established a global political framework for decarbonization, using top-down pressure to compel nations to set renewable energy targets.
	National-Level Incentive pOlicies (e.g., U.S. Inflation Reduction Act)	Translated global goals into concrete financial incentives (e.g., tax credits), directly reducing the investment cost and risk of wind power projects.
	Energy Independence and Security	Positioned domestic renewable energy development as a national security strategy, reducing reliance on external fossil fuels and providing political assurance for long-term investment.

systematically analyzes how three tiers of driving forces since 2015 (technological, economic, and geopolitical) interconnected to catalyze the transformation in wind field modeling research over hilly terrain.

Furthermore, a statistical analysis reveals a significant geographical imbalance in case studies within the literature. Large-scale field observation projects and key case studies are highly concentrated in Europe (e.g., the Alps, the Perdigão mountains) and North America (e.g., the Rocky Mountains, Askervein Hill). Europe and North America form data-rich “research highlands,” whereas South America, Africa, and large parts of Asia constitute data-sparse “research lowlands.” This geographical imbalance is not merely descriptive; it represents a significant scientific risk. This bias means current mainstream modeling methods may remain unvalidated in specific climates (such as tropical highlands) or unique geomorphologies. This clearly indicates an urgent future direction for the international atmospheric science community: the critical need to conduct similar large-scale, comprehensive field observation experiments in other representative, data-sparse complex terrain regions globally.

In the following sections, this review is structured into two main parts: “Methods for wind field modeling over hilly terrain,” which discusses research methods and tools; and “Wind Fields over Hilly Terrain: Current Practical Issues,” which discusses practical challenges. Given length constraints, this review cannot be exhaustive; therefore, it emphasizes general trends, research gaps in each category, and future research needs.

3. Methods for Wind Field Modeling over Hilly Terrain

There are four primary modeling approaches for wind fields over hilly terrain: field measurements, wind tunnel experiments, numerical simulations, and the more recently emerging data-driven methods. This section aims to provide a critical and comparative assessment of these four approaches. These four methods were selected because they represent the core strategies for addressing the problem from distinct philosophical and technological standpoints: field measurements provide “ground-truth” empirical data, wind tunnel experiments conduct scaled physical simulations in controlled environments, CFD relies on numerical solutions of fluid dynamics, and data-driven methods make predictions by learning patterns from data. Section 3.1, Section 3.2, Section 3.3, Section 3.4 will then elaborate on each method in detail.

Figure 5a shows a timeline for wind field modeling methods over hilly terrain. This evolution was not arbitrary but was driven by breakthroughs in key enabling technologies. Following the classic theoretical analyses of the 1950s [13,14], the maturation of wind tunnel techniques in the 1970s made physical simulation of flow over terrain feasible [15,16]. In the 1980s, significant advances in instrumentation and data acquisition systems enabled the widespread adoption of field measurements, leading to the accumulation of substantial mountain meteorology datasets [17,18]. Since the 1990s, the exponential growth in HPC has directly propelled numerical simulation methods, particularly CFD, into the research mainstream [19,20]. More recently, since the 2010s, the proliferation of remote sensing technologies (e.g., Lidar) and the maturation of machine learning algorithms have collectively spurred the rapid emergence of data-driven approaches [21,22].

As shown in Figure 5b, publications for wind fields over hilly terrain are increasing. CFD methods maintain a dominant position, fundamentally due to the ideal balance they strike between cost-effectiveness, flexibility in handling real complex geometries, and the ability to visualize the entire flow field—advantages that are difficult for physical experiments to match. Wind tunnel experiments and field measurements, essential for providing key physical insights and validation data, rank second. Notably, the number of studies employing data-driven models has tripled since 2019 (in Figure 5b), reflecting a profound paradigm shift: As vast datasets from both simulations and observations become available, the research community is actively exploring AI to enhance predictive efficiency and tackle complex, multi-parameter problems that are challenging for traditional methods. Meanwhile, Figure 5b also highlights a critical limitation of experimental approaches: the scarcity of high-quality observational and experimental data may constrain the development, calibration, and validation of both CFD simulations and data-driven models. Therefore, future efforts should not only advance numerical and data-driven methodologies but also prioritize the advancement of experimental techniques and the accumulation of high-quality datasets.

3.1. Field Measurement

Field measurements remain the most direct and accurate approach for obtaining wind characteristics to date and are essential for determining the actual conditions of wind fields over hilly terrain. However, compared to other methods, studies focusing on field measurements are relatively scarce. Table 3 highlights that frequently investigated variables are wind speed/direction, atmospheric pressure, temperature and humidity. To capture these parameters, various devices have been employed: anemometers for wind speed and direction [23]; meteorological masts and rainfall detection sensors for precipitation [24]; and, in recent years, Doppler lidar and unmanned aerial vehicles (UAVs) have been widely used to measure parameters such as temperature, humidity, wind speed, and solar radiation [25,26]. A significant recent trend is the shift from single-instrument limitations toward integrated, multi-instrument experimental campaigns designed to comprehensively capture complex atmospheric phenomena involving multi-scale and multi-physics coupling. Some large-scale international collaborations have produced unprecedented high-resolution turbulence datasets by deploying extensive arrays of state-of-the-art instruments. The CROSSINN project [27], for example, augmented an existing network of surface flux towers with a vast suite of instruments including Doppler lidars, Raman lidars, microwave radiometers, UAVs, and research aircraft. This synergistic integration of multiple instruments not only enabled rigorous cross-validation between different measurement systems, ensuring data quality, but more importantly, it revealed complex flow phenomena that no single instrument could capture alone. While multi-instrument synergistic observation is increasingly common, understanding the precision and limitations of each instrument is crucial for data fusion and validation. As indicated in Table 4, ultrasonic anemometers on meteorological masts provide “ground-truth” data, with very high temporal resolution (>10 Hz) and wind speed uncertainties below 0.1 m/s at a fixed point, making them the preferred choice for resolving fine-scale turbulence. In contrast, Doppler Lidar provides wide-area spatial wind fields but measures a volume-averaged value, which can introduce systematic biases in complex terrain. Its measurement accuracy is typically within 0.1–0.2 m/s, and it has a measurement blind zone near the ground. Although Unmanned Aerial Vehicle (UAV) sensors offer high mobility, rotor downwash can disturb the local flow field, requiring complex correction algorithms to ensure accuracy, and their uncertainty is also relatively high. Therefore, researchers must make trade-offs between spatial coverage, data resolution, and measurement accuracy when combining these instruments.

Despite these technological advancements, several key limitations persist. As indicated in Table 3, studies predominantly focus on core parameters for wind energy development, such as wind speed, direction, and temperature, while coupled meteorological phenomena like fog, snow, and precipitation, remain relatively under-investigated. This is partly due to the performance limitations and risk of damage to sensitive instruments in harsh weather, and also because research has been primarily driven by the demands of the wind energy sector, leading to less focus on other coupled factors. Future research should adopt multi-source data fusion strategies, combining ground-based remote sensing, UAVs, and satellite observations, to capture a complete picture of complex weather processes [28].

Furthermore, current field measurements commonly either neglect or oversimplify fine-scale surface features such as vegetation, infrastructure, and micro-topography, which significantly undermines the practical value of the findings. Many studies deliberately place measurement points in ‘ideal’ open areas far from such features to obtain ‘clean’ inflow data, but as a result, they lose the understanding of the true interactions between the surface and the atmosphere [29]. Other studies simplify the complex underlying surface into a single ‘surface roughness’ parameter, which fails to capture local flow variations caused by surface heterogeneity. To address this challenge, a more pragmatic strategy has been developed in engineering practice: dividing a large, complex hilly project site into several relatively homogeneous zones for independent assessment. Although this zoning approach requires more measurement points, it significantly improves the accuracy of wind resource assessment by reducing the complexity of each study unit [30]. To enhance the generalizability of research, future measurement campaigns should advocate for high-density observation networks combined with surface morphology measurement techniques, such as Terrestrial Laser Scanning (TLS), to provide realistic boundary conditions for high-fidelity simulations.

Finally, a review of major large-scale complex terrain wind field research projects over the past decade reveals a significant geographical imbalance in study locations. A statistical analysis of the case studies mentioned in the literature (in Table 2) shows that these pioneering studies are highly concentrated in Europe and North America. On one hand, this geographical concentration reflects the scientific strength and long-term investment of European and North American countries in this field. On the other hand, it introduces a potential scientific risk. The interaction between atmospheric circulation and topography is strongly region-specific. Physical models and parameterization schemes validated in regions like the European Alps or the North American Rocky Mountains may not be directly applicable to other areas with vastly different geomorphological and climatic characteristics, such as the Himalayas or the Andes. This imbalance thus points to a clear direction for the international atmospheric science community: there is an urgent need to conduct similar large-scale, comprehensive field observation experiments in other representative complex terrain regions worldwide, especially in data-sparse areas. This will help build more globally representative datasets and drive the development of wind field models toward greater universality and accuracy.

Table 3. Field measurement research of wind fields over hilly terrain.

Author (Year)	Location	Mountain Feature	Parameter	Detail	Device
Russell et al. [31] (2016)	Idaho, the United States	A complex terrain	WS, WD, AT	The forest canopy	Sonic anemometer
Fenerci et al. [32] (2017)	Hordaland, Norway	Hardangerfjord	WS	Dynamic response, wind characteristics	Sonic anemometer, accelerometer
Chaurasiya et al. [33] (2018)	Karyatal, India	A gentle slope	WS, WD	wind resource assessment	SODAR, LIDAR
Huang et al. [34] (2019)	western China	A “Y”-shaped valley	WS, WD, AT, RH, AP	thunderstorm wind; thermally developed wind	Ultrasonic anemometers
Zhang et al. [35] (2020)	Southwest of China	A typical canyon	WS, WD, AT	Wind resource assessment	Meteorological mast, SODAR; automatic meteorological station
Radünz et al. [36] (2021)	Morrinhos, Brazil	A mixture of hills, ridges and plateaus	WS, WD, AT	Atmospheric stability	Sonic anemometer
Radünz et al. [37] (2022)	Northeastern Brazil	A plateau	WS, WD, AT	Wind farm design	Meteorological mast
Jiang et al. [38] (2023)	southwest of China	A U-shaped canyon	WS, WD, AT, P	Mixed wind climate	Sonic anemometer, automatic meteorological station, meteorological mast
Adler et al. [39] (2021)	Inn Valley, Austria	Alpine valley	AT, WS, RH, TI	Atmospheric phenomenon	Doppler, microwave radiometer, unmanned aerial vehicle, ground flux tower array
Coimbra et al. [40] (2025)	Perdigão, Portugal	Double parallel ridges	WS, TI	Wind field characteristics	Dual Doppler scanning Lidar, acoustic anemometer
Desnijder et al. [41] (2024)	Krummendeich, Germany	Wind farms in complex terrains	WS, TI	Wind farm design	High-frequency sensor, unmanned aerial vehicle swarm

WS: wind speed; WD: wind direction; AT: air temperature; RH: relative humidity; AP: air pressure; P: precipitation; TI: turbulence intensity.

Table 3. Field measurement research of wind fields over hilly terrain.

Author (Year)	Location	Mountain Feature	Parameter	Detail	Device
Russell et al. [31] (2016)	Idaho, the United States	A complex terrain	WS, WD, AT	The forest canopy	Sonic anemometer
Fenerci et al. [32] (2017)	Hordaland, Norway	Hardangerfjord	WS	Dynamic response, wind characteristics	Sonic anemometer, accelerometer
Chaurasiya et al. [33] (2018)	Karyatal, India	A gentle slope	WS, WD	wind resource assessment	SODAR, LIDAR
Huang et al. [34] (2019)	western China	A “Y”-shaped valley	WS, WD, AT, RH, AP	thunderstorm wind; thermally developed wind	Ultrasonic anemometers
Zhang et al. [35] (2020)	Southwest of China	A typical canyon	WS, WD, AT	Wind resource assessment	Meteorological mast, SODAR; automatic meteorological station
Radünz et al. [36] (2021)	Morrinhos, Brazil	A mixture of hills, ridges and plateaus	WS, WD, AT	Atmospheric stability	Sonic anemometer
Radünz et al. [37] (2022)	Northeastern Brazil	A plateau	WS, WD, AT	Wind farm design	Meteorological mast
Jiang et al. [38] (2023)	southwest of China	A U-shaped canyon	WS, WD, AT, P	Mixed wind climate	Sonic anemometer, automatic meteorological station, meteorological mast
Adler et al. [39] (2021)	Inn Valley, Austria	Alpine valley	AT, WS, RH, TI	Atmospheric phenomenon	Doppler, microwave radiometer, unmanned aerial vehicle, ground flux tower array
Coimbra et al. [40] (2025)	Perdigão, Portugal	Double parallel ridges	WS, TI	Wind field characteristics	Dual Doppler scanning Lidar, acoustic anemometer
Desnijder et al. [41] (2024)	Krummendeich, Germany	Wind farms in complex terrains	WS, TI	Wind farm design	High-frequency sensor, unmanned aerial vehicle swarm

WS: wind speed; WD: wind direction; AT: air temperature; RH: relative humidity; AP: air pressure; P: precipitation; TI: turbulence intensity.

