Automated multifilter rotating shadow-bandradiometer: an instrument for optical depth andradiation measurements

Lee Harrison, Joseph Michalsky, and Jerry Berndt

The multifilter rotating shadow-band radiometer is a ground-based instrument that uses independentinterference-filter-photodiode detectors and the automated rotating shadow-band technique to makespectrally resolved measurements at seven wavelength passbands (chosen at the time of manufacturebetween 350 nm and 1.7 pim) of direct-normal, total-horizontal, and diffuse-horizontal irradiances. Thisinstrument achieves an accuracy in direct-normal spectral irradiance comparable with that of trackingradiometers, and it is more accurate than conventional instruments for the determination of the diffuseand total-horizontal spectral irradiances because the angular acceptance function of the instrumentclosely approximates the ideal cosine response, and because the measured direct-normal component canbe corrected for the remaining angular acceptance error. The three irradiance components are measuredwith the same detector for a given wavelength. Together with the automated shadow-band technique,this guarantees that the calibration coefficients are identical for each, thus reducing errors when onecompares them (as opposed to measurements made with independent instruments). One can use thedirect-normal component observations for Langley analysis to obtain depths and to provide an ongoingcalibration against the solar constant by extrapolation to zero air mass. Thus the long-term stability ofall three measured components can be tied to the solar constant by an analysis of the routinely collecteddata.

Key words: Atmospheric radiometry, turbidity, optical depth, Langley regression.

Automated Rotating Shadow-Band RadiometryThe basic geometry of a computer-controlled rotatingshadow-band radiometer can be seen in Fig. 1. Theshadowing band is a strip of metal formed into acircular arc that lies along a celestial meridian (theface of the Lambertian detector is the center for thisarc). It can be accurately rotated in 0.40 steps aroundthe polar axis by a direct-coupled stepping motor thatis in turn controlled by a microprocessor. This bandblocks a strip of sky with an umbral angle (Zp)l of3.270, which is more than sufficient to block the solardisk. The tracking accuracy must be substantiallybetter than Zp because of the presence of the solaraureole within the field of view. For this instrumentthe limiting accuracy is ±0.3° because of stepping

J. Berndt is with the Pacific Northwest Laboratory, P.O. Box999, Richland, Washington 99352; the other authors are with theAtmospheric Sciences Research Center, State University of NewYork at Albany, 100 Fuller Road, Albany, New York 12205.

Received 25 January 1993; revised manuscript received 4 Febru-ary 1994.

0003-6935/94/225118-08$06.00/0.o 1994 Optical Society of America.

precision and error. (Contributions from an allow-ance for approximately 10 of misalignment of thepolar axis and the computational accuracy of theephemeris are negligible in comparison.) The mecha-nism permits a simple mechanical adjustment for thelatitude. This adjustment, together with the azi-muth alignment to the Earth's pole (of either thenorthern or southern hemisphere, depending on thesite latitude), is done when the instrument is installedat a site; no further mechanical adjustment is neces-sary.

The operation of the instrument is controlled by itsself-contained microprocessor. At each measure-ment interval it computes the solar position by usingan approximation for the solar ephemeris. The mea-surement sequence starts with a measurement madewhile the band is at nadir; this is the total-horizontalirradiance. The band is then rotated so that threemeasurements are made in sequence; the middle oneblocks the Sun and the other two block strips of sky 90to either side. These side measurements permit afirst-order correction for the excess sky blocked by theband when the Sun-blocking measurement is made.One subtracts the average of these two side measure-

5118 APPLIED OPTICS / Vol. 33, No. 22 / 1 August 1994

Detector

SteppingMotor

i -

/1 Polar Axis

SignalConnector

Fig. 1. Basic geometry of an automated rotating shadow band(shown in the position where the measurement of the total-horizontal irradiance is made).

ments from the total-horizontal measurement andthen adds this correction to the Sun-blocked measure-ment to determine the diffuse-horizontal irradiance.The 90 offset must be larger than one half of angle Z1(see Table 1) plus one half of the solar disk, or 6.750.(Modeling demonstrated that 90 yields a better first-order correction for sky radiances expected withtypical optical depths and scattering phase functions,given the Zp angle of 3.27°.) Finally, one can sub-tract the diffuse component of the irradiance from thetotal-horizontal component to produce the direct-horizontal component. Division by cosine of thesolar position angle from the zenith (available fromthe ephemeris calculation) then produces the direct-beam flux on a normal surface. The entire measure-ment sequence is completed in less than 10 s and isnormally programmed to occur four times per minute.

