Uncertainties in modeled and measured clear-sky

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. D22, PAGES 25,881-25,898, NOVEMBER 27, 1997 Uncertainties in modeled and measured clear-sky surface shortwave irradiances Seiji Kato, Thomas P. Ackerman, Eugene E. Clothiaux, James H. Mather, Gerald G. Mace, '2 Marvin L. Wesely, 3 Frank Murcray, and Joseph Michalsky s Abstract. A comparison of five independent measurements of the clear-sky downward shortwave irradiance at the surface shows that they scatter within a 5% range depending on their calibration constants. When the measurements are corrected using data from two cavity radiometers, three of the five independent measurements agree within 3 W m -2 over three clear-sky days, which is well within the estimated error limit of :1:1.5%. A comparison of these three sets of irradiance measurements with the computed irradiance by a 52-stream model reveals that the model overestimates the irradiance by 5%. Detailed investigation of the approximations and uncertainties associated with the computations (including the measurement error in the water vapor and ozone amounts, neglecting the state of polarization and trace gas absorption, the 2-stream approximation, the neglect of the spectral dependence of the surface albedo, and the uncertainties associated with aerosols) demonstrates that the discrepancy not due to these approximations. Further analysis of the modeled and measured irradiance shows that the discrepancy is almost entirely due to the difference between modeled and measured diffuse field irradiances. An analysis of narrow-band diffuse to total irradiance ratios shows that this discrepancy is the largest near 400 nm and decreases with wavelength. These results rely on the absolute calibrations of two cavity radiometers, two shaded pyranometers, and one unshaded pyranometer, as well as ratios of irradiances measured by a multifilter rotating shadow-band radiometer. Therefore, in order for instrumental error to account for the diffuse field discrepancy, three independent measurements of the diffuse field irradiance must be biased low by at least 40%. For an aerosol to account for this discrepancy, it must be highly absorbing with a single-scattering albedo as low as 0.3. The unlikelihood of instrumental errors of 40% and aerosol single-scattering albedos of 0.3 suggests a third possibility: the neglect of some gaseous absorption process at visible wavelengths. 1. Introduction Our ability to measure and compute clear-sky irradiances accurately is a matter of fundamental scientific interest because it is directly related to our understanding of atmospheric composition, gaseous absorp- tion, molecular and particle scattering, and radiative transfer theory. In addition, it impacts on studies of climate, particularly the Earth radiation budget and on remote sensing of the atmosphere and surface. The accuracy of such computations of the clear-sky shortwave irradiance, however, is not well known. For example, a comparison of shortwave radiation models [Fouquart X Department of Meteorology, The Pennsylvania State et al., 1991] shows that the computed downward irra- University, University Park, Pennsylvania. diances scatter over a wide range. In addition, recent 2Now at Department of Meteorology, University of Utah, studies indicate that theoretical computations overes- Salt Lake City, Utah. timate the downward shortwave irradiance at the sura Argonne National Laboratory, Argonne, Illinois. 4Department of Physics, University of Denver, Denver, face compared with observations [Charlock and Alberta, Colorado. 1996; Wild et al., 1995]. 5Atmospheric Sciences Research Center, State University In this study, we use a high-quality data set obof New York at Albany, Albany, New York. tained during the Atmospheric Radiation Measurement Enhanced Shortwave Experiment (ARESE), which was Copyright 1997 by the American Geophysical Union. held from September 25, 1995, to November 1, 1995, in Paper number 97JD Oklahoma, and two state-of-the-art radiative transfer /97/97JD $09.00 models to quantify the accuracy of clear-sky radiation 25,881

2 25,882 KATO ET AL.- CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE calculations. Sun photometer derived aerosol optical thicknesses, measured pressure, temperature, water vapor, and ozone profiles, as well as the measured surface albedo, serve as inputs to the models. In the following sections, we first discuss the radiation and model input data, attempting to identify the uncertainties associated with the data. We then evaluate the magnitudes of the errors in the radiative transfer model that we used in the study. Finally, we compare the radiative transfer model results with the best estimate of the measured downward shortwave radiation at the surface. 2. Surface Downward Shortwave Radiation Data In this study, we used three clear-sky days that occurred on October 14, 15, and 18 during ARESE. On each of these days, there were no visible clouds anywhere in the sky throughout the day. The lack of clouds on these days is confirmed both by the lack of structure in the ratio of the diffuse to total irradiance [Long, 1996] and Sun photometer derived optical thicknesses that are temporally smooth, low in magnitude, and decreasing with increasing wavelength. The smooth variation of the measured downwelling shortwave surface irradiances on all three days (Figure 1) is the final indication that the skies were cloudless during the three case study days. Three types of radiometers are utilized in this study: unshaded pyranometers, which provide a measure of the total downwelling shortwave irradiance at the surface; shaded pyranometers, which provide a measure of the downwelling shortwave diffuse irradiance at the surface; and normal incidence pyrheliometers, which provide a measure of the downwelling shortwave direct nor- 8OO 700 mal irradiance at the surface within a 5.7øfield of view. These radiometers are deployed at the Southern Great Plains (SGP) central facility (latitude øN, longitude øW) of the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Program in two groups, each consisting of an unshaded pyranometer, a shaded pyranometer, and a pyrheliometer. One group of radiometers is part of a broadband radiometer system (BR, hereinafter), while the other is part of the Solar and Infrared Radiation Observation System (SIROS). The BR and SIROS radiometers are installed 1.5 m above the ground over pasture. The BR radiometers measure irradiances at I s intervals and output a 60 s average, while the SIROS radiometers measure and output instantaneous irradiances every 20 s. During the experiment period, the Atmospheric Radiation Branch of the NASA Langley Research Center supported the deployment of a third unshaded pyranometer near the ARM SGP central facility. It was located at øN latitude and øW longitude and 2 m above ground covered with new wheat (C. Whitlock and G. Schuster, personal communication, 1996). All of the pyranometers were of the current standard design manufactured by Eppley Laboratory; they were calibrated independently (Table 1). To check for consistency in the BR and SIROS irradiance measurements, we compared the total irradiances computed from the BR and SIROS pyrheliometers and shaded pyranometers, which we call "reconstructed" irradiances, with the irradiances measured by the BR and SIROS unshaded pyranometers. The reconstructed irradiance is the sum of a diffuse field irradiance, measured by a shaded pyranometer, and the direct beam irradiance, measured by a pyrheliometer, multiplied by the cosine of the solar zenith angle. To compare the measured irradiances, we define the absolute difference AFxZ, y between two irra- diances as and the fractional difference f,y as AF Z,y = F Z - F;, (1) 600 E500 m 400 c: 300 2OO loo ({ Figure 1. The downward shortwave irradiances at the surface measured by an unshaded pyranometer for the three clear-sky days. The solid, dash-dotted and dashed lines represent measurements for October 14, 15, and 18, respectively. f:,y -- AF:,y/F;, (2) where the superscript z represents a direct beam (db), diffuse field (dr), or total (t) irradiance and x and y represent one of the three (BR, SIROS, NASA) radiometers or reconstructed irradiances from the BR (rebr) or SIROS (resiros) data sets. We also define the average absolute difference between two irradiances F and F from 1600 to 2000 UT as I 20UT, - (F: - F )dt - F: - F, (3) AF y 16UT where t is the time and F and F are the averaged insolations between 1600 and 2000 UT measured by instruments x and y, respectively. The average insolations FiR, FrteBR, F IROS, and FrteSIROS for the three clear-sky days are summarized

3 KATO ET AL.: CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,883 Table 1. Calibration and Operation Date for Radiometers Used in This Study Shortwave radiometers Calibration Operation (From) BR unshaded pyranometer BR shaded pyranometer BR pyrheliometer SIROS unshaded pyranometer SIROS shaded pyranometer SIROS pyrheliometer NASA unshaded pyranometer September 1995 October 13, 1995 June 1995 October 13, 1995 July 1993 March 17, 1994 June 1995 July 25, 1995 June 1995 July 25, 1995 September 1994 July 25, 1995 post-arese ARESE in Table 2. Using (3), we find that the differences liometers were 0.5% greater and 2.1% smaller, respect t AFreBa,B a and AFreSiROS,SiRO S averaged over the 3 tively, than the irradiances measured by two cavity radays are 4.3 and 10.7 W m -2, respectively. The two diometers [Michalsky et al., 1997] that have an accuracy reconstructed irradiances obtained from the B R and of 4-0.3% (T. Stoffel, personal communication, 1996). SIROS data sets and the total irradiances measured by three independently calibrated unshaded pyranometers When we multiply the direct beam irradiances measured by the BR and SIROS pyrheliometers by scatter within a 5% range (Figure 2). The separation and 1.021, respectively, these two pyrheliometers agree of the fractional difference curves of each total irradi- within 3 W m -2 over the 3 days. Therefore the unance against the BR unshaded pyranometer measure- certainties in the measured direct beam irradiances are ments is nearly constant with time (Figure 2). Since 4-0.5% (3 W m -2 out of 600 W m - ) after these corthe fractional differences are nearly independent of the solar zenith angle, we conclude that the differences in the measured irradiances by the three unshaded pyrarections are applied. In addition, if we assume that the uncertainty in measuring the diffuse field irradiance by a shaded pyranometer is at most 10%, which is approxnometers are due to relative offsets in their calibration imately equivalent to the fractional differences between constants. The discrepancy between the BR and SIROS unshaded pyranometer calibration coe cients may resuit from a difference in calibration techniques; the BR unshaded pyranometer was calibrated using the broadband outdoor radiometer calibration (BORCAL) technique, while the SIROS unshaded pyranometer was calibrated with the Eppley factory calibration method. As determined in a recent calibration exercise, the irradiances measured by the BR and SIROS pyrhethe diffuse field irradiances measured by the BR and SIROS shaded pyranometers, the subsequent additional uncertainty in the total irradiance is --1% because the diffuse irradiance is.- 10% of the total irradiance (70 W m -2 out of 700 W m-2). Therefore the uncertainties in the reconstructed irradiances, after correcting the direct beam irradiance biases, are at most 4-1.5%. The corrected insolations FrteBand FrteSiROS averaged over the 3 days are 678 and 675 W m -2, respectively, while Table 2. Average Insolation Between 1600 and 2000 UT Measurement/Model Oct. 14 Oct. 15 Oct. 18 Average Reconstructed BR 706 (647) 692 (633) 648 (555) 682 (612) SIROS 687 (633) 671 (619) 628 (545) 662 (599) Best measurement 703 (646) 687 (632) 645 (557) 678 (612) Unshaded pyranometer BR SIROS NASA Model No aerosol Sulfate 740 (648) 728 (637) 694 (560) 720 (615) Mineral 734 (648) 723 (637) 680 (560) 712 (615) Soot 707 (648) 689 (637) 615 (560) 670 (615) irradiance. Units of W m -2. The numbers in parentheses the average insolations due to the direct beam

4 25,884 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE (a) Oct. 14, 1995 (b) Oct. 15, 1995 (c) Oct. 18, 1995 I ',., O.lO Figure 2. The absolute and fractional differences of the measured downward shortwave irradiances at the surface relative to the irradiances measured by the BR unshaded pyranometer. The thick lines represent reconstructed irradiances (see text); the reconstructed irradiance from the BR data set is always greater than that from the SIROS data set at given time. The upper and lower thin lines represent measured irradiances by the SIROS and NASA unshaded pyranometers, respectively. F a averaged over the 3 days is 678 W m -2. These three total irradiances are within 3 W m -2, which is well within the estimated error limit of approximately +1.5%. In the following comparisons with the model irradiances, we use the SIROS pyrheliometer irradiances after multiplication by and the average of the BR and SIROS shaded pyranometer measurements for the measured direct beam and diffuse field irradiances, respectively. The best estimate of the measured total irradiance is simply the sum of the these two irradiances. Hereinafter, we refer to these three quantities as the measured direct beam, diffuse field, and total irradiances. We opt for the SIROS pyrheliometer mea- surements in the comparisons because its Sun-tracking mount was more reliable than the BR pyrheliometer mount during the ARESE period. Since there were no known problems with either the BR or the SIROS shaded pyranometers, we take the average of these two measurements to represent the measured diffuse field irradiances. 3. Radiative Transfer Model Input Data 3.1. Atmospheric Pressure, Temperature, Water Vapor, and Ozone Profiles Values of surface pressure, temperature, and relative humidity were obtained directly from surface observa- tions. To obtain vertical profiles of water vapor concentration, pressure, and temperature, we interpolated soundings taken at 3 hour intervals to 5 min intervals using the scheme of Mace [1994]. The good agreement between the total column amounts of water vapor derived from the soundings and from the microwave radiometer retrievals indicates that the water vapor profiles that we used in the irradiance calculations are reasonable (Figure 3). To extend the sounding profiles from maxi- mum altitudes of approximately km to 70 km, we used the midlatitude summer profile of McClatchey et al. [1972]. To estimate the magnitude of the error in the column water vapor amounts, we define where W s and Wm are the column water vapor amount obtained from soundings and microwave radiometer retrievals, respectively. The maximum value of Rw occurred on October 14 with a value of 0.11 (Figure 3). Treating the difference w8 - w, as a measure of uncertainty in the model column water vapor amount implies an uncertainty of 10%. We averaged 32 ozone soundings taken during ARESE to determine the mean ozone profile up to 35 km, where the soundings terminated. To extend the ozone profile to 70 km, we used the standard midlat-