Table 4. Commonly used instruments for field measurement research.

Instrument	Advantages	Limitations	Cost	Typical Accuracy/Uncertainty	Spatial/Temporal Resolution	Ideal Application Environment
Ultrasonic Anemometer	Provides high-precision 3D wind velocity and high-frequency turbulence data.	Limited to single-point measurements, leading to poor spatial representativeness; high installation and maintenance costs.	Moderate instrument cost, but high costs for measurement towers and long-term maintenance.	Wind speed uncertainty < 0.1 m/s; accuracy of approx. ±1% of reading.	Spatial: Point measurement (~cm) Temporal: >10 Hz	Long-term, fixed-point, high-resolution observation of boundary layer structure and turbulence at a specific location.
Doppler Lidar	High spatial coverage and relatively good portability.	Performance degrades in extreme weather; the instrument is expensive and has a near-ground measurement blind zone.	Very high acquisition and maintenance costs.	Wind speed accuracy: ±0.1~0.2 m/s; affected by volume averaging effects.	Spatial: Gate length 10–50 m Temporal: ~0.1–1 Hz (scanning mode)	Capturing meso-scale wind field structures, such as the evolution of canyon and mountain-valley winds.
Sodar	Effectively measures low-level wind profiles; relatively sensitive to temperature fluctuations.	Data quality is susceptible to background noise and ground clutter; vertical detection range and stability are generally inferior to Lidar.	Significantly lower cost compared to Lidar.	Wind speed accuracy: ±0.2~0.5 m/s.	Spatial: Vertical resolution 10–30 m Temporal: On the order of minutes	Studies of the urban boundary layer, low-level atmospheric stability, and the nocturnal stable boundary layer structure.
UAV (Unmanned Aerial Vehicle)	High mobility and portability; enables flexible measurements to rapidly acquire high-spatial-resolution data.	Limited by flight endurance and weather conditions; rotor wash can disturb the local flow field, requiring data correction.	Relatively low hardware acquisition and operational costs.	Sensor-dependent; post-correction wind speed uncertainty >0.5 m/s.	Spatial: Variable (~m) Temporal: Dependent on flight speed	A powerful complement to traditional methods, for probing fine-scale structures (e.g., ridge flow, wake regions) and measuring in inaccessible areas.

Table 4. Commonly used instruments for field measurement research.

Instrument	Advantages	Limitations	Cost	Typical Accuracy/Uncertainty	Spatial/Temporal Resolution	Ideal Application Environment
Ultrasonic Anemometer	Provides high-precision 3D wind velocity and high-frequency turbulence data.	Limited to single-point measurements, leading to poor spatial representativeness; high installation and maintenance costs.	Moderate instrument cost, but high costs for measurement towers and long-term maintenance.	Wind speed uncertainty < 0.1 m/s; accuracy of approx. ±1% of reading.	Spatial: Point measurement (~cm) Temporal: >10 Hz	Long-term, fixed-point, high-resolution observation of boundary layer structure and turbulence at a specific location.
Doppler Lidar	High spatial coverage and relatively good portability.	Performance degrades in extreme weather; the instrument is expensive and has a near-ground measurement blind zone.	Very high acquisition and maintenance costs.	Wind speed accuracy: ±0.1~0.2 m/s; affected by volume averaging effects.	Spatial: Gate length 10–50 m Temporal: ~0.1–1 Hz (scanning mode)	Capturing meso-scale wind field structures, such as the evolution of canyon and mountain-valley winds.
Sodar	Effectively measures low-level wind profiles; relatively sensitive to temperature fluctuations.	Data quality is susceptible to background noise and ground clutter; vertical detection range and stability are generally inferior to Lidar.	Significantly lower cost compared to Lidar.	Wind speed accuracy: ±0.2~0.5 m/s.	Spatial: Vertical resolution 10–30 m Temporal: On the order of minutes	Studies of the urban boundary layer, low-level atmospheric stability, and the nocturnal stable boundary layer structure.
UAV (Unmanned Aerial Vehicle)	High mobility and portability; enables flexible measurements to rapidly acquire high-spatial-resolution data.	Limited by flight endurance and weather conditions; rotor wash can disturb the local flow field, requiring data correction.	Relatively low hardware acquisition and operational costs.	Sensor-dependent; post-correction wind speed uncertainty >0.5 m/s.	Spatial: Variable (~m) Temporal: Dependent on flight speed	A powerful complement to traditional methods, for probing fine-scale structures (e.g., ridge flow, wake regions) and measuring in inaccessible areas.

3.2. Wind Tunnel Experiment

While field measurements provide the most direct representation of wind fields over hilly terrain, their high costs restrict widespread application. In contrast, wind tunnel experiments establish a crucial link among theoretical analysis, numerical simulations, and full-scale field measurements, with the primary objective of reproducing the key physical principles governing atmospheric boundary layer flow over complex terrain in a controlled laboratory environment.

The core advantages of wind tunnel experiments lie in their high degree of controllability and repeatability. Compared to field measurements subject to changing weather, wind tunnels allow for the precise setting and repetition of boundary conditions like inflow wind speed and turbulence intensity. This facilitates parametric studies that systematically reveal the influence of key terrain parameters (e.g., slope, shape) on the wind field structure. Furthermore, wind tunnels can leverage advanced measurement techniques to acquire high spatiotemporal resolution flow field data that is difficult to obtain in the field, which is vital for an in-depth understanding of fine flow structures such as flow separation, vortex shedding, and reattachment on the leeward side of hills.

Despite these advantages, the inherent limitations of wind tunnel experiments cannot be overlooked. Among these, scaling similarity, especially the “Reynolds number mismatch” problem arising from the model’s reduced geometric scale, poses the most fundamental challenge. As shown in Table 5, experiments on regular terrain typically employ a scaling ratio of approximately 1:300, whereas those involving actual complex terrain often use ratios between 1:1000 and 1:2000. However, the significant reduction in characteristic length L (i.e., the lateral width of the scale model) poses challenges for achieving Reynolds number similarity. The Reynolds number is defined as follows [42]:

$$\mathit{Re}=(\rho \mathit{UL})/\mu$$

(1)

where ρ is the air density (International System of Units: kg/m³), U is the characteristic wind speed (International System of Units: m/s), L is the characteristic length (International System of Units: m), and μ is the air viscosity (International System of Units: kg/(m·s)). In scaled-down models, the value of L is very small, while the density and viscosity of air cannot be substantially altered in the experiment. As a result, the Reynolds number in wind tunnel tests is typically much lower than that of the actual wind field prototype, leading to the “Reynolds number mismatch” problem. Even increasing U to raise the Reynolds number is often not feasible due to equipment limitations and may introduce other issues. To address the challenges of insufficient Reynolds numbers and data limitations, numerical simulation methods such as CFD have increasingly become important complementary tools. Secondly, the simulation of thermal effects is another major limitation. As summarized in Table 5, the vast majority of experiments are confined to measuring wind speed and turbulence intensity under mechanically driven neutral stratification conditions. In real mountainous areas, however, thermally driven flows such as valley and slope winds, as well as stable or unstable stratification, are often dominant. Current wind tunnel technologies struggle to economically and effectively reproduce these complex thermodynamic coupling effects, which severely limits their applicability. Despite these challenges, recent efforts to simulate thermal effects have shown progress. Some environmental wind tunnels create temperature gradients by heating or cooling the test section floor, or by using heated/cooled grids at the inlet to simulate stable or unstable atmospheric conditions [43,44]. For instance, Hancock et al. simulated a stable boundary layer by controlling the inlet temperature profile and cooling floor panels, providing a physical basis for studying nocturnal inversions [43]. Other studies reproduced convective boundary layers over complex terrain by heating the hill model, revealing different flow structures on windward and leeward slopes crucial for understanding pollutant dispersion [45]. Although these techniques are currently applied mostly to idealized 2D terrains at low Reynolds numbers, they represent a key step toward more realistic physical simulations and offer possibilities for future research on thermodynamic coupling effects.

Furthermore, the oversimplification of boundary conditions can also introduce errors. For experimental convenience, the inflow is often set as a uniform stream or a standard logarithmic/power-law profile [46]. This assumption neglects the non-uniformity and anisotropic turbulence structures caused by complex upstream terrain in the real world, potentially leading to distorted predictions of wind field characteristics in specific areas, such as a valley entrance. Concurrently, most experiments neglect climate-related external loads like rain and snow.

The choice of measurement technology is a trade-off between research objectives and cost, and it directly determines the quality of the experimental data. The studies in Table 6 utilized various instruments, with the widespread use of the hot-wire anemometer [47] and the Cobra probe [48] reflecting the historical focus on acquiring mean flow and turbulence statistics at discrete points. However, the inability of these point-measurement techniques to capture the spatial coherence of the flow field has driven the development of new technologies. This “data gap” is now being bridged by full-field measurement methods like Particle Image Velocimetry (PIV) and by CFD. PIV can provide instantaneous spatial snapshots of the flow field, but it is often limited by its high cost [49,50]. CFD, on the other hand, can provide complete, three-dimensional spatiotemporal flow field information at a relatively lower cost. Therefore, modern wind engineering research tends to combine the precision of point measurements, the spatial insight of PIV, and the full-field simulation capabilities of CFD for a more comprehensive understanding.

Ultimately, the value of a wind tunnel experiment is demonstrated by its ability to be effectively extrapolated to the real world, which depends on the representativeness of the terrain model and its consistency with field data. While large scaling ratio models (e.g., 1:1000) can accommodate a wide expanse of actual terrain, this comes at the cost of smoothing out terrain details, affecting the accuracy of the near-ground flow. Therefore, direct comparative validation against field data serves as the ultimate standard for assessing the reliability of wind tunnel experiments. A milestone case is the international Askervein Hill project, which systematically compared full-scale field measurements, wind tunnel experiments, and numerical simulations, providing a gold-standard benchmark dataset for validating model predictive capabilities [51,52]. The project’s findings showed that wind tunnels could reasonably predict the mean wind speed-up at the hilltop but exhibited deviations in accurately simulating the leeward separation zone. Specifically, comparative studies indicated that the Root Mean Square Error (RMSE) between the wind tunnel predictions of the mean speed-up ratio and the field data was approximately 0.05. The prediction error for the speed-up factor at the hilltop was typically within 5–10%, but in the leeward slope region, the prediction error for turbulent kinetic energy could exceed 30%. Recent research has continued this “field-to-wind tunnel” validation approach. For example, the work by Lystad et al. [53] combined field and wind tunnel tests to reveal significant spatial variability of the wind field at a bridge site and to validate the wind tunnel’s ability to capture these primary features. Their study showed that at key measurement points for the bridge, the coefficient of determination (R²) between the wind angle of attack from the wind tunnel simulation and the field measurements exceeded 0.85, demonstrating the experiment’s reliability. Such studies demonstrate that, despite similarity challenges, well-designed wind tunnel experiments remain a powerful tool for understanding key characteristics of hilly terrain wind fields.

In summary, for wind tunnel experiments to be successfully applied, researchers must have a profound understanding of similarity theory, instrument performance, and inherent limitations (especially concerning thermal and scale effects). Its scientific value is ultimately realized through its synergistic use with field measurements (for validation) and CFD (for providing spatial completeness and exploring processes difficult to simulate in the lab), forming an integrated research framework of mutual supplementation and verification.

Table 5. Wind tunnel experiment research of wind fields over hilly terrain.

Author (Year)	Mountain Feature	Reduced Scale	Parameter	Detail	Device	Re
Mattuella et al. [47] (2016)	Actual complex terrain	1:1000	WS, TI	Wind power utilization	Hot-wire anemometer	-
Li et al. [48] (2017)	Actual canyon terrain	1:1000	WS, WD	Bridge site	Cobra probe	-
Lystad et al. [53] (2018)	Actual complex terrain	1:2000	WS, WD, TI	Long-span bridge; nonuniform wind field	Hot-wire anemometer	≈7.1 × 105
Tian et al. [54] (2018)	2D hill; 3D hill	1:320	WS, TI	Wind power utilization	Cobra probe	<7000
Kamada et al. [55] (2019)	2D hill	1:200	WS, TI	ABL	PIV	≈2.5 × 105
Shen et al. [56] (2021)	Actual mountain pass	1:1000	WS, WD	Long-span bridge; nonuniform wind field	Cobra probe	-
Zhu et al. [57] (2022)	2D slope	1:20	WS, TI	Railway infrastructure	Cobra probe	≈1.0 × 105
Raffaele et al. [58] (2023)	2D hill	-	WS, TI	Wind–sand coupling	PIV	=7.4 × 104
Wu et al. [59] (2025)	2D hill	1:1000	WS, TI	Pollutant dispersion	LDV	-

WS: wind speed; WD: wind direction; TI: turbulence intensity.