The microprocessor also acts as a data logger,accumulating the data from the shadow-band mea-surements as well as from ancillary measurementsfrom other instruments if desired. All analog sig-nals have conditioning amplifiers as needed, and theyare multiplexed to an analog-to-digital converter with12-bit-plus sign resolution (1 part in 8192) and 1-bitreproducibility over the range from -4.096 to 4.095V. The instrument can average over selected inter-vals; note that in this case the summation of thedirect-normal component is done subsequent to thedivision by the cosine of the solar zenith angle (whichis done individually for each measurement). This isnecessary to produce correct results at high solarzenith angles in which the cosine varies rapidly.The instrument stores and telemeters data and has abattery backup so that operation continues throughpower outages.

The basic rotating blocking-band method was devel-oped by Wesely.2 Instruments have since been devel-

Table 1. Field-of-View Full Anglesa

Instrument Zp (deg) ZO (deg) Z 1 (deg)

MFRSR 3.274 8.172 13.04Tracking radiometer 3.53 5.73 7.92

'Angles Zp, Z0, and Z 1 are defined in Ref. 1.

oped 3 4 to automate the Wesely method. The multi-filter rotating shadow-band radiometer (MFRSR)differs from these in that it uses a computed ephem-eris to position the band for the blocking measure-ments and does not depend on the detection of aminimum irradiance. This method permits muchlonger integration times for each measurement be-cause it requires measurements at only four positionsrather than a continuous scan across the sky. Thissubstantially improves measurement precision andpermits what would otherwise be impossible wave-lengths or passbands. The excess sky blockage cor-rection also significantly improves the measurementaccuracy, particularly under skies with fractionalcloud coverage. A disadvantage is that the instru-ment must be properly aligned. (The instrumentdeveloped by Guzzi et al.3 was intended for shipborneapplication, where no such alignment was possible.)

Blocking-band techniques have several advantagesover the traditional alternative of using two detec-tors, one fixed to measure the total-horizontal irradi-ance, and one mounted on a tracking mechanism tomeasure the direct-normal component (thus requir-ing a narrow field of view). They are simpler, lessexpensive, and more robust. Further, the threeirradiance components are derived from a singleoptical detector, greatly reducing our intercalibrationworries over both absolute sensitivity and spectralpassband and guaranteeing that the measurementsare synchronous. These features improve the utilityof calibration by means of Langley extrapolation(discussed below), because the measurements of thediffuse- and total-horizontal irradiances are cali-brated as well.

Seven-Passband Lambertian DetectorRadiometers intended to measure the flux incident ona surface must measure the input from a 27r sr field ofview, weighted by the cosine of the incidence anglefrom the surface norm. This ideal response is de-scribed as Lambertian. The empirical developmentof Lambertian diffusers optimized for various wave-lengths is not new; by the time of the early research ofKerr et al.,5 it was recognized that simple glass domescovering flat-plate detectors did not perform well(particularly at solar zenith angles greater than 700),and that flat diffusing receivers with carefully shapedsidewall and blocking-ring geometries were superior.

The performance of the inlet optic with respect tothe correct integration over the sky radiance distribu-tion is critical for many uses of the data and has beena continuing problem in radiometry. Many com-monly used radiometers have angular response func-tions that deviate from the ideal by more than 20% atsome angles, and often these angular response func-tions do not reproduce well from unit to unit of asingle design. In addition to the need for goodoptical performance, however, there are practicalconstraints stemming from the requirement that theinlet optic be suitable for field use. The optic musthave a sealed entrance and must be designed both to

1 August 1994 / Vol. 33, No. 22 / APPLIED OPTICS 5119

be readily cleaned and to minimize the optical conse-quences of small (but inevitable) soiling. It alsomust be designed to avoid aging degradation.

Figure 2 shows the design of our multifilter detec-tor assembly. The exterior, except for the opticalinlet, is black-anodized aluminum. The optical inletis a protruding diffuser surrounded by a raised block-ing ring. (Not shown is a drain hole that preventsrainfall or melted ice from filling the annular wellbetween the optical inlet and the blocking ring.) Thediffuser is made of Spectralon, a proprietary opticalplastic manufactured by Labsphere. The thin-walled external button acts as a transmission dif-fuser, and the thick internal sidewalls form a partialintegrating cavity. Two diaphragms of SchottGlaswerke frosted WG-280 glass act as transmissiondiffusers so that the randomization of the photontrajectories is increased. We arrived at the geometryof the protruding diffuser, the sidewall blocking rings,and the integrating cavity by extensive empiricaloptimization (cut and try), using the automated testfacility described below.

