8 Radiation Variables

8.1 Measurements of Irradiance and Radiometric Temperature

The following references, although in part obsolete now, have additional information on radiation measurements from NCAR aircraft: RAF Bulletin 25, Bannehr and Glover, 1991, NCAR Technical Note NCAR/TN-364+STR, and Albrecht and Cox, 1977.⁴⁷ The instruments are described in the “Radiation” section on the EOL web site. Some other radiometric measurements appear in Section 4 because the measurements fit better there with measurements of state variables for the atmosphere; these include two measurements of air temperature by radiometric thermometers, AT_ITR and OAT, and the Microwave Temperature Profiler MTP that measures temperature profiles above and below the aircraft by radiometric measurements.

Radiometric (Surface or Sky/Cloud-Base) Temperature (^∘C): RSTx

The equivalent black body temperature measured by an infrared radiometer. The radiometers used on the GV and C-130 are Heimann Model KT-19.85 precision radiation thermometers. The KT19.85 spectral band extends from 9.6 to 11.5 m, and it has a 2̊ field of view. The x in the variable name denotes the instrument location on either the bottom (B) or top (T) of the aircraft .The KT-19.85 instruments are calibrated using a NIST-referenced source over a range of sensor temperatures controlled by a cold bath.⁴⁸

Radiometer Sensor Head Temperature (^∘C): TRSTx

The temperature of the sensing head of the KT19.85 radiometer sensing head, usually applying to RSTB, the primary down-looking instrument. The down-looking instrument is normally heated to maintain a sensor-head temperature near the scene temperature. Consult the archived netCDF files or project reports for the calibration coefficients used, which often varied among projects.

Pyrgeometer Output (V): IRxV

The voltage representing long-wave irradiance, from a pyrgeometer manufactured by Kipp & Zonen. The CGR4 model used on the GV and C-130 includes a meniscus dome that provides a 180º field of view with negligible directional response error over the spectral range of 4.2 to 45 m. The thermal stability of the dome construction and coupling to the instrument body eliminates the need for dome temperature measurements or dome shading. It is calibrated at the Naval Research Lab over a range of temperatures encountered during flight according to procedures specified by Bucholtz et al. (2008).⁴⁹ The pyrgeometers are usually flown in pairs, one looking upward and one looking downward. The letter ’x’ denotes location on either bottom (B) or top (T) of the aircraft. The primary derived variable from this instrument is IRxC, below.

Pyrgeometer Housing Temperature (^∘C): IRxHT

The temperature of the modified pyrgeometer housing, measured by a platinum resistance temperature sensor. The calibrated temperature (IRxHT) is derived from the raw signal (IRxHTV) as described below:

Calibrated Infrared Irradiance (W m^-2): IRxC

The infrared irradiance measured by a Kipp & Zonen CGR4 instrument,⁵⁰ after application of a calibration function. The relationship between IRxV (V) and IRxC (W m^− 2) is determined by a calibration in which the CGR4 views a NIST-referenced source over a range of sensor temperatures controlled by a cold bath. The processing algorithm is described in the following box:

IRxHTV = voltage from a platinum resistance thermometer attached to the housing of the pyrgeometer [V]
{\(a_4,\,a_5\)} = calibration coefficients [\(^\circ\)C]
\(V_1\) = 1 V (for consistency of units)

\[\begin{equation} \mathrm{\{IRxHT\}} = a_4 + a_5\,\log_{10}(\mathrm{\{IRxHTV\}}\,/\,V_1) \tag{8.1} \end{equation}\]

Pyranometer Output (V): VISxV

The voltage from a pyranometer, representing visible irradiance. On the GV and C-130, Kipp & Zonen CMP22 pyranometers measure visible irradiance. A high-quality quartz dome allows for a wide spectral range, improved directional response, and reduced thermal offsets. The spectral range is 0.32 to 3.6 m. The pyranometers are usually flown in pairs, one looking upward and one downward. On the C-130, these sensors are mounted on stabilized platforms that remain level during aircraft pitch and roll variations. They are calibrated pre- and post-project at the Naval Research Lab (Bucholtz et al, 2008; see footnote [fn:Bucholtz-2008] on page ) using a sun-tracking shadow device and diffuse sunlight as a source. The letter ’x’ denotes either bottom (B, nadir-viewing) or top (T, zenith-viewing). The primary derived variable from this instrument is VISxC, below.