Table 5. Wind tunnel experiment research of wind fields over hilly terrain.

Author (Year)	Mountain Feature	Reduced Scale	Parameter	Detail	Device	Re
Mattuella et al. [47] (2016)	Actual complex terrain	1:1000	WS, TI	Wind power utilization	Hot-wire anemometer	-
Li et al. [48] (2017)	Actual canyon terrain	1:1000	WS, WD	Bridge site	Cobra probe	-
Lystad et al. [53] (2018)	Actual complex terrain	1:2000	WS, WD, TI	Long-span bridge; nonuniform wind field	Hot-wire anemometer	≈7.1 × 105
Tian et al. [54] (2018)	2D hill; 3D hill	1:320	WS, TI	Wind power utilization	Cobra probe	<7000
Kamada et al. [55] (2019)	2D hill	1:200	WS, TI	ABL	PIV	≈2.5 × 105
Shen et al. [56] (2021)	Actual mountain pass	1:1000	WS, WD	Long-span bridge; nonuniform wind field	Cobra probe	-
Zhu et al. [57] (2022)	2D slope	1:20	WS, TI	Railway infrastructure	Cobra probe	≈1.0 × 105
Raffaele et al. [58] (2023)	2D hill	-	WS, TI	Wind–sand coupling	PIV	=7.4 × 104
Wu et al. [59] (2025)	2D hill	1:1000	WS, TI	Pollutant dispersion	LDV	-

WS: wind speed; WD: wind direction; TI: turbulence intensity.

Table 6. Comparison of common measurement techniques in wind tunnel experiments for hilly terrain.

Instrument	Key Measured Parameters	Accuracy	Resolution	Advantages	Limitations	Cost and Feasibility	Ideal Applications
Hot-wire Anemometer (HWA)	Velocity magnitude, high-frequency turbulent fluctuations	~1–2%	Spatial: Very high (~1 mm) Temporal: Very high (>100 kHz)	Excellent for measuring turbulence spectra and Reynolds stresses. Relatively low cost	Intrusive and fragile probe. Requires frequent calibration; sensitive to temperature.	Medium cost, high maintenance. Probes are fragile and need frequent calibration; time-consuming for large-scale flow mapping.	Characterizing fine-scale turbulence in attached flows over hills. Quantifying Turbulence Intensity (TI) for wind energy.
Cobra Probe	3D mean velocity, turbulence intensity	~2–5%	Spatial: Moderate (~5–10 mm) Temporal: Low (~500 Hz)	Robust; provides 3D velocity vectors. Requires less frequent calibration	Intrusive; limited frequency response fails to capture fine turbulence. Accuracy degrades in high turbulence or reverse flow.	Higher cost, but durable. Simple operation, but low-frequency response is unsuitable for detailed turbulence studies.	Routine mapping of mean wind fields in complex terrain. Studies requiring robust instruments (e.g., bridge siting).
Laser Doppler Velocimetry (LDV)	1, 2, or 3 components of instantaneous velocity	~1%	Spatial: High (measurement volume ~0.1 mm) Temporal: High (>10 kHz)	Non-intrusive and highly accurate. Can measure reverse flow; no calibration needed	Requires tracer particles and expensive equipment. Time-consuming for flow field mapping (single-point).	High cost. A key advantage is its non-intrusive measurement, but it has low efficiency.	Precise, non-intrusive measurements at critical points (e.g., separation bubbles). CFD validation; pollutant dispersion studies.
Particle Image Velocimetry (PIV)	Instantaneous 2D or 3D velocity fields (“snapshots” of the flow)	~2–5%	Spatial: Good (dependent on camera resolution) Temporal: Low (typical systems <20 Hz)	Non-intrusive; provides full-field data. Excellent for visualizing complex flow structures	Requires optical access, particle seeding, and expensive equipment. Lower temporal resolution.	Highest cost. Provides instantaneous full-field data, but post-processing is complex.	Investigating large-scale turbulence, separation, and recirculation zones over hills
Surface Pressure Taps/Pressure Scanner	Mean and fluctuating surface pressure; pressure coefficient (C_p)	~1%	Spatial: High (dependent on tap density) Temporal: Variable (high-speed scanners can reach up to 500 kHz)	Directly measures wind loads on surfaces	Cannot provide flow field data away from the surface. Difficult to install on models with complex curvature.	The sensor itself is not expensive, but model fabrication is costly. Directly measures load data but offers no flow field information.	Wind load studies on structures in hilly terrain. Not used for characterizing free-stream flow

Table 6. Comparison of common measurement techniques in wind tunnel experiments for hilly terrain.

Instrument	Key Measured Parameters	Accuracy	Resolution	Advantages	Limitations	Cost and Feasibility	Ideal Applications
Hot-wire Anemometer (HWA)	Velocity magnitude, high-frequency turbulent fluctuations	~1–2%	Spatial: Very high (~1 mm) Temporal: Very high (>100 kHz)	Excellent for measuring turbulence spectra and Reynolds stresses. Relatively low cost	Intrusive and fragile probe. Requires frequent calibration; sensitive to temperature.	Medium cost, high maintenance. Probes are fragile and need frequent calibration; time-consuming for large-scale flow mapping.	Characterizing fine-scale turbulence in attached flows over hills. Quantifying Turbulence Intensity (TI) for wind energy.
Cobra Probe	3D mean velocity, turbulence intensity	~2–5%	Spatial: Moderate (~5–10 mm) Temporal: Low (~500 Hz)	Robust; provides 3D velocity vectors. Requires less frequent calibration	Intrusive; limited frequency response fails to capture fine turbulence. Accuracy degrades in high turbulence or reverse flow.	Higher cost, but durable. Simple operation, but low-frequency response is unsuitable for detailed turbulence studies.	Routine mapping of mean wind fields in complex terrain. Studies requiring robust instruments (e.g., bridge siting).
Laser Doppler Velocimetry (LDV)	1, 2, or 3 components of instantaneous velocity	~1%	Spatial: High (measurement volume ~0.1 mm) Temporal: High (>10 kHz)	Non-intrusive and highly accurate. Can measure reverse flow; no calibration needed	Requires tracer particles and expensive equipment. Time-consuming for flow field mapping (single-point).	High cost. A key advantage is its non-intrusive measurement, but it has low efficiency.	Precise, non-intrusive measurements at critical points (e.g., separation bubbles). CFD validation; pollutant dispersion studies.
Particle Image Velocimetry (PIV)	Instantaneous 2D or 3D velocity fields (“snapshots” of the flow)	~2–5%	Spatial: Good (dependent on camera resolution) Temporal: Low (typical systems <20 Hz)	Non-intrusive; provides full-field data. Excellent for visualizing complex flow structures	Requires optical access, particle seeding, and expensive equipment. Lower temporal resolution.	Highest cost. Provides instantaneous full-field data, but post-processing is complex.	Investigating large-scale turbulence, separation, and recirculation zones over hills
Surface Pressure Taps/Pressure Scanner	Mean and fluctuating surface pressure; pressure coefficient (C_p)	~1%	Spatial: High (dependent on tap density) Temporal: Variable (high-speed scanners can reach up to 500 kHz)	Directly measures wind loads on surfaces	Cannot provide flow field data away from the surface. Difficult to install on models with complex curvature.	The sensor itself is not expensive, but model fabrication is costly. Directly measures load data but offers no flow field information.	Wind load studies on structures in hilly terrain. Not used for characterizing free-stream flow

3.3. CFD Simulation

CFD simulations have played an increasingly important role in the study of wind fields over hilly terrain due to their flexibility and accessibility. In CFD simulations, the choice of a turbulence model is a critical trade-off between computational cost and simulation accuracy, requiring careful consideration of the specific terrain and flow phenomena. As shown in Figure 6a, the Reynolds-Averaged Navier–Stokes (RANS) method, due to its computational efficiency, remains the predominant approach for simulating wind fields over hilly terrain, with its related publications being nearly double those of Large Eddy Simulation (LES). This choice, however, is driven more by computational economy than universal high accuracy [60].

Table 7 summarizes the 3D studies on wind fields over hilly terrain, with particular emphasis on the comparison between grid resolution and simulation performance. The differences between RANS and LES in terms of computational resources and predictive accuracy are substantial.

In terms of computational cost and feasibility, switching from RANS to LES typically increases the computational load by one to two orders of magnitude (10 to 100 times) [61], as shown in Table 8. This cost difference stems from their disparate grid resolution requirements. A RANS simulation covering several square kilometers might be feasible with 5 to 10 million cells, whereas a corresponding LES requires a grid fine enough to resolve most energy-containing turbulent eddies, potentially increasing the cell count to hundreds of millions, making such simulations dependent on large high-performance computing (HPC) clusters. Furthermore, capturing high-frequency turbulent fluctuations requires much smaller time steps for LES than for RANS/URANS, further increasing total computation time [62]. This reality reframes the model selection process as a “trilemma” among cost, accuracy, and project feasibility. A project manager may find a low-cost, lower-fidelity RANS solution feasible, whereas a high-cost, high-fidelity LES solution, while theoretically superior, may be practically infeasible. This trilemma explains the persistence of RANS in industrial applications and motivates the development of hybrid models and AI surrogates aimed at breaking this deadlock.

Regarding predictive validation, the scientific community uses standardized quantitative metrics (e.g., MAE, RMSE, MB) to quantify model uncertainty against “gold-standard” datasets from international field campaigns. The classic Askervein Hill project and the more recent Perdigão project are key “touchstones” for testing CFD models. The Askervein Hill project, using the Fractional Speed-up Ratio, showed that RANS/URANS models systematically underestimated the wind speed-up effect at the hilltop (by about 8–15%) [63]. Their most significant deficiency was in the leeward separation zone, where they predicted a recirculation region nearly 30% larger than observed and also incorrectly predicted the sign of the Reynolds shear stress [64]. These findings highlighted the inherent weakness of time-averaged models in handling flow separation, thereby motivating higher-fidelity methods like LES [65]. The Perdigão project, focusing on a real-world double-ridge topography, elevated the complexity of validation by using spatio-temporal statistical metrics to evaluate coupled models (e.g., WRF-LES) [66]. Studies revealed that even for high-resolution LES, predictive accuracy varied significantly in space (RMSE up to 5.65 m/s on the ridge vs. 2.28 m/s in the valley) [67]. Furthermore, a model-intercomparison challenge found that while LES offered superior physical fidelity, RANS models, due to their lower cost, could simulate a wider range of wind conditions. This broader coverage sometimes led to more accurate predictions of the Annual Energy Production (AEP) than LES runs limited to a few specific cases [68]. Nevertheless, the superiority of LES in resolving complex flow structures is indisputable. Research at Perdigão confirmed that only LES could reliably reproduce the high turbulence levels, reattachment points, and the distribution of Turbulent Kinetic Energy (TKE), while keeping the mean wind speed bias below 0.1 m/s. However, the accuracy of LES remains highly sensitive to grid resolution and the inflow turbulence generation method.

Table 7. CFD simulation research of wind fields over hilly terrain.

Author (Year)	Turbulence Model	Mountain Height/Mesh Size	Mountain Feature	Reduced Scale	Detail	Tool
Liu et al. [69] (2016)	LES	540 m/3 m	Real terrain	1:2000	The forest canopy	Fluent
Dhunny et al. [70] (2017)	Steady RANS	825 m/-	Real terrain	1:1	Wind power utilization	WindSim
Yan et al. [71] (2018)	Steady RANS	100 m/12 m	3D hill	1:1	Wind power utilization	Fluent
Huang et al. [72] (2019)	Steady RANS	700 m/20 m	Real terrain	1:4000	ABL	Fluent
Hu et al. [73] (2021)	LES	210 m/10 m	3D hill/Real terrain	1:1000	ABL	Fluent
Zhou et al. [74] (2022)	URANS	600 m/3 m	3D hill	1:1000	ABL	OpenFOAM
Cao et al. [75] (2023)	LES	200 m/10 m	3D hill	1:1	ABL	WRF/OpenFOAM
Huang et al. [76] (2024)	LES	288 m/8 m	2D hill/3D hill	1:1	Wind–snow coupling	-
Zhou et al. [77] (2024)	LES	60 m/2 m	3D hill	1:1000	Thermally driven flow	Fluent

Table 7. CFD simulation research of wind fields over hilly terrain.

