a. Basic concepts

The other absorbers here include stratospheric and tropospheric nitrogen dioxide (NO₂), uniformly mixed gases, and water vapor. These absorbers can be considered to be secondary to the aerosols, ozone, and Rayleigh terms. The NO₂ absorption is most pronounced in the ultraviolet end of the spectrum (Davidson et al. 1988), and water vapor is strongest at the infrared end and beyond. Therefore, because this paper is focused on the technique of measurement and not on the details of the absorption chemistry, we will combine all other extinction terms with the aerosol scattering term (k_A).

In the atmosphere k_λ 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 = secθdz and

View Expanded

where I_λ(h) is the irradiance at the observer at height h above sea level, and I_λT is the irradiance at the TOA. 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 k_λ is constant through the air column, as in Rayleigh scattering, it can be moved outside the integral. In the cases when it is nonuniform in the column, as for aerosol and ozone, an effective extinction coefficient can be defined. The resulting effective total extinction coefficient is given by k̃_λ = k̃_A + k_R + k̃_O and is defined by

View Expanded

The terms with tildes are effective mean values that produce the same extinction 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 AOT is defined as

View Expanded

The resulting formulation for the irradiance becomes

I_λhI_λTe^{−(τ_A+τ_R+τ_O)m(θ)}(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 a definition of the optical thicknesses that must be derived by observation of the extinction of the solar beam through the atmosphere.

The air mass, also called atmospheric mass, m(θ), is a function of the path of the ray through the atmosphere. When refraction and the earth’s curvature are ignored, the simple equation m = secθ_T, where θ_T is the solar zenith angle at the top of the atmosphere, can be used. This approximation is accurate to within 1% when θ_T ⩽ 70°. Kasten and Young (1989) include both curvature and refraction in a formulation of air mass and use the ISO standard atmosphere for density and index of refraction. They use an index of refraction profile at 700 nm for all wavelengths and then fit the computations to an empirical curve,

View Expanded

where θ_r is the solar zenith angle relative to the observer in radians, a = 0.505 72, b = 96.079 95, and c = 1.364. A pointing sun photometer locates the solar beam and thus automatically measures θ_r, but a shadowband instrument must compute it. The ephemeris algorithm by Michalsky (1988; Spencer 1989) is used to determine θ_r and θ_T given the time and geographic position of the observer and including refraction and curvature.

In (7), the last two normal optical thickness terms can be determined by a combination of measurements and theory. Rayleigh scattering is well understood, and τ_R can be computed by theoretical formulation. Tables of Rayleigh scattering coefficient, using the relationships from Penndorf (1957), were computed for each channel wavelength and for the atmospheric pressure at the time of the measurement with an empirical equation:

View Expanded

where (a₁, a₂, a₃, a₄) = (117.2594, −1.3215, 0.000 320 73, −0.000 076 842), p is the atmospheric pressure (in hPa) at the time of the measurement, p₀ = 1013.25 hPa, and λ is the wavelength (in μm).

The ozone optical thickness can be computed from measurements of the ozone distribution or inferred from known ozone climatology. The ozone corrections used in this paper are quite small and were provided by the National Aeronautics and Space Administration (NASA) (M. Wang 1999, personal communication).

b. Calibration considerations

Photometric instruments measure light through a bandpass filter and so all wavelength dependency must be integrated over the filter bandpass. Each detector has a different response function, w_i(λ), where i is the detector (channel) number. Each detector-filter response is calibrated relative to its maximum value at its center wavelength, λ_i, and w_i(λ_i) ≡ 1. Its values at other wavelengths are referenced to its response at λ_i. The measured irradiance is related to the actual incident irradiance by the integral

View Expanded

and all references to irradiance, as measured by an instrument, imply the above weighted mean based on a known bandpass filter response. The bandwidth of the filter is defined as the width of a top-hat unity-response function with the same area as the actual response

View Expanded

In all discussions after this point, the λ subscript will be dropped unless it is necessary for clarity. All development refers to monochromatic light, and wavelength dependency is implicit. The instrument bandpass and its effect on a spectrum of light are also hereafter implied. The discussion below is applied to all channels in the same fashion, and so unless it is necessary for clarity, the i subscript will be omitted.

