Learning Objectives 1. Be able to define reflectance qualitatively and quantitatively. 2. Understand the terms that describe the path of light from the sun to the earth and up to the satellite. 3. Understand the equations that define the amount of light at various places on the light path.
Learning Objectives (cont.) 4. What are reflectance spectra and what do they look like for common materials? 5. What leaf characteristics control the shape of its spectral reflectance curve?
Spectral Reflectance Definition: The amount of reflected radiation divided by that amount of incoming radiation in a particular wavelength range % Reflectance =100 x reflected/incoming % Reflectance =100 x reflected/incoming What are the units of reflectance?
Types of Reflectance Specular Mirrors or surfaces of lakes, for example Mirrors or surfaces of lakes, for example Angle of incidence = angle of reflection Angle of incidence = angle of reflection Diffuse (aka Lambertian) Reflects equally in all directions Reflects equally in all directions Usually we assume Lambertian reflectance for natural surfacesUsually we assume Lambertian reflectance for natural surfaces Idealized—not really found in nature but often closeIdealized—not really found in nature but often close
Reflectance Varies with wavelength Varies with geometry Diagnostic of different materials
Radiant Flux Rate of flow of energy onto, off of, or through a surface Φ λ (Watts)
Some Important Terms Irradiance (E λ ) (Incoming light from sun) Radiance (L λ ) (Light received at satellite) EλEλ L λ
Irradiance Radiant flux incident per unit area of a surface E λ = Φ λ /A (radiant flux/area in a particular wavelength) (So…what would the units be?)
Radiance (L λ ) Radiant flux per unit solid angle arriving at a satellite from a given direction per unit area. What are the units??
Radiance vs. Reflectance Satellites measure radiance (What are the units??) Objects on the ground are often characterized by their reflectance (What are the units??) Often we want reflectance but we measure radiance. How do we deal with this?
RADIANCE!!!Top of Atmosphere IRRADIANCE REFLECTANCE!!
Top of Atmosphere (TOA) Irradiance Incoming radiation from the sun (E 0 ) Amount is described by Stefan-Boltzmann Law which relates the absolute temperature of an object to amount of energy it gives off Peak wavelength is determined by Wien’s Displacement Law which relates object’s temperature to emitted wavelength
Top of Atmosphere Irradiance Top of atmosphere irradiance varies over time. Why? Is top of atmosphere irradiance equal to ground irradiance? Why or why not?
Stefan-Boltzmann Law Q = єσ*T 4 Where: Q = amount of energy radiated є = emissivity σ = Stefan Boltzmann constant (5.6697 x 10 -8 Wm -2 K -4 ) T = Temperature ( o K) What does this equation tell you?
Wien’s Displacement Law Peak λ(µm) = 2898/T( o K) Sun is 5778 o K So peak λ = 2898/5778 = 0.5 µm (green) What does this equation tell you about temperature and the energy of emitted light?
Wien’s Displacement Law http://phet.colorado.edu/sims/blackbody-spectrum/blackbody- spectrum_en.html Demo from UC Boulder
Calculating Irradiance at Ground E λ = E 0 t m cosθ E λ = Irradiance on ground for a particular wavelength (W/m 2 ) E 0 = Irradiance at top of atmosphere for that wavelength (W/m 2 ) t = atmospheric transmittance (fraction) m = relative air mass (fraction) θ = angle of incidence (degrees or radians)
Angle of Incidence (θ) Depends on slope of ground Depends on sun altitude Angle of sun above the horizon Angle of sun above the horizon Depends on time of year and time of day Depends on time of year and time of day Depends on sun azimuth The compass direction of sun The compass direction of sun Depends on time of year and time of day Depends on time of year and time of day
Solar Angle Zenith Angle We use the zenith angle for angle of incidence in the irradiance equation.
Calculating Radiance from Reflectance L λ = Et m r/π (+ L p ) L λ = Radiance at satellite (W/m 2 /sr) (not the same as DN – must convert!) E λ = Irradiance on ground t λ = Atmospheric transmittance m = Relative air mass r λ = Reflectance of object π = 3.1416 L p accounts for atmospheric scattering; will discuss later in semester.
Reflectance Spectra Reflectance spectra are graphs of reflectance vs. wavelength. Understanding reflectance spectra is fundamental to using remote sensing
Spectral Properties of Vegetation Unlike minerals, vegetation is composed of a limited set of spectrally active compounds Relative abundance of compounds, including water, indicates veg. condition Vegetation structure has significant influence on reflectance. Spatial scale of reflectance measurement is critical.
How do you get spectra? Measure in the field with field spectroradiometers Measure in the lab Collect from image data Look at spectral libraries: http://speclab.cr.usgs.gov/spectral-lib.html)