Sensors designed to measure electromagnetic radiative flux are generically called actinometers or radiometers. In meteorology, actinometers are usually oriented to measure downwelling or upwelling radiation. Sensors that measure the difference between down- and up-welling radiation are called net actinometers.
Special categories of actinometers are designed to measure different wavelength bands:
- pyranometer – broadband solar (short-wave) irradiance, viewing a hemisphere of solid angle, with the radiation striking a flat, horizontal plate (Figure 2.15).
- net pyranometer – difference between top and bottom hemispheres for short-wave radiation.
- pyrheliometer – solar (short wave) direct-beam radiation normal to a flat surface (and shielded from diffuse radiation).
- diffusometer – a pyranometer that measures only diffuse solar radiation scattered from air, particles, and clouds in the sky, by using a device that shades the sensor from direct sunlight.
- pyrgeometer – infrared (long-wave) radiation from a hemisphere that strikes a flat, horizontal surface (Figure 2.15).
- net pyrgeometer – difference between top and bottom hemispheres for infrared (long-wave) radiation.
- radiometer – measure all wavelengths of radiation (short, long, and other bands).
- net radiometer – difference between top and bottom hemispheres of radiation at all wavelengths.
- spectrometers – measures radiation as a function of wavelength, to determine the spectrum of radiation.
Inside many radiation sensors is a bolometer, which works as follows. Radiation strikes an object such as a metal plate, the surface of which has a coating that absorbs radiation mostly in the wavelength band to be measured. By measuring the temperature of the radiatively heated plate relative to a nonirradiated reference, the radiation intensity can be inferred for that wavelength band. The metal plate is usually enclosed in a glass or plastic hemispheric chamber to reduce error caused by heat conduction with the surrounding air.
Inside other radiation sensors are photometers. Some photometers use the photoelectric effect, where certain materials release electrons when struck by electromagnetic radiation. One type of photometer uses photovoltaic cells (also called solar cells), where the amount of electrical energy generated can be related to the incident radiation. Another photometric method uses photoresistor, which is a high-resistance semiconductor that becomes more conductive when irradiated by light.
Other photometers use charge-coupled devices (CCDs) similar to the image sensors in digital cameras. These are semiconductor integrated circuits with an array of tiny capacitors that can gain their initial charge by the photoelectric effect, and can then transfer their charge to neighboring capacitors to eventually be “read” by the surrounding circuits.
Simple spectrometers use different filters in front of bolometers or photometers to measure narrow wavelength bands. Higher spectral-resolution spectrometers use interferometry (similar to the Michelson interferometer described in physics books), where the fringes of an interference pattern can be measured and related to the spectral intensities. These are also sometimes called Fourier-transform spectrometers, because of the mathematics used to extract the spectral information from the spacing of the fringes.
You can learn more about radiation, including the radiative transfer equation, in the weather-satellite section of the Satellites & Radar chapter. Satellites use radiometers and spectrometers to remotely observe the Earth-atmosphere system. Other satellite-borne radiometers are used to measure the global radiation budget (see the Climate chapter).
Most differential equations describing meteorological phenomena cannot be solved analytically. They cannot be integrated; they do not appear in a table of integrals; and they are not covered by the handful of mathematical tricks that you learned in math class.
But there is nothing magical about an analytical solution. Any reasonable solution is better than no solution. Be creative.
While thinking of creative solutions, also think of ways to check your answer. Is it the right order of magnitude, right sign, right units, does it approach a known answer in some limit, must it satisfy some other physical constraint or law or budget?
Find the irradiance that can pass through an atmospheric “window” between wavelengths λ1 and λ2.
Find the Answer
Approach: Integrate Planck’s law between the specified wavelengths. This is the area under a portion of the Planck curve.
Check: The area under the whole spectral curve should yield the Stefan-Boltzmann (SB) law. Namely, the answer should be smaller than the SB answer, but should increase and converge to the SB answer as the lower and upper λ limits approach 0 and ∞, respectively.
- Pay someone else to get the answer (Don’t do this in school!), but be sure to check it yourself.
- Look up the answer in a Table of Integrals.
- Integrate it using the tricks you learned in math class.
- Integrate it using a symbolic equation solver on a computer, such as Mathematica or Maple.
- Find an approximate solution to the full equation. For example, integrate it numerically on a computer. (Trapezoid method, Gaussian integration, finite difference iteration, etc.)
- Find an exact solution for an approximation to the eq., such as a model or idealization of the physics. Most eqs. in this textbook have used this approach.
- Draw the Planck curve on graph paper. Count the squares under the curve between the wavelength bands, and compare to the value of each square, or to the area under the whole curve. (We will use this approach extensively in the Thunderstorm chapter.)
- Draw the curve, and measure area with a planimeter.
- Draw the Planck curve on cardboard or thick paper. Cut out the whole area under the curve. Weigh it. Then cut the portion between wavelengths, & weigh again.
- ...and there are probably many more methods.