decimal day = day + hour/24 + minute/1440
The conversion of a date to a decimal day in columns C-H is optional, but we believe it makes it easier to deal with time as an x-axis value.
Do different kinds of surfaces reflect solar radiation differently? Are there differences between surface reflectance that depend on wavelength? Does the reflectance depend on sky conditions or time of day? For vegetated surfaces, can the reflectance tell us something about the health of the vegetation? How does surface reflectance impact urban heat island effects? Does the reflectance of manmade surfaces affect our environment and the efficiency with which structures can be heated and cooled?
An interesting measurement that can be made with two of IESRE's pyranometers is surface reflectance (or reflectivity). One instrument points straight up at the sky and the second instrument points down at the ground. The ratio of the output from the downward-pointing instrument to the output from the upward-pointing instrument is equal to the reflectance of the surface. One advantage of this measurement is that the pyranometers do not necessarily need an absolute radiometric calibration, that is, a calibration that allows the output voltage from a pyranometer to be converted to insolation units of watts per square meter.
This is a conceptually simple measurement with many applications, as can be seen by the variety of research questions posed above. Two of these questions are dealt with in separate projects described on this website — "Surface Reflectance and the Health of Vegetation" and "Measuring the Surface Reflectance of Snow." For the first question, the obvious answer should be that, yes, different surfaces reflect solar radiation differently. Dark surfaces should reflect less radiation (and absorb more) and light surfaces should reflect more. The answers to the other questions are less obvious and, therefore, perhaps more interesting.
For IESRE's pyranometers, the fact that reflectance measurements do not require pyranometers with absolute radiometric calibrations is not quite the end of the story. The simple ratio calculation assumes that both instruments have the same output if they are facing in the same direction, side-by-side — only if this is true can the surface reflectance be calculated as the ratio of the downward- to upward-facing pyranometer outputs. But, this is not true for IESRE's pyranometers, as the output differs somewhat from sample to sample, based on the variations in the detectors themselves and how they are assembled. This difference must be accounted for by calibrating the output of one instrument relative to the other.
It is not hard to determine the relative calibration for a pair of instruments. Mount two instruments, A and B, side by side and record data for part of a day. You could start by pointing both instruments up. Later, you could point them both down. Designate one of the instruments as the "reference." Then determine the value C which, when multiplied times the output of the second instrument, causes the adjusted output voltage of the second instrument to agree with the reference instrument. Suppose the reference instrument is designated as the A instrument, which will point up when reflectance data are collected. The B instrument will be pointed down. Then the reflectance is:
(Bvolts*C)/Avolts
The images below shows results from calibrating two instruments. In this case, each instrument has two channels — a broadband channel using the pyranometer detector, and a near-IR channel that uses a detector sensitive only to radiation in the near-IR part of the electromagnetic spectrum. This is of interest because vegetation, for example, has different reflectivities in the visible and IR.
In this Excel file, the date recorded with the data logger, in column B, has been converted first to text in column C (using Excel's TEXT([cell containing a date],"mm/dd/yyyy hh:mm") function, and then to integers for the month, day, hour, and minute in columns D-G, using VALUE(LEFT(...)), VALUE(MID(...)), and VALUE(RIGHT(...)) functions. Then the date and time have been converted to a day expressed as a decimal fraction:
decimal day = day + hour/24 + minute/1440
The conversion of a date to a decimal day in columns C-H is optional, but we believe it makes it easier to deal with time as an x-axis value.
The lefthand image below shows a graph of the raw data from these two instruments. As expected, the outputs for the two instruments are not the same. In mid-afternoon, the upward-pointing instruments were both turned upside down to point down at the ground.
The righthand image shows the raw data adjusted by the values in cells M1 and N1 of the Excel worksheet. For this pair of instruments, it just happens that the constant is the same for the broadband and near-IR channels. In general, these two values will be different! You can see that the adjusted data cause the outputs from these two instruments to agree nearly perfectly under a range of sky conditions. The calibration value is the same whether the instruments are both pointing up or both pointing down — as should be the case.
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As a result of this calibration exercise, we can now be confident that accurate reflectance measurements can be made with these two instruments. But, the interpretation of these measurements is not so easy! The images below show an example. The first and most obvious thing to notice is that, even over the same surface, there is a lot of variability in surface reflectance during the day! It is important to remember that the detectors in these pyranometers collect radiation from the entire hemisphere above (or below) them. So, the downward-facing pyranometer "sees" not just the surface directly under it, but also radiation from around the entire site, with decreasing sensitivity as the line of sight moves from directly down to horizontal. This may include some sky and plants, and certainly includes, in this case, surfaces with varying amounts of direct sunlight/shadows as the sun moves across the October sky. We might reasonably conclude, then, that site selection is very important for reflectance measurements. A large expanse of homogeneous surface is the best choice. We might also consider limiting the influence of a hemispherical field of view by moving the detector closer to the surface. This shouldn't cause a problem if the surface being measured is homogeneous and representative of a larger area. As is always the case for experimental research, a great deal of care is required to limit input that makes data interpretation more difficult, and it is important to remember that there are always tradeoffs to be made in the design of an experiment!
