1. Introduction

• 1.1 Definition
• 1.2 Key Facts

2. Related Material

• 2.1 Solar Intensity
• 2.2 The Solar Spectrum
• 2.3 Solar Declination
• 2.4 Seasons
• 2.5 Sun-earth Distance
• 2.6 Milankovitch Cycles
• 2.7 Insolation and Latitude
• 2.8 Diurnal Insolation
• 2.9 Daylight Length
• 2.10 Solar noon & the equation of time
• 2.11 Atmospheric Impacts
• 2.12 Normal Optical Thickness
• 2.13 Optical Thickness & Atmospheric Species
• 2.14 Air Masses

3. Instrumentation

• 3.1 Pyronometer

4. Local Insolation Charts

• 4.1 Insolation Chart Example
• 4.2 Daylight, Sunrise, & Sunset Times
• 4.3 Downwelling Shortwave Radiation
  

-Incoming solar radiation is the intensity of incoming solar radiation on an object.
Incoming Solar Radiation (Eo) &nbsp Ref: Ahrens 2007

-Typical Units are Wm-2 (Flux/Unit Area)
Measures solar input on a horizontal surface.

-Incoming solar radiation is the intensity of incoming solar radiation on an object.
Incoming Solar Radiation (Eo) &nbsp Ref: Ahrens 2007

-Typical Units are Wm-2 (Flux/Unit Area)
Measures solar input on a horizontal surface.

• Represents input solar energy into the system
• Rsw = incoming – outgoing
• Incoming = Insolation*(1-albedo), where albedo=fraction of incident radiation that is reflected (value between 0 and 1, e.g. snow ~= 0.9 and grass ~= 0.3)
• Outgoing = Insolation*albedo
• Drives numerous physical and biological processes
• Absorbed energy heats the surface and air
• Diurnal variation controls surface and air temperatures
• Seasonal variation influences weather
• Latitudinal variation is a major control on climate
• Absorbed Photosynthetically Active Radiation drives photosynthesis while the full spectrum drives Evapotranspiration
  • Alternate units: Mole, or Mole/m2/sec
• Daylight Length (Photoperiod)
• Environmental cue used by plants

Solar Intensity

Solar intensity changes with distance.As distance is doubled, for example, the energy is spread over four times the area. This results in an intensity that is one-fourth its original strength.

The Solar Spectrum

Insolation is primarily short wave radiation: 350 to 3000 nm, and 50% of this energy is in the visible portion of the spectrum..

Solar Declination (δ)

-Earth's axial tilt is: 23.45º

-Solar Declination = Latitude of the subsolar point (where the sun is directly overhead at solar noon)

-Solar Declination (δ) changes seasonally, and is calculated by the day of year using the following equation:

δ =23.45*cos(2*π*(JD-172)/365)

Where:
JD = Julian Day (count the days from Jan.1st)

Solar dec. calculator

Seasons

• Describes the revolution of the Earth around the Sun
• Orbital tilt causes changes in the position of sun and local incidence
• Controls seasonal changes in solar zenith
• Controls seasonal changes in irradiance
• Controls daylight length
• Accounts for our four basic seasons

Sun-Earth Distance

The sun and earth are closest during perihelion and farthest away during aphelion. The Solar constant is the incoming solar radiation measured at the top of the Earth's atmosphere on a surface that is perpendicular to the incident rays. While the average is 1367 W/m2, it varies due to the earth-sun distance, since radiation intensity is proportional to the square inverse of the sun-earth distance. This is because the surface area (4*pi*r^2) over which the sun's energy is distributed will increase with r, the earth-sun distance, and therefore since the total energy is constant, the intensity (W/m2) must decrease.

