Evaluating weather impact on vehicles: a systematic review of perceived precipitation dynamics and testing methodologies

The performance of road vehicles degrades when driving in adverse weather conditions. Weather testing for vehicles is important to understand the impacts of precipitation on vehicle performance, such as driver visibility, autonomous sensor signal, tire traction, and structural integrity due to corrosion, to ensure safety. This tutorial summarizes the essential elements for performing realistic testing by applying physical and meteorological rationale to vehicle applications. Three major topics are identified as crucial steps for precise quantitative studies, including understanding the natural precipitation characteristics, estimating the perceived precipitation experienced by a moving vehicle, and selecting data collection strategies. The methods used in current practices to investigate the effects of rain and snow on road vehicles at common facilities of outdoor test tracks, drive-through weather chambers, and climatic wind tunnels are summarized. The testing techniques and relevant instrumentations are also discussed, with considerations of factors that influence the measured data, such as particle size distribution, precipitation intensity, wind-induced droplet dynamic events, accumulation behaviour, etc. The goals of this paper are to provide a tutorial with guidelines on designing weather testing experiments for road vehicles and to promote the idea of establishing standardized methodologies for realistic vehicle testing that facilitates accurate prediction of vehicle performance in adverse weather conditions.


Introduction
Road vehicle operation is affected by precipitation events, such as fog, rain, snow, and hail.During these events, precipitation particles impact the road and vehicle surfaces directly; indirect impacts of contaminants are deposited onto the vehicles, such as salt and dirt from the wet ground [1][2][3].
Often it is inevitable to commute in adverse weather conditions; understanding the effects and the potential risks associated with different weather types is crucial for transportation.The precipitation frequency in a region is a result of the interactions of thermodynamic, physical, and dynamical processes during which an increase in water vapor and a decrease in atmospheric stability can contribute to more frequent and heavier precipitations [4].
During precipitation events, road vehicles experience issues that cause performance degradation and risk of accidents, including but not limited to driver visibility [5], autonomous sensor signal [6], tire traction [7] and corrosion [8].As such, governments, industries, and academia are actively studying different weather effects and developing solutions for a variety of road vehicle applications [9][10][11][12].
Although weather testing for vehicles may seem to be an old topic, a common setback is to realistically simulate the climatic conditions encountered in the real world.Outdoor measurements are challenging, and creating a robust database for accurate statistical analysis can take years.For this reason, critical parameters must be identified so that they can be reproduced in a controlled environment, such as climatic wind tunnels.Efforts are needed in the direction of correlating meteorological factors such as particle size distributions and intensities perceived from the perspective of moving vehicles.Only very recently, a method was developed based on unsupervised machine learning to identify recurring precipitation events in southern Ontario, Canada [13].
Many methodologies exist related to introducing and quantifying precipitation on a test vehicle; there are a wide variety of facilities, weather simulation systems, and measurement instruments employed and reported in the open literature.However, a lack of standardized procedures is likely to hinder the advancement of automotive technologies.These are explained below.
Although some vehicle-in-weather related review topics exist, they are mostly application specific, such as contaminant particle deposition [1], visibility [14], and autonomous vehicle sensor performance [6]; however, there seems to be no comprehensive review exists on road vehicle testing methodologies in adverse weather conditions.This paper intends to provide guidelines to answer questions such as where to test, what to test, and how to test.It is the hope that this tutorial can contribute to shaping the field and provide directions and testing strategies.
The main goal of this work is to provide a comprehensive overview of the recent studies on road vehicle testing in rain and snow conditions.In the review, each of these forms of precipitation is subdivided into the natural precipitation (no vehicle system involved, fixed reference system) and perceived precipitation (with a vehicle system involved, standing or moving).Then, analysis is performed on different evaluation methods, and lastly, guidelines for designing weather testing experiments for vehicles are provided.

Analysis
In the analysis, a systematic approach was taken to identify the key parameters and the suitable methodologies for evaluating weather impacts on vehicles, as shown in figure 1.The three main steps include (1) understanding natural precipitation characteristics; (2) estimating the perceived precipitation that a moving vehicle experiences; and (3) evaluating the impacts of precipitation on the test vehicle based on the correlations between natural and perceived precipitation.

Natural precipitation
In order to evaluate perceived precipitation, first, natural precipitation needs to be understood well and quantified.In this section, the characteristics of natural rain and snow precipitation are summarized using observations.Since our ultimate research interest is related to weather impact on automotive applications, this section will briefly discuss related key meteorological factors affecting vehicle performance.

Natural rain
The raindrop characteristics that matter to road vehicle applications include rain intensity, drop size, and its fall velocity.These characteristics are especially critical to applications that are sensitive to the droplet impacting frequency, energy, size, and shape, such as optical sensors used in autonomous and modern vehicles [15].These features are reviewed and summarized into separate sub-sections.Then, particle size distribution (PSD) models used to describe natural rain are also presented.

