Multifilter Rotating Shadowband Radiometer Research Articles

Investigating anomalous absorption using surface measurements

Flux measurements from the 415 nm band of the multifilter rotating shadowband radiometer and liquid water path from the microwave radiometer were used to derive effective radii in warm boundary layer clouds at the U.S. Department of Energy Atmospheric Measurement Program Southern Great Plains site. Surface fluxes computed using the effective radii retrieved using 415 nm measurements showed no bias when compared with observed broadband fluxes. It is therefore inferred that there is no excess absorption at solar and near‐infrared wavelengths in the presence of warm boundary layer clouds.

Validation of surface retrieved cloud optical properties with in situ measurements at the Atmospheric Radiation Measurement Program (ARM) South Great Plains site

Cloud optical properties inferred from a multifilter rotating shadowband radiometer have been validated against in situ measurements during the second ARM Enhanced Shortwave Experiment (ARESE II) field campaign at the ARM South Great Plains (SGP) site. On the basis of eight aircraft in situ vertical profiles (constructed from measurements), Forward Spectra Scattering Probe (FSSP), we find that our retrieved cloud effective radii for single‐layer warm water clouds agree well with in situ measurements, within 5.5%. A sensitivity study also illustrates that (for this case) a 13% uncertainty in observed liquid water path (LWP, 20 g/m2) results in 1.5% difference in retrieved cloud optical depth and 12.7% difference in inferred cloud effective radius, on average. The uncertainty of the LWP measured by the microwave radiometer (MWR) is the major contributor to the uncertainty of retrieved cloud effective radius. Further, we conclude that the uncertainty of our inferred cloud optical properties is better than 5% for warm water clouds based on a surface closure study, in which cloud optical properties inferred from narrowband irradiances are applied to a shortwave model and the modeled broadband fluxes are compared to a surface pyranometer.

Raman lidar and sunphotometric measurements of aerosol optical properties over Thessaloniki, Greece during a biomass burning episode

Abstract The influence of biomass burning smoke on the aerosol loading in the free troposphere over Thessaloniki, Greece (40.5°N, 22.9°E) is discussed in this paper. A selected case during summer 2001 is presented, when very high aerosol optical depth values were observed, benefiting from the synergy of various remote sensing instruments. The data that were collected allow the characterization of the optical properties of the aerosols in this region, where only little information has so far been available. Four-day back trajectories indicated that air masses were advected from Bulgaria and the northern coast of the Black Sea, where strong forest fires occurred in early August 2001. In order to investigate the optical properties of biomass burning aerosols, we used a two-wavelength lidar system that combines Raman and elastic-backscatter observations, in addition to a Brewer spectrophotometer, a nephelometer and a multi-filter rotating shadowband radiometer. The lidar measurements on 9 August 2001 recorded an integrated aerosol optical depth at 355 nm of the order of 1.35 during cloud-free conditions. The estimated mean extinction–to-backscatter ratios from the Raman lidar were 60 sr for 355 nm and 50 sr for 532 nm. Estimated values of the single scattering albedo, using spectral UV measurements and modeling were of the order of 0.90, consistent with previous findings, indicating a weak contribution of absorption to the total extinction. The Angstrom exponent, calculated from the multi-filter rotating shadowband radiometer exhibited also high values around 1.78, indicating the presence of rather small particles.

Assessment of multiple scattering and horizontal inhomogeneity in IR radiative transfer calculations of observed thin cirrus clouds

