Lecture 9 Derivation of the EM signal detected by a spaceborne VIS/RIR radiometer 7 October 2008

Lecture 9Derivation of the EM signal detected by a spaceborne VIS/RIR radiometer7 October 2008

Source of Figures The figures used in today’s lectures are from Jensen, J.R., Remote Sensing of the Environment - An Earth Resource Perspective, 2nd Edition, 592 pp., Prentice Hall, Upper Saddle River, NJ, 2007.

Key components of VIS/RIR remote sensing Lecture 2 – Energy emitted from sun based on Stephan/Boltzman Law, Planck’s formula, and Wein Displacement Law VIS/RIR Satellite Lecture 9 – EM energy arriving at the sensor EM energy Lecture 3 EM Energy interacts with the atmosphere going to and coming from the earth’s surface Lectures 7-8 EM energy reflected/scattered from Earth’s Surface

The conceptual model presented by Jensen in Figure 2-22 is the focus of today’s lecture

Lecture Outline/Key Points • Terms used to describe EM radiation • Flux, Radiant Flux Density, Irradiance, Exitance • Hemispherical reflection, distance to the sensor, and the concept of the solid angle • Radiance • Terminology for defining radiance detected by a radiometer • Sources of surface irradiance • Path radiance • Model of total EM radiance detected by a spaceborne radiometer

Radiant Flux -  • The fundamental unit to measure electromagnetic radiation is radiant flux • Defined as the amount of energy that passes into, through, or off of a surface per unit of time • Radiant flux is measured in Watts (W)

Radiant Flux Density Radiant flux density is simply the amount of radiant flux per unit area Radiant flux density represents the amount of EM energy coming from the area represented by a pixel  Radiant flux density =  /area

Irradiance - E  Irradiance is the amount of incident radiant flux per unit area of a plane surface in Watts / square meter (W m –2 ) Fig 2-20 in Jensen

Exitance - M  • Exitance is the amount of radiant flux per unit area leaving a plane surface in Watts per square meter (W m –2 ) Fig 2-20 in Jensen

Irradiance versus Exitance • Irradiance (E) is the radiant flux density that is incident on a surface • Exitance (M) is the radiant flux density that exits a surface

Sources of Exitance (M) • Reflected irradiance M = r E, Where r is the hemispherical reflection coefficient 2. Emitted radiation based on the temperature of the surface – not important for VIS/RIR EM energy

For the purposes of this discussion, let us assume that: • The irradiance striking the surface is 1,000 W m-2 • Our target area has a size of 1 by 1 m = 1 m2 • The surface is Lambertian and has a hemispherical reflectance (r) of 0.8 • This means the total E Total M = 800 W m-2 But this EM energy is being equally distributed throughout a hemisphere, can be thought of the total radiant flux () = 800 watts E = 1,000 W m-2

QUESTION – what is the radiant flux density at a distance of 10 m from the ground? Surface area of a hemisphere (A) = 2  R2 where R = radius of the hemisphere = distance from the ground At 10 m, A = 2 x 3.14159 x 102 = 628.3 m2 The radiant flux density at 10 meters from the ground = 800/628.3 = 1.27 W m-2

QUESTION – what is the radiant flux density at a distance of 20 m from the ground? Surface area of a hemisphere (A) = 2  R2 where R = radius of the hemisphere = distance from the ground At 10 m, A = 2 x 3.14159 x 202 = 2513.3 m2 The radiant flux density at 10 meters from the ground = 800/ 2513.3 = 0.32 W m-2

Radiant flux density at a sensor =  / d2 / a =  / a / d2 1. The radiant flux () from a surface decreases by a factor of the distance to the surface squared, e.g., at a distance d,  (d) =  /d2 2. The density of the energy captured by a detector is proportional to the size of the detector surface – a e.g., radiant flux density at the sensor, i.e., the irradiance at the sensor at a distance, d, I (d) =  (d) / a Detector: surface area - a d

Solid angle of the sensor a Flux from a surface is actually being emitted or reflected in all directions equally, i.e., it is being distributed into a hemisphere d The radiometer intercepts a fraction of the exitance from a surface, this fraction is defined by the solid angle, Ω, of the sensing system, which can defined by the area of the detector surface (a) and the distance to the target area (d) Ω = a/d2

Radiance - L  • Radiance – the radiant flux per unit solid angle in a given direction per unit of projected surface in the direction considered • Radiance is the measure of EM radiation detected by the Remote Sensing system

Detection of exitance by a remote sensing system Satellite Radiometer θ – Sensor viewing angle Area as seen by the sensor (projected area) = A cos θ A = area on ground being sensed

Same as Figure 2-21 in Jensen • Figure 2-10 from Elachi, C., Introduction to the Physics and Techniques of Remote Sensint, 413 pp., John Wiley & Sons, New York, 1987.