Rain intensity
Rain intensity is calculated by measuring the water mass per unit time using a weighing gauge or PSD using an optical instrument [16].Measurements are then converted to mm h −1 normalized by the sampling area.There are two main types of weather reports: Meteorological Aviation Report (METAR) for aviation purposes and Surface Synoptic (SYNOP) observations for general weather forecasts.The classifications of rain intensity are listed in table 1.Some researchers may classify using their own metrics [17], potentially due to the capacity of custom instrumentation.Despite the differences, the amount of rain is still described in similar ranges.

Raindrop size
Raindrops are formed when extremely small cloud droplets in the size range of 1-50 μm grow by vapor diffusion, collision, and coalescence processes and finally fall as raindrops by overcoming vertical air velocity magnitude.Raindrops may undergo different dynamic events, such as collision, breakup, and coalescence during the fall, which would impact the final size that lands on a surface, resulting in a droplet size distribution [19].Volume mean diameter represents one of the raindrop size distribution (DSD) parameters and it is defined as [20], where n i and d i are the number count and droplet diameter at bin number i, respectively, and N = ∑n i .The subscripts 3 and 0 are weights for the type of mean calculation according to the moment-ratio-notation for particle analysis [21].
As an example, Wen et al [22] measured droplet size during three different types of rain, namely shallow, stratiform (rain), and convective (showers), and found that the mass weighted mean droplet diameters were 0.64 mm, 1.16 mm, and 1.41 mm, respectively.Droplet size is also influenced by geographic location, it was measured by Bringi et al [23] that convective precipitation in continental areas have D m close to 2.75 mm in size and is larger than maritime areas by about 1 mm.Besides the types and locations of precipitation, droplet size is also influence by temperature and evaporation.Seela et al [24] measured stratiform and convective precipitations in summer and winter times; it was found that droplets tend to be larger in the summer period.
The data trend fitted to observations shows a power law relation between the median droplet size (D 50 [mm], 50% of droplets are smaller or larger than the D 50 ) and rain intensity (I [mm h −1 ]) as D 50 = aI b [25] where a and b are a constant in the unit of h and a unitless constant, respectively.According to this relationship, droplet size tends to be larger in heavier rain cases.

Raindrop terminal velocity
When raindrops fall from the cloud, they accelerate until they reach terminal velocity, at which the falling speed will remain constant in a homogeneous environment with a fixed relative humidity.Terminal velocity ) is achieved when gravitational force and drag force are in equilibrium; it is a function of droplet size (D [mm]) and can be estimated from empirical models such as the one by Atlas et al [26], obtained through experiments in a controlled environment.The equation for terminal velocity as a function of droplet diameter can be written as v t (D) = 9.65-10.3 -0.6D .

Particle size distribution models
In order to accurately describe the overall rain characteristics, drop size distributions are needed.The first moment of PSD is the total drop number concentration [27].For each bin width (Δd [mm]), the number concentration (N d [m −3 mm −1 ]) can be derived as where n, v z , t, SA are the count of drops, fall velocity [m s −1 ], sampling time interval [s] and sampling area [m 2 ], respectively.
There are various models for drop size distribution, such as the exponential or gamma size distributions [28].Marshall and Palmer [29] fitted a regression line to the observations where N d decreases with increasing D that is given as N d (D) = N o e − ΛD , where N o is a constant representing the spatial density and Λ [cm −1 ] is a fit constant, respectively; thus, D here has a unit of cm.Intensity (I [mm h −1 ]) can be calculated by using N o = 0.08 cm −4 (or 8000 m −3 mm −1 ) and Λ = 41 I −0.21 .
The use of the gamma function was proposed by earlier studies [27], which includes an additional shape parameter to better fit a broader range of observations, especially in regions of smaller droplet sizes.However, it was debated that the use of the gamma model may be of little practical difference compared to the exponential model [28], as there are a lot of uncertainties in the measured data with the current state-of-the-art instruments [16].In a brief summary, the raindrop characteristics discussed in this section can be used as a reference for realistic parameters that should be considered in simulated weather experiments on vehicles in a controlled testing platform.In addition, the relationships and models presented are useful tools to classify the conditions of interest when studying vehicle performance in rain.

Natural snow
Snow is a more complex problem than rain because it can possess various particle shapes and spectral characteristics.Often, snow begins to affect vehicle performance as it accumulates on the surface.The accumulation behaviours of snow highly depend on snow type and wind effect, as snow particles have lower density; therefore, they are easily carried away by the wind.Snow characteristics that accumulation is dependent on are explained below.

