Warming The Earth And The Atmosphere – Incoming Solar Radiation

All objects no matter how big or small whose temperature is above absolute zero emit radiation. Absolute zero is the temperature in which all molecular activity comes to a stop. Even though everything emits IR energy, we usually do not notice it because it is often weak, and we can’t see infrared light like you can sunlight.

The incoming solar radiation from the sun is scattered through the atmosphere and depending how saturated or dry the atmosphere is determines if the solar radiation will be reflected back out to space or absorbed and used modify the air mass it enters.

The most popular event that takes place from incoming solar radiation and the effect the earth’s atmosphere has on it is the greenhouse effect. Although this is the most noticeable effect, there are many other interactions between the earth and the sun’s radiation.

Earth vs. Sun

The sun is approximately 20 times warmer than the earth (using Kelvin scale). How much more solar radiation will the sun emit? Answer: The amount of radiation emitted is proportional to the fourth power of the temperature. If the sun in 20 times warmer than the earth, it will emit 20⁴ times more radiation. (20)⁴ = 1.6 x 10⁵ more radiation emitted by the sun.

Incoming Solar Radiation

This is energy from the sun. It is also called short-wave radiation because the sun is hotter than the earth and emits shorter wavelengths of radiation. These fall mainly in the ultraviolet and visible portions of the electromagnetic spectrum.

Radiation

Radiation is the transfer of energy by electromagnetic waves (have electrical and magnetic properties).

Characteristics of Waves

Wavelengths are measured from crest to crest. Wavelength is symbolized by the Greek symbol lambda (λ).

The shorter the wavelength, the higher the frequency.

Electromagnetic Spectrum

Spectra of emitted radiation from the earth and sun cover different intervals of the electromagnetic spectrum. Wavelengths important to weather are the short waves emitted by the sun called solar radiation
(UV or ultraviolet), and long waves emitted by the earth called terrestrial radiation (visual and IR or infrared).

The popular visible spectrum is the rainbow. A rainbow will appear when the sun is behind you and the rain in in front of you. The rain will act as a prism and scatter the light.

Blackbodies

These objects are both a perfect absorber and emitter. It absorbs all radiation, which hits it and emits all possible radiation. (Examples: Earth and sun are assumed to be blackbodies). Blackbodies are “ideal” objects. Real objects are selective absorbers. They absorb and emit only selected wavelengths.

Definitions

Emissive Power – This is the measure of the total radiant energy emitted per unit time, per unit area. A black body is a hypothetical body that emits and absorbs all energy incident upon it.

Emissivity – It is the ratio of the actual amount of energy emitted at a specific wavelength and temperature to that of a black body at the same wavelength and temperature.

Absorptivity – It is the fractional part of the incident radiation that is absorbed by the surface. It is a measure of how efficiently an object absorbs energy.

Reflectivity – It is the fractional part of the incident radiation that is reflected by a surface.

Transnulcsivity – It is the fractional part of the radiation transmitted through a medium per unit of thickness along the path of the radiant beam.

Radiation Laws

Kirchoff’s Law

This law states that good absorbers of a certain wavelength are good emitters at that wavelength. Poor absorbers of a certain wavelength are poor emitters at that wavelength. The earth’s surface and the sun a blackbodies because they are good absorbers as well as good emitters of radiation.

Planck’s Law

This law describes the amount of energy emitted by a blackbody at a specific temperature for each wavelength of the electromagnetic spectrum. The figure below shows the Planck curves for blackbodies at several different temperatures.

Note each curve has the same distinct shape with a single peak, but the location of this peak differs for each object. Also, note the height of the curve is greater for objects with higher temperatures.

Stefan – Boltzmann Law

This law states that the amount of radiation emitted by an object is proportional to the fourth power of its surface temperature. (E = σ T⁴) In other words, hotter objects radiate more total energy per unit area than colder objects.

Wien’s Law.

The wavelength at which the maximum amount of energy is emitted by an object (the most popular wavelength at which an object emits) is inversely proportional to the temperature of the object).

λ_max = W/T

The hotter the radiating body, the shorter the wavelength of maximum radiation.

Scattering

This is the process of redirecting incident radiation in all possible directions. (This is common with small particles suspended in the atmosphere.) Scattering is a major source of attenuation.

Scattering and absorption are beneficial when an aircraft does not want to be detected by radar. A radar emits a beam and looks for the return. If the object scatters or absorbs the beam, little to no signal will get back to the radar receiver and the aircraft can go undetected.