5 KATO ET AL.- CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25, Oct. 14, 1995 Oct. 15, 1995 i i i i i i i i i Oct. 18, i i i I '6 Figure 3. The column water vapor amounts for the three clear-sky days derived from soundings (asterisks) and microwave radiometeretrievals (dotted line). The solid line indicates the column water vapor amounts actually used in the model; we obtained these values from an interpolation scheme that we applied to the sounding data. itude summer ozone profile [McClatchey et al., 1972]. The column ozone amount of the average profile is 16% less than that of the standard midlatitude summer ozone profile. Since 16% is much greater than the standard deviation of ozone amounts obtained from the soundings, we assume that the uncertainty in the ozone amount is at most 16% Aerosol Properties Absorption and scattering of solar radiation by aerosol are important components of clear-sky radiative transfer studies. Since in situ measurements of Surface Albedo The surface albedo at the ARM SGP central facility changed during the day as the solar zenith angle varied. To characterize the surface albedo as a function of time of day, we used the ratio of the shortwave irradiance measured by a downward looking pyranometer located 10 m above the surface to the shortwave irradiance measured by an upward looking pyranometer located 1.5 m above the surface. The shortwave surface albedo for the three clear-sky days changed during the day and slightly from day to day (Figure 4); its average value between 1400 and 2200 UT for the 3 days was For the model calculations, we incorporated the surface albedo by using 1 min averages at 5 min intervals. Our initial calculations assumed a spectrally invariant albedo. However, we do consider the effects of the spectral dependence of the surface albedo on the model calculations in section [ 14 Figure 4. The shortwave surface albedo for the three clear-sky days derived from upward and downward pointing unshaded pyranometers. The thick solid, dashed, and thin solid lines represent the shortwave surface albedo for October 14, 15, and 18, 1995, respectively.

6 25,886 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE aerosol properties were not made during the experi- The impacts on the surface irradiance due to sulfate and ment, we used the Pennsylvania State University Sun soot aerosol envelop the uncertainties in the surface irphotometer to measure the direct beam shortwave irradiance in a 2øfield of view at wavelengths of 400, radiance due to uncertainties in the properties of the aerosol for a fixed extinction optical thickness. Based 441, 519, 670, 872, and 1029 nm with a nominal band on prior aerosol studies [Delany et al., 1973; Huser et width of 20 nm for each channel. The total atmo- al., 1981] and personal observations the site during spheric extinction optical thickness at each wavelength ARESE, the most plausible aerosol composition is minwas recovered from the direct beam measurements by eral aerosol, which is weakly to moderately absorbing. application of Bouguer's law. To obtain the aerosol op- Note that the properties of soot that we used are estical thickness from the extinction optical thickness, the sentially equivalent to the properties of the particulates Rayleigh optical thickness, deduced from the surface that are generated by diesel engines; hence it is much pressure, was subtracted from the extinction optical more absorbing than typical aerosol that is generated by thickness at each wavelength. The Rayleigh optical biomass burning and unlikely to be a significant comthickness r t was obtained from [Hansen and Travis, ponent of aerosol in rural Oklahoma. The retrieved 1974] lognormal distributions that we obtained using these aerosol types are consistent with the results of Whitby P [1978], Patterson and Gillette [1977], and Twitty and rr -- --{ A-4(1 q A-2 q A-4)}, P0 (5) where p mbar, p is the atmospheric pressure at the ground in millibars, and A is the wavelength in micrometers; the error in the Rayleigh optical thickness is negligible [Young, 1981; Telllet, 1990]. At this point we assumed that the remaining optical thickness at each wavelength was due to the effect of aerosol present in the atmosphericolumn. Because the aerosol optical thickness values were typically uniform in the morning with a slight increase in the afternoon, for each day we generated two to three sets of average aerosol optical thicknesses as a function of wavelength, correspondingly roughly to the morning, noon and afternoon periods. We then applied the algorithm of King et al. [1978] to these sets to obtain a particle size distribution for the aerosol. From these distributions, we were able to obtain the mode radius and the standard deviation of an assumed lognormal size distribution for the aerosol [Whitby, 1978]. Since we had no composition information, we carried out size distribution retrievals for three aerosol types: sulfate, mineral and soot. In each case, we used the refractive indices provided by d'almeida et al. [1991]. Weinman [1971] for sulfate, mineral and, soot aerosols, respectively. To minimize the propagation of errors from the size distribution retrievals into our model irradiance calcu- lations, the actual measured aerosol optical thickness values averaged over a 30 min period centered on the time of interest are used in the irradiance calculations rather than those optical thicknesses derived from the retrieved size distributions using Mie theory. In other words, the aerosol optical thicknesses used in the model are constrained by measurements; at a given time, we used the same aerosol optical thickness regardless of the type of aerosol used in the model. Since the aerosol optical thicknesses are constrained by the Sun photometer measurements, uncertainties in the retrieved size distribution parameters lead only to uncertainties in the aerosol asymmetry parameter and single-scattering albedo. The shapes of mineral and soot particles are not spherical. Hpwever, Mishchenko et al. [1995] showed that the errors introduced into the single-scattering albedo and asymmetry parameter by the use of the spherical particle assumption are small. Hence as long as the measured aerosol optical thickness is used in the Table 3. Retrieved Aerosol Optical Properties at a Wavelength of 545 nm Sulfate Mineral Soot Date Time, UT r g w g w g Oct. 14, Oct. 14, Oct. 15, Oct. 15, Oct. 15, Oct. 18, Oct. 18, Oct. 18, Here r, g, and indicate averaged optical thickness, asymmetry parameter, and single scattering albedo, respectively. Since r is constrained by measurements, it remains constant for all three aerosol types.