Snow type
Snow events are called flurries or showers depending on the intensity when snow falls in a relatively calm environment, and blowing and drifting snow events occur in the presence of wind, which may escalate into squalls or blizzards depending on the duration [30].Blowing and drifting snow are similar in nature; the difference lies in their flying height [31].Blowing and drifting snow events are identified as hazardous conditions for road vehicles because visibility is affected [16,32].
Snow can be classified as wet or dry based on its liquid water content (LWC), which is significantly influenced by the temperature profile.Wet snow occurs when a portion of the snow melts as it falls, typically at temperatures just above freezing.Dry snow is powdery and occurs when temperatures are well below freezing, allowing it to remain low in LWC and can be easily blown by the wind [33].Temperature variations between day and night, ground temperature, and sunlight exposure further affect the wetness of snow.Research into the formation of wet snow reveals varying temperature thresholds across multiple studies [34,35].Typically, snow exhibits adhesive properties to surfaces at temperatures between −2 °C and 5 °C [36].

Snow shape
When ice crystals reach sizes of 0.2-0.3mm, they start to fall down and collect other particles and then become snow.The formation of ice crystals is governed by ice nuclei and then heat transfer and vapor diffusion [37]; thus, temperature and humidity play important roles in the morphology of the ice crystals.While collisions and agglomerations can lead to multi-crystal snowflakes [38], there can be as many as over 120 categories of snow and ice crystals [39].Among all the possible structures, the hexagonal crystal was found to be the most prevalent form [33].

Snow crystal size
Snow crystals can be suspended in the air by turbulent diffusion, causing further thermodynamic and mechanical alteration of the crystals [38]; as a result, their size varies over wide ranges.The crystals continue to grow through collisions and coalescence processes as they fall; thus, the measured diameters can be as large as 30 mm [40,41].Falling snow crystal sizes usually are less than 50 mm.Snow as ice crystals exist in the range of 2-15 mm and averaged at around 5 mm.Dry dendrites were measured to have the widest range of 5-20 mm, and had a larger average size of about 15 mm.
Wind-induced breakup of snow crystals is evident by the much smaller diameters measured for blowing and drifting snow; the two types of snow were measured in Canada and Switzerland to have a similar mean diameter of around 0.1-0.3mm and a size range between 0.04-0.8mm [42,43].

Snow packing density
Unlike rain, for which there is surface drainage of water in typical scenarios, snow tends to pile up on a surface.As mentioned in the section 'Snow type', snow crystals are carried along by the wind and turbulence, causing accumulation in solid form with different particle densities.Parameters such as crystal size and terminal velocity [44], air temperature [45], and wind speed [46] all have an impact on the agglomeration process of snow crystals [40].The classifications of snow based on accumulated densities are listed in table 2.
The snow characteristics discussed serve the purpose of categorizing of snow conditions in the experimental design, where the vehicle is stationary.However, when the vehicle is in motion, additional dynamical parameters become significant which may cause differences in the measured precipitation perceived by the moving vehicle.

Perceived precipitation
In the previous section, the characteristics of natural precipitation were discussed, as experienced by stationary vehicles.In this section, the physical condition experienced by moving vehicles is introduced, i.e., perceived precipitation, where a vehicle travels through a precipitation event.The amount of precipitation perceived by a moving vehicle depends not only on the vehicle speed but is also explained as a function of the shape, dimension, and orientation of the vehicle surfaces.The problem is analyzed first by looking at the dynamical concepts, then models from the literature are applied to a moving vehicle, and lastly, limitations of the models are identified, and the challenges are discussed when implementing them in vehicle studies.

Concepts 4.1.1. Reference frames
The concept of vehicle driving in a precipitation event can be explained using two perspectives: (1) the stationary observer or (2) the moving observer within the vehicle [48], shown in figures 2(a)-(b).A stationary observer will see precipitation falling vertically (if there is no wind) and a vehicle moving horizontally.From the moving observer's perspective, the precipitation will strike the moving vehicle at an angle.
Extending the picture of the moving vehicle perspective, Bocci [49] discussed the perceived precipitation velocity as a density vector resulting from precipitation fall velocity, wind speed, and vehicle velocity.Assuming driving velocity is constant, the perceived impacting angle (α in figure 2(b)) increases if there is a headwind or decreases if there is a tailwind.

Surface orientation
A moving vehicle has surfaces having different orientations with respect to the incoming rain; the major groups are horizontal, vertical, and slanted, corresponding to hood and roof, front and rear bumpers, and front and rear windscreens, respectively.
Bocci [49] suggested that there can be both wet and dry surfaces when the vehicle is in translational motion with respect to falling precipitation.This is evident by observing the rain strikes on the rear windscreen, where  the surface remains dry when the windscreen surface is parallel to the apparent rain vector.The amount of precipitation received by simple geometries having horizontal and vertical surfaces was discussed in earlier studies [50,51].At slower speeds, most of the precipitation lands on the horizontal surfaces; however, as speed increases, the vertical surfaces begin to collect more precipitation.