Langley plots are constructed as often as possible as a quality assurance tool because they provide an excellent means of detecting calibration changes. The measured TOA irradiance, I_T, depends on the sun–earth separation, but its corrected value, I₀ = I_Tr², should not change significantly over time. The absolute calibration of the instrument can be compared to the mean reference solar irradiance at the top of the atmosphere, I_REF, (Colina et al. 1996) by integrating the reference solar spectrum over the bandpass of the sensor [see Eq (11)] to obtain

View Expanded

In a well-calibrated absolute instrument, I₀ ≈ I_0REF. However, as long as the calibration constant I₀ is constant, as determined from multiple Langley plots, accurate AOT estimates are possible. While many investigators use raw voltages to calibrate their instruments, the extra step of computing I₀ is important, since it defines the radiative impact of the aerosol at the surface.

Once I₀ is established for an instrument, (13) is used to estimate aerosol optical thickness for each instantaneous measurement of I_N. From the time and geographic location of the measurement, I_T can be computed from the calibration constant, I_T = I₀/r², and m can be computed accurately from (9) or estimated by secθ_T. After the contributions by Rayleigh scattering and ozone absorption are accounted for, τ_A remains.

c. Theory of shadowband radiometers

An estimate of τ can be made for every measurement of the solar beam irradiance I_N when there are no clouds in front of the solar disk. Two sun photometer designs are commonly used: a narrowbeam detector mechanically pointed in the direction of the sun or a wide-field-of-view radiometer with a solar occulting apparatus. The first type of sun photometer (see Holben et al. 1998) requires careful angular positioning but can provide additional information on forward scattering phase functions and thus help characterize the aerosol constituents. The latter type of radiometer, a shadowband radiometer, measures the diffuse and global (upper hemispheric) irradiance and computes I_N as the difference between the two. The device gets its name from the hemispherical metal strip that rotates around the detector and blocks the direct solar beam to yield a signal that is from the sky only (after the effect of the arm is included).

One of the first rotating shadowband devices was a broadband device introduced by Wesely (1982). A more advanced broadband instrument using a thermopile-type broadband pyranometer has been developed by Long et al. (1996). The multifrequency rotating shadowband radiometer (MFRSR), developed by Harrison et al. (1994), uses independent interference-filter-photodiode detectors and an automated rotating shadowband technique to make spatially resolved measurements at seven wavelength passbands. The MFRSR achieves an accuracy in direct-normal spectral irradiance comparable with that of narrowbeam tracking devices. A significant advantage of the shadowband technique is that the global and diffuse irradiance measurements can be used to study overall radiative budgets (Long 1996). Our FRSR makes use of the MFRSR detector head.

a. Hardware description

The complete radiation package, shown in Fig. 1, is an integration of five primary components (Fig. 3): 1) a broadband pyranometer, model PSP from The Eppley Laboratory, Inc.; 2) the FRSR, which is the subject of this paper; 3) an attitude sensor that measures platform pitch, roll, and azimuth; 4) a small, low-power data-control unit that performs the sweep-by-sweep processing algorithms; and 5) an uninterruptable power supply and backup battery module that eliminates power surges, minimizes power supply noise, and supports wind or solar power operation for remote operation. This paper concentrates on the operation of the FRSR and the specialized data processing that is required to derive accurate spectral decomposition of solar insolation.

The FRSR shadowband rotates continuously and moves across the upper hemisphere in 3.4 s. The hemispherical shape of the shadowband ensures that the sensor will see a shadow, regardless of its azimuth heading and at all but minimal solar elevations. Typically, the shadow moves across the face of the sun in a few tenths of a second, and the head is in full shadow for about one-tenth of a second.

The multispectral FRSR head is manufactured by Yankee Environmental Systems, Inc. It is a modified version of the comercially available MFRSR spectral radiometer head and has seven detectors (channels): a broadband channel and six 10-nm-wide bandpass-filtered channels at 415, 500, 660, 860, 870, and 940 nm. The head construction, adeptly described by Harrison et al. (1994), is environmentally sound, robust, and suitable for use in a marine environment. Figure 2 shows the Colina et al. (1996) reference solar spectrum at the top of the atmosphere and a typical spectrum for the earth’s surface. Superimposed on the graph are the FRSR pass bands, the silicone cell photodiode (called broadband here), and the six narrowband spectral channels. Passbands on the SeaWiFS satellite are shown for comparison.