7 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,887 irradiance computations, the error introduced by assuming spherical particles is small. Therefore all particles are assumed to be spherical and Mie theory is used to compute the asymmetry parameter and the singlescattering albedo from the retrieved lognormal distributions (Table 3). (The variations of the single-scattering albedos and asymmetry parameters in Table 3 are due to variations in the retrieved aerosol size distributions.) Even if there are large errors in the retrieved aerosol size distributions, the resulting errors in the values of the asymmetry parameter and single-scattering albedo are not necessarily large because only the shape of the size distribution, and not the absolute number densities of the aerosol particles in the distribution, affects these parameters. For retrieved size distributions that were multimodal, we used only the single mode radius closest in size to the wavelength of the incident radi- ation ( 0.5 / m) for the single-scattering albedo and asymmetry parameter calculations because that mode contains the most effective scatterers [Twomey, 1977]. Since the Sun photometer measures the optical thicknesses at only six wavelengths, we used the Lundholm relation -. (6) where,k is the wavelength (/ m) and c and are free parameters determined by a fit to the Sun photometer data, to estimate values of the aerosol optical thickness throughout the shortwave spectrum (Figure 5). (The Lundholm relation is often referred to as the ngstrsm , I ( U. UI:i - 0 0, o. OOdo,, 015 I 1.5 Wavelength (!.Lm) Figure 5. The aerosol optical thickness from 1800 to 1900 UT October 14 as a function of wavelength. The asterisks represent the mean optical thicknesses obtained from the Sun photometer data, while the pluses represent the standard deviations in the optical thicknesses during this period. A curve fit to the optical thicknesses derived from the Sun photometer measurements leads to the relation -(,k) = 0.026,X -x'2, which is shown by the solid line. The open circles represent the mean aerosol optical thicknesses obtained from the multifilter rotating shadowband radiometer aerosol retrievals. relation, although /[ngstrsm[1929] acknowledges that he did not initially develop it.) To further verify that the Sun photometer derived optical thickness values are reasonable, we also plot in Figure 5 values derived from multifilter rotating shadow-band radiometer (MFRSR) measurements [Harrison et al., 1994]. The aerosol optical thickness values, measured independently by these two different instruments, agree relatively well so we conclude that there are no gross errors in the aerosol optical thickness retrievals. 4. Model Calculation of the Downward Shortwave Surface Irradiance 4.1. The 52-Stream Radiative Transfer Calculations We used a 52-stream radiative transfer method based on the numerical algorithm of Toon et al. [1989] to compute instantaneous d9wnward shortwave irradiances at 5 min intervals for the three clear-sky days. Inputs to the model were derived from the measurements of the aerosol properties, atmospheric state, and surface albedo that we described in section 3. We incorporated the solar insolation at the top of the atmosphere provided in MODTRAN3 [Kurucz, 1995]. The model atmosphere was divided into 250 m thick layers from the surface up to km, a 1.25 km thick layer from to 17 km, I km thick layers from 17 km to 25 km, 5 km thick layers from 25 to 50 km, and a 20 km thick layer from 50 to 70 km. The 1.25 km thick layer from to 17 km was an artifact of the way in which we combined the mid-latitude atmospheric profile with the sounding data. For the vertical distribution of the aerosol, we assume that aerosol is evenly distributed throughout a planetary boundary layer with a depth of I km. The Rayleigh optical thicknesses for each model layer are obtained from (5) by differencing the optical thicknesses that are computed from the pressures of neighboring layers. An important feature of the radiative transfer model calculations is the incorporation of a new spectral integration scheme based on k distribution and correlated-k techniques e.g., [Goody and Yung, 1989; Fu and Liou, 1992]. In developing this scheme, we divided the entire solar spectrum from 0.24 to 4.6 / m into 32 intervals. The new scheme incorporates gaseous absorption by water vapor, including the water vapor continuum, carbon dioxide, ozone and oxygen [Karo et al., 1997]. The wavelength dependent absorption cross sections of these species are generated from the HITRAN database [Rothman et al., 1987] using the line-by-line code developed by Clough and Iacono [1995] at a range of temperatures, pressures and water vapor amounts that attempts to cover the full range of possibilities that occur in the atmosphere. In each spectral interval, these cross sections are sorted into cumulative frequency distributions, which are quadratured to produce sets of absorption cross sections. The number of quadrature points

8 25,888 KATO ET AL.: CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE was selected by ensuring that the averaged transmission from the quadrature method agreed with that from line- by-line computations to better than 1% in all cases. The correlated-k technique is used to compute the transmission for each spectral interval through an inhomogeneous layer based on look-up tables that contain these quadratured gaseous absorption cross sections. missivity provided by the absolute solar transmittance interferometer (ASTI) Uncertainties in the 2-Stream Model The ASTI is a solar tracking interferometer that measures the direct beam radiance in a 0.25øfield of view Computations centered on the solar disk at spectral wavelengths from Estimating the error due to neglect- 1 to 5 / m with a resolution of 1 cm -1. The instruing polarization. Recent studies by Mishchenko et ment was operated for several weeks at the ARM SGP al. [1994] and Adams and Kattawar [1993] show that significant errors can be introduced into radiance calculations if the state of polarization is neglected. However, the magnitude of the error introduced into modelderived clear-sky surface irradiances by neglecting pocentral facility in support of the ARESE and other experiments. The instrument was operating on October 8, 1995, which was a clear day. To obtain an estimate of the atmospheric transmissivity from the ASTI that we can compare with the model-derived transmissivities, larization