Dynamic models
Hence, in quantitative terms, how much precipitation amount does a moving vehicle experience?Several models attempted to answer this question with a simplified object geometry traveling in a straight trajectory and under constant precipitation conditions.Most of the existing models focus primarily on rain but not snow as they do not consider the aerodynamics and atmospheric dynamics, which would alter the flow paths of snow crystals but less on raindrops.
A first attempt was to determine the number of droplets strikes [52]; this model calculates the number of raindrops striking on projections of the moving surfaces.The total number of strikes (N S [drops]) is defined as the droplet intensity (S [drops cm −2 s −1 ]) experienced by the vertical (A z ) and horizontal (A x ) components of the surface area in a given amount of time (t [s]), expressed as N s = S (A z + A x ) t.A similar approach was followed by De Angelis [48], some researchers presented a similar method to find the optimal speed to reduce the volume of rainfall encountered by the moving body in rain and wind scenarios [50,53].The use of oversimplifying hypotheses of travel distances at slow speeds, has led to questionable conclusion that moving faster can minimize weather impact on vehicle performance.Moreover, driving faster in adverse weather is generally not a safe solution.These studies were also insufficient to answer the question fully of how much precipitation amount does a moving vehicle experience.
Although the number of impacts provides a qualitative insight on the amount of water encountered by the vehicle, it is limited as a parameter, as it does not consider the average size of the droplets.Therefore, both the number of strikes and optimal speed models are impractical; they have limited usefulness for evaluating the precipitation impact on vehicle applications.To pair the drop size distribution (DSD) data with the number of strikes model, thus connecting the natural and perceived precipitation characteristics, a different metric is required for the correct evaluation of the problem, and the flux model is the more appropriate choice.Rain rate, often used in meteorology, is defined as precipitation mass passing through a unit area for a given time, and it has a unit of kg m −2 s −1 ; in perceived precipitation scenarios, it is referred to as rain flux.
Holden [51] introduced the concept of rain flux as a volume swept by the surface components with only vertical rainfall without wind.Another flux model based on equations from electromagnetism was proposed by Bocci [49].This approach allows the formulation of a more robust model since it is possible to consider more complex geometries with different orientations.The calculation of the rain flux (Φ) is given by a surface integral, expressed as the dot product of the rain density vector (j) and the vector normal to the surface area (dA) exposed to precipitation, given by Φ

S wet
When the shape and dimensions of the measurement surface are known, the flux calculation becomes trivial.This model, however, does not consider the rain flux as a particle flux nor is any mention made of data collection methods.Although it is suitable for vehicle applications, the model needs adjustments to directly input instrumentation data, and was reported in the work of Carvalho and Hangan [54] who carried out computational simulations of precipitation rates on surfaces with different orientations and speeds along non-linear paths.The developed algorithm is inspired by the flux equation of Bocci [49] but incorporates the required experimental aspects for the implementation of the model in real-life applications.
On the other hand, Lanza and Barbera [55] derived a simplified perceived intensity model, similar to that of flux, but now the rain rate is expressed in mm h −1 .The perceived intensity approach allows for the direct implementation of measurable quantities of surface orientation (θ [deg]), rain intensity, vehicle speed, and raindrop falling velocity.The perceived rain intensity (I p [mm h −1 ]) on a surface is the sum of the horizontal and vertical perceived precipitation rates, defined as where the horizontal perceived precipitation intensity can be estimated as the rain density in the environment which is being swept by the vehicle at the speed of u x [m s −1 ]; and I is the natural precipitation intensity and v z [m s −1 ] are the total volume of all droplets measured, area, time elapsed, and falling velocity, respectively.
Further looking at the perceived intensity equation, a perceived-to-natural precipitation intensity ratio (I p /I) can be obtained, the ratio approach was also reported in the work of Rabiei et al [56].A qualitative implementation of the perceived intensity model is shown in figure 3 for surfaces oriented at different angles, it was found that multiple I p /I ratios are possible for the same driving speed.Suggested by Pao et al [15], the ratio is affected by a critical parameter of the droplet falling velocity (v z ), which depends on the droplet size and aerodynamic upwash.
Since aerodynamics play a role in the perceived intensity on a moving vehicle, it is challenging to place instruments to measure perceived precipitation on the surface as it will alter the aerodynamics.Thus far, the perceived precipitation data for vehicles under a wide range of conditions is not available in the open literature.There is no simple solution to quantifying perceived precipitation on a vehicle, since it depends on several variables such as wind direction, variation of precipitation rate, exposure time, and aerodynamics.Still, the dynamic models that correlate natural and perceived precipitation intensities are useful to define a cost function to be evaluated in real-time between a vehicle and a weather station.Crucial pieces of information such as wind and aerodynamic influences on perceived precipitation would be beneficial to realistic weather studies for vehicles.

Vehicle testing methodologies
Test conditions possibility and results repeatability are highly dependent on the capacity of the investigative tools, e.g., facility, vehicle speed limit, weather conditions, and controllability of experimental parameters.The state-of-the-art instrumentations and weather testing methodologies are summarized in this section.

Facilities
Testing on public roads may be associated with higher risks and liability.Special permits may also be required depending on city bylaws.There are three well-established classes of facilities that can provide convenient weather testing conditions for vehicles: (1) outdoor test tracks, (2) indoor controlled weather chambers, and (3) wind tunnels.These are discussed below.