Radiation traveling through the atmosphere decreases in intensity as it moves further from the emitting surface. Due to absorption and scattering by atmospheric constituents, the further the energy travels through the atmosphere, the more attenuation that takes place.

Types of Scattering

There are three types of scattering

Rayleigh/molecular scattering – This occurs when the size parameter (x) is much less than 1μm and caused by air molecules scattering out a portion of the electromagnetic spectrum. This is why the sky is blue. The blue wavelengths are scattered out of the visible spectrum during the day. Rayleigh scattering is the least amount of atmospheric scattering expected.

Mie/aerosol scattering – It occurs when the size parameter is greater than 1μm but will stop when the size approaches 10μm. Aerosols in the atmosphere cause Mie scattering. It is forward scattering.

Geometric scattering – This happens when the relative humidity is over 90%. It is backward scattering as opposed to the forward scattering of Mie scattering.

Absorption

Absorption is the process by which incident radiant energy is retained by a substance. Gases are selective absorbers, meaning that they absorb strongly in some wavelengths, moderately in others, and only slightly in still others. Substances tend to absorb in specific wavelength intervals called absorption bands. The atmospheric window is a large “gap” between 8 and 11μm in which none of the gases are effective absorbers of radiation.

Continuum Absorption

Continuum absorption varies slowly with wavelength, across broad regions of the electromagnetic spectrum. Water vapor is the most significant absorber. An increase in the concentration of waver vapor increases absorption. The absolute humidity is a measure of the actual amount of water in the air, while relative humidity indicates how close the air is to saturation. Desert areas may have a low relative humidity but a high absolute humidity.

Absorptivity is a measure of how efficiently an object absorbs energy. Values lie between zero and one; one is a perfect absorber.

Angle of Incidence

Not all places on earth receive the same amount of radiation from the sun. The angle in which the sun’s radiation enters the atmosphere greatly determines the amount that part of the earth will heat up.

The angle at which the sun’s rays strike the earth’s surface is the angle of incidence. It is dependent on latitude. Small angles near the equator where there is a large concentration of heating per unit area. Large angles near the poles where there is a small concentration of heating per unit area. The slanting rays will spread over a greater area and will pass through a greater thickness of atmosphere. Only 1/2 the earths surface is receiving solar radiation at any given time. The earth emits radiation in all directions at ALL times (day and night).

Terrestrial Radiation

This is energy from the earth. It is also called long-wave radiation because the cooler temperatures of the earth and its atmosphere emit longer wavelengths. These fall in the infrared portion of the electromagnetic spectrum.

Greenhouse Effect

Gases in the troposphere (CO₂ and water vapor) strongly absorb most of the long-wave radiation emitted from the earth’s surface. These substances then reemit the long-wave radiation in all directions including back towards the ground. A portion of this energy reaches the surface of the earth and is reabsorbed by the ground (heating it). This causes the surface temperature to be greater than if no water vapor or CO₂ existed in the atmosphere.

The absorption varies with the wavelength of the radiation. Some long-wave radiation passes through the atmosphere and out to space. CO₂ and water vapor absorb very little radiation with wavelengths of 8μm to 11μm. This range is called the atmospheric window since radiation in these wavelengths is radiated out to space.

The reason why the air cools so quickly on a clear, dry evening is because the lack of humidity and clouds allows large amounts of IR radiation to escape rapidly to outer space as it is emitted upward by the ground and other surfaces.

Radiation Budget

The earth as a whole is not heating or cooling with time. Therefore, on a global scale the incoming radiation must equal the outgoing radiation. On smaller time scale, the incoming radiation does not equal outgoing. In the daytime incoming is greater than outgoing. And at night, incoming is less than outgoing. Solar radiation enters the top of atmosphere. Clouds and the earth’s surface reflect a certain amount. The atmosphere absorbs some. The rest makes it through to the surface of the earth and is absorbed. For energy leaving the surface of the earth: terrestrial radiation is emitted by the surface of the earth. Some is absorbed by the atmosphere and reemitted in all directions and the atmosphere radiates some. The rest makes it through to the top of the atmosphere and is emitted to outer space. Also, latent heat and sensible heat are transferred from the surface to the atmosphere.

Reflectivity

Objects are discriminated from their background due to differences in reflectance. They have texture due to the nonuniformity of the reflection process on rough and variable surfaces. An object’s albedo (reflectivity over a range of wavelengths expressed as a percentage) and the albedo of the background affect this discrimination. Reflection is the most important process in seeing an object, unless it emits significant amounts of energy.