Outgoing longwave (LW) radiation (OLR) and infrared heating rate errors due to the neglect of multiple scattering by clouds and horizontal cloud inhomogeneity in infrared radiative transfer parameterizations are assessed with a modified version of the Fu and Liou [1992] radiative transfer model and field measurements of optically thin cirrus that were observed during the fall 1997 and spring 2000 intensive observation periods conducted at the Atmospheric Radiation Measurement Southern Great Plains site in Oklahoma. A rigorous method is first introduced for incorporating atmospheric and cloud optical and geometric properties derived from measurements in radiative transfer calculations and for ensuring the consistency of these calculations with observations. Part of that method is the use of optical depth derived from measurements of a Multi Filter Rotating Shadowband Radiometer (MFRSR) at 415 nm to determine the cloud ice water content for the longwave and shortwave radiative transfer calculations. The optical depth is corrected to account for forward scattering by cirrus crystals, which is dominant under the thin cirrus conditions observed. Surface downwelling fluxes from the radiative transfer calculations are compared against observations from the Baseline Surface Radiation Network for consistency, with primary emphasis placed on achieving good agreement between the observed and calculated direct normal components. For all cases considered, there is very good agreement in the solar direct irradiance and reasonably good agreement in the solar diffuse irradiance, but without the forward scattering correction the agreement for both would degrade; the diffuse agreement, in particular, would do so by 12 W m−2 (>30%). Very good agreement is achieved in the LW with an absolute mean difference of 0.02 W m−2. For the observed cases considered, neglecting multiple scattering of LW by thin cirrus overestimates OLR by 6–8 W m−2 or less (depending on cloud optical depth and particle size) because of exclusion of reflection of upwelling LW at the cloud base and results in heating rate errors of as much as 0.2 K d−1. The effect of horizontally homogeneous clouds is approximated by employing the half hourly mean of the derived optical and geometric properties in the calculation. The impact of the combined effect on OLR and LW heating rates is shown from these calculations to be as high as 30 to 35 W m−2, and heating rate errors are on the order of 0.5 to over 1 K d−1, which are very significant errors.

Aerosol single scattering albedo retrieved from measurements of surface UV irradiance and a radiative transfer model

Aerosol single scattering albedo (ω), the ratio of aerosol scattering coefficient to total aerosol extinction coefficient, at UV wavelengths is an important aerosol radiative parameter in determining surface UV irradiance. Surface measurements of total and diffuse UV irradiance in the summer and fall of 1999 at the seven narrowband wavelength channels of an UV multifilter rotating shadowband radiometer (UVMFR‐SR) at Black Mountain, N. C., were coupled with a tropospheric ultraviolet radiative transfer model to produce values of ω. Its value ranged from 0.65 to 0.91 at 300 nm, 0.71 to 0.96 at 305.5 nm, 0.73 to 0.97 at 311.4 nm, 0.74 to 0.91 at 317.6 nm, 0.76 to 0.96 at 325.4 nm, 0.77 to 0.97 at 332.4 nm, and 0.80 to 0.99 at 368 nm. Error in this procedure decreases with increasing aerosol optical depth (AOD), from ±0.63 at AOD = 0.05 to ±0.04 at AOD = 1.0 averaged over the seven wavelengths. The current values of ω have a slightly wider variation than values reported from a previous study at the same site. The lower values of ω could indicate that, over the site, preferential absorption of UV radiation by black carbon aerosols could be occurring. More values of ω in the UV spectrum will allow for better estimation of this parameter for UV radiative transfer modeling and will lessen error in estimation of surface UV irradiances.

Determination of Angstrom’s turbidity coefficient over Thailand

Values of the Angstrom’s turbidity coefficient, β, at 53 meteorological stations covering Thailand were determined by using three different methods. A selection of the methods was based on input data available at each station. It was started with the calculation of β at Nakhon Pathom (13.81 °N and 100.4 °E) using narrow-band spectral irradiance data obtained from a multi-filter rotating shadow band radiometer. Langley’s method was employed to calculate β from the spectral data. The values of β derived from this method were used as references to validate a method for computing β from broad-band direct irradiance proposed by Louche et al. (Solar Energy 38(2)89). It was found that this method was valid for a tropical climate. Then Louche et al.’s method was used to calculate β at meteorological stations situated at four main cities, namely Chiang Mai (18.78 °N, 98.98 °E) located in the north, Ubon Rachathani (15.25 °N, 104.87 °E) in the northeast, Songkhla (7.20 °N, 100.60 °E) in the south and Bangkok in the central region. Based on values of β of these cities, a new model relating β to visibility, suitable for the tropical climate was developed. This model was used to estimate β at the other 48 meteorological stations where the visibility was routinely observed. Finally, seasonal variations of β were investigated. It was found that for the stations in the north, the northeast and the central region, the values of β are relatively high in the dry season (November–April). They decrease in the wet season (May–October). For most stations in the south, β was relatively low and remained nearly constant all year round. It was also inferred that the northeast monsoon and the southwest monsoon had a strong influence on the seasonal variations of β.