Outdoor test tracks
Proving grounds are outdoor test tracks exposed to natural precipitation.The test tracks normally can accommodate a wide range of vehicle driving speeds as well as different types of pavements and ground conditions [57][58][59].
Conducting experiments outdoors is the most realistic method, but the environment is less controlled, which may be subjected to geometric track parameters, such as curvature and banking; variability of atmospheric conditions, such as crosswinds and turbulence.Based on this, the results may not be repeatable, and it is difficult to compare data obtained from different days and times.This type of experiments also requires extensive instrumentation to quantify the perceived conditions and vehicle performances.

Indoor weather chambers
Weather chambers are indoor facilities that employ artificial precipitation systems.The length of the chamber varies across different facilities, and that determines the maximum driving speed possible for each test case.A shorter chamber is likely to be used for stationary vehicle testing such as the Cerema R&D Fog and Rain Platform in Clermont-Ferrand, France [60].Whereas a longer chamber can allow a vehicle to move through, such as the indoor facility at the Center of Automotive Research on Integrated Safety Systems and Measurement Area (CARISSMA) at Technische Hochschule Ingolstadt, Germany, featuring a 123 m long building with over 4000 m 2 floor space [61]; and the indoor snow test track at the Test World (a test facility under UTAC CERAM Millbrook), Finland, featuring a maximum track length of 410 m with snow and ice grounds [62].A Drive-thru Climate Tunnel (DCT) was developed by Pao et al recently as a facility for weather event testing on a moving vehicle [63].A prototype scaled setup was constructed and validated the perceived precipitation concept discussed in the 'Perceived Precipitation' section of this paper.
Conducting experiments indoors can ensure better control of the test conditions.Most chambers allow for driving in a straight path in a single direction only; the driving speed is limited by space.The realistic simulated condition depends on the type of artificial precipitation systems used, as well as the capability of other environmental controls such as road wetness, temperature, humidity, lighting, etc.

Wind tunnels
Climatic wind tunnels (CWT) are indoor facilities that are equipped with various climatic controls, together with the addition of an artificial precipitation system.Inside the wind tunnel test section, the perceived precipitation is brought onto the stationary test vehicle through water injection into the wind stream and then particles are carried along by the wind [64] termed wind-driven precipitation (referred to as dynamic precipitation here).The aerodynamics of a moving vehicle is simulated by airflow controls around the test vehicle.
An example of a modern CWT is the one at the Automotive Centre of Excellence (ACE), Oshawa, ON, Canada.The ACE CWT is capable of varying wind speeds up to 300 km h −1 and temperatures between −40 to +60 °C.Several weather simulation methods are framed in Hangan et al [65] using new instrumentation as well as previous weather instrumentation methods reported in Gultepe et al [16].
CWT testing is controlled and repeatable.It is also rapid to vary conditions with the push of a button [66].However, the primary challenge of wind tunnel weather simulation is that a predetermined dynamic precipitation target on each surface is required prior to testing because the test vehicle is stationary, following the reference frame shown in figure 2(b).Therefore, it is important to determine the relation between natural and perceived precipitation.During wind tunnel experiments, various droplet dynamic events, such as collision and break up, are induced by the wind flow, which results in precipitation characteristics that deviate from real life scenarios.Therefore, the range of possible realistic simulated conditions is limited by the capacity of the precipitation simulation strategies, and their ability to overcome these deviations.

Artificial weather systems
There are review articles that have already focused on artificial precipitation systems; they present the system design, capacity, and quality of the simulated precipitation, for rain [67,68] and for snow [69,70].These systems are summarized in conjunction with the facilities to create a controlled environment and simulate natural and perceived precipitation.