Perfect (specular) reflector – A perfect reflector results in the angle-of-incidence equal to the angle-of-reflectance, so the reflected energy has the same wavelength as the incident energy. The sensor must be in line with the angle of reflectance.

Diffuse Reflector – A diffuse reflector reflects energy (EMR) evenly in all directions.

Transmissivity

It is the ratio of transmitted radiation to the total radiation incident upon the medium. For electro-optics use, it measures how well the contrast between a target and its background is transmitted or sent through the atmosphere. Transmissivity is limited by varying weather conditions such as clouds, precipitation, aerosols, and high absolute humidities.

Contrast – This is the brightness difference between the target and its background that is received at the weapons sensor. This difference must exceed a minimum contrast threshold in order to be seen by the sensor. The ability to see the target depends on the: Inherent contrast (Co). It is the contrast that exists at the target and its background as measured at
the target.

Apparent contrast [Co (x)] – The apparent contrast is the contrast measured at some distance from the target. This is the contrast that appears to exist. As the distance from the target (path length) increases, the apparent contrast decreases.

Threshold contrast [Co(th)] – Where the target just barely becomes visible to the sensor is called the threshold contrast. The ability to detect an object using a visual sensor is affected by the reflectance of the target versus the reflectance of the background. Generally, a bright object on a dark background shows up better than a dark object on a bright background.

Contrast Transmission – Contrast transmission deals with the loss of contrast due to the intervening atmosphere between the target, background, and sensor. Regardless of how great the inherent contrast between the target and background, that contrast must be transmitted to the sensor to be seen.

Path radiance, path length, weather, and absorbing gases affect contrast transmission. The apparent contrast received at the sensor is directly enhanced or degraded depending upon the variation of these effects.

Path radiance (glare) – This occurs when the target has a bright background. The target is hard to see or may be hidden because of the background. A pilot flying toward a target with the sun rising/setting behind the target would experience path radiance while trying to acquire the target in the visual. Whenever the background is brighter than the target, path radiance (glare) can occur.

Path length – The distance between the target and sensor is the path length. As the path length increases, the amount of absorbing gases, lithometeors, and hydrometers increases. This decreases the chance of being able to see the target.

The higher the concentration of aerosols (smoke, dust, etc.) and absorbing gases (water vapor, carbon dioxide, ozone, oxygen) the more EMR is attenuated. Of the absorbing gases, water vapor is the most important absorber, accounting for some absorption at all wavelengths. Because of their shorter wavelengths, visible systems are often more weather sensitive.

Far-Infrared Wavelengths – Sensors in the far-IR range use emitted energy to detect a temperature contrast between the target and the background. The wavelengths range from 8 to 12μm. As with visible sensors, the target /
background contrast (thermal with IR) received at the detector must exceed a minimum operating threshold. Factors determining the detection of thermal contrast include:

• Thermal characteristics of the target and background
• Present and recent weather
• Characteristics of the sensor

Radiative Temperature (RAT)

The temperature an object appears to have is related to the amount of energy it emits. How much energy an object (target) emits is dependent upon its characteristics of absorptivity/emissivity, thermal conductivity, and thermal capacity. These variables directly affect the radiative temperature throughout the thermal cycle (heating and cooling of the object (target). Remember, an IR sensor “sees” the SURFACE temperature of an object, NOT the interior/core.

Absorptivity/Emissivity

Absorptivity and emissivity is a measure of how rapidly an object absorbs or emits by a radiative process. Objects with high absorptivity/emissivity heat faster during the day and cool faster during the night (with constant conductivity and capacity). Objects with low absorptivity/emissivity are slow to heat and cool.

Thermal Conductivity

The thermal conductivity is a measure of how rapidly heat is transferred within a material (how quickly it ‘is transferred from the skin surface to the core/interior of the object). Objects with low conductivity appear to heat up quickly, but core temperatures remain cool. At night, objects with low conductivity cool quickly (heat energy remaining near the surface is released quickly). Objects with high conductivity appear to heat slowly, due to heat being transferred from the surface into the core/interior. At night, the object’s skin (surface) cools slowly as this “stored” energy is conducted back. An example of objects with low vs. high conductivity is plastic and metal.

Thermal Capacity

The thermal capacity is a measure of how much heat (energy) an object can store. It is a function of two parameters, mass and specific heat. The larger the mass, the more heat it can store. The higher the specific heat of a substance, the more heat it can store. An object (target) with a high thermal capacity will heat and cool slower than an object with a lower thermal capacity – with all characteristics being the same.