An Automated Method of MFRSR Calibration for Aerosol Optical Depth Analysis with Application to an Asian Dust Outbreak over the United States

Abstract Over the past decade, networks of Multifilter Rotating Shadowband Radiometers (MFRSR) and automated sun photometers have been established in the United States to monitor aerosol properties. The MFRSR alternately measures diffuse and global irradiance in six narrow spectral bands and a broadband channel of the solar spectrum, from which the direct normal component for each may be inferred. Its 500-nm channel mimics sun photometer measurements and thus is a source of aerosol optical depth information. Automatic data reduction methods are needed because of the high volume of data produced by the MFRSR. In addition, these instruments are often not calibrated for absolute irradiance and must be periodically calibrated for optical depth analysis using the Langley method. This process involves extrapolation to the signal the MFRSR would measure at the top of the atmosphere (Iλ0). Here, an automated clear-sky identification algorithm is used to screen MFRSR 500-nm measurements for suitable calibration da...

Irradiance-based cross-calibration of Landsat-5 and Landsat-7 Thematic Mapper sensors

On 2 June 1999 Landsat-5 and Landsat-7 passed over north-central Nebraska collecting Thematic Mapper (TM) data for essentially the same spatial location, with an acquisition time differing by less than 20 min. At the Niobrara Nature Preserve, Nebraska site, two multifilter rotating shadowband radiometers (MFRSRs), a Cimel sunphotometer, a Microtops sunphotometer, and an ASD-FR spectroradiometer were used to take ground-based readings. This dataset offered a unique opportunity to absolutely calibrate both instruments, and also to cross-calibrate TM with Enhanced Thematic Mapper Plus (ETM+) the new thematic mapper aboard Landsat-7. ModTran3 radiative transfer code, based on the Nebraska datasets, was calibrated to match observed atmospheric transmittance and diffuse-to-global ratios, employing ground reflectance values, for each individual overpass. Having replicated those conditions, models were then extrapolated to satellite orbits, and exoatmospheric irradiances calculated. Finally, by obtaining actual imagery from each satellite, a cross-calibration comparison of the two satellites' TM sensor's responses was made.

Aerosol Measurement in the Australian Outback: Intercomparison of Sun Photometers

The low background aerosol loadings prevailing over much of the Australian continent necessitate careful attention to the calibration of sun photometers. The validity of such calibrations can only be assessed objectively by intercomparison of independent systems operating side by side. This paper documents two intercomparisons: the first between three dissimilar photometers collocated at Alice Springs using independent calibration methods, and the second between identical photometers sited at Tinga Tingana in the Strzelecki Desert of South Australia. The intercomparison of total optical depth derived from two Cimel CE318 systems at Tinga Tingana shows negligible biases (<0.0004) at all four wavelengths. Instantaneous differences in total optical depth are used to infer 95% uncertainty intervals, which range from 0.003 at 670 nm to 0.005 at 870 nm. The Alice Springs intercomparison shows negligible bias between the Carter–Scott SPO1A and Cimel CE318 at 500 nm, while a bias of 0.004 between the two at 868 nm is identified as sideband leakage in one of the filters. The 95% uncertainty interval for each instrument is <0.007 at both 500 and 868 nm. The multifilter rotating shadowband radiometer (MFRSR) shows a consistent positive bias of 0.012–0.014 at the three wavelengths studied, most probably related to issues of alignment and angular response characterization. The 95% uncertainty interval is greater than 0.02, comparable with the typical background midvisible aerosol optical depth at these sites. Hence this instrument is unsuitable for the measurement of background aerosol under Australian conditions without careful characterization. The impact of uncertainties in surface pressure and ozone on aerosol optical depth is shown to be negligible for the case where the surface pressure is measured on site, and the ozone amount is taken from monthly mean data from stations of commensurate latitude to the observing site. Comparison with previous work suggests that calibration of collimated sun photometers at remote inland sea level Australian sites yields accuracy exceeding that obtained from techniques presently in use in the Northern Hemisphere involving calibration at high altitude sites.

Measurement errors in diffuse irradiance with non-Lambertian radiometers

Experimental errors in measurements of solar irradiance resulting from the departure of angular response of real sensors from the Lambertian ideal are evaluated. The errors include polarization independent and dependent components. The polarization independent component is relatively independent of solar zenith angle and thus is substantially correctable by scaling. It was estimated to be as high as m 6.0% for some commonly used radiometers. The polarization dependent component for the multifilter rotating shadowband radiometer (MFRSR) was estimated to be between m 1.5% for the Sun at the zenith and +1.0% for the Sun at the horizon. The zero crossover for this error occurs around 55° solar zenith angle. These errors do not explain the discrepancy between measured and modelled diffuse shortwave irradiance, but in some instances they can reduce the difference.