Author (Year)	Turbulence Model	Mountain Height/Mesh Size	Mountain Feature	Reduced Scale	Detail	Tool
Liu et al. [69] (2016)	LES	540 m/3 m	Real terrain	1:2000	The forest canopy	Fluent
Dhunny et al. [70] (2017)	Steady RANS	825 m/-	Real terrain	1:1	Wind power utilization	WindSim
Yan et al. [71] (2018)	Steady RANS	100 m/12 m	3D hill	1:1	Wind power utilization	Fluent
Huang et al. [72] (2019)	Steady RANS	700 m/20 m	Real terrain	1:4000	ABL	Fluent
Hu et al. [73] (2021)	LES	210 m/10 m	3D hill/Real terrain	1:1000	ABL	Fluent
Zhou et al. [74] (2022)	URANS	600 m/3 m	3D hill	1:1000	ABL	OpenFOAM
Cao et al. [75] (2023)	LES	200 m/10 m	3D hill	1:1	ABL	WRF/OpenFOAM
Huang et al. [76] (2024)	LES	288 m/8 m	2D hill/3D hill	1:1	Wind–snow coupling	-
Zhou et al. [77] (2024)	LES	60 m/2 m	3D hill	1:1000	Thermally driven flow	Fluent

Table 8. Comparison of Turbulence Models for CFD in hilly terrain.

Model	Typical Topography	Advantages	Disadvantages and Quantitative Limitations	Computational Cost and Feasibility
RANS	Gentle slopes, no significant flow separation	Extremely high computational efficiency	Severely underestimates the size of separation zones; unable to capture unsteady effects.	Mesh Size: 5–20 million Time Step:/(steady-state) CPU Hours: 10–100 Cost Factor: 1×
URANS	Moderately complex terrain	Balances efficiency and accuracy; capable of capturing large-scale unsteady structures	Still relies on modeling assumptions; cannot resolve small-scale turbulence.	Mesh Size: 5–25 million Time Step: Large (e.g., 10−2–10−1 s) CPU Hours: 100–1500 Cost Factor: ~10–50×
LES	Steep hills/cliffs/canyons	High-fidelity prediction of turbulent structures and separated flows	Computationally very expensive; sensitive to inflow boundary conditions.	Mesh Size: 50 million—500+ million Time Step: Very small (e.g., 10−5–10−3 s) CPU Hours: 10,000–100,000+ Cost Factor: ~1000×

Table 8. Comparison of Turbulence Models for CFD in hilly terrain.

Model	Typical Topography	Advantages	Disadvantages and Quantitative Limitations	Computational Cost and Feasibility
RANS	Gentle slopes, no significant flow separation	Extremely high computational efficiency	Severely underestimates the size of separation zones; unable to capture unsteady effects.	Mesh Size: 5–20 million Time Step:/(steady-state) CPU Hours: 10–100 Cost Factor: 1×
URANS	Moderately complex terrain	Balances efficiency and accuracy; capable of capturing large-scale unsteady structures	Still relies on modeling assumptions; cannot resolve small-scale turbulence.	Mesh Size: 5–25 million Time Step: Large (e.g., 10−2–10−1 s) CPU Hours: 100–1500 Cost Factor: ~10–50×
LES	Steep hills/cliffs/canyons	High-fidelity prediction of turbulent structures and separated flows	Computationally very expensive; sensitive to inflow boundary conditions.	Mesh Size: 50 million—500+ million Time Step: Very small (e.g., 10−5–10−3 s) CPU Hours: 10,000–100,000+ Cost Factor: ~1000×

To clearly define the application scenarios for different models, Table 8 summarizes their characteristics. The RANS model is cost-effective for gentle slopes with no significant flow separation due to its very low computational cost. For flows with strong separation and complex turbulent structures, such as canyon winds and mountain peak wakes, LES is the preferred choice for high-accuracy results. Positioned as a middle ground between RANS and LES, the Unsteady Reynolds-Averaged Navier–Stokes (URANS) model aims to capture unsteady large-scale flow structures like vortex shedding at an acceptable computational cost. Its performance is a significant improvement over steady RANS, making it an attractive option for simulations of moderately complex terrain.

In terms of simulation tools (Figure 6b), the majority of CFD applications employ ANSYS Fluent [78], followed by the mesoscale meteorological model WRF [79], and the open-source framework OpenFOAM [80]. Together, these three tools account for a dominant majority of terrain wind field simulations. Their dominance stems from their unique advantages in their respective technological niches, as compared in

Table 9. Comparison of mainstream Software for CFD in hilly terrain.

	ANSYS Fluent	OpenFOAM	WRF
License Model	Commercial license, high cost	Open-source, free	Open-source, free
Primary Simulation Scale	Microscale (10−2–103 m)	Microscale (10−2–103 m)	Mesoscale (103–105 m)
User Interface	Graphical User Interface (GUI), user-friendly	Command-line	Command-line
Core Strengths	Industry standard, reliable and easy to use	Flexible, free, suitable for large-scale parallel computing	Provides realistic atmospheric background fields
Core Limitations	High cost, poor customizability	High technical barrier to entry	Coarse resolution, unable to resolve local flow details
Role	Microscale wind field solver	Microscale wind field solver	Provides boundary conditions for microscale simulations

. ANSYS Fluent, as a prime example of commercial software, significantly lowers the barrier to entry for CFD technology with its user-friendly graphical interface and comprehensive technical support. OpenFOAM, with its open-source and free nature, provides researchers with great flexibility to customize and develop new algorithms [81]. WRF is not a traditional CFD software but a mesoscale meteorological model; its widespread adoption is due to its ability to provide more realistic, time-varying atmospheric boundary conditions for microscale CFD simulations, playing an indispensable role in coupled simulation methods [82]. In recent years, coupled simulation approaches have been increasingly applied to hilly terrain wind field studies [64]. These methods combine CFD with wind distribution tools to enable joint simulation across temporal and spatial scales. Typical coupled approaches utilize global Numerical Weather Prediction (NWP) models, such as WRF, or observational data to supply detailed boundary conditions (e.g., air temperature and pressure, or wind speed) for CFD simulations over hilly terrain, thereby enhancing the accuracy of wind field modeling and wind resource assessment in mountainous areas [83,84].

Although wind tunnel experiments or field measurement data are usually adopted to verify the simulation’s validity, the challenges of the validation process itself are often overlooked in the literature. Firstly, the quality, representativeness, and uncertainty of the validation data are core issues. While wind tunnel data are highly controllable, they are often plagued by the “Reynolds number mismatch” problem, leading to inherent biases in reproducing the details of the real atmospheric boundary layer turbulence [85]. Field measurement data, though authentic, typically have very low spatial resolution (e.g., a single meteorological mast) and are limited by specific weather conditions, making it difficult to cover all scenarios [86]. Consequently, “validation” in many studies is limited to a qualitative comparison of basic parameters like mean wind speed, lacking a quantitative error analysis of key statistics such as turbulence intensity and integral scales. Future research needs to establish more rigorous validation protocols to assess the uncertainty and spatio-temporal representativeness of validation data. Furthermore, most coupled methods still lack comprehensive validation and calibration, particularly where observational data is limited, and thus their stability and reliability require further investigation.

Overall, the application of CFD methods has expanded from investigating wind characteristics over hilly terrain to assessing regional energy and modeling extreme natural events, including downbursts, thermally driven flows, and snow loads. Such studies usually adopt wind tunnel tests or field measurement data for comparison to verify the simulation’s validity. Additionally, as shown in Figure 7, research on real terrain and 3D hills has increased annually, while the proportion of studies on 2-D idealized terrain has declined. This trend reflects not only growing computational capacity but also a deeper understanding of the 3D nature of atmospheric flows.

3.4. Data-Driven Models

With the rapid development of machine learning and data science, data-driven models have provided a new paradigm for wind field modeling over hilly terrain [87]. Their core value lies in the potential to significantly reduce computational costs while enhancing prediction efficiency by learning complex nonlinear patterns from high-dimensional data, offering a critical complement to computationally expensive Computational Fluid Dynamics (CFD) methods. However, despite their promising prospects, the application of these methods is still in its early stages, facing significant challenges in model validation, generalization, and standardization.

Current data-driven approaches can be broadly categorized into two types: Reduced-Order Models (ROMs) and machine learning-assisted models. On one hand, ROMs, represented by Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), excel at extracting dominant spatio-temporal coherent structures from high-fidelity data such as CFD simulations [88,89]. As shown in Table 10, they are widely used for flow field reconstruction and feature analysis [90,91,92,93]. When the research objective focuses on revealing physical mechanisms and the flow structures are relatively stable, ROMs are preferred for their computational efficiency and strong physical interpretability. However, their limitations are also apparent: model performance is strongly correlated with the training data, and their generalization to new conditions is limited. On the other hand, machine learning models, such as Multilayer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs), demonstrate superior performance in learning the complex nonlinear relationships between multi-source inputs (e.g., terrain, meteorological data) and wind field outputs [94,95]. These models can effectively handle heterogeneous data from both CFD simulations and field observations, showing powerful nonlinear fitting capabilities in tasks like wind resource assessment and short-term wind speed forecasting [96,97]. Therefore, when sufficient training data are available and prediction accuracy is the primary goal, deep learning models are generally more advantageous, although their inherent “black-box” nature makes the interpretation of physical mechanisms difficult.

To address the inherent spatio-temporal coupling in wind field modeling, researchers have introduced more advanced architectures such as Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM) networks, and Transformers. While the first two have been highly successful in time-series forecasting, a fundamental limitation is their difficulty in adequately accounting for spatial dependencies between different locations. The Transformer architecture overcomes this weakness through its core self-attention mechanism, which can be tuned to weigh the importance of different spatial locations, thus explicitly capturing spatial correlations and making it potentially more powerful than traditional RNNs or LSTMs for regional wind field prediction [98]. Model accuracy varies by application. For time-series forecasting at a point, sequential models like LSTM are accurate with sufficient historical data. For spatial downscaling, CNNs are advantageous as they effectively process gridded data and capture terrain-induced flow features [97,99]. The Transformer architecture shows potential for regional forecasting with complex spatio-temporal dependencies. With sparse data, Physics-Informed Neural Networks (PINNs), incorporating physical constraints, often achieve higher accuracy in wind field reconstruction than purely data-driven methods [100]. The value of these architectures has been validated in several applications. For instance, GANs have been used to upscale low-resolution data to high-resolution 3D velocity fields [99]. Notably, the FuXi-CFD model, pre-trained on a large CFD dataset, downscaled kilometer-scale forecasts to a 30 m resolution 3D wind field with CFD-comparable accuracy, reducing inference time from hours to under a second [101]. In regional forecasting, a model by Zhang et al. (2025) reduced the 1 h forecast RMSE by 66% over NWP models in northeastern China [102]. Furthermore, PINNs integrate physical knowledge by embedding governing equations as soft constraints in the loss function, enabling plausible solutions with sparse data. For instance, one study reconstructed a 2D wind field from sparse, LIDAR-like data, achieving an MRMSE of just 0.32 m/s for the streamwise velocity [100]. These results illustrate the potential of different architectures for specific tasks.

However, the high efficiency of data-driven models comes at a cost, concentrated in the training phase. First, building a robust model requires massive, high-quality training datasets, often generated by hundreds or thousands of high-fidelity CFD simulations. Second, the training process itself is computationally intensive, relying on HPC clusters with GPUs and taking days or weeks to converge. In stark contrast, the inference (prediction) stage is extremely cheap. Once trained, a model can make rapid predictions on standard hardware (hours down to seconds), enabling real-time applications and large-scale parameter optimization. Thus, feasibility assessment involves a trade-off between the high, one-time training investment and the long-term, low-cost application benefits.

In terms of Technology Readiness Level (TRL), data-driven methods are at various stages. Traditional machine learning (e.g., MLP) for tasks like single-point forecasting is relatively mature (approx. TRL 6-8) and used in some commercial software [96]. Deep learning models like CNNs and LSTMs for complex spatio-temporal prediction are in the validation and demonstration phase (approx. TRL 4-6), with generalization and robustness being a key research focus [97]. In contrast, cutting-edge models like GANs, FuXi-CFD, and PINNs are in the proof-of-concept stage (approx. TRL 2-4) [99,100,101]. They face challenges in training stability, data dependency, and physical consistency before becoming reliable engineering tools.