These three characteristics interact in a complex manner to give a substance its radiative temperature (thermal emission). Radiative temperature is the temperature an object will appear to have based on the amount of energy it is emitting. The temperature of an object/target as seen in infrared is actually the temperature of the surface of the object (or the “skin” temperature). For targets being heated by sunlight the skin temperature depends on how rapidly the object absorbs heat (absorptivity), on how rapidly the heat is transferred within the object (conductivity), and
how much mass is available to contain the heat (thermal capacity). For example, a truck and tank have essentially the same absorptivity/emissivity and conductivity characteristics, but the tank has a larger thermal capacity because there is more mass available to distribute absorbed energy. At night this internally stored heat is available to be conducted to the surface to maintain the skin temperature. As a result, the tank will show a smaller diurnal temperature variation than a truck. The following equation
summerizes the relationships between absorptivity/emissivity, conductivity and thermal capacity:

Radiative Temperature = Absorptivity/Emissivity + Conductivity + Thermal Capacity

Radiative Temperature Crossover

The radiative temperature crossover occurs when the target and background achieve the same radiative temperature. The sensor will not distinguish the target from its background; hence the target becomes invisible.

Radiative temperature crossover is a function of the diurnal temperature cycle, thermal conductivity, and thermal capacity of the target and its background. The actual time of crossover is highly dependent on the thermal characteristics of the targets and environmental conditions. Normally, it occurs shortly after sunrise and near sunset. The natural environment can affect the thermal response of an object in two ways. First, moisture increases thermal conductivity, so wet dirt will have a smaller diurnal temperature variation (due to its higher thermal capacity and absorptivity) than dry dirt. Second, natural objects (trees, grass) have smaller diurnal variations when they are growing than when they are dormant. The growing process acts as an internal heat source at night and a cooling process during the day (evapotranspiration).

At night a cold tank will appear warmer, relative to its rapidly cooling background (dry dirt) but during the day the background (dry dirt) heats up more rapidly, and the cold tank will appear cooler. The nighttime skin temperature of the target will not only depend on its thermal characteristics but will also be strongly affected by the radiative characteristics of the sky (if the target is highly reflective in IR). This will greatly affect an IR forecast.

The angle of the sun also changes thermal crossover by unequal heating of the target, the east side of objects in the morning and the west side of objects in the evening. In the morning, the east side of the target will be warmer (positive contrast) than the relatively cooler (negative contrast) west side. This could affect the ability of the IR system to see the target if the imager was looking for a positive contrast. If an attack came from the west and the target had a negative contrast the sensor would not achieve lock-
on.

Contrast Transmission

Transmission of thermal contrast from the target to the sensor is affected by the amount of water vapor (absolute humidity) and aerosols in the air. The more water vapor, the greater the absorption. Aerosol (Mie) scattering is significant to extremely significant for IR, depending on the type. Moderate to heavy precipitation will reduce contrast transmission to unacceptable levels. Molecular scattering is negligible for IR, and path radiance (glare) is not significant.

Near-Infrared (Laser) Wavelengths

Near infrared (Laser) sensor systems detect reflected EMR that a laser designator has put on a target. The wavelength is 1.06μm. The laser designator produces a concentrated beam of Near IR (1.06μm) energy, which is aimed at a target. This beam is reflected off of the target and is located by a sensor.

Refraction of EMR is significant only for near-infrared (laser) wavelengths. When lasers are used to “highlight” a target, the beam used could be refracted (called beam wander) away from the target due to small particles in the air. Visual examples of bending EMR are mirages of water on a hot road or a straw seemingly bent in a glass of water. Both are due to changes in density of the transmitting medium.

Generally, target to background contrast transmission is the same as for Far IR refraction.

Millimeter/Microwave Wavelengths

Millimeter/microwave (MM/MW) sensors detect EMR in one of three different ways, depending on the weapon. The wavelengths range from 0.1 mm to 10 cm. It may respond to EMR, which originates from an operating target itself. It may sense EMR reflected off of the target by and outside source, or it may sense EMR, which originates from the weapon. This will be covered in greater detail under Guidance System Types on the next page.
MM/MW systems use the longest wavelengths of all E-0 weapon systems. This makes them generally less weather sensitive than IR or visual units. Under normal conditions, only heavy cloudiness and precipitation effect MM/MW systems to some extent. A drawback to this is the longer wavelengths make target resolution the poorest of all systems.