Remote Sensing of Atmospheric Aerosols and Trace Gases by Means of Multifilter Rotating Shadowband Radiometer. Part II: Climatological Applications

Abstract Measurements from ground-based sun photometer networks can be used both to provide ground-truth validation of satellite aerosol retrievals and to produce a land-based aerosol climatology that is complementary to satellite retrievals that are currently performed mostly over ocean. The multifilter rotating shadowband radiometer (MFRSR) has become a popular network instrument in recent years. Several networks operate about a hundred instruments providing good geographical coverage of the United States. In addition, international use of the MFRSR has continued to increase, allowing MFRSR measurements to significantly contribute to aerosol climatologies. This study investigates the feasibility of creating a ground-based aerosol climatology using MFRSR measurements. Additionally, this analysis allows for testing of the performance of the retrieval algorithm under a variety of conditions. The retrieval algorithm is used for processing MFRSR data from clear and partially cloudy days to simultaneously ret...

Remote Sensing of Atmospheric Aerosols and Trace Gases by Means of Multifilter Rotating Shadowband Radiometer. Part I: Retrieval Algorithm

Abstract A retrieval algorithm for processing multifilter rotating shadowband radiometer (MFRSR) data from clear and partially cloudy days is described and validated. This method, while complementary to the Langley approach, uses consistency between the direct normal and diffuse horizontal measurements combined with a regression technique to simultaneously retrieve daily time series of column mean aerosol particle size, aerosol optical depth, NO2, and ozone amounts along with the instrument's calibration constants. Comparison with the traditional Langley calibration method demonstrates two advantages of the approach described here: greater calibration stability and a decreased sensitivity of retrievals to calibration errors.

A differential technique to retrieve column water vapor using sun radiometry

Techniques for retrieving column water vapor from Sun radiometer measurements involving the 940‐nm water vapor absorption band have been around for the better part of a century. Arguably, the best method to use for this retrieval is the modified Langley technique. However, to apply this method one must obtain the instrument response at the top of the atmosphere using modified Langley plots on clear days with a very stable water vapor column. Using subsequent measurements in this filter, ratioed to the top‐of‐the‐atmosphere response allows one to determine the transmission in the 940‐nm water band. In this paper, we present an approach that does not require an absolute knowledge of the extraterrestrial instrument response. The method discussed here relies, instead, on relative measurements of a calibration lamp and the extraterrestrial spectral irradiance within and just outside the 940‐nm absorption band. We execute these retrievals for the rotating shadowband spectroradiometer (RSS) on 3 days during the Department of Energy's Atmospheric Radiation Measurement program's 1997 Water Vapor Intensive Observation Period. We compare the results to those retrieved from a colocated multifilter rotating shadowband radiometer (MFRSR) that uses an empirical calibration and from a colocated microwave radiometer. Since our optical method of retrieving column water vapor from RSS measurements does not depend on a calibration performed against another water vapor measurement, it contributes an independent estimate in the search for absolute accuracy. The major contributors to the uncertainty of this retrieval are the water vapor band strength calculations, the difference in aerosol extinction in and near the water vapor band, the relative spectral irradiance output of the calibration lamp and the Sun at the nonabsorbing and band‐centered wavelengths, and the stability of the spectral response of the instrument, which will be discussed in detail.

April 1998 Asian dust event over the Columbia Plateau

Surface‐based radiometers can be used to assess the atmospheric aerosol burden. During 1998, two multifilter rotating shadow‐band radiometers (MFRSRs), operated by Washington State University (WSU) and by the USDA UV‐B program, were used to collect data on the Columbia Plateau atmosphere. Analysis of these data by an automated Langley algorithm provided retrievals for total optical thickness, allowing for calculation of aerosol optical thickness (AOT) and the top‐of‐atmosphere (TOA) instrument signal. Statistical evaluation of the TOA signal permitted recalculation of optical thickness using the Bouguer‐Lambert‐Beer law and resulted in improved estimates of aerosol optical thickness (AOT). Results for AOT and the associated Ångström parameters are presented here for an April 1998 dust event for two colocated Columbia Plateau sites. AOT at 500 nm went from background levels (seasonally dominated by regional windblown dust) of ∼0.2 to more than 0.4 during the event maximum on April 27, not returning to normal levels until April 30. Comparison of 500‐nm AOT between the two MFRSR showed a root‐mean‐square (RMS) difference of 0.016. The Ångström exponent α reached a minimum of ∼0.2, and the β coefficient reached a maximum of ∼0.35, both on April 27, coincident with the AOT maximum. Contemporaneous aerosol sampling in Spokane, Washington, provided (1) elemental data that strongly support our interpretation of this event as an influx of Asian dust without significant sulfur enrichment and (2) event maximum PM10 measurements ∼80 μg/m3 consistent with Pullman event maximum AOT results, assuming a 3–4 km thick dust layer.