Rain simulation systems
According to Yakubu and Yusop [68], there are two main types of rain systems categorized based on droplet formation methods, which are pressure spraying and drop-forming.
Spray nozzle rain systems.The spray type rain simulation system is a low-cost method to achieve large area coverage; an example was demonstrated by Rasshofer et al [71], who used only 32 nozzles to produce rainfall in 228 m 2 of space.Because of the small number of nozzles used, it is inexpensive to configure the matrix and implement individual activation control, similar to the setup constructed by Hasirlioglu et al [72].To mimic natural rain, the nozzle openings are typically pointed downward [73].Downward spraying has been reported in wind tunnel use as well [74], while some have simulated wind-driven rain with horizontal spraying [75].
However, the convenience of using spray nozzles comes with disadvantages.Spray nozzles usually produce an extensive amount of small droplets.Hasirlioglu [76] used a screen at 1 m below the spray nozzles to force the formation of larger droplets as they accumulate and drip from the mesh.In natural rain conditions, mean droplet size increases with rain intensity; this relationship cannot be achieved by spray nozzles as increasing pressure (P) for a higher flow rate will reduce the droplet size (D) following the general rule of D 1 /D 2 = (P 1 /P 2 ) −0.3 [77].If used with a wind tunnel, wind force will cause a reduction in the critical Weber number (We < 5) and may further reduce the droplet size [78].
Besides, spray nozzle systems tend to have difficulty producing low rain intensity, for example, the single nozzle system constructed by Tossell et al [73] could achieve as low as 17.5 mm h −1 after varying different heights and pressures.Each nozzle geometry has its own spray pattern [77].Spray nozzle systems often create nonuniform intensity coverage at the test section [71].This issue is exacerbated in the wind tunnel.Cacciotti et al [74] proposed a downward spraying calibration procedure in a wind tunnel and correlated measured intensities with spray rate, pipe pressure, and the number of nozzles.Their calibration was performed with an empty wind tunnel.It is worth mentioning that rain characteristics are extremely sensitive to the airflow field, presence of a test vehicle will alter the aerodynamics in the test section; thus, rain calibration together with the test vehicle is highly desired for precise studies.
Drop-forming rain systems.Very few researchers have considered using drop-forming rain systems as compared to the number of spray systems in the literature.This may be due to the complexity of the system and the cost to configure for large scale coverages with individual controls of dripping devices; for example, Regmi and Thompson [79] designed a rain system using capillary tubes and actuators.Drip nozzles may be connected together and share the same control to reduce cost, such as the drip tray constructed by Vahabi and Nikkami [80].
Since droplets fall vertically, the placement of drip nozzles determines the spacing between wet and dry spots.A drop-forming rain system would require more nozzles to obtain the same area coverage as a spraying rain system.Therefore, the drop-forming rain system is likely to be heavier, especially if a reservoir is mounted overhead.Water supply pump can be used to minimize the overhead weight but head loss may occur.
The major advantage of a drop-forming rain system is being able to produce realistic droplet density.It can also achieve lower intensity since a much lower flow rate is required to activate the nozzle, unlike a spray nozzle.However, naturally dripping droplets tend to be too large regardless of nozzle opening size; Hignett et al [81] measured droplet size of at least 2.7 mm by using 16-gauge (1.29 mm) needles.This issue is eliminated when used in a wind tunnel, because large droplets are unstable under wind force; a volume mean diameter of about 1 mm was achieved by Pao et al using a drop-forming type rain system in the wind-driven rain environment [82].

Snow simulation systems
Artificial snow generally consists of small ice crystals, which differ from the flakes in natural snow [83].Artificial snow does not possess all features of natural snow [84].The extent of similarity depends on how the snow is generated; two of the most common methods are introduced: snow guns and shaving.
Artificial snow normally has a higher density than natural fresh snow (<100 kg m −3 , presented in the 'Natural snow' section) as its structure is closely packed, evidenced by the measured densities of 250 kg m −3 [85] with a snow gun and 430 kg m −3 with shaved ice [86].Additionally, artificial snow is more resilient than natural snow and better tolerates environmental fluctuations [83,87].
Snow gun.An artificial snow-making machine utilizes atomization techniques, the water droplets are discharged and cooled as they exit the nozzle [87,88].There are two typical types of snow guns; the air-water gun uses pressurized air whereas the fan gun uses pressurized water with blowing fans [89].
Snow guns are suitable for high-volume snow-making; in general, more snow can be yielded at lower temperatures at the expense of more water input [90].At the same time, a large number of parameters should be considered to generate desired snow characteristics.Factors such as air-water mixture, air humidity, pressure, temperature, and wind velocity are all crucial for creating artificial snow [91].
The water droplets produced with snow guns are usually small, around 0.1-0.5 mm [92], and they are susceptible to the wind forces.Therefore, when used in the wind tunnel, one should make sure that small water droplets have sufficient time to freeze when travelling in the air.To accommodate this, snow guns can be placed inside the settling chamber of a wind tunnel where the air speed is slower [93].
Snow/ice shaving.One advantage of snow testing is that snow can be stored for later testing by discharging from a snow system.Also, fresh and deposited natural snow can be collected outdoors.Real snow was reported as the primary source of snow feed in several wind tunnel experiments [84,94].The same strategy applies to artificial snow as well, which can be premade, stored, and dispensed from a container.Villeneuve et al [85] used a snow gun to generate artificial snow in a cold environment, and then the snow was kept inside a freezer.The snow particles were dispensed onto the test object later, where the snow feeding was facilitated by a rotating cylinder and air circulation inside the container.
As the name suggests, shaving is a process of slicing and grinding off smaller quantities from a bigger bulk material.An ice shaving system was designed by Landolt et al [92] that uses a drill press and a stepper motor to grind the side surface of an ice cylinder.The system can generate larger flakes to mimic natural snow, and a size range of 0.5−10 mm was reported [92].Desired snow particle sizes can be screened to produce different types of snow, such as the rotating drum with an internal crusher and 6 mm mesh constructed by Oda et al [95].Overall, the shaving type of artificial snow system involves a lengthier preparation and has a slower snow production rate; it is more suitable for small-scale testing.