Spectralon is a halocarbon with excellent resistanceto chemical and ultraviolet degradation. (The mate-rial must be baked in vacuo at 90° C for several hoursto drive off residual oils from manufacture. Afterthis the material shows excellent resistance to weath-ering and irradiation.6 ) Consequently, we believethat these detectors will have stable long-term perfor-mance in the field environment. In addition, diffus-ers are inherently less sensitive to surface soiling bytypical atmospheric aerosols than are transmissionwindows (e.g., instruments with domes such as ther-mopile pyranometers). The reason is that the depo-sition of a small increment in scattering on thesurface of the diffuser makes a negligible change in itsthroughput because the optical depth is already large.In contrast, transmission of a window is affectedlinearly. The single-scattering albedo of most natu-ral aerosols is in excess of 0.9 (except soot); theirdeposition does not substantially affect an opticallythick diffuser coupled to an integrating cavity.

The entire detector consists of the diffuser-integrator described above that illuminates an inter-nal hexagonal close-packed array of seven photodi-odes with interference filters. These diodes aremounted to the interior of a five-sided cubic printedcircuit board that provides a separate transimped-

t_ To SignalConnector

Spectralon

Schott WG 280

Bakelite(Thermal Insulator)

Fig. 2. Multifilter detector cross section (not to scale).

ance amplifier (zero-bias current-to-voltage amplifier)for each of the photodiodes. We use an alignmenttool to position them during soldering so that the faceof each is normal to, and centered on, a line from thecenter of the exit aperture of the diffuser. No rayentering the filter is more than 7.5° from normal.The circuit-board assembly mounts to an internalaluminum shroud that has a grooved and anodizedsurface that reduces stray trajectories to the detec-tors, which also serves as the support for the heatingstrip (not shown).

We operate the photodiodes in the photovoltaic(rather than photoconductive) mode to reduce noiseand increase sensitivity and stability. We imple-ment transimpedance amplifiers by using individualLinear Technologies LTC1050 commutating-auto-zero (i.e., chopper-stabilized) devices to reduce varia-tions in input offset and bias current. The amplifierfor each channel has a first-order feedback timeconstant that is set from 0.02 to 0.06 s. The motionalgorithm guarantees that the band has been station-ary for 1 s before any of the channels are sampled;this ensures that the signal has settled well beyondthe accuracy of the digitization.

The interior of the detector assembly is thermallyinsulated with a phenolic spacer around the diffuserand with a Kapton film with glass wool insulationaround the electronics. It has a thermostatic electri-cal heater (25-W maximum) that holds the tempera-ture of the internal detector assembly at a set pointfrom 35 0C to 45 0C (for hot sites). Temperaturestabilization is necessary to improve the accuracy inseveral ways. Both the passband and transmissionof interference filters are sensitive to temperature,although these effects are most pronounced withpassbands that are significantly narrower than thosewe employ. More importantly, the photodiodes ex-hibit changes in sensitivity with temperature, and thebias currents of the amplifiers are temperature sensi-tive as well. Finally, the elevated and stable tempera-ture improves the long-term stability of the interfer-ence filters by eliminating temperature-cycle-inducedmechanical fatigue of the dielectric lamina (that havediffering expansion coefficients) and by guaranteeinga low internal humidity. (Provision is made for anadditional desiccator for environments that are warmand humid.) An important operational side benefitof this temperature control is that the heat loss keepsthe detector ice free in all but the worst icing condi-tions.

Silicon photodiodes are optimum over the wave-length range 350-1000 nm. We currently use DFSeries integrated photodiode-interference-filter as-semblies manufactured by EG&G Optoelectronics.The typical detector photocurrent is wavelength de-pendent, but it nears 1 nA for a 10-nm passband atwavelengths below 380 nm. We require at least 1part in 103 sensitivity and precision, which in turnrequires picoampere current stability. Beyond 1050nm either germanium or indium gallium arsenidephotodiodes are required. As a result of a decreasing

5120 APPLIED OPTICS / Vol. 33, No. 22 / 1 August 1994

irradiance at longer wavelengths and poorer shuntresistance of the detectors, passbands greater than 20nm are needed at wavelengths beyond 1.3 Rm.