The FRSR head is modified to decrease its electrical response time to about 1 ms. The response of the silicone cell detector is well below 1 ms, but the internal preamplifiers in the stock head have integrating low-noise amplifiers, that slow the overall response. The head response times are decreased by reducing their low-pass filter capacitors. This is accomplished easily, and laboratory tests do not show additional noise in the measurements.

b. Laboratory calibrations

Calibration is the most essential element of a radiation measurement program. Climate studies require insolation averages to a few watts per meters squared in absolute accuracy, and photometric studies require zero drift in the end-to-end calibration constants for reliable estimates of optical thickness. A thorough and on-going calibration process is required before the FRSR can make accurate photometric measurements at sea.

Laboratory calibration is done in two parts: the electronics and the optical head. The end-to-end electronic gains are carefully calibrated using the data collection software and a precision millivolt reference source in place of each radiometer channel. One-minute averages and standard deviations of voltages for each channel are logged for a full range of input voltages. The output voltage range is approximately 0–3000 mV and standard deviations are typically <1 mV over the entire range. Electronic calibrations are repeated at regular intervals and for a variety of ambient temperatures. Calibration of the electronics is performed before and after each deployment, and the gain equations are constant.

The FRSR radiometer head comes fully calibrated by the manufacturer in the form of three tables. First is a linear, direct-normal irradiance gain equation with units of mV (W m⁻²)⁻¹ for the broadband channel and mV (W m⁻² nm⁻¹)⁻¹ for the narrowband channels. These calibration equations are corrected for the individual bandpass spectral responses for the head. The second calibration product is the bandpass spectral response for each narrowband channel. This is the w_i(λ) function in Eq. (11). Each of the narrowband filters has a bandwidth of approximately 10 nm, and the calibration provides gain figures at 1-nm spacing. Finally, zenith angle correction is measured on two planes, one on a south-to-north plane and one on a west-to-east plane. The zenith angle corrections are determined by holding the head in a tilting fixture under a collimated beam and tilting the head through 180° in 1° steps from horizon to horizon in each plane. Calibration tilt angles are θ_SNj and θ_WEj for j = 1, 2, . . . , 181. As an example, θ_SN1 = 90° in the south direction, θ_WE136 = 45° in the east direction, and so forth. A plot of the calibration zenith error corrections for the S–N and W–E planes are shown as a function of atmospheric mass in Fig. 4.

The electronic gains are combined with the direct-normal head irradiance gains coefficients to make a single calibration equation relating direct-normal irradiance to the electronic measurement in millivolts:

I_hc₁υc₂(18)

where I_h is the irradiance, which is computed from the measured voltage υ, and (c₁, c₂) are the calibration constants. In the case of a parallel beam of radiation, the measured irradiance flux into a plane that is parallel to the head surface is given by

View Expanded

where χ is the cosine correction calibration; α_h and θ_h are the beam azimuth and elevation angle, respectively, relative to the plane of the head; I_λ is the beam irradiance spectrum in a plane normal to the beam vector; and w_λ is the filter bandpass discussed above.

By combining (18) with (7), the measured voltage for a solar beam becomes

View Expanded

and as long as the response is linear and the bias term is negligible (i.e., |c₂/c₁| ≪ 1), one can use the voltage output to measure τ. A silicone cell photodiode has a small leakage current called a “dark current.” After amplification in the electronics, a dark voltage results, and if the dark voltage, −(c₂/c₁), is not negligible, it must be measured and removed. Electronic bias is a consideration in interpreting Langley calibrations. In some instruments, such as the MicroTops handheld sun photometer (Solar Light Company 1996), the operator covers the detector before taking a solar measurement. For an autonomous instrument, it is better to choose an electronic design that eliminates the dark voltage. For the FRSR, the largest deviation from a straight line fit is 0.2 W m⁻² for the broadband channel and 0.002 W m⁻² nm⁻¹ for the narrowband channels, which is less than 0.1% of full scale.