Pyranometer Housing Temperature (^∘C): VISxHT

The temperature of the modified housing unit of a pyranometer, measured by a platinum resistance temperature sensor. A calibrated temperature (VISxHT) is derived from the raw signal, VISxHTV, which is normally not included in archive netCDF files. The equation used for the calibration is VISxHT = a₁ + a₂log₁₀({VISxHTV}/V₁) where V₁is 1 V and {a₁, a₂} are calibration coefficients having dimensions of [^∘C].

Calibrated Visible Irradiance (W m^-2): VISxC

The visible irradiance measured by a Kipp & Zonen CMP22 pyranometer. The relationship between VISxV (V) and VISxC (W m^− 2) is determined by calibration procedures in which the CMP22 views a clear sky source while a sun-tracking device blocks direct solar radiation. The normal processing algorithm is to apply a simple linear calibration, as follows:

VISxV = voltage output by a pyranometer [V]
\(a_{1}\) = linear calibration coefficient [W m\(^{-2}\) V\(^{-1}\)]

\[\begin{equation} \mathrm{\{VISxC\}}=a_{1}\mathrm{\{VISxV\}} \tag{8.2} \end{equation}\]

8.1.0.1 Stabilized Platform Angles (^∘): SPxPitch, SPxRoll {-spx}

The pitch and roll angles of the stabilized platforms, relative to the aircraft reference frame. Upward- and downward-looking pyrgeometers and pyranometers on the C-130 are mounted on stabilized platforms that compensate for aircraft pitch and roll. These variables record the movement of the top (x=T) and bottom (x=B) platforms in response to aircraft pitch and roll changes. The platforms are mounted with 2.85^∘ downward pitch angle to compensate for the normal upward pitch of the aircraft. The range of motion is  ± 5^∘ in pitch and  ± 10^∘ in roll. The sign convention is that of the aircraft, for which nose-upward pitch and right-wing-down roll are positive.

8.2 Spectral Irradiance and Actinic Flux

The HIAPER Atmospheric Radiation Package (HARP) includes separate components that measure spectral irradiance (both upwelling and downwelling) and actinic flux. The instrument is described at this URL. Data are recorded on dedicated disk drives associated with the instrument, not in the standard aircraft data-system files. This is an ancillary data set, for which special Matlab and IDL analysis routines have been developed, but the measurements are not merged into the netCDF archives produced by EOL. For data access and assistance with analysis routines, contact EOL/RAF data managers at mailto:raf-dm@eol.ucar.edu.

8.3 Solar Angles

The calculations described in this group are used primarily when interpreting the calibrated visible irradiance (VISxC) but can be used by themselves or in conjunction with other measurements that need them. For additional documentation see Bannehr and Glover, 1991, NCAR Technical Note NCAR/TN-364+STR and this NOAA web site.⁵¹ The calculator at this link can also be used to find these angles from the position and time in data files.

Solar Declination Angle (radians): SOLDE

The solar declination angle, the angular distance of the sun north of the earth’s equator. (Negative values are south.) To obtain this, the solar hour angle is calculated (taking leap years into account).

\(N\) = day number
    = number of days (corrected for leap years) since 1 January 1980
       (including fractional day from UTC time)
   = (year-1980)365+(int)(year-1980)/4+day
      + (hour+min/60.+sec/3600.)/24.+\(M\)
   where \(M\)=(int)(k+(int)((month-i)30.6+b)
      with {i,b,k}={1,0.5,0} for month <= 2
      and otherwise {3, 59.5, (1 for leap years, else 0)}
\(\Theta_h\): UTC time expressed as radians after solar noon
\(f,\ \alpha.\ \epsilon\): internal-calculation variables defined below
{SOLDE}: solar declination angle

\[\begin{equation} \theta_{h}=2\pi\frac{N}{365.25} \tag{8.3} \end{equation}\] \[\begin{equation} f=-0.031271-4.53963\times10^{-7}N+\theta_{h} \tag{8.4} \end{equation}\] \[\begin{align} \alpha &= \theta_{h}+4.900968+0.000349\,\sin(2f)+3.67474\times10^{-7}N\notag \\ &+(0.033434-2.3\times10^{-9}N)\,\sin(f) \tag{8.5} \end{align}\] \[\begin{equation} \epsilon=0.409140-6.2149\times10^{-9}N \tag{8.6} \end{equation}\] \[\begin{equation} \mathrm{{\{SOLDE\}}=}\arcsin(\sin\alpha\sin\epsilon) \tag{8.7} \end{equation}\]

Solar Elevation Angle (radians):SOLEL

The solar elevation angle, describing how high the sun appears in the sky. The angle is measured between a line from the observer to the sun and the horizontal plane on which the observer is standing. The elevation angle is negative when the sun drops below the horizon, and the sum of the elevation angle and the zenith angle is π/2.