The MFRSR instruments built for the AtmosphericRadiation Measurement and Quantitative Links ex-periments have six filtered detectors with a nominal10-nm FWHM bandwidth at wavelengths of 415, 500,610, 665, 862, and 940 nm and an unfiltered siliconphotodiode. The filtered passband curves are shownin Fig. 3. We measure these simultaneously, testingthe complete detector assembly as a unit, and theydemonstrate the expected small shift and broadeningof the passbands compared with those of the samefilters tested at uniform normal incidence. We chooseall the filtered passbands except 940 nm (a water-vapor band) to permit a Langley analysis for thedirect determination of optical depth. We choose thewavelengths to span a useful range for flux calcula-tions and to permit the maximum amount of informa-tion about the aerosol extinction to be retrievedthrough inversions.7-9 An additional goal (that wehave yet to demonstrate) is the estimation of columnozone from Chappuis band absorption.

Lambertian PerformanceWe constructed an automated test facility to measurethe angular response functions of detectors.10 Thelight source is a 300-W, 1-in.- (2.54-cm-) apertureaxial xenon arc with an encapsulated parabolic rearreflector and a plane exit window (by ILC Corpora-tion). This produces an output beam with residualpolarization less than 1%. We project this through a5.08-m-long, black-walled tube with internal bafflesto eliminate off-axis light, to an enclosed black-walledworking cavity with a 70-cm working swing radiusaround the central beam point. The working opticalaperture is slightly greater than 5 cm in diameter,with a measured intensity uniformity of better than1%. The maximum beam divergence is 0.50, with84% of the radiance having a beam divergence of lessthan 0.25°. The calibration process is automated bya computer that controls the angular rotation of theapparatus under test and that also samples and storesthe detector output. Such automation is critical tothe development of good Lambertian detectors (par-ticularly if they must operate over a range of wave-lengths), because repeated measurements (and some

1.0

0.6-

I-0.4-

Ez

Wavelength, X

Fig. 3. Filtered passbands of the MFRSR.

cut-and-try iteration) are required for us to arrive atan acceptable design. We need repeated back-and-forth scans to average the inevitable lamp fluctua-tions of the xenon arc.

Measurements are made from -90° to 900 (withrespect to the normal axis of the detector) along twoorthogonal planes corresponding to the east-westand north-south azimuth orientation in the field.The measurement at two independent azimuth orien-tations make any azimuthal dependence of the detec-tor apparent, and it permits an accurate correction ofthe direct-beam component for the remaining devia-tions in the angular response function. This is ofparticular importance for the correct determinationof optical depths.

A major part of our development effort for themultifilter instrument was the development of thediffuser geometry. We need adequate light through-put, good approximation to an ideal cosine responseat all wavelengths, and low azimuthal variation. Inaddition, a practical requirement is reproducible co-sine behavior within the limits of achievable manufac-turing tolerances. We found these goals to be muchmore difficult for a design that must illuminatemultiple-interference filters at near-normal incidence(implying a substantial standoff distance from theexit aperture to the filter) than for a simple diffuserwith a large-area diode immediately behind (as istypical of single-passband designs). Initial guessesfor trial geometries were based on Monte Carloray-tracing simulations, but the lack of accurate dataconcerning the scattering phase functions and absorp-tion coefficients of our optical media prevented thesefrom being anything more than the starting point forexperimental iteration. Early designs had strongazimuthal dependence because of the diode position.(The first test of each design is done with identicalunfiltered detectors in all seven positions.) Most ofour effort was directed toward minimizing this effectwhile retaining adequate light throughput. Onceresults similar to those shown below were achieved inazimuthal dependence, then minor tailoring of thick-ness and height ratios optimized the Lambertianbehavior over the wavelength range.

The performance of our diffuser geometry for allseven passbands is shown in the graphs of Figs. 4aand 4b, which show error ratios for each of thepassbands for the two orthogonal scans. Figure 4(c),for comparison, shows three Eppley PSP instruments.At all wavelengths the cosine response of our diffuseris competitive with the best single-passband scientificinstruments. We have the design freedom to tradeoff errors to some extent. Our primary criterion is toproduce correct total irradiance for typical diffuseskies (as we discuss further below), because we cancorrect the direct-beam component. Additional con-siderations are maintaining smooth correction func-tions through the zenith angles used for Langleyextrapolation to decrease the sensitivity of thesecalculations to the corrections, and, of course, thesensitivity to manufacturing tolerances.