Calibration drift in the multifrequency head has caused a great deal of consternation to the sun photometer community. Calibration shift is detectable as a permanent change in I₀ (or its voltage analog υ₀) as computed by the Langley method. Calibration shift is erratic and quite variable; it can occur suddenly, over a few weeks, or can degrade slowly over months. The 610- and 660-nm channels are most prone to drift, though all narrowband channels are suspect. Researchers suspect that the gain drift is due to a shifting bandpass response. In earlier heads, the filter material, a stack of laminated films, apparently became delaminated as a result of temperature cycling and humidity. A different filter material became available after approximately December 1998 (Barr Associates; see their Web site: barrassociates.com/terms/temperature.html), and many researchers are in the process of retrofitting their heads with the new material. The filter material is also sensitive to temperature, and the shift in center frequency for any narrowband filter is approximately 10⁻⁵λ₀ΔT. Thus, if the head temperature varies from 20° to 30°C, the 500-nm filter will drift by less than 1 nm (M. Beaubean, Yankee Environmental Systems, 1999, personal communication).

The MFRSR head is well insulated (thermal time constant ≈ 15 min) and has a 25-W heater circuit. A temperature regulation circuit easily maintained the head internal temperature at 35°C. An added benefit from heating is that condensation inside the head and on the diffuser is eliminated by the elevated temperature. The electronic amplifier circuits were carefully designed and tested from −20° to 65°C, and no significant temperature dependence was observed.

c. Installation and operation

The control data unit, shown in Fig. 3, is custom-made and packaged in a waterproof housing that resides in close proximity to the sensors. The complete datalogger package incorporates radio interference and surge protection, operates over a −40° to 65°C temperature range, and is waterproof and immune to shock and vibration. The low-level analog signals from the FRSR head are digitized with a high-speed 12-bit analog-to-digital converter circuit.

The installation location of the instrument on a ship must be carefully selected. Ideally, the FRSR should be mounted in an exposed location as high as possible and free of nuisance shadows from other objects. This is often difficult. Radiative flux measurements on a ship always need to consider errors from the ubiquitous masts and antennas. A ship’s communication antennas have highest vertical priority, as do the running lights, and one must be careful of radar beams, which can cause severe electronic noise.

Several external observations are necessary for data analysis. Accurate time, latitude, and longitude are needed to compute solar zenith and azimuth angles. To correct the sensor’s cosine response, one also needs the ship’s pitch, roll, and heading so the exact angle between the normal of the head and the solar beam can be derived. A pitch-roll-compass sensor is read twice during each cycle of the shadowband. A GPS receiver provides time, position, and magnetic variation each second.

The control data unit performs several functions during each shadowband cycle (Fig. 5). Broadband and housekeeping measurements are taken when the arm is at each horizon. During the sweep, when the shadowband crosses the upper hemisphere, 250 measurements are made for each channel. The first and last 10 samples of each sweep are averaged, and we refer to these measurements as the global measurements, υ_G1 and υ_G2. Global measurements are computed for each filter channel. To minimize electrical interference, the heater is operated only while the shadowband is below the horizon, and in cruises thus far, a constant head temperature of 35° ± 0.5°C is easily maintained.

At the end of each sweep of the shadowband, the channel-1 voltage measurements are examined, and a decision is made whether a viable shadow was present. The shadow ratio is a sensitive measure of the intensity of the direct solar beam and is computed by the equation

View Expanded

where υ_av is the mean signal voltage for the entire sweep, υ_min is the minimum signal voltage, and σ_υ is the standard deviation for the sweep. (Measurements at the time of the minimum signal ±0.3 s are excluded from the computation of mean and standard deviation.) After extensive field testing, an empirical criterion of κ ≥ 2.3 has been found to capture almost all true shadow cases and seldom permits a false positive. A statistical argument for this value is as follows. In a completely overcast situation, the 250 sweep measurements could be considered to be independent samples with a Gaussian probability distribution, and there is approximately a 13% chance that any of the 250 samples would have a minimum that exceeded the 2.3 criterion. On sunny days, the shadow ratio can exceed a value of 200.

