## Water drop 3a – Physically based wet surfaces

Version : 1.3 – Living blog – First version was 19 March 2013

This is the third post of a series about simulating rain and its effect on the world in game. As it is a pretty big post, I split it in two parts A and B:

Water drop 1 – Observe rainy world
Water drop 2a – Dynamic rain and its effects
Water drop 2b – Dynamic rain and its effects
Water drop 3a – Physically based wet surfaces
Water drop 3b – Physically based wet surfaces
Water drop 4a – Reflecting wet world
Water drop 4b – Reflecting wet world

Physically based rendering (PBR) is now common in game (See Adopting a physically based shading model to know more about it). When I introduce PBR in my company few years ago we were actually working on rain. At this time we were questioning about how our new lighting model should behave to simulate wet surfaces. With classic game lighting model, the way everybody chose was to darken the diffuse term and boost the specular term (Here I refer to the classic specular use as RGB color to multiply with the lighting). The wet diffuse/specular factors being eye calibrate. I wanted to go further than simply adapt this behavior to PBR and this required to better understand the interaction between water and materials. This post is a mix of the result of old and recent researches. I chose to provide up to date information including experimental (not complete) work because the subject is complex and talking about it is useful. This might be of interest for future research. The post describe how water influence materials and provide ways to simulate wet surfaces with physically based lighting model.  I suppose here that’s the reader know the basics of reflected/refracted lights with Snell’s law and index of refraction (IOR).

## Wet surfaces – Theory

People are able to distinguish between a wet and a dry surface by sight. The observation post show many pictures to illustrate this point. The main visual cue people retain is that wet surfaces look darker, more specular and exhibit subtle changes in saturation and hue when wet:

This behavior is commonly observed for natural or human made rough material/porous materials (brick, clay, plaster, concrete, asphalt, wood, rust, cardboard, stone…), powdered materials (sand, dirt, soil…), absorbent materials (paper, cotton, fabrics…) or organic materials (fur, hair…). However this is not always the case, smooth materials (glass, marble, plastic, metal, painted surface, polished surface…) don’t change. For example, there is a big difference between a dry rough stone and a wet rough stone but a very small difference between highly polished wet stone and highly polished dry stone.
In the following discussion, wet surfaces refer mostly to rough and diffuse materials quenched in water and having a very thin water layer on their surfaces.

Why rough wet surfaces are darker when wet ? Because they reflect less light.
There is two optical phenomena imply in this decrease of light reflection and they are details in [3] and [4]. A rough material has small air gaps or pores which will be filling by water when wetting process begin. When pores are filled, there is  “water saturation”, water propagates onto the material as a thin layer.

Let’s first see the impact of the thin layer of water. The rough surface leads to a diffuse reflection (Lambertian surface).  Some of the light reflected from the surface will be reflected back to the surface by the water-air interface due to total internal reflection. Total internal reflection occur when moving from a denser medium into a less dense one (i.e., n1 > n2), above an incidence angle known as the critical angle (See [1] for more detail). For water-air interface, this is $\theta_c=arcsin(\frac{n_{air}}{n_{water}})=arcsin(\frac{1.0}{1.33})=48.75^{\circ}$

Source [1]

This reflected light from the surface is then subject to another round of absorption by the surface before it is reflected again. This light’s back and forth result in darkening of the surface.

Source [2]

Now take a look at the water filling in the pore inside the rough material. There is a concentration of water beneath the surface. The water which replace the air have an index of refraction higher than that of air (1.33 against 1.0) which is closer to index of refraction of most rough dielectric material (1.5). Consequence, following the Snell’s law, light entering in material will be less refracted due to the reduced index of refraction difference: The scattering of light under the surface is more directional in the forward direction. The increase scattering events before the light leave the surface increases the amount of light absorbed and thus reduce the light reflection.

Source[5]

The darkening of the material is also accompanied by a subtle change in saturation and hue. In [11] the spectral reflectance (i.e the “RGB” representation of real world color, the visible range of the spectrum is around 400nm blue to 780 nm red) of a dry and wet stone has been measured to highlight these characteristics. Analyze show that’s there is a significant reduction in reflectance across the whole range of the visible spectrum when the surface gets wet. Which confirm the darkening of the surface. It also show that’s the surface color becomes more saturated because of this reduction.

Source [11].