Weather testing methodologies
Physical experimental studies are discussed in this section.Upon analysis of the existing strategies reported in the literature, including instrumentation and quantification, insights are provided to help the process of selecting the appropriate methodology.In general, weather testing methodology for vehicles can be divided into three main steps: (1) Deposition mechanism.This step identifies the relevant scenarios.Rain and snow depositions on vehicle surfaces are often referred to as soiling or surface contamination [1], primary deposition is when precipitation directly impacts the vehicle, secondary deposition results from other nearby vehicles or road objects, and lastly, self-deposition occurs due to the vehicle's own rotating tires and wake regions.
(2) Reference frame.This step determines the facility of choice and how the experiments are conducted.Relating back to the 'Perceived precipitation' section, there are two perspectives of viewing the precipitation on vehicles: (i) static precipitation with a moving vehicle, or vice versa, (ii) dynamic precipitation with a stationary vehicle.For (i), it is easily achievable, the limiting factor is the precipitation characteristics produced by the artificial system.Where (ii) needs to account for the wind effect on the simulated precipitation and determine the perceived precipitation target prior to experiments.For most vehicle applications, it is more realistic to be able to simulate the relative impact of precipitation which allows for observation of the post-impact behaviours; thus, static precipitation with the stationary vehicle is not considered in this section.
(3) Quantification strategy.For quantitative studies, it is important to know what is being simulated and what is the impact on the vehicle surfaces.The calibration process for (2-i) can be performed with typical instruments found at a weather station.The use of the vehicle to measure the perceived precipitation can be performed afterward.The calibration process for (2-ii) first requires an estimation of what the vehicle surfaces oriented at different angles would perceive at various driving speeds.In this case, the presence of the test vehicle during the calibration process is preferred, and the perceived precipitation on the surfaces is also measured at the same time.The challenge when measuring the perceived precipitation on the vehicle surfaces lies in the choice of instrumentations and their locations to ensure that it does not affect the aerodynamics.
Some examples of weather testing methodologies, including the experimental design and instrumentations, are discussed below for the two categories:

Static precipitation with moving vehicle
A 56 m long static artificial rain system using sprinkler nozzles and connected pipes was built on top of a 2.1 km long outdoor straight runway at the Texas A&M Research Annex [5].The static rain intensity was measured with a custom funnel with 30.5 cm diameter as a rain gauge.Two test groups were conducted: the same driving speed with varying rain intensities and the same rain intensity with different driving speeds to evaluate the effect of perceived intensity on camera visibility behind the windshield, which is similar to human vision; both test groups showed visibility degradation.With a more comprehensive study for a wider range of driving speeds, rain intensities, and droplet size distributions, this relationship can be used as a perceived intensity correlation strategy using a camera.
Only slow driving speed can be achieved when space is limited.Hasirlioglu [76] studied rain on vehicle sensor perception at CARISSMA in Germany at a speed of 20 km h −1 .Earlier, Rabiei et al [56] used an innovative method to simulate the vehicle movement via a rotation of the arm that mounts the test surface.However, their setup only achieved slightly higher speed, up to 45 km h −1 , and their method is only suitable for small-scale studies.The constant rotation also incurs complexity to the problem with added vectors.
In Hasirlioglu's study [76], a tall spray nozzle rain system was used, and the rain was characterized by an optical disdrometer.An optical disdrometer is comprised of photodiodes, where the sheets are illuminated by an infrared laser when rain and snow particles pass through [96].Rainfall and snowfall rates can be estimated from the disdrometer data; total precipitation accumulation, for example, can be obtained by integrating the droplet volumes recorded at the laser plane.Although there are often uncertainties found for this type of equipment [97]; laser technology generally is more suitable for moving vehicle studies, as it provides a wider working range at a higher resolution than an impact-based disdrometer.
Impact-based instruments, such as an acoustic disdrometer are less expensive method than laser-based instruments.An acoustic disdrometer relies on the electric signal sent from the piezoelectric sensor, which can be translated as impact force and kinetic energy to estimate the droplet size and velocity [98].This method may be appropriate for natural precipitation characterization since the instrument is stationary with respect to the precipitation.However, it is not suitable to be used on a moving vehicle as the impact behaviour is now factoring in the vehicle motion in addition to droplet size and terminal velocity.
The use of automotive rain sensors as a perceived rain intensity measurement method was proposed by several studies [56,99]; this type of instrument is widely used on vehicles as an automatic wiper sensor, which measures the difference in light beam intensity due to the presence of droplets to estimate intensity.The wiper speed or the water film thickness removed can also be used to back correlate for intensity [55].Rain sensors are the least expensive type but also have lower capacity and accuracy; also, they are not suitable for obtaining droplet size distributions.