is not discussed. The magnitude of this error we must take into account the fact that the ASTI field can be evaluated by numerically integrating the analyt- of view is limited to a fraction of the solar disk. The ical solution for a single layer given by Chandrasekhar ASTI views only the central region of the Sun where and Elbert [1954] over a hemisphere and comparing the resulting irradiances with those computed by the twothe radiance is significantly larger than toward the limb of the Sun; the drop in solar radiance away from the stream model. Since our tow-stream radiative transfer model for this single layer case is identical to the twostream model of Liou [1974], we compared the transmission Tc of a homogeneous layer obtained from the expression of Chandrasekhar and Elbert with the transmission Tl obtained from Liou. Defining the fractional error as we find that the two-stream error- (Tl - Tc)/Tc, (7) solution overestimates the transmissivity for all solar zenith angles and the error increases with increasing solar zenith angle. Because the degree of polarization at the zenith and the magnitude of the diffuse irradiance increase as the solar zenith angle increases, we would expect the error introduced into the model by neglecting polarization to increase with the solar zenith angle. The magnitude of the error, however, is small; the fractional error is less than 2% of the diffuse field irradiance at the lowest solar zenith angles, which amounts to no more than approximately 2 W m -2. Because the solar radiation incident at the top of the atmosphere is not polarized, the direct beam irradiance at the surface is not polarized, and any effect due to polarization must be contained in the diffuse irradiance. Therefore we conclude that the effects due to neglecting polarization are negligible Estimating the error in the near- error. To test the accuracy of the radiative transfer model treatment of gaseous absorption, we compared the spectral transmissivity of the atmosphere derived from the radiative transfer model with relatively high spectral resolution measurements of atmospheric trans- center of the Sun is known as limb darkening. Therefore the ASTI measured radiances must be decremented by an amount that attempts to model what the ASTI radiance would be if the ASTI viewed the entire solar disk. The multiplicative limb darkening coefficient cf is a function of wavelength and is obtained by numerically integrating the equation [Minnaert, 1953; Pierce and Waddell, 1961] cf(a) = fo (a q- b l su, q- c [1 - tsun ln(1 q- 01/Zsund/zsun ts- ln)]) sund sun ' (s) where sun is the cosine of the angle between the line of sight from the center of the Sun to the ASTI and the solar radius that connects the center of the Sun to the point on the solar surface in question. The factor in brackets is an empirical fit to data that describes the radiance of the Sun both as a function of the location on the Sun through /Zsun and of wavelength through the empirically determined coefficients a,, b,, and c, [Pierce and Waddell, 1961]. Values of cf are 0.88 at 1.0 rn and 0.94 at 2.40 rn; beyond 2.40 rn the coefficient is essentially constant. infrared gaseous absorption. Uncertainty in cal- To obtain an estimate of the downward shortwave diculating gaseous absorption in our model arises both because of the correlated-k assumption and uncertainties in the gaseous absorption cross sections from the rect irradiance at the surface, this limb darkening correction is applied to the ASTI data after the ASTI measured radiances are multiplied by the solid angle of the HITRAN database itself. Moreover, we developed a Sun. These irradiances are integrated over the spectral model of absorption for each gaseous constituent independently for each spectral interval. Combining these intervals used in the model and divided by the total solar insolation across the corresponding spectral inmodels in regions of the shortwave spectrum where tervals to create the final set of transmissivities that two or more gases have significant absorption produces we can compare to transmissivities computed by the

9 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,889 Oct. 08, 1995, 1810 UT,,, i,!?. /,. I "i, i i i i i I i 0.2[ " Wavelength ( m) with the earlier measurements of the solar constant on which the MODTRAN3 solar spectrum is based. With this adjustment applied to the ASTI transmissivities, the overall differences between the measured and modeled transmissivities were significantly less (Figure 6b). Apart from the measurements at the two shortest wavelength intervals, the ASTI-derived transmissivities were quite close to the MODTRAN3-derived transmissivities. The accuracy of the model gaseous absorption can be ascertained by comparing the transmissivities derived from MODTRAN3 with those derived from the two- stream model. The measure of accuracy that we use is given by 0.5 _>, 0.4.>_. _ 0.3 E m 0.2 ß - o.1.e o._ -o Wavelength ( m) Figure 6. (a) Transmissivities of the atmosphere obtained from the absolute solar transmittance inter- ferometer (ASTI) (solid line), the two-stream model (dashed line), and MODTRAN3 (dash-dotted line) between and 4.61/ m. The entire spectral region between and 4.61/ m is divided into 11 bands and the transmissivities are plotted at the center of each band. (b) Differences in the MODTRAN3 (solid line) and two-stream (dashed line) transmissivities relative to the ASTI transmissivities, where we have corrected the ASTI transmissivities by a factor of The solar zenith angle at 1810 UT was 42.5 ø. greater than both model derived transmissivities, and they exceed unity in the two spectral regions from 1.52 to 1.61 / m and 2.15 to 2.28 / m. To make a consistent set of transmissivities for comparison, we multiplied the ASTI results by 0.904, which is the ratio of the MODTRAN3-derived transmissivity (0.940) to the ASTI transmissivity (1.040) in the spectral region from 2.15 to 2.27 / m. The factor is not unity because the ASTI calibration has not yet been reconciled (b) - - (9) n i--1 where T is the transmissivity, n is the number of spectral intervals in the comparison, and the superscripts t and m represent the two-stream model and MOD- TRAN3, respectively. The agreement in these transmissivities is quite good from I to 2 m, where AT is This slight difference in transmissivity is due to neglecting aerosol in MODTRAN3. The relatively poor agreement between the two-stream model and MOD- TRAN3 transmissivities