The practical value of these advanced architectures has been validated in several cutting-edge applications. For instance, in spatial downscaling, Wold et al. [99] leveraged Generative Adversarial Networks (GANs) to successfully upscale low-resolution wind field data to high-resolution 3D velocity fields. Recently, the notable FuXi-CFD model, pre-trained on a large CFD dataset, achieved downscaling from kilometer-scale forecasts to a 30 m resolution 3D wind field with accuracy comparable to CFD, while reducing inference time from hours to under a second—a computational efficiency improvement of over three orders of magnitude [101]. In short-term regional forecasting, a model proposed by Zhang et al. (2025) [102] reduced the Root Mean Square Error (RMSE) by 66% for 1 h forecasts in northeastern China compared to operational NWP models. Furthermore, a highly promising direction is the integration of physical knowledge with data-driven methods. Physics-Informed Neural Networks (PINNs) embed governing equations (e.g., the Navier–Stokes equations) as soft constraints into the loss function, enabling the model to generate physically plausible solutions even with sparse data. For example, one study successfully reconstructed the 2D wind field upstream of a wind turbine using only sparse, LIDAR-like data points, achieving a Mean Root Mean Square Error (MRMSE) of just 0.32 m/s for the streamwise velocity component [100].

Despite the rapid development of model architectures, their effectiveness is fundamentally limited by the quality of training data and the rigor of validation methods—precisely the weakest links in current research. Model training data typically come from two sources: high-fidelity CFD simulations or real-world observations (e.g., SCADA, LIDAR). CFD data can provide complete, noise-free 3D flow fields, but they are an approximation of reality and may contain systematic biases [103,104]. A model trained exclusively on CFD data might “learn” these simulation-specific artifacts, leading to degraded performance on real-world data [105]. Conversely, observational data represent the “ground truth” but are often sparse, noisy, and incomplete. Therefore, the future direction inevitably points toward a hybrid data strategy: for example, pre-training a model on a large volume of CFD data to learn the general laws of fluid dynamics, followed by fine-tuning on a smaller, site-specific observational dataset to correct simulation biases. More importantly, the validation of spatio-temporal models presents significant challenges beyond standard statistical metrics. While metrics like Mean Absolute Error (MAE) and RMSE are crucial for quantifying average errors, they can mask critical issues [106,107]. For instance, a model might perform excellently on overall RMSE but completely fail to predict a single, high-impact extreme wind event, rendering it unreliable for practical engineering applications [108]. Therefore, the field urgently needs standardized validation protocols and open benchmark datasets, drawing on experience from related disciplines. For instance, computational wind engineering uses “gold standard” public datasets from projects like Askervein Hill [51,52] and Bolund Hill to validate terrain flow models. Similarly, meteorology uses the ERA5 reanalysis data [101] as a recognized benchmark for mesoscale simulations. Inspired by ImageNet in computer vision, creating a benchmark platform for AI models of mountain wind fields—with multi-source data (e.g., high-precision LES, Lidar, masts)—is a critical step. This will ensure model reproducibility, facilitate fair comparisons, and advance the field from academic exploration to engineering practice.

Table 10. Data-driven modeling research of wind fields over hilly terrain.

Author (Year)	Sources of Data	Method	Detail	Key Quantitative Results	Mountain Feature
Lou et al. [90] (2020)	CFD	POD	Design of transmission tower lines	Not provided in text; focused on extracting wind field characteristics for design.	3D valley
Zhou et al. [91] (2020)	CFD	POD	Time–space characteristic	Not provided in text; focused on spatio-temporal analysis of wake turbulence.	3D hill
Wang et al. [92] (2023)	CFD	POD	Dynamic soaring	Not provided in text; used for prediction of wind shear layers.	2D ridge
Zhou et al. [93] (2021)	CFD	DMD	High-rise buildings	Not provided in text; focused on analyzing the flow field around buildings.	-
Quiroga et al. [94] (2021)	Field measurement	k-NN	Wind power utilization	MAE: 1.29%	Actual complex terrain
Lee et al. [96] (2022)	Field measurement	MLP	Wind power utilization	Mean error: 2.92 m/s	Actual complex terrain
Sheehan et al. [97] (2022)	CFD	CNN	ABL	MAE: 0.03–0.04 m/s	Actual complex terrain
Wold et al. [99] (2024)	Low-resolution wind field data	GAN	ABL	No error metric provided; successfully upscaled low-res data to high-res 3D fields.	Actual complex terrain
Zhang et al. [102] (2025)	ERA5 reanalyzes the data	MFWPN	Wind speed forecast	RMSE: 0.42 m/s	Actual complex terrain
Lin et al. [101] (2025)	CFD	U-Net	ABL	RMSE: 0.4 m/s. Reduced inference time by over three orders of magnitude (hours to <1 s) with accuracy “comparable to CFD”	Actual complex terrain
Hidalgo et al. [100] (2025)	CFD	PINN	Rebuild the wind farm	MRMSE: 0.32 m/s	Actual complex terrain

Table 10. Data-driven modeling research of wind fields over hilly terrain.

Author (Year)	Sources of Data	Method	Detail	Key Quantitative Results	Mountain Feature
Lou et al. [90] (2020)	CFD	POD	Design of transmission tower lines	Not provided in text; focused on extracting wind field characteristics for design.	3D valley
Zhou et al. [91] (2020)	CFD	POD	Time–space characteristic	Not provided in text; focused on spatio-temporal analysis of wake turbulence.	3D hill
Wang et al. [92] (2023)	CFD	POD	Dynamic soaring	Not provided in text; used for prediction of wind shear layers.	2D ridge
Zhou et al. [93] (2021)	CFD	DMD	High-rise buildings	Not provided in text; focused on analyzing the flow field around buildings.	-
Quiroga et al. [94] (2021)	Field measurement	k-NN	Wind power utilization	MAE: 1.29%	Actual complex terrain
Lee et al. [96] (2022)	Field measurement	MLP	Wind power utilization	Mean error: 2.92 m/s	Actual complex terrain
Sheehan et al. [97] (2022)	CFD	CNN	ABL	MAE: 0.03–0.04 m/s	Actual complex terrain
Wold et al. [99] (2024)	Low-resolution wind field data	GAN	ABL	No error metric provided; successfully upscaled low-res data to high-res 3D fields.	Actual complex terrain
Zhang et al. [102] (2025)	ERA5 reanalyzes the data	MFWPN	Wind speed forecast	RMSE: 0.42 m/s	Actual complex terrain
Lin et al. [101] (2025)	CFD	U-Net	ABL	RMSE: 0.4 m/s. Reduced inference time by over three orders of magnitude (hours to <1 s) with accuracy “comparable to CFD”	Actual complex terrain
Hidalgo et al. [100] (2025)	CFD	PINN	Rebuild the wind farm	MRMSE: 0.32 m/s	Actual complex terrain

In summary, the integration of numerical simulation and AI is not a single path but a multi-level, objective-driven framework. Based on current research, we can categorize it into the following four key modes:

• AI as Surrogate/Accelerator: This mode uses deep learning models (e.g., CNNs, GANs) to learn and replace high-cost CFD solving processes. After training on massive CFD datasets, the model can achieve rapid, second-level predictions at a very low cost, supporting large-scale parameter studies and real-time forecasting.
• AI as Data Fusion & Corrector: This mode uses AI to resolve the conflict between the systematic biases of CFD models and the sparsity of field observation data. Its core is the “CFD pre-training + observation fine-tuning” strategy, where the AI model corrects CFD’s predictive biases using sparse but real observation points, generating a more accurate wind field than either source alone.
• AI as Physics-Informed Extractor: Represented by PINNs, this mode embeds governing equations like Navier–Stokes into the AI’s loss function as a physical constraint. This forces the model to generate physically self-consistent solutions even with sparse data, making it ideal for reconstructing flow fields or discovering unknown parameters from limited measurements.
• AI as Intelligent Boundary Generator: In multi-scale coupled simulations (e.g., WRF-CFD), AI acts as a bridge connecting models of different scales. By learning the complex relationship between mesoscale meteorological fields and microscale boundary conditions, the model can rapidly generate dynamic and realistic inlet conditions for CFD, thereby replacing or accelerating the slower mesoscale model and improving the efficiency of the entire simulation chain.

In conclusion, although data-driven models hold immense potential, their application to wind fields over hilly terrain requires a more critical and systematic research approach. Current work often focuses on optimizing the predictive models themselves, with insufficient attention paid to feature engineering, data quality control, and validation protocols, which severely limits the models’ generalization ability and predictive accuracy. Future research must not only explore novel model architectures but also commit to building high-quality open-source datasets, establishing standardized validation protocols, and effectively integrating physical principles into model design. Only then can the full potential of data-driven methods in this complex field be truly unlocked.

4. Wind Field Modeling over Hilly Terrain: Current Practical Issues

The advancements in modeling methods for wind fields over hilly terrain, detailed in Section 3, are driven by the need to address pressing real-world engineering and environmental challenges. Specifically, these methods are concentrated in three critical domains: wind resource development, the design of buildings and infrastructure, and pollutant dispersion. As illustrated in Figure 8, the volume of research focused on these practical applications showed a continuous and significant upward trend from 2015 to 2024, reflecting the growing urgency of these topics.

This trend highlights that, against the backdrop of a global push for renewable energy in complex terrain, wind resource assessment has become a focal point. As a multi-billion-dollar industry, wind energy development demands models capable of accurately optimizing Annual Energy Production (AEP), where minor inaccuracies in wake modeling can translate to millions of dollars in revenue loss [109]. Similarly, for buildings and infrastructure, inaccurate wind load predictions can have catastrophic safety and economic consequences, with a single extreme wind event potentially causing billions of dollars in damage, thus necessitating models that can inform robust designs compliant with codes such as ASCE 7 [110]. In the environmental realm, the accumulation of pollutants in valleys poses a severe threat to public health, with associated annual economic costs reaching billions of dollars in affected regions, requiring that models reliably simulate complex transport and dispersion phenomena [111]. Collectively, these issues form the core concerns of current scientific research and engineering practice.

Nevertheless, applying the methods from Section 3 to these practical issues is not straightforward, as critical challenges persist across all three areas. The primary difficulty lies in accurately capturing the extreme spatiotemporal variability of the wind field induced by complex topography. Furthermore, the modeling process is often complicated by multi-physics coupling effects, such as the interplay between thermal phenomena and airflow, which are frequently oversimplified or neglected. The main factors influencing these domains include not only environmental conditions (wind speed, direction, and air temperature) and geomorphological features (2D/3D hills and real terrain) but also surface characteristics like vegetation and forest cover, which add further layers of complexity. In the following subsections, this paper will delve into the specific applications of modeling methods for each practical issue, analyzing the unique challenges, recent progress, and remaining knowledge gaps in each domain.

4.1. Wind Resource Development

As a clean and renewable energy source, wind energy has attracted considerable attention, given the growing demand for green energy and the abundance of wind resources in mountainous areas. Wind farm siting requires a careful balance between wind resource potential and terrain-induced effects, particularly in minimizing wake losses and improving turbine layout efficiency. Currently, wind resource assessment primarily relies on field measurements, wind tunnel experiments, and Computational Fluid Dynamics (CFD) simulations. Among these, CFD has become the predominant tool due to its flexibility (Figure 9b). However, each method has its own scope of application and limitations, necessitating a synergistic approach at different stages of the assessment, as shown in

Table 11. Comparison of wind resource assessment methods for hilly terrain.

Method	Advantages	Limitations	Optimal Application Scenarios
Field Measurement	Provides authentic “ground-truth” data, serving as a benchmark for validation. Captures long-term wind climate characteristics at specific locations.	High cost and sparse measurement points hinder comprehensive capture of spatial variability in the wind field. Instrument installation and maintenance are challenging in remote areas.	Micro-siting for critical turbine locations. Supplying boundary conditions and validation data for CFD and wind tunnel models.
Wind Tunnel Experiment	Allows for efficient and repeatable testing of terrain effects on the wind field in a controlled environment. Aids in understanding the physical mechanisms of complex flows.	Reynolds number mismatch makes it difficult to fully simulate the atmospheric boundary layer and thermal effects. High cost and model scaling ratios limit the precision of fine details.	Fundamental research on physical mechanisms (e.g., flow over hills, wake model development). Preliminary validation of parameterization schemes in CFD models.
CFD Simulation	Relatively low-cost; provides high-resolution, full-domain wind field data. Offers flexibility to simulate various terrains and atmospheric conditions.	Accuracy is highly dependent on mesh quality, turbulence model selection, and boundary conditions. Requires rigorous validation and calibration against high-quality field measurement data.	Macro-siting, micro-siting, and layout optimization. Analysis of wake effects and energy yield prediction in complex terrain.

.

The fundamental challenge of wind resource assessment in hilly terrain is the high spatial variability of the wind field. Unlike flat terrain, complex geomorphological features such as ridges and valleys induce significant local flow perturbations, including hilltop speed-up, leeward slope separation, and valley channeling effects. This leads to drastic changes in wind speed, direction, and turbulence intensity within a scale of hundreds of meters, making it difficult for traditional methods based on single-point measurements to represent wind conditions across an entire project site [112]. This spatial heterogeneity severely violates the horizontal homogeneity assumption that standard assessment models rely on. Studies have shown that without correction, systematic errors from remote sensing instruments can exceed 10% in complex terrain [113].