1 August 1994 / Vol. 33, No. 22 / APPLIED OPTICS 5121

a)0)a00.

a)Ir10a)N

E0z

0!

0,

0

0,

-50 0 50

MFRSR Angle from West to East

a)Wr

a)

0

z

0

0

-50 0 50

MFRSR Angle from South to North

aU)

0

I.a)

a)

0Cd

EoZ

02

0,

0

0

0

-50 0 50

Eppley Angle from South to North

Fig. 4. Angular response error of a, MFRSR angle from west toeast; b, MFRSR angle from north to south, both for sevenpassbands; c, Eppley PSP angle from south to north.

Laboratory radiometric calibrations are usuallydone at normal incidence only; this is physically theleast interesting angle. When the Sun is visible theirradiance is dominated by the direct beam, and hencethe instantaneous solar zenith angle is the mostimportant one. Rarely is it at the zenith. Fordiffuse skies the total flux is given by the integral

rs2

= L(0)cos(0)sin(0)d0,

where L(O) is the almucantar-averaged radiance as afunction of zenith angle 0. Function cos(0)sin(0)peaks at 45°. Realistic diffuse skies exhibit a zenithbrightness (a consequence of the ground albedo being< 1), but this rarely decreases the zenith angle of thepeak contribution to the flux integral to < 35°. If theangular response cannot be ideal, then a responsefunction that mildly overcompensates at high zenithangles (so that midrange angles near 450 are moreaccurate) is substantially better at producing correctflux integrals than a response such as that of theEppley PSP that monotonically declines at increasingzenith angles.

The angular misalignment error between the ac-tual optical axis of the instrument and the geometric

axis can be estimated by the mean angle of themeasured angular irradiance function.

= /2

E(O)OdO-T/2

Oerror f /2

E(O)dO-s/2

This is the maximum-likelihood estimator, if we aregiven uncorrelated normally distributed measure-ment errors. The small residual azimuthal varia-tions among the passbands (caused by diode positionsaround the outer hexagon) are well modeled as anindividual plane tilt relative to the normal opticalaxis. These angles typically range from 0.01 to0.50, and they are comparable with those of single-passband instruments.' 0

If left uncorrected, tilt errors can be important to ameasurement error budget when high accuracy isrequired. A 0.250 error in east-west alignment (i.e.,hour angle) corresponds to 1 min of time. Errors ininferred direct-beam components and the resultingcomputation of optical depth are sensitive to sucherrors." In contrast, the diffuse-sky irradiances areless affected. The error is sin(Oerror) for the artificialcase of a uniform sky irradiance and a zero surfacealbedo: in this case an error of 0.25° in the zenithaxis causes an error of 0.5%. [This error is notnegligible when judged against the admittedly diffi-cult goal of the Atmospheric Radiation Measurement(ARM) program for measurement accuracies betterthan 1%.] The sensitivity of the measurements tosmall tilts demonstrates the need for accurate charac-terization of the detector response, careful alignmentof the instrument in the field, and concern about itslong-term stability. Correction of the data (as de-scribed below) based on the measured angular re-sponses as well as a leveling accuracy of 0.1 isrequired for reduction of these errors so that theymake a small contribution to a 1% budget. (Thedetector head is designed for the provision of a largeflat fiducial leveling surface, and all measurements,both in the laboratory and the field, are referenced toit. This also illustrates the great difficulty of makingaccurate observations from ships, or even meteorologi-cal towers. Many buildings sway more than 0.10,either from wind loads or from the diurnal thermalcycle.)

Example DataFigure 5a shows the time series of direct-beam irradi-ances measured by a MFRSR at the RattlesnakeMountain Observatory (RMO, 46.400 N, 119.600 W,elevation 1088 m) on 6 October 1992. The direct-beam irradiance is derived by difference; thus it is themost sensitive to experimental error. We chose thisday for presentation because it had a clear interval inthe morning for Langley regression and scatteredcloud passages in the afternoon. Figure 5b showsthe morning Langley plots for all the filtered pass-

5122 APPLIED OPTICS / Vol. 33, No. 22 / 1 August 1994

.................... . . .. .

0C,0

'T

-0

0

C.)a)0

50 C:6 CDI

0( I0=0D

0D

280.3 280.4 280.5 280.6 280.7

Day of Year Plus Fraction

0

aIV'a

is

U,

r

0

0co

3 4 5 6

Air MassFig. 5. a, Time series of MFRSR data forLangley regressions.

one day; b, associated

bands except 940 nm, for which this method of opticaldepth analysis is inappropriate. The direct-beamcomponent has been corrected for the remainingangular error of the detector as described below, andwe performed Langley analyses by using algorithmsdescribed by Harrison and Michalsky.12 The linear-ity of the regressions demonstrates the accuracy towhich this can be done. The total optical depthsretrieved for these cases are shown in Table 2.

