Remote Measurements & Research Company 214 Euclid Av. Seattle WA 98122 [email protected] cel/text 631-374-2537 MLO19 frsr langley calibration.tex ARM MOSAIC MENTOR REPORT | v1 MLO19|FRSR and ShipRad Calibration at Moana Loa Observatory (MLO) Instrument FRSR and ShipRad Serial Number FRSR 3 and SR1{3 ID 1906 Techs M. Reynolds, L. Riihimaki Calibration Start Time 2019-05-30 Calibration End Time 2019-06-05 Location LANL Beta Test Results Attached sheets. After calibration The FRSR was returned to Seattle for final preparation. Some operational data is presented (page9). It will be returned to LANL. DISCUSSION: (left) The three ShipRad radiometer systems on the roof of the Moana Loa Observatory (MLO). (right) The ARM FRSR mounted nearby. This document reports on the FRSR calibration by the method of Langley plots. We were operating for five days and clouds were a problem. Nevertheless, There were sufficient clear morning skies that we were able to derive V0 calibrations with a repeatability of 1%. 2 1 Methods The mathematics behind the FRSR is well described in the original 2000 paper, http://rmrco.com/docs/pub00 reynolds jtec frsr.pdf and the Langley method of calibration is described in Wikipedia: https://en.wikipedia.org/wiki/Langley extrapolation where one derives a top of the atmosphere value of V0 which can be used in AOD calculations. In a nutshell, for each channel a top-of-the-atmosphere voltage, ln(V0) and the atmospheric extinction, τ, is calculated by ln(V ) ln(V ) τ = 0 − n m where ln(V0) is determined by the Langley analysis, ln(Vn) is the direct-normalvoltage determined from analysis of the FRSR sweep, and m is the atmospheric mass for the solar zenith angle at the sweep time. Vn is the direct-normal voltage computed from the \edge" amd \shadow" voltages. and corrected for zenith angle and for the MFR head zenith angle correction, kze, the \whisker curve." The figure below shows the corrections for June 1. The correction equation is Vn = Vn0 =kze and is based on the solar zenith and azimuth and the MFR pitch, roll and heading. 3 2 Observations Observations took place on five mornings, June 1 ::: 5, 2019. The figure are plots of the FRSR voltage for total (direct plus diffuse) irradiance versus time of day. Note: the time zone here was -10 hr so 20 z corresponds to 10 am. These plots clearly show times of cloud. The optimum times for a Langley plot are evident in these plots. Global measurements for the five observation days. 6/4 was cloudy all morning. 4 3 Results 3.1 June 01 2019 5 3.2 June 02 2019 6 3.3 June 03 2019 7 3.4 June 05 2019 8 4 Results from the Langley Analysis MLO19 Langley Results Day 2 3 4 5 6 6/1 6.876 6.626 6.626 6.505 6.679 6/2 6.864 6.617 6.618 6.497 6.672 6/3 6.887 6.624 6.621 6.501 6.680 6/5 6.957 6.667 6.659 6.539 6.718 MN 6.896 6.633 6.631 6.510 6.687 Std .0417 .0227 .0190 .0193 .0208 Mn1 6.876 6.622 6.622 6.501 6.677 St1 .0115 .0047 .0040 .0040 .0044 .16% .07% .06% .06% .06% The best estimates of V0 for days 1,2,3 and for channels 2,3,4,5,6 are 6.876 6.622 6.622 6.501 6.677 9 5 Sea-level operation We were testing the system and noticed that the sky was perfectly clear. Such splendid skies are quite rare in Seattle so we set out the frsr and began collecting data. Shadow values were around 480. The left panel shows the computed direct normal irradiance in millivolts. We focus on the short time in the first 40 minutes of the record. The right panel shows ten sweeps in the clear sky period. Edge and shadow values are repeatable. After applying the MLO calibrations and subtracting the Rayleigh and Ozone optical depth, the resulting aerosol optical depth (AOD) for channels 2,3,4,5,6 are plotted in the above figure. 10 A Appendix: FRSR Theory Remote Measurements & Research Company 214 Euclid Av. Seattle WA 98122 [email protected] November 27, 2017 frsr data description.pdf FRSR Theory and Calibration This document is a review of the data stream from the Fast-Rotating Shadowband Radiometer (FRSR) during normal operation. A basic description of the FRSR system and a description of the installation are provided in [1] and [2] below. A knowledge of these will help the reader in reading this description of the data. Background documents [1] Basic description [2] Installation & Operation Estimating the Solar Direct Beam Figure 1: By measuring the direct solar beam, the aerosol optical depth can be