To address this challenge, the industry has developed a “zonal measurement approach,” which involves geographically dividing a complex terrain site into multiple relatively homogeneous sub-regions for independent assessment. By increasing the coverage of measurement points, this strategy effectively overcomes the limitations of single-point extrapolation and improves assessment accuracy, although it also places higher demands on measurement costs and data management [114,115,116]. This practical need has fostered a crucial synergistic feedback loop between measurement and modeling: the demand for high-spatial-resolution data has promoted technologies like scanning LiDAR, while the inherent biases revealed by these new technologies (such as systematic errors from flow curvature) have in turn driven innovation in modeling—utilizing high-resolution CFD simulations to correct measurement data. This “model-assisted measurement” strategy provides a higher-fidelity validation benchmark for CFD models, creating a powerful synergy that systematically reduces project uncertainty [113].

An accurate resource assessment ultimately serves to optimize wind farm layouts for maximum economic benefit. Accurate resource assessment serves to optimize wind farm layouts for maximum economic benefit. The core economic metric is Annual Energy Production (AEP), which directly determines revenue. For investors and lenders, however, the primary concern is the uncertainty associated with the AEP forecast, which is quantified through “Probability of Exceedance” (p-values). The P50 AEP represents the “expected” output (50% chance of being met or exceeded), while the P90 or P99 AEP is a conservative forecast serving as the key “bankable” figure for lenders. All sources of uncertainty in the assessment process (including measurement, modeling, and climate variability) collectively determine the spread between P50 and P90. A wider spread implies higher risk and potentially more stringent lending terms. Studies have shown that traditional Gaussian wake models severely underestimate wake losses in complex terrain [117]. In contrast, high-fidelity CFD simulations offer a dual value: they increase the P50 AEP—the “expected” output—by 3–5% through more accurate modeling and also significantly reduce overall assessment uncertainty, thereby narrowing the P50-P90 spread [118,119]. This reduction in uncertainty boosts the “bankable” P90 value, directly increasing the project’s valuation. For a major wind project, a 3–5% increase in P50 AEP translates to millions in additional lifetime revenue. Furthermore, studies indicate that each 1% reduction in energy forecast uncertainty can add USD 0.5 M to USD 2 M in project value [120]. Therefore, the upfront investment in high-fidelity CFD is a critical financial risk management investment that “de-risks” the project, offering a high return through long-term economic benefits and financing advantages [121]. Furthermore, considering the variable wind directions in hilly regions, Song et al. [122] emphasized the importance of incorporating wind direction variability into economic performance assessments. Integrating atmospheric stability, a critical but often overlooked factor, into the model can also significantly improve the accuracy of wind speed estimation [123,124,125]. These methodological advancements have benefited from advanced tools such as WindSim and OpenFOAM [126]. For instance, Dhunny et al. [70] utilized WindSim to develop high-resolution wind energy potential maps of Mauritius, providing a scientific basis for national-level energy planning.

Given the heavy reliance of the assessment on numerical models, rigorous validation is a core element in ensuring the reliability of their predictions. The standard validation process requires a direct comparison of CFD results with high-quality on-site measurement data (typically wind speed, direction, and turbulence intensity at hub height). Table 12 synthesizes key performance metrics for wind resource assessment in complex terrain as reported in recent literature. Quantitative studies have shown that for steady-state RANS simulations over complex terrain, the deviation of predicted wind speed from measured values is typically within 10–20%, and the wind direction deviation is within 30° [86]. Accuracy can be improved by integrating more advanced methods. For instance, using CFD to correct LiDAR data can reduce the mean wind speed deviation from −2.4% to −0.1% [127]. Similarly, a coupled meso-microscale (e.g., WRF-CFD) modeling framework, in a large validation study involving 45 observation points, demonstrated a mean bias of only +0.05 m/s and reduced the variability of prediction errors by 35% [118].

Table 12. Performance metrics of wind resource assessment methods in hilly terrain.

Evaluation Method	Performance Metric	Reported Error Range	Key Influencing Factors
Steady RANS [86]	Mean wind speed deviation	10–20%	Terrain complexity, turbulence model selection
	Wind direction deviation	<30°	Inflow boundary conditions
Lidar + CFD Correction [127]	Mean wind speed deviation	Reduced from −2.4% to −0.1%	Correction algorithm, terrain curvature
Meso-microscale Coupling (WRF-CFD) [128]	Mean wind speed deviation	+0.05 m/s	Coupling scheme, physics parameterization
	Variability of prediction error	Reduced by 35%	Mesoscale model accuracy

Table 12. Performance metrics of wind resource assessment methods in hilly terrain.

Evaluation Method	Performance Metric	Reported Error Range	Key Influencing Factors
Steady RANS [86]	Mean wind speed deviation	10–20%	Terrain complexity, turbulence model selection
	Wind direction deviation	<30°	Inflow boundary conditions
Lidar + CFD Correction [127]	Mean wind speed deviation	Reduced from −2.4% to −0.1%	Correction algorithm, terrain curvature
Meso-microscale Coupling (WRF-CFD) [128]	Mean wind speed deviation	+0.05 m/s	Coupling scheme, physics parameterization
	Variability of prediction error	Reduced by 35%	Mesoscale model accuracy

At the same time, it is necessary to acknowledge the geographical limitations of current research. Most case studies are concentrated in specific regions such as Europe, East Asia, and North America, and whether their conclusions can be directly extrapolated to mountainous areas in other climate zones (e.g., tropical or polar) requires further verification [129,130]. Future research should aim to broaden the geographical coverage to enhance model generalizability. To systematically address the current lack of geographical representativeness and enhance the global generalizability of models, future research should advance in the following directions:

• Establish global, open benchmark datasets: Foster international collaborations to conduct large-scale field campaigns in data-sparse but representative mountainous regions (e.g., the Andes, African highlands), similar to the New European Wind Atlas (NEWA) project. The resulting high-quality data should be integrated into standardized, open-access datasets to provide a “gold standard” for researchers worldwide to validate and develop models.
• Develop physics-constrained transfer learning models: Utilize data-driven methods, particularly transfer learning, to adapt models trained in data-rich regions to target areas with sparse observational data. By incorporating physical constraints (e.g., the continuity equation), these models can ensure that predictions in data-scarce regions remain physically plausible.
• Initiate systematic model intercomparison projects: Define standardized simulation cases for different types of mountain geomorphologies and organize multiple research groups globally to perform simulations using various models. Comparing these results against high-quality observational data will help quantify model uncertainties and lead to the development of more robust parameterization schemes.

Furthermore, high-precision wind resource assessment technology has become a bridge connecting scientific research and energy policy. High-resolution wind resource atlases generated by combining NWP and CFD can assist governments in formulating scientific renewable energy development roadmaps [112]. Accurate modeling also helps meet increasingly stringent environmental regulations, for example, by simulating noise propagation to ensure safe distances from residential areas or by supporting the core requirements of Environmental Impact Assessments (EIAs) by evaluating wake impacts on ecosystems [131,132,133].

In summary, research on wind resource development in hilly terrain is advancing towards more refined, comprehensive, and practical directions. The focus has shifted from single-factor analysis to a comprehensive consideration of the synergistic effects of terrain, atmospheric stability, and surface roughness, with increasing attention being paid to the environmental impacts of wind farms and their coordination with socio-economic factors. These research outcomes are directly related to the technical feasibility, economic returns, and sustainable development of wind power projects in mountainous regions.

4.2. The Design of Buildings and Infrastructure

A substantial portion of infrastructure in mountainous regions (including high-rise buildings, bridges, and transmission towers) is directly exposed to complex wind environments, demanding higher levels of structural safety and operational reliability. Compared to flat terrain, hilly topography profoundly alters the characteristics of the near-surface wind field through mechanisms such as flow acceleration, separation, and induced strong turbulence, often rendering traditional design code-based methods inapplicable. Therefore, adopting high-fidelity wind field assessment tools and gaining a deep understanding of structural responses under extreme weather events are crucial for ensuring the resilience of mountainous infrastructure. Publication statistics indicate that bridge siting receives the most attention (Figure 10a), while studies focusing on high-rise buildings and transmission towers remain relatively limited. The vast majority of these studies rely on CFD simulations, with data-driven approaches only recently emerging as a nascent technique (Figure 10b).

For large-span bridges, the dynamic analysis of wind loads is particularly crucial. Studies show that the spatial variability of wind parameters is especially significant in hilly terrain [134,135]. To accurately capture these complex characteristics, research typically employs an integrated approach of field measurements, wind tunnel experiments, and CFD simulations, each with unique advantages and limitations. As the most direct method, field measurements can capture the true spatial distribution of turbulence at a bridge site; for instance, the study by Lystad et al. [53] revealed significant spatial non-uniformity in wind speed and turbulence. However, this method is hampered by high costs and a limited number of measurement points, making it difficult to comprehensively capture spatio-temporal wind field dynamics. Wind tunnel testing, a classical technique for studying bridge aeroelasticity, can replicate topography and the atmospheric boundary layer in a controlled environment but is constrained by scaling effects, such as Reynolds number similarity, which may lead to deviations from reality. CFD simulation, with its flexibility in providing full-field details, has become the primary tool for investigating the wind environment of mountainous bridges. Nevertheless, its accuracy is highly dependent on the choice of turbulence models, grid resolution, and boundary conditions, and the results must be rigorously validated against field or wind tunnel data [58,60]. The outcomes of these refined studies have begun to exert a substantial impact on engineering practice and design codes. For example, addressing strong crosswinds at mountain tunnel portals, a novel transition section design by Peng et al. [136,137] was verified via numerical simulations to reduce the local wind speed amplification effect by 15–20%, significantly enhancing traffic safety. Such findings challenge and supplement existing design specifications (e.g., China’s JTG/T 3360-01 or the Eurocode). Current codes predominantly base wind parameters on flat terrain, whereas findings on the spatial correlation and non-stationary characteristics of mountain wind fields provide a critical scientific basis for future code revisions.

In contrast to bridges, wind-resistance research on buildings in mountainous areas, though less common, is of growing importance. The core impact of topography on building wind loads is twofold: the hill’s acceleration effect significantly increases wind pressure on the windward face, while leeward separation and wake zones induce complex, non-uniform negative pressures on the roof and side walls, posing a severe challenge to the building envelope [138,139,140]. Methodologically, wind tunnel tests can directly measure wind pressure distributions, but accurately simulating upstream inflow conditions remains a technical challenge. CFD simulations, particularly Large Eddy Simulation (LES), show great potential in resolving the fine details of the flow field around buildings, but their widespread application is limited by high computational costs [141]. As an emerging frontier, data-driven models offer a novel solution. For instance, An et al. [138] utilized neural networks to improve the prediction accuracy of peak surface pressures on buildings in complex terrain by approximately 25%, demonstrating their potential for rapid wind load assessment. These studies also reveal the limitations of current loading codes like ASCE 7. Research by Kim et al. [139] indicated that abrupt changes in terrain roughness can cause local wind pressure coefficients on low-rise buildings to be over 30% higher than specified by the code, directly threatening the building envelope’s safety. This suggests that modification factors in current codes, based on idealized topography, fail to accurately reflect the influence of real three-dimensional terrain. These cutting-edge outcomes thus lay the foundation for developing more universally applicable terrain correction methods.

As critical “lifeline engineering,” transmission tower-line systems in mountainous areas face even more unique challenges, including highly non-uniform wind loads due to long spans and large elevation differences, coupled ice–wind effects in high-altitude regions, and the significant amplification of extreme weather by micro-topography [142]. In this context, CFD (especially LES) has become a powerful tool for assessing micro-topographical impacts. The study by Meng et al. [143] confirmed that specific pass-like terrain can amplify typhoon wind speeds by over 25%, drastically increasing the risk of tower collapse; this quantitative result provides refined load inputs for design. Concurrently, dynamic models considering the coupling of multi-physics fields like wind, rain, and ice have been developed [144,145]. Although these models are theoretically more advanced, their complexity necessitates a large amount of measured data for validation, which remains a primary bottleneck.