Multiyear measurements of aerosol optical depth in the Atmospheric Radiation Measurement and Quantitative Links programs

The U.S. Department of Energy funded the development of the multifilter rotating shadowband radiometer (MFRSR) as part of the Atmospheric Radiation Measurement (ARM) program. This seven‐channel radiometer began operation at the first ARM site in 1992 and at the Department of Energy Quantitative Links (QL) sites in the fall of 1991; three of the QL sites continue to operate, although this program was discontinued after 1995. This paper describes the use of the MFRSR in acquiring aerosol optical depth data, including the in‐field calibration procedure and a partial validation of this process. Multiyear measurements of aerosol optical depth from three of the sites indicate similar phasing of seasonal and interannual changes, but with notable differences in the magnitude of the aerosol optical depth. Published papers that use these aerosol data are highlighted, and public access to these and future data sets for scientific studies are explained.

A study of the aerosol radiative properties needed to compute direct aerosol forcing in the southeastern United States

To assess the direct radiative forcing due to aerosols in southeastern United States where a mild cooling is under way, an accurate set of data describing the aerosol radiative properties are needed. We report here aerosol optical depth (AOD) and diffuse to‐direct solar irradiance ratio (DDR) at three operational wavelengths (415, 500, 673 nm) determined by using Multifilter Rotating Shadowband Radiometers (MFRSR) at two sites (a mountain top site: Mount Gibbes, 35.78°N, 82.29°W, 2006 m mean sea level (msl); a valley site: Black Mountain, 35.66°N, 82.38°W, 951 m msl), which are separated horizontally by 10 km and vertically by 1 km. The characteristics AOD and DDR were determined from the field measurements obtained during 1995. It was found that the representative total AOD values at 500 nm at the valley site for highly polluted (HP), marine (M) and continental (C) air masses were 0.68±0.33, 0.29±0.19, and 0.10±0.04, respectively. The fact that the ratio of the mean 1 km layer optical depth to total mean optical depth at 500 nm from the valley site was 71% indicates that the major portion of the atmospheric aerosol was located in the lowest 1 km surface boundary layer (SBL). There was a significant linear correlation between the DDR and the total AOD at both sites. A simple, fast, and operative search‐graph method was used to retrieve the columnar size distribution (number concentration N effective radius reff, and geometric standard deviation σg) from the optical depth observations at the three operational wavelengths. The ground albedo, single‐scattering albedo, and imaginary part of the refractive index are calculated using a mathematically unique procedure involving a Mie code and a radiative transfer code in conjunction with the retrieved aerosol size distribution, AOD, and DDR. It was found that N, reff, and σg were in the range of 1.9×10 to 1.7×104 cm−3, 0.09–0.68 μm, and 1.12–2.70, respectively. The asymmetry factor and single‐scattering albedo were in the ranges of 0.63–0.75 and 0.74–0.99 respectively. The ground albedo over the forested terrain and the imaginary part of refractive index were found to be in the range of 0.08–0.29 and 0.005–0.051, respectively.