Any sweep with κ ≥ 2.3 is block averaged and stored in a compressed binary packet. Block averaging of the sweep retains all of its significant shape characteristics but significantly reduces data storage requirements. Block averaging begins at the minimum index value, i_min, and moves left and right through the sweep array with increasing block sizes. Twenty-three contiguous block averages, b_ij, where i is the channel number 1–7 and j is the bin number, are computed according to Table 1. The shadow index, i_min, depends on the solar azimuth and zenith angles, the ship heading, and the pitch and roll, and thus can occur anywhere in the 250-point sweep array. In the block averaging process, some bins fall outside the sweep and are given a “missing” value.

The sweep data must be transmitted over long cables in noisy electronic environments, and therefore, standard packet conventions are used to ensure error-free communication. The compressed binary packet, with global and sweep data for all detectors, is transmitted as an EIA422, 19 200 bps, serial stream to the base computer. An EIA422 balanced-line transmission is highly immune to electronic noise and radio interference and can be transmitted over long transmission lines. The binary packet has start and end character strings and a cyclic redundancy checksum (CRC) for error-free transmission. Once the packets are transmitted, the shadowband cycle begins again.

a. Sweep averaging

On a moving platform, some smoothing of the data is necessary. It was found that simple averages over a 2-min period (16 sweeps) would reduce the sampling uncertainty by a factor of approximately 4 and yield worst-case measurement uncertainties of about 5 W m⁻² for the global values and less than 1 W m⁻² for the shadow value. For perspective, 2 min is the approximate time for the sun to move by one diameter across the celestial sphere.

An example of the effectiveness of the 2-min averaging process is shown in Fig. 6, taken during the Aerosols99 cruise (discussed below). For this example the sun was high in the sky, and ship pitch and roll had a standard deviation of about 2°. (This amount of motion is typical for an 88-m ship in fair-weather ocean conditions.) When the detector was in full shadow, the standard deviations were extremely low and amounted to less than ±1 W m⁻². During the time the detector was partially covered, the standard deviations were quite high due to the rapid transition and platform motion. When the detector was out of the shadow, standard deviations were small but were larger than the full-shadow case. Strict requirements are placed on the acceptability of any 2-min block. At least 14 sweeps must pass the shadow ratio criterion. Otherwise, that particular 2-min period is excluded from further analysis.

The diffuse component of total irradiance is insensitive to platform motion. Clouds alter the integrated diffuse irradiance on a timescale that is slow compared with the averaging times considered, as long as they do not block the direct beam. The minimal standard deviations in the shadow measurement in Fig. 6 are evidence to this fact.

The effectiveness of a 2-min averaging scheme was demonstrated by tests with an automated tilting table. During a cloud-free day, the tilting table was set to ±5° in pitch and roll and to a rocking period of 6.7 s, and it was turned on and off in half-hourly intervals. Figure 7 compares the individual sweep measurements to the averages. The black curve shows mean global voltages from individual sweeps, and the white line is the result from the 2-min averaging process.

b. Decomposing the solar signal

The shadowband theory [outlined in Eqs. (15) and (16)] must be modified for a moving platform when the head might not be on a horizontal plane. Three measurement quantities for each channel are computed from the 2-min mean voltages: the global signal υ^′_G, the shadow signal υ^′_S, and the edge value υ^′_E. The primes indicate that the measurement is referenced to the plane of the head, which can be different than a horizontal plane. The two global measurements υ_G1 and υ_G2 are combined to produce the best estimate global voltage, υ^′_G. The mean shadow voltage is υ^′_S. The edge value is selected from the 2-min composite sweep using an objective algorithm that accounts for the fact that the width of the shadow depends on solar zenith and relative azimuth. The objective selection of the edge voltage uses one or a mean of both edge measurements to get the best estimate of υ^′_E.

The direct-beam irradiance on a horizontal plane relative to the instrument, υ^′_H, is converted to a direct-beam irradiance into a plane normal to the solar beam using the relationship

View Expanded

The global and horizontal voltages are recomputed for the earth frame of reference:

υ_Hυ_Nθ_rυ_Gυ_Hυ_D(26)

The calibration equation, (18), is used to compute I_G, I_D, I_H, and I_N from υ_G, υ_D, υ_H, and υ_N, respectively. From these terms, Eq. (13) can be used either for estimating the calibration constant I₀ or for estimating τ_A.