It is important to emphasize that the aforementioned studies largely focus on the influence of topography on statistically steady atmospheric boundary layer (ABL) wind fields. However, an increasingly prominent frontier is the interaction between complex terrain and transient, non-stationary extreme wind events, such as downbursts and typhoons [146,147,148]. These events possess physical characteristics fundamentally different from the conventional ABL, with more complex wind field structures and greater destructive power, for which existing design assumptions are often inadequate. The coupling of downbursts with hilly terrain creates exceptionally hazardous conditions: the inherent acceleration over a hilltop can superimpose on the already high near-ground winds of a downburst outflow, posing a severe and often underestimated threat to infrastructure on ridges. LES has proven to be an effective tool for simulating these transient, strong interactions [109,149]. Meanwhile, the interaction of large-scale cyclonic systems like typhoons with complex terrain presents a formidable multi-scale modeling challenge, requiring the capture of both the mesoscale storm structure and the microscale flow features around topography [150,151]. To this end, hybrid methods such as embedded Large Eddy Simulation (ELES) have been developed. By embedding a high-resolution LES grid in a critical region while using a more computationally efficient RANS model elsewhere, ELES achieves an effective balance between computational accuracy and cost [152]. Therefore, the study of extreme events is not merely an application of existing computational tools but a core driver for the advancement of computational wind engineering methodology.

Table 13. Quantitative effects of hilly terrain on wind loads and effectiveness of mitigation strategies.

Phenomenon/Application	Key Quantitative Finding	Implications for Design/Codes	Source
Wind loads on low-rise buildings	Due to abrupt changes in terrain roughness, local pressure coefficients can exceed ASCE 7 code values by more than 30%.	Correction factors in current codes, which are based on idealized terrain, are insufficient to reflect the influence of real 3D topography.	Kim et al. [139]
Typhoon amplification effects at mountain gaps	Specific gap topographies can amplify typhoon wind speeds by over 25%.	Extreme event load assessment must consider the amplification effects of micro-topography.	Meng et al. [143]
Wind environment mitigation at mountain tunnel portals	A novel transition section design can reduce local wind speed amplification effects by 15–20%.	Targeted aerodynamic shape design can significantly enhance traffic safety.	Peng et al. [136,137]
Peak pressure prediction on building surfaces	Neural networks can improve the prediction accuracy of peak pressures on building surfaces in complex terrain by approximately 25%.	Data-driven models provide a new pathway for rapid, site-specific load assessment.	An et al. [138]

integrates the key findings from these studies, quantifying the impact of hilly terrain on wind loads and the effectiveness of advanced engineering mitigation strategies, thereby providing a solid scientific basis for subsequent economic and regulatory analysis. The ‘risks’ identified in these studies have immense, quantifiable economic consequences, underscoring the urgency for advanced simulations. The macroeconomic impact of extreme wind events is staggering, with U.S. losses reaching trillions of dollars [153]. The economic fallout from a recent bridge collapse is illustrative: reconstruction may cost nearly USD 2 billion, while indirect losses from shipping disruptions reach USD 15 million daily [154]. This shows indirect costs of infrastructure failure can far exceed direct costs. This economic vulnerability exposes a critical issue: current design codes may underestimate wind loads in complex terrain by over 30%, meaning infrastructure built to code may carry a substantial hidden risk [155]. These potential failure costs are not in initial budgets, creating a negative incentive to use simplified methods, sacrificing long-term safety for lower upfront design costs. From a societal perspective, therefore, high-fidelity simulation is not a ‘luxury’ but an essential risk-mitigation investment with a high potential Return on Investment (ROI).

Finally, a systematic review of the research in this section reveals a geographical concentration of existing case studies, with the majority located in regions such as southwestern China, the European Alps, and the North American Rocky Mountains. The unique topographical and climatic features of these areas have guided the current research focus. Consequently, caution must be exercised when extrapolating these findings to other types of mountainous terrain, such as plateaus or coastal ranges, as their generalizability remains to be verified. Overall, a common challenge in current research is the insufficient consideration of multi-hazard coupling effects (e.g., wind–rain, wind–snow, wind–earthquake), and the pathway for translating cutting-edge research into design code provisions needs strengthening. To overcome these limitations and promote the generalizability of research findings, future studies should focus on the following directions:

• Developing Parameterized Terrain Influence Models: Use extensive CFD and data-driven methods for parametric studies on typical mountain terrains to develop universal terrain influence prediction models or correction factors, providing a basis for revising design codes.
• Establishing a Standardized Validation Database: An international collaborative effort is needed to establish an open-access benchmark database for “Wind Loads on Infrastructure in Mountainous Terrain.” Similar to the “Askervein Hill” project, this would involve long-term monitoring of representative infrastructure to create a public validation platform for researchers to systematically evaluate and improve models.
• Promoting a Universal Framework for Multi-Hazard Coupling Research: Develop a universal numerical simulation framework capable of coupling multiple physical effects. This should be used to systematically investigate the amplification mechanisms of these coupled effects on structural loads, enabling a more comprehensive and safer resilience design for infrastructure in mountainous regions.

4.3. Pollutant Dispersion

In recent years, with accelerated industrialization and urbanization in mountainous regions, pollutant dispersion has become a critical component of hilly terrain wind field studies. Although the number of publications in this area remains relatively low compared to fields like wind energy development, it has garnered sustained research interest due to its direct implications for ecological safety and public health. In contrast to flat terrains, hilly topography introduces unique challenges for pollutant dispersion modeling through complex mechanical and thermal effects, profoundly influencing the transport pathways and concentration distributions of pollutants.

First, mechanical effects are among the primary challenges. As airflow passes over ridges, it often generates large-scale separation and recirculation zones on the leeward side. These zones, characterized by low wind speeds and swirling flow patterns, form “mechanical traps” that can capture and accumulate pollutants, leading to localized concentrations far exceeding those in surrounding areas [156,157]. For instance, combining monitoring data with the WRF model, Lai et al. [158] found that leeward vortices in the mountainous areas of Taiwan play a dominant role in the accumulation and transport of PM2.5 pollution events. In urbanized hilly regions, the combined effect of buildings and terrain can further exacerbate pollutant stagnation in areas such as street canyons [159,160]. Accurately identifying and quantifying the extent and intensity of these recirculation zones is crucial for assessing local air quality risks.

Second, thermal effects often play a more critical role in mountain environments, especially under clear-sky conditions with weak synoptic forcing [161]. The energy exchange between the surface and the atmosphere is strongly modulated by slope aspect and gradient, driving unique local thermal circulation systems such as valley and slope winds. These circulations not only transport pollutants along specific paths but can also “lock” them in valley bottoms during the formation of nocturnal temperature inversions, causing sharp increases in concentration [162,163]. Furthermore, diverse surface covers like vegetation and snow can significantly affect near-surface wind field structures and the dry/wet deposition of pollutants by altering surface properties [156,157]. Therefore, pollutant dispersion in mountainous areas is a classic multi-scale problem, where accurately coupling physical processes across different scales remains a core difficulty in modeling.

To address these challenges, Computational Fluid Dynamics (CFD) has become an indispensable research tool [164,165]. Among CFD methods, Reynolds-Averaged Navier–Stokes (RANS) models are often used for preliminary engineering assessments due to their lower computational cost, but their accuracy is limited in simulating highly separated flows and anisotropic turbulence [166]. In contrast, Large Eddy Simulation (LES) can more accurately resolve the transient structures of turbulence, offering significant advantages in predicting peak concentrations and studying the unsteady characteristics of dispersion, albeit at a much higher computational expense. For particulate matter (PM) dispersion, the Euler–Lagrange approach, combining CFD with a Discrete Phase Model (DPM), has become a mainstream technique [167,168]. This method tracks the trajectories of a large number of representative particles, fully accounting for particle inertia, gravitational settling, and interactions with turbulent eddies. This enables a detailed analysis of the transport and deposition differences among particles of various sizes (e.g., PM2.5 and PM10), which is vital for health risk assessments [169]. To overcome the limitations of standalone microscale CFD models, coupling mesoscale meteorological models (like WRF) with microscale CFD models (WRF-CFD) has become a state-of-the-art solution [170]. This coupling allows realistic, time-varying meteorological fields from the mesoscale model to drive high-resolution local CFD simulations, thereby greatly enhancing the accuracy and realism of pollutant dispersion predictions. However, the reliability of any numerical model depends on validation against physical observation data from field measurements or wind tunnel experiments [165,171,172]. Yet, each validation method has inherent limitations: field measurements, while providing the most realistic data, are costly and spatially sparse; wind tunnel experiments, though conducted under controlled conditions, face challenges with strict similarity criteria (e.g., Reynolds number mismatch) and struggle to fully replicate real-world atmospheric thermal stratification.

Table 14. Comparison of pollutant dispersion models.

Method	Core Principle	Main Advantages	Key Limitations	Best Application Scenarios
Field Measurement	Direct measurement in real environments	Provides “ground truth” data for validation	High cost; difficult to capture 3D structure	Long-term monitoring; numerical model validation
Wind Tunnel	Scaled-down lab simulation	High controllability and repeatability	Significant thermal effect errors	Basic physical research; model verification
RANS-CFD	Solves time-averaged equations	High computational efficiency, low cost	Poor accuracy for peak concentrations	Preliminary screening and long-term average concentration assessment for industrial site selection and environmental impact
LES-CFD	Solves large-scale eddies directly	High fidelity; captures turbulent structure	High computational cost and demands	Consequence assessment of sudden accidents; refined risk assessment in high-risk areas
WRF-CFD	Couples meteorological and CFD models	High accuracy for forecasting	High computational complexity	Regional air quality forecasting; pollutant diffusion research under complex weather conditions

provides a systematic comparison of these methodologies.

As indicated in

Table 15. Comparison of field measurement strategies for validating diffusion models.

Feature	Intensive Observation Period (IOP)	Long-Term Routine Monitoring
Main Objective	Understanding physical mechanisms	Regulatory compliance and statistical validation
Time Coverage	Short-term (days to weeks)	Long-term (months to years)
Measurement Frequency	High (e.g., 1 Hz to 100 Hz)	Low (e.g., hourly averages)
Typical Instruments	Multi-wavelength LiDAR, UAVs, sodar, research aircraft	Fixed-site gas/particle analyzers
Core Advantages	High spatiotemporal resolution data	Cost-effective; strong statistical representativeness
Core Limitations	Limited time coverage, high cost	Low spatial resolution, missing turbulent data
Ideal Model Match	LES, high-fidelity CFD models	RANS, Gaussian, operational forecast models

, field data collection follows two complementary paradigms: short-term, high-intensity Intensive Observation Periods (IOPs) and long-term routine monitoring. These strategies are not interchangeable; they serve the validation goals of different model types. Applying inappropriate validation data to a specific model is a fundamental methodological error. For example, using hourly averaged data from routine stations to validate an LES model (designed to resolve high-frequency eddies) is akin to evaluating a high-performance sports car by its average speed on a long trip. This ignores the model’s core capability: capturing transient flow structures. This mismatch often yields uninformative or misleading results. Hourly averaged data filter out the unsteady structures in LES; thus, it cannot test the model’s unique high-fidelity capabilities. A flawed LES model (e.g., with an improper subgrid-scale model) might perform adequately averaged statistics, while a correct LES, if compared against unrepresentative points, might appear to perform poorly. This mismatch is the fundamental reason for “huge discrepancies among participants’ calculations” in model inter-comparisons, weakening the field’s credibility. Therefore, the validation strategy must be conceptually aligned with the model’s purpose.

Furthermore, mismatch between modeling capabilities and validation data creates a “validation gap”: we have LES models capable of resolving fine-scale, transient turbulent structures, but lack the experimental data with corresponding spatiotemporal resolution for rigorous validation [173]. To bridge this gap, the academic community is increasingly adopting standardized quantitative validation metrics, such as Fractional Bias (FB), Normalized Mean Square Error (NMSE), and the fraction of predictions within a factor of two (FAC2), to objectively evaluate and compare the performance of different models [170,174]. In classic complex terrain dispersion experiments, these metrics are widely used as quantified benchmarks [175]. For instance, one study comparing the CFD model FLUENT against wind tunnel and field tests showed the model achieved an FAC2 of 77.9% for wind speed, yet its relative error for peak concentration reached 72.5% [176]. This indicates that accurately predicting critical peak concentrations remains a challenge, even when the overall flow field is captured. Furthermore, evaluating the regulatory model AERMOD with experiment data showed it predicted the highest 1 h concentration magnitude within ±30%, but specific location predictions could differ from observations by nearly a factor of 1.9 [175]. Studies also consistently show CFD simulations tend to underestimate maximum concentration values compared to physical models [177]. In contrast, high-fidelity methods (like LES) validated against high-quality lab data achieve a near-perfect match (FB as low as 0.02, FAC2 as high as 0.98), directly confirming the positive trade-off between computational investment and predictive accuracy [178].

Despite significant progress, current research exhibits systematic limitations. The existing literature is often concentrated on specific geographical regions (e.g., the European Alps), with insufficient research on other important mountain ranges, limiting the generalizability of findings. Concurrently, studies tend to favor neutral stratification conditions, with less exploration of dispersion mechanisms under the strong stable or unstable conditions common in mountains. Furthermore, most models neglect the coupling effects of key multi-physics processes such as complex chemical reactions, precipitation scavenging, and absorption by vegetation canopies—gaps that future research urgently needs to address.