Dynamic precipitation with stationary vehicles
The perceived precipitation concept is often not considered in most wind tunnel studies; sometimes, an assumed intensity or a selected water flow rate is used as a case study.Hagemeier et al [2] pointed out that a free driving (dynamic) rain intensity (I d ) should be simulated during wind tunnel testing, which is defined as where u x , v z , and I s represent horizontal wind speed, droplet falling velocity, and static rain intensity, respectively.The relationship is similar to the dynamic models discussed in the 'Dynamic Models' section; however, it is only limited to horizontally dispensing systems and a vertically oriented vehicle surface.
It has been noted that simulating the rain density in the air alone and introducing wind flow may not result in targeted perceived intensity at the test surface as it is not a steady-state problem.Droplets of different sizes will be accelerated to a different extent by the horizontal wind before impacting the test vehicle.
More recently, a methodology was proposed and developed by Pao et al [15,82] to produce dynamic rain in wind tunnels.Their artificial rain system injects droplets from an elevated height outside of the wind stream.The falling droplets are then broken down and deflected towards the test surface by the wind.The test conditions are calibrated using predetermined rain conditions, including perceived intensity and droplet size.A laser disdrometer [16] is employed for the calibration process prior to introducing the test vehicle; the instrument is positioned at the same location and with the same orientation as the test surface.The procedure is split into two steps due to limited space in the model wind tunnel test section to avoid significant blockages.The same method was demonstrated in full-scale wind tunnel testing and improved precision by calibrating in the presence of the test vehicle.
The most obvious difference between snow and rain is that snow accumulates on a surface and continues to pack.The cohesion strength of snow particles onto each other and adhesion strength on a surface highly depend on the liquid water content (LWC) of the snow.It was found that snow tends to accumulate when the LWC increases, but it peaked at 20%, and the strength began to drop [100].
Snow accumulation on an automotive camera at different wind speeds (up to 64 km h −1 ) and the LWC (up to 28%) was studied by Mohammadian et al [101] using a small-scale setup.The artificial snow was produced with snow guns inside a cold room and injected into the connected wind tunnel.The LWC was controlled by adjusting the temperature in the cold room and varying the distance to the test surface.A LWC sensor that records electrical resistivity was employed to quantify the simulated snow in close proximity with the test surface.The snow particle size was characterized using a high-speed camera at 10,000 fps externally with postprocessing on the images.
There are fewer snow studies for vehicles using controlled set ups as snow formation is a complex phenomenon that is influenced by various properties [40].It is challenging to replicate outdoor conditions in the laboratory [70]; it is also difficult and expensive to control the cold climate for a long chamber.

Summary
To summarize the selection of weather testing methodology, examples of weather simulation studies that are categorized based on the types of artificial precipitation systems and the testing strategies for both rain and snow are provided in table 3.
The decision criteria are explained in the flow diagram shown in figure 4. The decision-making process follows the systematic approach proposed in figure 1 to first determine the precipitation characteristics such as inflow rate and droplet size distributions, then estimate the impact velocity and intensity experienced by the moving vehicle at different surfaces, and finally define the strategy to quantify the performance of vehicle applications of interest with respect to both driving and weather conditions.

Conclusions
Driving in adverse weather can become dangerous as vehicle performance degrades, therefore, it is essential for vehicle applications to be evaluated in different precipitation conditions.For this reason, a comprehensive overview of weather testing strategies for road vehicles is presented.As a tutorial for readers, this work provides basic and extensive characterization of the natural and perceived precipitation conditions experienced by the vehicle, as well as selecting testing methodology.Important parameters such as wind speed, precipitation type (rain or snow) and droplet size distribution (DSD) are determined to be critical for the driving conditions that response to this tutorial objectives.The concept of perceived precipitation on a moving vehicle is also found to be strongly related to the vehicle speed, surface physical characteristics such as surface orientation, as well as aerodynamics.
This work is intended to bridge the knowledge gap between different scientific fields, e.g., aerodynamics of a driven vehicle and meteorological environment.This knowledge can be used realistically to design realistic experiments for testing vehicles in rain and snow.The choice of facility (outdoor or indoor) and methodology (static or dynamic) of testing driving-in-weather conditions depends on the testing objectives criteria and the importance of the perceived precipitation characteristics, such as droplet size, shape, intensity, accumulation density, etc, in relation to the specific vehicle applications.
Overall, several literature gaps were identified related to weather impact on vehicles that could hinder the development of autonomous vehicles and technology applications.Some of the current practices in measuring and simulating weather precipitation and dynamic conditions are unrealistic; therefore, new analysis methods and platforms need to be tested to facilitate standardization of testing methodologies.

Figure 1 .
Figure 1.A systematic approach for evaluating weather impact on vehicles.

Figure 2 .
Figure 2. Reference frames for (a) stationary and (b) moving observers in precipitation, adapted from [48] with permission.

Figure 3 .
Figure 3. Schematic of perceived-to-natural precipitation ratios obtained by implementing the perceived intensity model for surfaces oriented at different angles.

Figure 4 .
Figure 4. Flow diagram for decisions on weather testing methodologies for vehicles.

Table 3 .
Summary of studies on weather impact on vehicles (or test object) using artificial rain and snow systems for different evaluation methodologies.