in the 2.28 to 3.00 m spectral region is most likely due to applying the multiplication rule [Goody and Yung, 1989] to the overlapping water vapor and carbon dioxide absorption band in the twostream model. The relatively poor agreements in the spectral intervals from 2.00 to 2.15 m and 3.64 to 3.80 m are due to neglecting absorption by water vapor in the two-stream model. Finally, the relatively poor agreement in the spectral interval from 3.00 to 3.64 m is either due to applying the multiplication rule to the overlapping water vapor and ozone absorption bands or neglecting the absorption by methane in the two-stream model. Using the MODTRAN3 transmissivities to derive the direct beam irradiance at the surface in the spectral intwo-stream model, which includes the measured aerosol terval from to 4.61 m, we find that the irradiance optical thickness (Figure 6a). In Figure 6a, we also at the surface derived from MODTRAN3 is 8.8 W m - show the transmissivities calculated from MODTRAN3 greater than the corresponding irradiance derived from [Kneiz!ts et al., 1988] for the same spectral intervals, the two-stream model. This difference between MODwhere we neglected the presence of aerosol but included TRAN3 and the two-stream model is almost entirely the trace gases CO, CH4, N20, NH3, NO, NO2, SO2, due to the lack of aerosol in the MODTRAN3 calculaand CFC, in addition to H20, CO2, 02, and 03. tions. If we remove the aerosol from the two-stream cal- The transmissivities obtained from ASTI data are culations, the difference between the model calculations is only 1.6 W m -, where the two-stream irradiance is now slightly higher. We also computed the direct beam irradiance by MODTRAN3 in the spectral interval from to 4.61 m, where we again neglected aerosol and included only water vapor, ozone, oxygen,and carbon dioxide. The difference in the irradiance between this result and the calculation including all of the trace gases is 1.5 W m -. Furthermore, the difference between the ASTI and two-stream irradiances, where the aerosol op-

10 25,890 KATO ET AL.: CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE tical thickness was included in the two-stream model runs, is 1.6 W m -2 after we applied the global adjustment to the ASTI data, with the two-stream model derived irradiance being larger. Therefore we conclude that the two-stream model for gaseous absorption exhibits consistency with the ASTI measurements across the near-infrared region of the shortwave spectrum and excellent overall accuracy relative to MODTRAN Estimating the error in the two-stream approximation. To evaluate errors associated with the two-stream approximation, we computed the total and direct beam irradiances using the 52-stream model with and without the 5 assumption, respectively. The diffuse field irradiance is simply the difference between the total and direct beam irradiances. These irradiances are compared with the corresponding irradiances computed by a Monte Carlo radiative transfer model with the same spectral integration scheme, atmospheric inputs, and solar insolation at the top of the atmosphere. The comparison shows that the difference in the total downward irradiance at the surface computed by the 52-stream model is less than 1% greater than the corresponding irradiance computed by the Monte Carlo model. This result agrees with Liou et al. [1988], who show that the error due to the 52-stream approximation is less than 1% when the scattering optical thickness of the atmosphere is small and the solar zenith angle is not large. To estimate the error in the 52-stream calculation that is attributable to the diffuse field, we subtracted the 52-stream model diffuse field irradiance from the Monte Carlo model diffuse field irradiance and averaged the difference over the 3 days. We found that the 52- stream model results are biased high by 2.7 W m -2 averaged over the 3 days with respect to the Monte Carlo model results. This result agrees with the conclusion of Toon et al. [1989] that the error in the diffuse field irradiance due to the 52-stream approximation for the molecular atmosphere is less than 10% when the solar zenith angle is not large Spectral dependence of the surface albedo. The surface albedo used in the model simulations was obtained by taking the ratio of the irradiance measured by a downward pointing pyranometer to the irradiance measured by an upward pointing pyranometer. The actual surface albedo, however, has a wavelength dependence that is a function of the surface type. During ARESE, the upward and downward pointing pyranometers were located over pasture. Inspection of the surface albedo versus wavelength for vegetation [Rock et al., 1994; Vogelmann and Moss, 1993] and soil [Irons et al., 1989] shows that the albedo in the visible spectral region is generally smaller than at longer wavelengths, especially for vegetated surfaces. This would suggest that the surface albedo in the visible region of the shortwave spectrum is less than the broadband albedo. Since scattering by the atmosphere in the near-infrared spectral region is less than that in the visible, decreasing the surface albedo in the visible and increasing it in the near-infrared spectral region reduces the amount of energy scattered back to the surface from the atmosphere. Consequently, taking into account the spectral dependency of the surface albedo reduces the model downward shortwave irradiance at the surface. To test the magnitude of this effect, we incorporated into the 52-stream model the spectral dependence of the surface albedo of vegetated ground [Rock et al., 1994] and soil [Irons et al., 1989]. To keep the shortwave surface albedo the same as the observed albedo value, we scaled the magnitudes of the two spectrally varying surface albedos until they matched the measured surface albedo at local solar noon. Incorporating these spectrally varying surface albedo values into the model, the average surface insolation Ft a averaged over the 3 days dropped by 3.6 and 3.9 W m -2 for vegetation and soil, respectively Wavelength dependent solar constant. In our current 52-stream model, we have incorporated two different data sets that provide the solar insolation at the top of the atmosphere as a function of wavelength. One solar spectral irradiance curve is derived from Thekaekara [1970] and the second one is from Kurcsz [1995]. The Kurcsz [1995] spectrum is incorporated into MODTRAN3 [Kneizys et al., 1988,] and it is the solar spectrum