Looking forward, a suite of cutting-edge technologies heralds a shift from a data-scarce to a data-rich era in this field. Mobile observation platforms, represented by unmanned aerial vehicle (UAV) swarms, can perform in situ, three-dimensional, and synchronous measurements of pollutant plumes, offering a direct solution to fill the “validation gap” [41,179]. Simultaneously, Digital Twin technology presents a revolutionary approach by integrating real-time sensor data, high-fidelity physical models (such as WRF-CFD), and artificial intelligence (AI) algorithms to create a dynamic virtual replica of the physical world, enabling real-time prediction, scenario simulation, and proactive decision support [180,181].

Finally, the findings from research on pollutant dispersion in mountainous areas must be closely integrated with practical applications. High-resolution dispersion models can inform the scientific siting of industrial parks and the formulation of dynamic emission standards. For sudden chemical release accidents, fully validated rapid-response models are core to building early warning systems, providing critical information for emergency evacuation and decision-making. This transition from academic research to operational, real-time management signifies a deep integration of environmental science and smart city operations, providing powerful technological support for building healthier and more resilient mountain communities.

5. Discussion and Challenges

This review reveals significant advancements in wind field modeling over hilly terrain since 2015, yet it also highlights persistent challenges that remain to be addressed. These challenges are not merely technical bottlenecks of individual methods but are systemic issues that cut across different methodologies and applications. As shown in Table 16, existing research methodologies face the following four interrelated core challenges, which constrain the translation of research findings into reliable engineering practices and are ranked below in order of importance:

• The Validation Chasm—A Fundamental Contradiction Between High-Fidelity Models and Sparse Validation Data

This is the most critical bottleneck currently facing the field. Although high-precision CFD (particularly LES) and advanced data-driven models can generate meter-scale spatiotemporal wind field information, the corresponding validation data are exceptionally scarce. Field measurements, due to high costs, are often limited to sparse point data, making it difficult to capture complete three-dimensional flow structures. This “chasm” means that many cutting-edge models can only be validated using qualitative descriptions or coarse statistical metrics, lacking rigorous quantitative verification of key physical phenomena such as turbulent fluctuations and flow separation. This uncertainty severely impedes the transition of advanced models from academic research to engineering practice.

2.

The Inherent Complexity of Multi-physics and Multi-scale Coupling

Wind fields in hilly terrain are not driven by mechanical forces alone but are the product of complex coupling between multiple physical processes, including thermodynamics, precipitation, and vegetation. At night, thermal effects leading to temperature inversions can completely alter pollutant dispersion patterns. During extreme weather, the synergistic effects of wind, rain, and ice on structures like transmission towers are far greater than a simple superposition of individual factors. Integrating these factors into a single model can increase computational costs by one to two orders of magnitude and introduce additional model uncertainties. Neglecting these coupled effects can lead to unsafe or uneconomical design decisions. For example, research has quantitatively demonstrated that micro-topography can amplify typhoon wind speeds by over 25%, directly proving its critical impact during extreme weather.

3.

The Pervasive Lack of Data Standardization, Quality Control, and Heterogeneity Management

The rise of data-driven models has made data itself a core challenge. Training data originate from multiple heterogeneous sources, including CFD simulations, field measurements, and LiDAR, each with different quality, resolution, and error characteristics. This makes building a universal and robust AI model a formidable task. Furthermore, traditional cross-validation methods (e.g., k-fold, mean errors, RMSE) are fundamentally unsuitable for spatiotemporally correlated meteorological data. The field currently lacks unified protocols for data quality control and model validation, severely limiting the comparability and reproducibility of research findings.

4.

The Generalizability and Geographical Limitations of Research Findings

Most of the cutting-edge research cited in this review is highly concentrated in specific geographical regions, such as the European Alps and the North American Rocky Mountains. Consequently, the generalizability of models or parameterization schemes validated in one region to other climatic zones or different topographies is questionable. This highlights an urgent need for international collaboration to conduct large-scale field observation campaigns in data-sparse regions (such as the Andes and African highlands) to build more globally representative datasets, thereby advancing models toward greater universality.

Table 16. Core challenge and research directions in wind field modeling over hilly terrain.

Core Challenge	Key Quantitative Evidence	Impact	Corresponding Research Direction
1. Validation Chasm	RANS overestimates leeward zone size by up to 30% [64]. LES shows RMSE up to 5.65 m/s on Perdigão ridge [67].	Increases AEP prediction uncertainty (P50–P90), directly raising project financing risk [153].	Establish global benchmark datasets similar to IEA Task [182]. Conduct Perdigão-level high-density observation experiments in data-sparse regions [67].
2. Multi-physics Coupling Complexity	Micro-topography can amplify typhoon wind speeds by over 25% [143]. Nocturnal thermal inversions “trap” pollutants [162,163].	Current design codes (e.g., ASCE 7) underestimate loads by over 30%, posing significant safety risks [139].	Develop multi-scale coupled models like WRF-LES. Study the impact of multi-hazard coupled effects (wind-rain-ice) on infrastructure [66].
3. Data-Driven Paradigm Dilemma	AI reduces inference time from hours to seconds, but training data from unvalidated CFD risks “bias amplification” [102].	Fast, incorrect predictions are more dangerous than slow, accurate ones.	Develop Physics-Informed Neural Networks (PINNs) to integrate physical constraints into AI. Establish data quality and validation protocols as advocated by IEA Task 51 [183].
4. Generalizability Limitations	Most benchmark experiments are concentrated in specific regions (e.g., Europe, North America, like NEWA) [40], questioning model applicability in other climate zones (e.g., tropical, polar).	Limited global generalizability of models and parameterization schemes.	Conduct new international collaborative field observations in representative regions (e.g., Andes, African highlands) to fill “climate mechanism gaps.”

Table 16. Core challenge and research directions in wind field modeling over hilly terrain.

Core Challenge	Key Quantitative Evidence	Impact	Corresponding Research Direction
1. Validation Chasm	RANS overestimates leeward zone size by up to 30% [64]. LES shows RMSE up to 5.65 m/s on Perdigão ridge [67].	Increases AEP prediction uncertainty (P50–P90), directly raising project financing risk [153].	Establish global benchmark datasets similar to IEA Task [182]. Conduct Perdigão-level high-density observation experiments in data-sparse regions [67].
2. Multi-physics Coupling Complexity	Micro-topography can amplify typhoon wind speeds by over 25% [143]. Nocturnal thermal inversions “trap” pollutants [162,163].	Current design codes (e.g., ASCE 7) underestimate loads by over 30%, posing significant safety risks [139].	Develop multi-scale coupled models like WRF-LES. Study the impact of multi-hazard coupled effects (wind-rain-ice) on infrastructure [66].
3. Data-Driven Paradigm Dilemma	AI reduces inference time from hours to seconds, but training data from unvalidated CFD risks “bias amplification” [102].	Fast, incorrect predictions are more dangerous than slow, accurate ones.	Develop Physics-Informed Neural Networks (PINNs) to integrate physical constraints into AI. Establish data quality and validation protocols as advocated by IEA Task 51 [183].
4. Generalizability Limitations	Most benchmark experiments are concentrated in specific regions (e.g., Europe, North America, like NEWA) [40], questioning model applicability in other climate zones (e.g., tropical, polar).	Limited global generalizability of models and parameterization schemes.	Conduct new international collaborative field observations in representative regions (e.g., Andes, African highlands) to fill “climate mechanism gaps.”

Based on the analysis of these challenges, we propose the following specific and actionable future research roadmap:

• Integration of Multi-scale, Multi-physics Models: Efficiently couple mesoscale meteorological models (e.g., WRF) with microscale CFD simulations (especially LES) to balance computational cost and accuracy, while utilizing emerging high-resolution NWP (e.g., ICON, IFS regional configurations [184,185]) to provide higher-precision inflow boundary conditions. Furthermore, explore methods such as Physics-Informed Neural Networks (PINNs), which embed physical information as soft constraints, to generate physically plausible wind field predictions in data-sparse scenarios.
• Standardization of Data and Validation Protocols: Through international collaboration (drawing from initiatives like IEA Tasks [182,183]), conduct large-scale, multi-physics field observation campaigns in globally representative regions (e.g., the Perdigão experiment), especially by making full use of ground-based scanning LIDAR and SODAR technologies [24,25]. These remote sensing technologies are key weapons to bridge the “validation chasm,” providing 4D (3D space + time) wind field structures rather than sparse point data. Future standardized protocols must require models not only to match meteorological mast data but also to quantitatively reproduce key flow structures observed by LIDAR (e.g., recirculation region dimensions, wake morphology) and turbulence statistics (e.g., spectra and PDFs).
• Deepening and Broadening of Application Domains: Conduct in-depth research on the interaction mechanisms between extreme wind events (e.g., downbursts, typhoons) and complex terrain. Investigate the response of infrastructure to multi-physics coupling effects (wind–rain, wind–ice–snow) to enhance structural safety and energy security in mountainous regions. The ultimate future application form is the construction of “Wind Engineering Digital Twins” for mountainous areas [181]. For example, building a wind farm digital twin that fuses high-resolution NWP, live LIDAR scanning data, and sensor information in real-time, utilizing AI and reduced-order models to predict turbulence and loads for every turbine in the next hour, thereby enabling active dynamic yaw control and extreme load avoidance. Apply wind field models to assess pollutant dispersion in mountains (environmental health) and turbine noise propagation to provide a scientific basis for sustainable energy and environmental planning.

6. Conclusions

This review has systematically examined the key advances in wind field modeling over hilly terrain since 2015. The research paradigm has undergone a fundamental shift, moving from a focus on idealized, two-dimensional terrain simulations toward a comprehensive exploration of multi-physics, multi-scale coupled problems over real, complex three-dimensional terrain. This transition has been primarily driven by the leap in high-performance computing capabilities and pressing practical demands in areas such as wind energy development and infrastructure safety.

Over the past decade, significant, quantifiable progress has been made. In terms of model accuracy, coupling mesoscale meteorological models with microscale CFD simulations can reduce the mean wind speed prediction bias to below 0.1 m/s. For engineering applications, optimized designs for infrastructure in mountainous areas can mitigate local wind speed amplification effects by 15–20%, while wind farm layout optimization can increase annual energy production by 3–5%. Regarding computational efficiency, data-driven models, particularly those based on AI, have achieved a revolutionary breakthrough, reducing the inference time for high-resolution wind fields from hours to under a second.

Nevertheless, despite these achievements, wind field modeling over hilly terrain still confronts a series of deep-seated, systemic challenges. These challenges are interconnected and constrain the translation of research findings into reliable engineering practices. As detailed in Section 5, they can be categorized into four main areas: the fundamental contradiction between high-fidelity models and sparse validation data; the inherent complexity of multi-physics and multi-scale coupling; the widespread lack of data heterogeneity and standardization; and the generalizability of research findings versus their geographical limitations.

To address these challenges and steer future progress, we recommend that future research prioritize the following strategic directions:

• Establishing global benchmark datasets and advancing observational technologies: Foster international collaborations to create high-quality, open access benchmark datasets from representative terrains worldwide to bridge the “validation gap.”
• Developing efficient multi-scale coupled and physics-data fusion models: Focus on developing frameworks that efficiently couple mesoscale models (e.g., WRF) with microscale LES, and explore cutting-edge methods like PINNs to generate physically plausible predictions in data-scarce scenarios.
• Deepening application-oriented research with a focus on extreme events: Enhance the investigation of interaction mechanisms between extreme wind events, such as downbursts and typhoons, and complex terrain, and apply high-fidelity wind field models to the resilience assessment of infrastructure under multi-hazard coupling effects.

In summary, wind field modeling over hilly terrain is at a pivotal juncture, transitioning from ‘simulation’ to ‘replication’ and from ‘point-based’ to ‘domain-wide’ analysis. The ultimate goal is to construct a “Digital Twin” of the mountainous environment. This vision is built upon solid quantitative progress: our demonstrated ability to reduce point-based prediction bias to below 0.1 m/s and shorten domain-wide inference to the scale of seconds via AI jointly confirms the capability to make the leap from ‘simulation’ to ‘replication’. In the future, this “Digital Twin” system will no longer be limited to providing a “scientific foundation” but aims to deliver actionable decision-making tools: for instance, providing real-time, multi-scale coupled power generation forecasts and operational commands for wind farms (expanding the currently validated 3–5% AEP improvement potential to regional wind cluster management), or issuing street-scale infrastructure risk warnings for urban managers during extreme weather transit. Achieving this vision requires not only continuous breakthroughs in computational science and atmospheric physics but also a broader international data-sharing and model-validation framework established upon specific initiatives, such as NEWA or IEA-Wind Tasks, to ultimately provide robust decision support for the sustainable development of energy, environment, and infrastructure in mountainous regions.