Correction of the Direct-Normal Irradiance forLambertian Receiver ErrorThe direct-normal irradiance can be corrected for theresidual errors of the Lambertian receiver, providedthat adequate calibrations such as those shown aboveare available. There are two reasons for us to makethese corrections: the direct-normal irradiance mustbe corrected for us to obtain accurate optical depthretrievals, and the accuracy of the estimation of thetotal-horizontal measurement can be improved whena direct beam is present.

Table 2. Total Optical Depths (r) at the RMO

Wavelength Optical Depth (T)

(10-nm FWHM) MFRSR Tracking Radiometer

415 0.402 0.408500 0.265 0.262610 0.220 0.221665 0.184 0.182862 0.130 0.133

This is similar to the method routinely used for theimprovement of pyranometer measurements oftotal-horizontal irradiance; data taken with a shadedpyranometer measure the diffuse component, and asecond narrow-field-of-view normal-incidence pyran-ometer measures the direct beam. One then aggre-gates the results by using the known cosine of thezenith angle,

Etotal-horiz = Ediffuse + cos(Z)*Edirect-normal

With the MFRSR one needs only a single instrument,thereby avoiding the problem inherent in this methodof matching the calibrations if two independent detec-tors are used for the separate components.

The correction of the direct-normal irradiance isdone to each observation as table-directed linearinterpolation from the angular calibrations shownabove. The solar azimuth angle is resolved into thefour quadrants, and then zenith-angle dependence isproportioned from the two orthogonal axes of mea-surement linearly with respect to angle (the north-to-east quadrant equation):

90 - 1I 1C(+, 0) = 90 fnorth( 0 ) 90 fet t (0)

Here C is a multiplying correction factor, 0 is the solarzenith angle, is the solar azimuth angle in degrees,and north and feast are the normalized angular re-sponse functions shown in Figs. 4a and 4b. Weretain tables for each instrument, storing the f valuesalong the four quadrant axes at 1° increments, and welinearly interpolate in between. This interpolationscheme is accurate for Lambertian receivers that donot show strong azimuthal variation, and in whichthe effective tilt of the optical axis as discussed aboveis sufficiently small that the approximation sin(x) xis valid. If the effective tilt is larger, then two-stepinterpolations based on the resolved projection axesof the solar position in Cartesian coordinates followedby separate corrections for effective tilt (as estimatedabove) and then residual diffuser errors would beneeded. Characterization of the receiver along morethan two azimuthal axes would be required if thevariation were larger.

Intercomparison with Sun-Tracking Radiometry

The MFRSR at RMO also acquires data from aseven-passband tracking radiometer. We constructedthis instrument by placing a multifilter detectorassembly (including the housing and diffuser) at theend of a tube with an entrance aperture; we selectedthe length and aperture size to mimic the acceptanceangles of the Eppley normal incidence pyranometer.The angles for the tracking radiometer and MFRSRare shown in Table 1. This radiometer is continu-ously pointed at the Sun by a LiCor solar tracker.Our purpose for this detector is to demonstrate theaccuracy of the optical depths retrieved from theMFRSR. Intercomparison of the data from theMFRSR with that from the tracking instrument tests

1 August 1994 / Vol. 33, No. 22 / APPLIED OPTICS 5123

Table 3. Correlation Coefficients for Optical Depths Retrieved byColocated MFRSR's and Tracking Radiometers

Passband Center (nm) Correlation Coefficient

415 0.92500 0.95610 0.97665 0.97862 0.97

the entire MFRSR measurement system, includingall the calibration and correction algorithms.

Close matching of passbands must be maintainedfor any intercomparison of optical depths. All instru-ments will intrinsically measure the total opticaldepth, although in most cases it is only the variableaerosol and trace-gas components that are of interest,for which the Rayleigh extinction is subtracted.However, mismatch in perceived optical depth isdominated by the Rayleigh contribution, both be-cause it is the dominant extinction process at all butthe longest wavelengths and because it has the stron-gest wavelength dependence, varying as A-4 for

1= CA-a,

the differential

(-) =-a

Consequently, for a passband at 500 nm, a wave-length accuracy of 1 nm is required for us to obtain1% accuracy in the determination of total opticaldepths.