Three Orbital Parameters of Milankovitch
1. Precession: Changes the timing of when the Earth is closest to the Sun

Current Configuration:

• Perihelion (closest): December
• Aphelion (farthest): June
• Northern hemisphere has warmer winters, cooler summers than Southern hemisphere

2. Obliquity: (Axial Tilt) Changes the severity of the seasons

• 21.5 degrees, least extreme
• 24.5 degrees, most extreme

3. Eccentricity: Changes the overall radiation balance of Earth

• Eccentric: Most variable
• Least Eccentric: Least variable
  
  Images from Dylan Parenti 2008

Insolation and Latitude

• Insolation decreases with increased latitude
• E_θ=E₀cos(θ)
• θ=|β-δ|

Comparison of measured insolation at Coal Oil Point on December 22 to modeled insolation with and without an atmosphere

Diurnal Insolation

• Varies with Solar Zenith
• Varies with Direct vs Diffuse Beam
• Peaks at Solar Noon
  • What is solar noon?
  • When does it occur?
• Solar Zenith (θ_sun)
  • cos θ_sun=sin(δ)sin(β)+cos(δ)cos(β)cos(ω-λ)
• Solar Azimuth(phi;_sun)
  • tanφ_sun=cos(δ)sin(ω-λ)/(cos(δ)sin(β)cos(ω-λ)-sin(δ)cos(β))
• Where,
  δ = solar declination
  ω= solar longitude
  β = observer latitude
  λ = observer longitude
  ω-λ = hour angle

Daylight Length (Photoperiod)

Solar Noon and the Equation of Time

• What is the Equation of Time?

  • Determines the timing of Solar Noon
  • Sun fast (early) or sun slow (late)
• It is a product of a combination of Earth’s orbital eccentricity and tilt
• The modern formula consists of two periodic functions

  • ET = 0.170*sin[4π(JD-80)/373]-0.129*sin(2π(JD-8)/355]
  • Where JD = Julian day
  • ET = decimal hours
• SN = 12+(Daylight Savings Time)-ET +/-(Longitude-Meridian)*hr/15º

Atmospheric Impacts

• The atmosphere absorbs and scatters shortwave
  • Absorption reduces direct beam radiation
  • Scattering reduces direct beam, adds diffuse beam
• The atmosphere absorbs and reemits longwave

NORMAL OPTICAL THICKNESS

Quantifies attenuation by scattering and absorption

• E = E₀e^{-(α+β)*pathlength}
  • α = absorption coefficient
  • β = scattering coefficient
• Combined, α+β attenuate light
• In an atmosphere we need to weight attenuation by absorbers and scatterers by the change in particle density with height
• We call that weighted extinction coefficient normal optical thickness (τ)
• E_surf = E₀e^-τ

Optical Thickness & Atmospheric Species

• τ provides a unitless measure of attenuation at different wavelengths

  • E=E₀*e^-τ
• τ is scaled to one atmosphere. As the atmosphere changes, so does τ

  • If you double the pathlength, what happens to τ?
• Normal Optical Thickness is the sum of all absorption and scattering mechanisms as they vary with wavelength for one atmosphere

  • τ_N = τ_ray + τ_aer + τ_h20 + τ_O2 +τ_O3 + τ_CO2 + τ_CH4 etc.
• Each constituent can be understood separately given a spectrum

Air Masses

How do you relate pathlength to zenith angle?
Pathlength = 1/cos(θ) = airmasses (m)

Instrumentation

Other Measures of Light:

• Diffuse light (Diffuse=Total - Direct)
  • Block out direct beam with a shadowband
  • Highest early or late in the day or in overcast or partially overcast conditions
• PAR: Photosynthetically Active Radiation
  • Restricted to 400 to 700 nm
  • Sensitivity weighted to compensate for variable photon energy
    • Q = hc/λ
  • Units (Moles of Photons), 1 mole = 6.02x10²³ photons
• PPFD: Photon Flux Density
  • Restricted to 400 to 700 nm
  • Photons per unit area and time (moles/m2/sec)

Pyranometer at Coal Oil Point Reserve, Photo by Dar Roberts; July 18, 2007.

LI200X Silicon Pyranometer
The LI200X Silicon Pyranometer is used to accurately measure sun plus sky radiation in the 400 to 1100 nm waveband. It is used extensivly in solar, agricultural, and meteorological applications.
The sensor includes diffuser, cosine correction and level bubble. It should be nstalled in a location where it will not be shaded (such as the south end of tower crossarm). Installed at: COPR, Airstrip, Lisque

Time: UTC
Units: Watts/m2

Click here for a full size version of downwelling radiation at the surface.

Click here for a full size image of downwelling radiation at the top of the atmosphere.

(Both images will open in a new window)