computed. Left. The radiance at the top of the atmosphere is absorbed as it travels to the surface. Middle. The total solar irradiance at the surface is comprised of the direct beam and the diffuse radiance from cloud and molecular interaction. Right The shadowband technique, explained below, is used to separate the direct beam from total irradiance. Basic Concepts A sun photometer measures the directional solar irradiance in discrete wavelength channels along a vector from the instrument detector to the solar disk. The atmosphere both absorbs and scatters light along this vector, and these effects are treated together through the mass extinction cross section, kλ (Liou 1980). Because the different scattering and absorbing processes may be assumed to be independent of each other, the total extinction coefficient is a simple sum from all the contributors: kλ = kA + kR + kO + kN , (1) where the terms on the right represent the mass extinction cross sections, as a function of wavelength, for aerosol scattering, Rayleigh scattering, ozone ( O3) absorption, and nitrogen dioxide (NO2) absorption. A parallel beam of radiation, denoted by its irradiance, Iλ, will be reduced in the direction of its propagation by an amount given by dI = k ρ I ds, (2) λ − λ λ where kλ is defined by (1), ρ is the air density, and ds is the differential path length. If kλ is constant, the classical Beer-Bouguer-Lambert law results: kλu Iλ(s2) = Iλ(s1)e− , (3) where u = ρ ds is called the optical thickness or optical path and integration proceeds along the path the ray takes from s to s . R 1 2 2 In the atmosphere kλ and ρ are not homogeneous and so the full integration of (2) is required. A reasonable approximation is that the atmosphere is horizontally stratified, and this allows integration of (2) along the vertical axis, z, in a coordinate system on the Earth’s surface. Then ds = sec θ dz, and ∞ I (h) = I exp k ρ sec θ dz , (4) λ λT − λ Zh where Iλ(h) is the irradiance at the observer at height h above sea level, and IλT is the irradiance at the top of the atmosphere. Integration follows the ray in its refracted path through the atmosphere and, for completeness, must include the curvature of the Earth. In the case that kλ is constant through the air column, as in Rayleigh scattering, it can be moved outside the integral. In the cases when it is non-uniform in the column, as for aerosol, O3, and NO2, an effective extinction coefficient can be defined. The resulting effective total extinction coefficient is given by k˜λ = k˜A + kR + k˜O + k˜N and is defined by ∞ ∞ ρ sec θ dz k ρ sec θ dz = k˜ ρ sec θ dz = τ . (5) λ λ λ ρ dz Zh Zh R The terms with tildes are effective mean values that produce the same extinctionR if uniformly distributed through the atmosphere. The bracketed fraction is defined as the air mass, m(θ) and is a function of the zenith angle, θ. When the solar beam is normal to the geoid, m = 1, the normal atmospheric optical thickness (AOT) is defined as ∞ ∞ τλ = kλ ρ dz = k˜λ ρ dz . (6) Zh Zh The resulting formulation for the irradiance becomes (τA+τR+τO +τN ) m(θ) Iλ(h) = IλT e− , (7) which is a working analog to the classical Beer-Bouguer-Lambert equation, (3). Without knowing the vertical and horizontal distribution of the different contributing attenuators, (7) serves as definition of the optical thicknesses which must be derived by observation of the extinction of the solar beam through the atmosphere. The instantaneous solar irradiance at the top of the atmosphere, IT , is the solar constant modulated by the 2 Earth-Sun distance, IλT = Iλ0/r , where Iλ0 is the mean solar irradiance at the top of the atmosphere and r is the ratio of the Earth-sun distance to its mean value (Paltridge and Platt 1977): r = 1 cos (a [J 4]) , (8) − − where = 0.01673 is the eccentricity of orbit, and J is the day of the year (sometimes referred to as the Julian 2 day). The r correction results in an annual modulation of Iλ0 of approximately 6%. This is comparable to an uncertainty of about 5% in the measured solar spectrum (see Colina et al. 1996) (Fig. ??). The air mass, m(θ), is a function of the path of the ray through the atmosphere. When refraction and the Earth curvature are ignored, the simple equation m = sec θT , where θT is the solar zenith angle at the top of the atmosphere, can be used. This approximation is accurate to within 1% when θT 70◦.