The results of the intercomparison of optical depthsretrieved by the MFRSR with those from narrow-field-of-view tracking detectors are shown in Table 3 andFig. 6. Table 3 shows the correlation coefficientsbetween the two instruments for inferred opticaldepths. Figure 6 shows the statistics of aggregatedmeasurements for the assessment of the bias. Thebias between the two instruments is smaller than

U,

.

a c 415

0 cio ~~~~ ~500

g2 610 65

C-i ~~~~~~~~~~~862-

Wavelength (nm)

Fig. 6. Bar statistics of optical depths measured by a MFRSR (leftitem of each passband pair) and a tracking radiometer (right itemof each passband pair). Central boxes represent the central 50%of the data; white central bars represent the median. Dashedlines and vertical brackets illustrate the extrema.

that expected because of an assumed limit of passband-matching accuracy of 1 nm for all wavelengths except415 nm, and it is comparable with this limit for the415-nm passband.

Worst-case estimates of the accuracy of the opticaldepths inferred by this shadow-band technique can bederived easily from the statistics in Table 3 andFigure 6, if we assume that all variation is to beattributed to the shadow-band measurements. Inthis case the standard error of the inferred opticaldepths is approximately 0.0125 for measurements at500 nm and 0.0055 for those at 610 nm. (Statisticsare presented for these wavelengths for the purposeof comparison against the World Meteorological Orga-nization standard of 0.05 optical depth for photopicmeasurements.) More realistic estimates involvesome discretion in analysis, but they plausibly regressto remove residual bias caused by wavelength mis-match and attempt to apportion the variance inretrieved optical depths between the two measure-ments on the basis of variance observed within theLangley regression. In this case the standard errorsare reduced by slightly more than 21/2 and arecomparable for both measurement technologies.

Optical depths become highly variable when thetotal extinction is dominated by large particles, e.g.,thin cirrus. In this case, differing effective fields ofview of the direct-beam measurements (see Table 1)change the perceived optical depth because of thelarge fraction of light scattered into small forwardangles by particles that are large compared with thewavelength. The larger effective field of view of theMFRSR would cause it to report a smaller opticaldepth. However, these cases are readily identifiedby the noise in the Langley regression caused by thespatial and temporal variability of such clouds, andbecause the non-Rayleigh extinction becomes nearlyindependent of the wavelength. These signaturesprovide a ready indicator of the presence of subvisualclouds; Langley optical depths inferred from eitherinstrument are normally discarded.

In Situ Calibrations That Use Air-Mass ExtrapolationIn Figs. 5a and 5b the irradiance scale is uncalibrated(it is simply digitized millivolts). The Langley regres-sion for the determination of optical depth is aratiometric method that does not depend on anabsolute calibration. A second major use of theLangley analysis is in the attainment of the extrapo-lated intercept of this regression with zero air mass,E0. When corrected for the variation in the Earth-Sun distance (Eo*A2, where A is the distance from theEarth to the Sun in astronomical units), this value isthe inferred solar constant at the passband. Attain-ment of this value requires an extrapolation of atleast one air mass, so small errors in 7 can cause muchlarger errors in E0.

At exceptional sites (e.g., Mauna Loa) individualLangley regressions taken under favorable conditionswill show variations in Eo*A2 of less than 1%. This isremarkable and exceeds the precision of all but the

5124 APPLIED OPTICS / Vol. 33, No. 22 / 1 August 1994

best laboratory spectral calibrations. More typicalsites show much larger variations in the extrapolatedE0. Single regressions, then, do not yield good esti-mates. However, these variations are not system-atic, and we demonstrated that it is feasible for us toobtain calibrations against the solar constant byaveraging the results of a series of regressions. Thiswas done at a site atop the National Oceanic andAtmospheric Administration complex within the Den-ver, Colorado, basin; this is a site known as a difficultone and that is considered unsuitable for photometerintercomparisons, both because of variable air-masstrajectories across the front range to the west andbecause of local flows that perturb the urban pollution.Thus if the instrument has adequate short-termstability to permit the acquisition of a sufficientnumber of Langley extrapolations (under all but themost unfavorable conditions in less than 3 months),then the long-term stability of calibration can bemaintained by an analysis of the returned data to aprecision of approximately 1%. The absolute accu-racy depends on the precision to which the passbandis known, and the accuracy and stability of the solarconstant.