Radiance - L  • Radiance is what all satellites detect • It is measured as Watts per square meter per steradian (W m-2 sr -1 ) L  = ( / ) / (A cos )

Summary of terms used to describe EM radiation

What are the sources of irradiance at the target area? Satellite radiometer i – incident solar flux at the outer edge of the atmosphere – or incident solar irradiance - Eo Eg – all sources of irradiance reaching the target area Target area

Sources of irradiance on a target • Incident solar irradiance (Eo) • Diffuse sky irradiance (Ed) • Irradiance reflected from adjacent areas (En)

Sky Irradiance • Atmospheric scattering results in much EM radiation entering into the field of view of the radiometer • This indirect EM radiation is referred to assky irradiance • Sky irradiance that reaches the target area is referred to as diffuse sky irradiance Sky irradiance Atmospheric Scattering Diffuse sky irradiance Target area

Satellite radiometer En Target area En is irradiance reflected into the target area from adjacent areas

Model for describing total radiance (Ls) at a satellite radiometer Satellite radiometer Ls = radiance intercepted by the radiometer Lp = path radiance = radiance from outside the target area intercepted by the radiometer Lt = radiance from the target area intercepted by the radiometer

Sources of Path Radiance • Sky irradiance • Detection of irradiance from adjacent pixels – the effects of the detector point response function

Sky Irradiance • Atmospheric scattering results in much EM radiation entering into the field of view of the radiometer • This indirect EM radiation is referred to assky irradiance Radiometer Sky irradiance Atmospheric Scattering

Sky Irradiance • Sky irradiance is EM energy that is the result of scattering within the atmosphere • Sky irradiance is important for two reasons • Some sky irradiance reaches the earth’s surface, e.g., it illuminates the target area – this is called diffuse sky irradiance • Some sky irradiance is scattered into the area being viewed by the remote sensing system

Sensor Point Response Function • Sensors are not precise enough where they only detect energy from the target area of interest • All sensors detect some energy coming from areas adjacent to the area of interest Figure from Cahoon et al. 2000. Wildland fire detection from space: Theory and application. Pages 151-169 in J. L. Innes, M. Beniston, and M. M. Verstraete, editors. Biomass Burning and its Inter-Relationship with the Climate System. Kluwer Academic Publishers, Dordrecht.

Fig. 14 Sensor Point Response Function • In the AVHRR radiometer, 50% of signal comes from intended area, and 50% from outside of this area Figure from Cahoon et al. 2000. Wildland fire detection from space: Theory and application. Pages 151-169 in J. L. Innes, M. Beniston, and M. M. Verstraete, editors. Biomass Burning and its Inter-Relationship with the Climate System. Kluwer Academic Publishers, Dordrecht.

What are the impacts of an impulse response function on reflectance of the pixels being imaged by a sensor? Assume a radiometer is detecting a series of pixels that consist of bright sand and darker water 1 2 3 4 5 6 7 8 9 10 11 12 Sand – reflectance = 0.7 Water – reflectance = 0.1

Reflectance assuming that 50% of detected energy comes from target pixel and 25% comes from the pixels before and after the target

Figure 2-22 from Jensen Jensen discusses the sources for the radiance detected by the satellite, e.g., Ls He describes 5 pathways for the EM energy that contribute to Ls

Simple model for estimating total radiance (Ls) at a satellite radiometer i – incident solar flux Eo – solar irradiance Satellite radiometer Ls θo θv Assumptions -No atmosphere -Lambertian surface Ω A r

In our simple model, what do we know? i – incident solar flux – can calculate Eo A – area of the ground that is within the viewing geometry of the detector Ω – solid angle formed by the detector r – reflectance of the ground in the direction of the detector θv- viewing angle of the sensor where the detector is housed θo– Incident angle of the incoming solar radiation

Effects of variations in θo Just like outgoing emittance, the area over which the incoming solar irradiance (Eo) is projected onto the ground surface varies as a function of incidence angle To account for this, the solar irradiance reaching the ground is calculated as Eo cos θo Where Eo = i/A At θo = 0, cos θo = 1, and then decreases as θo increases

Simple model for estimating total radiance at the top of the atmosphere in our simple model Ls = [(Eo cos θo r)] / [(A cos θv) / Ω]

Sources of variation in total radiance (L s ) at a satellite radiometer Satellite radiometer i – incident solar irradiance Ls θo θv ivaries throughout the year – thus, it will affect Ls In addition, Ls varies as a function of the cos Θv r – reflectance in sensor direction

Sources of variation in Radiance (Ls) in our simple model • Changing sensor angle – θv • Changes projected surface area • Changes Bidirectional Reflection of surface • Changing solar illumination angle • Changes area of projection of solar flux • Changes Bidirectional Reflection of surface • Variations in solar flux i (daily and seasonal) • Changes in surface reflectance

The amount of solar radiation reaching the earth’s surface varies over the growing season Thus, even if the reflectance remains constant over the entire year, the radiance detected by a sensor will change

Complex model for estimating total radiance (L s ) at a satellite radiometer Satellite radiometer Ls Lt In reality, estimating Ls is much more complicated because we have to account for the effects of the atmosphere

Accounting for effects of the atmosphere • When we add the atmosphere to our model, we increase the complexity of our model – From here on, we will define Ls – the energy detected by the satellite Lt– the energy leaving the atmosphere (e.g., top of the atmosphere) from the target area • When no atmosphere is present, then Ls = Lt • When atmosphere is present, then Ls  Lt

Effects of the atmosphere on Ls • Through scattering and absorption, attenuates incoming and outgoing radiance through scattering and absorption of EM energy – determines atmospheric transmittance • Scattered light from the atmosphere results in reflection of EM energy into the field of view of the radiometer • Scattering of light results in diffuse sky irradiance, which also illuminates the target area

Fig. 10 Ls is the total radiance at the sensor Eo is the solar irradiance at the top of the atmosphere T is the atmospheric transmittance in the direction of the sun(θo) and sensor (θv) r is the surface reflectance Li is the total radiance from the area of interest at the earth’s surface Lt is the total radiance from the area of interest at the top of the atmosphere Path 1 – Accounts for reflection from the target of solar irradiance and attenuation by the atmosphere

Lecture 9 Derivation of the EM signal detected by a spaceborne VIS/RIR radiometer 7 October 2008