\(\theta_{G}\) = Greenwich hour angle [radians]
\(\theta_{L}\) = local hour angle [radians]
\(N\) = day number [see SOLDE box above]
\(Y\) = year (format as in 1980) \(\lambda\) = latitude [radians]
\(\psi\) = longitude [radians] \(h\) = fractional hour = (hour + minute/60. + second/3600.)
\(\alpha\)      see (8.5) in the SOLDE box above
\(\epsilon\)      see (8.6) in the SOLDE box
{SOLDE} = solar declination angle (radians) described above; cf. (8.7).

\[\begin{equation} \theta_{G}=\arctan(\frac{\sin\alpha\cos\epsilon}{\cos\alpha}) \tag{8.8} \end{equation}\] \[\begin{align} \theta_{L} = & \theta_{G}+\psi-2\pi\frac{h}{24}-1.759335\notag \\ - &2\pi(\frac{N}{365}-Y+1980)-3.694\times10^{-7}N \tag{8.9} \end{align}\] \[\begin{equation} \mathrm{\mathrm{\{SOLEL\}}=\arcsin\left(\sin\lambda\sin\mathrm{\{SOLDE\}+\cos\lambda}\cos\mathrm{\{SOLDE\}}\cos\theta_{L}\right)} \tag{8.10} \end{equation}\]

Solar Zenith Angle (radians): SOLZE

The angle of the sun from the zenith, or the solar zenith angle. Cf. also the discussion of the solar elevation angle, SOLEL. {SOLZE} = (π/2) − {SOLEL} with {SOLEL} given by (8.10) above.

Solar Azimuth Angle (radians): SOLAZ

The solar azimuth angle, the angular distance between due south and the projection of the line of sight to the sun on the ground. A positive solar azimuth angle indicates a position east of south (i.e., morning).

\(\theta_{L}\) = local hour angle (radians): see (8.9)
{SOLDE} = solar declination angle (radians): see (8.7)
{SOLEL} = solar elevation angle (radians): see (8.10)
{SOLAZ} = solar azimuth angle [radians]

\[\begin{equation} \mathrm{\{SOLAZ\}=\arcsin\left(\frac{\cos\mathrm{\{SOLDE\}\sin\theta_{L}}}{\cos\mathrm{\{SOLEL\}}}\right)} \tag{8.11} \end{equation}\] If sin({SOLAZ}) < sin({SOLDE})/sin(\(\phi):\)
\[\begin{equation} \mathrm{\{SOLAZ\}} = \pi/2-\mathrm{\{SOLAZ\}} \tag{8.12} \end{equation}\]

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47. Albrecht, B. and Cox, S.K.: 1977, Procedure for Improving Pyrgeometer Performance, J. Appl. Meteorol., 16, 188–197.↩︎

48. Some archived projects used this variable name for measurements from a narrow bandwidth, narrow field-of-view (2º) Barnes Engineering Model PRT-5 precision radiation thermometer. This instrument is now retired. The spectral bandwidth available was either 8 to 14 μm or 9.5 to 11.5 μm. Its cavity temperature was monitored and recorded as either TCAVB or TCAVT.↩︎

49. Bucholtz , Anthony, Robert T. Bluth , Ben Kelly, Scott Taylor, Keir Batson, Anthony W. Sarto , Tim P. Tooman , Robert F. McCoy, 2008: The Stabilized Radiometer Platform (STRAP) — An Actively Stabilized Horizontally Level Platform for Improved Aircraft Irradiance Measurements. J. Atmos. Oceanic Technol. , 25, 2161 – 2175.↩︎

50. Prior to 2009, IRx and IRxC were used to denote measurements from Eppley pyrgeometers. Processing methods for these obsolete variables are described in Section 10.↩︎

51. The descriptions of SOLZE, SOLEL, and SOLAZ in Bulletin 9 were incorrect, but the code in use has been consistent and correct and continues to be used unchanged. For reference, that code is contained in the nimbus subroutine ’solang.c’.↩︎