Radiometric variables describe "incident light", a.k.a. the light from the sun shining down on the ocean or atmosphere. Incident light tells us how many photons are interacting with the atmosphere/ocean including their wavelength.
To begin, let’s consider light shining onto a single point on the ocean. If we look at the light shining onto that point from a single direction, that would be a measure of Spectral Radiance, which describes the spatial, temporal, directional, and spectral structure of light coming onto that point. In the ocean, Spectral Radiance can be broken down into light (L) at a specified point (think, latitude/longitude or x,y on a coordinate plane), depth (z), time (t), direction the light is traveling (θ, ɸ), and wavelengths of that light (λ).
Not all of these parameters are as important as others, however, in terms of understanding this point of light in the ocean. For example, in the ocean, changes in the horizontal direction of light are much smaller than changes in the vertical direction. In other words, if you drove a boat along the sea surface, the light seen from the boat would appear pretty much the same along your travel path. If you were in a submarine, one the other hand and you steered it to dive down into the ocean, the light would change rapidly as you descended. So we don’t really need to worry about the x & y position in our equation, just z.
Similarly, timescales that change properties in the ocean are very long compared to the exact microsecond a light photon hits the ocean, so we don’t need to worry about time (t) either. After that, our equation is left with light as a function of depth (z), direction, and wavelength.
Radiance vs Irradiance
Realistically, an ocean sensor would not be able to measure light from each individual direction so we would never actually measure Spectral Radiance in the ocean. Instead we would focus on measuring Irradiance, light coming to a point from all directions, i.e., spectral radiance summed across all directions. Since Irradiance is the sum spectral radiance across all angles, the resulting values are simply a function of depth and wavelength.
Total Irradiance can be envisioned as a sphere surrounding our point with light coming in from all angles. If you split this sphere in half you would get measures of downwelling and upwelling irradiance. Thinking again about our ocean sensors, a sensor deployed in the ocean facing upward toward the sun would measure the downwelling irradiance, a sensor facing downward, toward the bottom of the ocean would measure upwelling irradiance. Since not much light is coming off of the bottom of the ocean, save for some particularly reflective white sand in shallow waters, we’ll focus the rest of this section on downwelling measurements.
Radiance vs Irradiance
Realistically, an ocean sensor would not be able to measure light from each individual direction so we would never actually measure Spectral Radiance in the ocean. Instead we would focus on measuring Irradiance, light coming to a point from all directions, i.e., spectral radiance summed across all directions. Since Irradiance is the sum spectral radiance across all angles, the resulting values are simply a function of depth and wavelength.
Total Irradiance can be envisioned as a sphere surrounding our point with light coming in from all angles. If you split this sphere in half you would get measures of downwelling and upwelling irradiance. Thinking again about our ocean sensors, a sensor deployed in the ocean facing upward toward the sun would measure the downwelling irradiance, a sensor facing downward, toward the bottom of the ocean would measure upwelling irradiance. Since not much light is coming off of the bottom of the ocean, save for some particularly reflective white sand in shallow waters, we’ll focus the rest of this section on downwelling measurements.
Three different values of irradiance are typically measured in ocean sciences by integrating (or summing) light in different ways across angles and focusing on specific wavelengths – scalar irradiance, spectral plane irradiance, and Photosynthetically Active Radiation (PAR). Simply taking the sum of light from all angles onto a point on the ocean is a measure of Scalar Irradiance.
Knowing how much light is coming in from all angles is great; however, the intensity of light that hits the ocean straight on versus from a wide angle is much different. For those of us who live at higher latitudes, it’s like the difference between the intensity of the sun in summer when the sun is at a more direct angle versus in winter when the sun is at a more oblique angle.
In our light function, when we talk about angles we are referring to the direction of light in terms of its angle away from straight down at the sensor. So, if an ocean sensor is oriented vertically within the water column, some incoming light will come from straight down (i.e., be orthogonal) and other light will come in at an angle. Johann Heinrich Lambert figured out in 1760 that the intensity of light hitting a flat surface (i.e., the top of the sensor) is proportional to its angle relative to orthogonal.
By adding this to our previous equation we can obtain a measure of Spectral Plane Irradiance. Another way to visualize this is the beam of a flash light. If you shine a flash light straight down on the floor you see a small, bright circle. If you move the flash light so the beam of light hits the floor at a greater angle, the circle of light from the flashlight grows in size and the brightness of the circle decreases. This is because the photons of light from the flashlights bulb are now spread over a larger area.
Average Cosines (an Apparent Optical Property ) connect the dots between Scalar and Spectral Plane Irradiances. By taking the ratio between these two irradiances, researchers can determine the average angular distribution of the light field entering the ocean or the atmosphere.
So far these two irradiance values tell us a lot about what a sensor would encounter in the ocean. But what about marine organisms that want to use light energy, such as phytoplankton? Phytoplankton, and all plants that contain chlorophyll, primarily use light in the spectrum of 400-700 nm wavelength for photosynthesis, a.k.a. Photosynthetically Active Radiation (PAR).
Different wavelengths of light have different amounts of energy (see Fundamental Properties of Light ), but phytoplankton don’t care about that. For photosynthesis, phytoplankton just need photons in their preferred range of 400-700nm to provide the energy they need for photosynthesis. So when we measure PAR, we are no longer interested in total energy, we just need to count the photons.
Radiometric variables provide very important information about the light reaching and moving through the atmosphere and ocean. These variables then become very important for calculating various AOPs, which will be addressed in the following sections. The key radiometric variables discussed above can be summarized as follows – Spectral Radiance, the amount of light reaching a specific point in the ocean at a certain depth and wavelength, and from one direction. By integrating across all directions of light we get a measure of Scalar Irradiance. And then if we scale the amount of light based on the cosine of the direction it comes from, we get the Spectral Plane Irradiance. You can directly compare them by examining the images below.
For more details and equations check out the Light and Radiometry section of the Ocean Optics Web Book .