ConclusionsThe MFRSR is a single instrument that can replace asuite of standard instruments. It provides spec-trally resolved measurements at seven passbands ofthe direct-normal, diffuse-horizontal, and total-horizontal irradiance. Demonstrated accuracies arecomparable with tracking instruments for the direct-normal components (and thus optical depths), andthey are superior to those of existing Lambertianradiometers for the diffuse-horizontal and total-horizontal irradiances. An important advantage ofthe MFRSR is that the diffuse- and total-horizontalirradiance measurements are guaranteed to have thesame passband and sensitivity as the direct-normalirradiances. This greatly reduces the errors in analy-ses that compare these components (versus tradi-tional measurement techniques that require separateinstruments), and it permits the measurements oftotal- and diffuse-horizontal irradiances as a wayto share the utility of long-term calibration by Lang-ley regression and zero-air-mass extrapolation.MFRSR's are currently being deployed by both theQuantitative Links measurement program and at theClouds and Radiation Testbed sites of the ARMprogram. Instruments are also being used in theTropical Oceans-Global Atmosphere, Coupled Ocean-Atmosphere Response experiment and are being de-ployed by individual investigators as well.

Research at the Atmospheric Sciences ResearchCenter was supported by the U.S. Department of

Energy (DOE) Quantitative Links program andthrough grant DE-FG02-90ER61072 (ARM pro-gram), and by the New York State Energy Researchand Development Authority under grant 1725-EEED-IEA-92. At Pacific Northwest Laboratory the re-search was supported by the Quantitative Linksprogram and the Office of Basic Energy Scienceswithin the DOE. The Pacific Northwest Laboratoryis operated for the DOE by Battelle Memorial Insti-tute under contract DE-AC06-76FLO 1830.

References and Notes1. M. Iqbal, An Introduction to Solar Radiation (Academic, New

York, 1983). Note that Fig. 12.5.1 of Iqbal shows definitionsof the half angles, whereas his associated table, Table 12.5.1,shows full angles = 2* half angles. The Zp, or umbral angle,is of particular importance for a blocking method because it isthe angle for which every point on the detector is blocked.

2. M. L. Wesely, "Simplified techniques to study components ofsolar radiation under haze and clouds," J. Appl. Meteorol 21,373-383 (1982).

3. R. Guzzi, G. C. Maracci, R. Rizzi, and A. Sicardi, "Spectroradi-ometer for ground-based measurements related to remotesensing in the visible from a satellite," Appl. Opt. 24, 2859-2863 (1985).

4. T. Stoffel, C. Riordan, and J. Bigger, "Joint EPRI/SERIproject to evaluate solar energy radiation measurement sys-tems for electric utility solar radiation resource assessment,"in Proceedings of the IEEE Photovoltaic Specialist's Confer-ence (Institute of Electrical and Electronics Engineers, NewYork, 1991).

5. J. P. Kerr, G. W. Thurtell, and C. B. Tanner, "An integratingpyranometer for climatological observer stations and meso-scale networks," J. Appl. Meteorol. 6, 688-694 (1967).

6. A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, "Vstability and contamination analysis of Spectralon diffusereflectance material," Opt. Eng. 32, 799-804 (1993).

7. M. D. King, D. M. Byrne, B. M. Herman, and J. A. Reagan,"Aerosol size distributions obtained by inversion of spectraloptical depth measurements," J. Atmos. Sci. 35, 2153-2167(1978).

8. M. D. King and B. M. Herman, "Determination of the groundalbedo and the index of absorption of atmospheric particles byremote sensing, part 1: theory," J. Atmos. Sci. 36, 163-173(1979).

9. G. E. Shaw, "Inversion of optical scattering and spectralextinction measurements to recover aerosol size spectra,"Appl. Opt. 18, 988-993 (1979).

10. J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser III,"Cosine response characteristics of radiometric and photomet-ric sensors," presented at the 1992 Annual Conference of theAmerican Solar Energy Society, Cocoa Beach, Fla., 15-181992.

11. L. W. Thomason, B. M. Herman, R. M. Schotland, and J. A.Reagan, "Extraterrestrial solar flux measurement limitationsdue to a Beer's law assumption and uncertainty in local time,"Appl. Opt. 21, 1191-1195 (1982).

12. L. Harrison and J. J. Michalsky, "Objective algorithms for theretrieval of optical depths from ground-based measurements,"Appl. Opt. 33, (1994).

1 August 1994 / Vol. 33, No. 22 / APPLIED OPTICS 5125