that we used in all of the model calculations. To test the sensitivity of the model results to the solar spectrum, we renormalized the solar data of Thekaekara [1970] to the Kurcsz value of W m -2. The surface irradiance due to using the data of Thekaekara [1970] was 1.8 W m -2 lower than using the data of Kurcsz [1995] at 1800 UT on October Comparison of Modeled and Measured Downward Shortwave Clear-Sky Irradiances 5.1. Total Shortwave Irradiance Comparisons We performed a detailed comparison between measurements and model calculations for the three clear-sky days selected from the ARESE period. The aerosol optical thicknesses at 0.519/ m ranged from 0.04 to 0.13; the values around local solar noon on October 14, 15, and 18 were 0.05, 0.05, and 0.13, respectively. Since the actual aerosol composition was unknown for each day, we performed three sets of model calculations for each 5 min time period, where each calculation used the properties of one of the three aerosol types discussed earlier. For the comparison, we use the same notation defined by (1), (2), and (3); the subscripts x and y represent the molecular atmosphere (ma), sulfate aerosol (su), mineral aerosol (mi) or soot aerosol (so) model calculations in addition to the radiometer sets defined earlier. As a standard for comparison, we chose the computed irradiance for a molecular atmosphere, i.e.,

11 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,891 (a) Oct. 14, 1995 (b) Oct. 15, 1995 (c) Oct. 18, i i i i i i i i 8 -o.o5 i ', , v, O 14 16', Figure?. The absolute and fractional differences of the modeled and measured downward shortwave irradiances at the surface relative to the computed downward shortwave irradiance of the molecular atmosphere. The thin solid lines represent the differences of the model irradiances based on one of the three aerosol types (sulfate, mineral and soot). The magnitudes of the absolute and fractional differences for sulfate and soot aerosol are the smallest and largest, respectively, at all times over all 3 days. The thick line represents the absolute and fractional differences of the measured irradiance. The aerosol size distribution in the model calculations was changed at times that are indicated by a "v" on the abscissa. an atmospheric column with the observed surface pressure and water vapor profile, but with no particles. We compare the molecular atmosphere model results both to the total irradiance measurements and the model re- sults derived from the three aerosol types; that is, we for the 34 W m -2 discrepancy, we independently incompute AFxt,rna and fxt,rna (X-- ms, su, mi, so, where creased the column water vapor and ozone amounts, as ms indicates the best set of measurements discussed at the end of section 2). 'The results for October 14, 15, and 18 are illustrated in Figures 7a, 7b, and 7c, respectively. The conclusion drawn from this comparison is that none of the model results based on a single aerosol type accurately reproduces the measured irradiances consistently for all three days. For example, the model results that are based on a soot only aerosol agree with the measurements when the aerosol loading is moderate on October 14 and 15. When the aerosol loading is large, however, soot produces surface irradiances that are too small. Both sulfate and mineral aerosol produce surface irradiances that are too large compared with the measurements for all three days. The larger fractional errors at large solar zenith angles are due to dividing by a smaller F a, which decreases the solar zenith angle increases. The modeled irradiance for mineral aerosol falls outside of the measurement uncertainty of +1.5%. The difference AFtmi,ms averaged over the three days is 34 W m -2, which is 5.0% relative to the measured average insolation. To test if errors in the model input data could account well as the aerosol optical thickness, in the model by the amounts illustrated in Table 4. As Table 4 illustrates for October 14, the resulting changes in the surface irradiances are considerably smaller than the discrepancy. Gross errors in the water vapor are an unlikely candidate for causing the discrepancy. To match the model irradiance to the measured total surface irradiances at local solar noon on October 14, the column water vapor amount must be increased by a factor of 3 from 0.91 to 2.91 g cm -, which is neither a plausible amount for this day nor a plausible error in the water vapor measurements. When the standard mid-latitude summer ozone profile is used in the model computations for October 14, which corresponds to a 16% increase of the column ozone amount, F a decreases by 3.4 W m -. In addition, a 10% increase in aerosol optical thickness decreases F i by 1.8 W m - for October 14. Therefore errors in the column water vapor and ozone amounts, as well as the aerosol optical thickness, used as inputs

12 25,892 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE Table 4. Summary of Sensitivity Studies Discussed in Sections 4 and 5 Item Perturbation Difference in Irradiance, W m -2 Input data Water vapor amount :t:10% Ozone amount +16% Rayleigh optical thickness Extinction optical thickness 10% Model approximation Polarization Two-stream Trace gas absorption Surface albedo Solar constants neglected neglected spectral dependence spectral dependence Difference Direct beam model- measurement Diffuse field model- measurement :t: negligible 1.8 negligible 2.7 negligible 3.9 negligible Numbers are averaged over 3 days except the sensitivity studies of input data, which are 1 day averages for October 14, to the model lead to changes in the surface irradiances extremely large with the model significantly overestithat are significantly less than 34 W m -2. mating the measurements by more than 40% (Figure 9). As Figure 9 also shows, the measured diffuse fields on 5.2. Direct Beam Shortwave Irradiance October 14 and 15 are close to the model diffuse field Comparisons To assess the accuracy of the 2-stream direct beam irradiances across the shortwave spectrum from 0.3 to 4.6/zm, we removed the assumption from the model. The resulting model direct beam irradiance should be close to the measured direct beam irradiances if the model treatment of gaseous absorption and the measured extinction optical thickness are accurate. Comparisons of the model direct beam irradiances with the irradiances of a molecular atmosphere. One interpretation of this result is that the photons removed from the direct beam by