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For these data, taken during a clear day (except for one small mid-afternoon "blip" due to reflections from the side of a small cloud somewhere in the sky), there is obviously a relationship between time of day (sun elevation angle) and surface reflectance. This is not at all surprising. The distribution of solar radiation falling on a surface depends on a combination of diffuse radiation from the sky and direct radiation from the sun. In a clear sky, about 85% of the radiation around mid-day is direct radiation.
The response of surfaces to incoming solar radiation is complicated! A surface reflects some of the incoming radiation, acting more or less like a mirror, depending on its characteristics, and scatters some of it, acting like a rough diffusing surface. This behavior influences how much radiation the downward-facing detector sees. It may never see some of the "mirror-reflected radiation" and under cloudy skies and at different times during the day it will receive relatively more of the scattered radiation. During a clear day, the constantly changing interactions between a surface subjected to both direct solar radiation and diffuse sky radiation, changing with solar position, means that surface reflectance will have a range of values rather than being a single number.
In late afternoon (at about 22.67 days), this site starts to fall into shadow, with the proportions of sunlit and shadowed surface changing quickly and, in the midst of these changes, the upward-facing detector falling into shadow. At these low signal levels, rather than looking like a continuous function, the reflectance values vary among several "discrete" values, due to the limited resolution of the data logger that converts the analog output of the detectors to a digital value. These values can be ignored in any analysis of the properties of the surface being studied. At a different site, with a larger expanse of homogeneous surface and fewer obstructions around the horizon (there are lots of trees and bushes around this site, and a two-story house about 10 m behind the location from which the photo was taken), it might be possible to extend the analysis to smaller solar elevation angles (earlier and later in the day).
Because of the obvious link between solar position and reflectance, a reasonable research project would be to find a mathematical way to characterize the variability in surface reflectance under clear skies as a function of solar elevation angle. Given a specific surface under clear skies, it should be possible to predict at least the shape of a curve relating reflectance to elevation angle. It may also be possible to paramaterize, for example, the minimum reflectance value at solar noon as a function of sky and surface conditions. There is also the question of how reflectance behaves under cloudy and even overcast skies; parameterizing this behavior will probably be more challenging than the clear-sky case.
Over vegetated surfaces, there may be some systematic dependence of reflectance on precipitation (or lack of it) because the health of vegetation is often related directly to precipitation. It may also be possible to characterize some differences between broadband and near-IR reflectance — see the "Surface Reflectance and the Health of Vegetation" project on this website. Note, however, that understanding the relationship between reflectance and vegetation health depends also on understanding the relationship between reflectance and solar position, as described in the previous paragraph.
These research suggestions are good examples of how important (and difficult!) it is to isolate the influence of several variables when you are collecting data for the purpose of constructing mathematical models to explain observed changes in natural systems. The "real world" is always complicated and will not behave as neatly as controlled experiments you can conduct in a lab! Understanding the relationships suggested here will require a lot of data collected over the seasons in order to gather data over a wide range of elevation angles and over a range of vegetation health conditions. In a temperate climate, the health of the lawn used as the data collection site for the measurements shown here will change dramatically from conditions in a rainy spring (the grass will be bright green and the soil will be damp) to a hot and dry summer (the grass will look brown and dead and the soil will be dry). And, of course, the maximum solar elevation angle changes significantly over this same time period, with a maximum in June and a minimum in December.
Finally, note that a lot of the scientific literature about surface reflectance deals with the spectral dependence of reflectance and what is called "bidirectional reflectance" because of the importance of being able to interpret surface reflectance data obtained from spacecraft. For measurements made from a spacecraft, the challenge is to interpret reflectance not just as a function of the solar elevation angle, but also as a function of the angular position from which the reflectance is measured within a narrow field of view over a range of viewing angles relative to the sun and surface. In the measurements described here, the downward-pointing detector integrates the reflected radiation over an entire hemisphere, so there is no "directional" component in what is being measured. The detectors don't have much in the way of spectral sensitivity, either. The broadband detector measures all wavelengths across visible and near-IR wavelengths, and the near-IR detector response is limited just, as the name implies, to the near-IR part of the spectrum, around 1000 nm. Nonetheless, these ground-based measurements of "bidirectionally integrated" reflectance are extremely useful, as they represent what scientists would like to measure from space, but cannot.