A comparison of the aerosol thickness derived from ground‐based and airborne measurements

The extinction optical thickness of particles obtained from scattering and absorption coefficients measured by an airborne integrating nephelometer and particle soot absorption photometer, respectively, is compared with the aerosol optical thickness derived from a ground‐based multifilter rotating shadowband radiometer, a Sun photometer, and a Raman lidar for 9 days. These 9 days are selected from intensive operation periods of the Atmospheric Radiation Measurement in April 1997, September 1997, and August 1998 at the southern Great Plains. For April 1997 and September 1997 cases the difference between the extinction optical thickness of particles estimated from vertical profiles and the extinction optical thickness of aerosol derived from the multifilter rotating shadowband radiometer is not significant. For August 1998 cases when the boundary layer relative humidity is higher than April 1997 and September 1997 cases, the extinction optical thickness of particles is 0.03 to 0.07 less than the extinction optical thickness of aerosol. The difference corresponds to 25% to 31% of the extinction optical thickness of aerosol. Based on these comparisons, the upper and lower limits of the single‐scattering albedo of particles present in the lower part of troposphere are 0.97 and 0.84, respectively.

Observational constraints on non-Lorentzian continuum effects in the near-infrared solar spectrum using ARM ARESE data

Uncertainties exist in the magnitude of the water vapor continuum at solar wavelengths and many models do not include a solar continuum. We assess whether the neglect of the continuum in some models could explain a significant amount of the excess solar absorption found by several recent studies, in which the observed atmospheric solar absorption is significantly greater than that modeled. Towards this goal, we constrain the magnitude of the near-infrared water vapor continuum absorption using observations from the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE). Narrowband irradiances measured by two independent Multifilter Rotating Shadowband Radiometers (MFRSRs) are used to infer the clear-sky transmission by water vapor in the 0.94 μm band. Over 16 000 such observations are compared to non-continuum (i.e., a pure Lorentzian model) and continuum calculations using a correlated- k distribution model, which shows excellent agreement with a line-by-line model and uses coincident measurements of the pressure, temperature and water vapor profiles. Continuum calculations use the CKD super-Lorentzian formulation. The data suggest the need for a far wing continuum in the 0.94 μm band with an absorption that falls between that computed for pure Lorentzian lines and the CKD continuum. A sensitivity analysis presents the effects of uncertainties in parameters affecting the calculations, including those in the line parameters, continuum magnitude and atmospheric state. Upper estimates for the absorption of broadband solar radiation by the continuum, beyond that computed for pure Lorentzian far wings, are only 1 to 2 W m −2 for a diurnal (24 h) average, and 4 to 6 W m −2 for local noon. Thus, uncertainties in or the neglect of the water vapor continuum at solar wavelengths are not likely explanations for excess absorption of the order of 15 to 30 W m −2 (diurnal average).

The USDA Ultraviolet Radiation Monitoring Program

The U.S. Department of Agriculture's Ultraviolet (UV) Radiation Monitoring Program has been measuring UV radiation since 1994. The initial network of 12 stations employed broadband meters to measure UVB irradiance and included ancillary measurements of temperature, humidity, and irradiance at seven wavelengths in the visible produced by a Multi-Filter Rotating Shadowband Radiometer (MFRSR). Since that beginning the network has expanded to more than 20 stations and the broadband meters have been supplemented with a seven-wavelength Ultraviolet Multi-Filter Rotating Shadowband Radiometer (UV-MFRSR). The network has been designed to include 30 stations, each with a full complement of instrumentation. Annual characterizations of the network's filter radiometers indicate that gradual shifts in instrument response are manageable but must be accounted for to achieve accurate and precise measurements of UV irradiance. The characterization and calibration of the filter instruments is discussed along with filter stability and instrument precision. Broadband instruments are shown to be quite stable and collocated instruments are shown to agree to within 2.3% for zenith angles less than 80° under all sky conditions. Preliminary investigations into the accuracy of the UV-MFRSR calibrated with the Langley method are presented and successful column ozone retrievals are demonstrated with the UV-MFRSR under clear skies.

Remote Sensing of Cloud Optical Properties from Ground-Based Measurements of Transmittance: A Feasibility Study

Abstract The authors present a retrieval technique for the inference of cloud optical depth from data obtained by a ground-based multichannel radiometer for use in climate-related studies. The basic steps of the analysis procedure are considered, including accurate calculations of the atmosphere and cloud properties. An approach is described that uses observed and model-simulated transmittances rather than irradiances and that does not depend on an absolute calibration of the instrument. This approach, which specifically deals with the transmittances, also offers substantial computational advantages. The resulting algorithm is applied (but not limited) to the measurements of incoming solar irradiance by a particular ground-based instrument, the so-called Multi-Filter Rotating Shadowband Radiometer (MFRSR). Sample results of inferred cloud optical depth obtained from MFRSR measurements in Fairbanks, Alaska, are presented.