Why is Enceladus's albedo greater than 1?

Question

Enceladus, one of Saturn's moons, has a geometric albedo of 1.38 and a bond albedo of 0.81. How can the geometric albedo of Enceladus be greater than one? What are the similarities or differences between a geometric albedo and a bond albedo?

Answer 1

To answer this, one really has to understand how the geometric and bond albedos are defined. Let's start with the bond albedo since its simpler.

Bond Albedo

The Bond Albedo is just the fraction of energy hitting a surface that gets reflected. To simplify the process, let's say I shoot 100 photons of all the same energy at Enceladus. Of those 100 photons that hit the surface, 81 of them will be reflected back and 19 of them will be absorbed. That means the bond albedo will be $81/100 = 0.81$.

Simple right? As such, the bond albedo can never be greater than 1 because you obviously can't reflect back more photons than you received. This means that a bond albedo of zero implies no light was reflected and all of it was absorbed, whereas a bond albedo of one implies all light was reflected and no light was absorbed.

Geometric Albedo

The definition of the geometric albedo is a bit more complicated. The first thing you have to realize though is that it is not a straight zero to one scale. A geometric albedo of one doesn't mean all the light got reflected like it did for the bond albedo. So let's try to define the geometric albedo.

There are two important points about the geometric albedo that make it differ from the bond albedo.

For the bond albedo, we talked solely about the total amount of incident light and the total amount of reflected light. This says nothing about an observer of said light. We just have some magical way of knowing about every photon that hits and is reflected by your surface and that allows us to calculate the albedo according to the bond albedo definition. The geometric albedo on the other hand specifically takes into account your ability to observe the light from a specific vantage point.

The second major point is that the geometric albedo is a measure of how well your particular surface reflected the light back to you compared to a reference surface. Imagine now you have two surfaces, one is the surface of Enceladus, the other is your "reference surface". This reference surface is an "idealized" reflector which means that it reflects every photon that hits it (making it have a bond albedo of 1). The key here though, is that it reflects light isotropically. What I mean by that is that the light doesn't get reflected in any preferred direction, but rather gets reflected in all directions equally. So now you have your 100 photons hitting your reference surface and all 100 photons get reflected, but because they're all reflected in random directions, only 10 photons actually get to your camera/eye/detector. What can happen with Enceladus though, is that the surface has just the right properties such that 100 photons hit the surface, and 14 photons get reflected to your detector because the surface preferentially reflects light in a specific direction. It's sending more photons to your detector than the reference surface. The geometric albedo is the ratio of how much light gets reflected to your detector by Enceladus over how much light gets reflected to your detector by the reference surface. In this case, $14/10 = 1.4$.

One small, additional point, is that this definition relies on your detector being in the same direction as your light source. In other words, the geometric albedo is a measure of how much your surface can retro-reflect (i.e., reflect back to the source of the photons) compared to the reference surface. Technically, the geometric albedo attains a maximum value when your surface is made up of retroreflectors.