aerosol particles must be either absorbed or scattered back to space. Since aerosol particles are predominately forward scatterers, this interpretation actually implies almost complete absorption of photons during extinction events, which is the case in the soot-based model results where the single-scattering albedos are extremely small. Clearly, in this study the measurements are illustrated in Figure 8. Since the field of view of the pyrheliometer is 5.7øand the aerosol optical thickness was relatively small during the three clear-sky days, the error in the direct beam measure- ments by the pyrheliometers due to forward scattering by aerosol and air molecules into the instrument field of view is less than 1% [Box and Deepak, 1979]. In fact, based on a Monte Carlo simulation at 1800 UT on October 14 when the aerosol optical thickness at /zm is 0.05, only 0.2% of the total number of photons recorded in the forward 5.7 øcone have undergone a scattering event. As Figure 8 demonstrates, the direct beam irradiances computed by the two-stream model are in very good agreement with the measurements for all 3 days. The average measure direct beam irradiance between 1600 to 2000 UT for the 3 days is 612 W m -e, while that computed by the two-stream model is 615 V 5.3. Diffuse Field Shortwave Irradiance Comparisons In contrast to the direct beam irradiances, the fractional differences between the modeled diffuse field ir- radiances for mineral aerosol and the measurements are major discrepancies between the model results with realistic values of the single-scattering albedo and measured downward shortwave irradiances at the surface are in the diffuse field Diffuse Field Narrowband Irradiance Comparisons We would expect the discrepancy between the modeled and measured irradiances to occur primarily at visible, or shorter, wavelengths, and not in the near- infrared spectral region, because the fraction of the diffuse field that is in the near-infrared region of the spectrum is small. To address this issue, we use the MFRSR measurements of the diffuse and total surface irradi- ance in four 10 nm wide bands centered at wavelengths of 0.415, 0.499, 0.644, and 0.860/zm. Using the Langley technique, we first determine the irradiances in the four bands that would be measured by the MFRSR at zero airmass; these irradiances correspond to the top of the atmosphere irradiances for each of the four bands. Using these top of the atmosphere irradiances, the total and diffuse downward surface irradiances for each of the four bands are computed using the 52-stream radiative transfer model. The model includes scattering

13 ß, KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,893 0 (a) Oct. 14, 1995 (b) Oct. 15, 1995 (c) Oct. 18, loo -12o ß =_-O.lO ' o _ u_ O '8 2' T'rme (UT) Figure 8. The absolute and fractional differences of the modeled (thin solid line) and measured (thick solid line) direct beam irradiances relative to the direct beam irradiances of the molecular atmosphere. The absolute and fractional differences of the Monte Carlo modeled direct beam irradiances are shown by asterisks. by atmospheric molecules and scattering and absorption by one of the three types of aerosol with optical thicknesses constrained by the Sun photometer measurements (section 3). We then compare the modelderived to MFRSR-derived diffuse-total ratios, defined as the ratio of the diffuse irradiance to the total irradiance, to determine if the model diffuse-total ratios based on any one of the aerosols can reproduce the measurements. As Figure 10 demonstrates, soot produces modelderived diffuse-total ratios that are close to the ob- servations at two of the four wavelengths but are substantially low at the longest wavelength. The diffusetotal ratios based on the properties of mineral or sul- fate aerosol are too high for all four wavelengths. Since the MFRSR-derived diffuse-total ratio utilizes the same detector, the ratio does not depend on the calibration constant of the detector. One possible error in the diffuse-total ratio may be due to the slight underestimate of the MFRSR-derived extinction optical thick- nesses compared with the Sun photometer (Figure 5). The MFRSR-derived extinction optical thicknesses are based on the direct beam irradiances that are in turn the difference between measurements of the total irradiance and the diffuse field irradiance. MFRSR-derived extinction optical thicknesses that are small compared with Sun photometer derived optical thicknesses imply that the diffuse field irradiances measured by the MFRSR are too small. However, we estimate that the uncer- tainty in the MFRSR-derived diffuse-total ratio is less than 2%. The model diffuse-total ratios based on soot are within this error at 499 nm wavelength, but they progressively shift from an overestimate to underestimate of the MFRSR diffuse-total ratios as the wavelength increases. This trend implies that even if the error is much greater than the above estimation, model diffuse-total ratios based on soot cannot reproduce the MFRSR diffuse-total ratios unless the error in MFRSRderived diffuse field is wavelength dependent, which is highly unlikely. 6. Discussion During the ARESE period, three of the five independent sets of measurements of the downward shortwave irradiance at the surface agreed to within the expected accuracy of the instruments. Our major finding from comparing the 52-stream model downward shortwave irradiances to these three sets of measurements is that the model irradiances are 34 W m -2 higher than the measured irradiances from 1600 to 2000 UT over the three clear-sky days. An analysis of the direct beam and diffuse field irradiances indicates that the modeled and measured direct beam irradiances agree to within 3.4 W m -2, while the corresponding diffuse field irradiances are different by 30.3 W m -2. The difference between the modeled and measured direct beam irra- diances amounts to less than 1% of the measured di-

14 ß 25,894 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE loo (a) Oct. 14, 1995 (b) Oct. 15, 1995 (c) Oct. 18, , v,, V ¾, Figure 9. The absolute and fractional differences of the modeled and measured diffuse field irradiances relative to the diffuse field irradiances of the molecular atmosphere. The thin solid lines represent the differences of the model irradiances based on one of the three aerosol types (sulfate, mineral, and soot). The magnitudes of the absolute and fractional differences for sulfate and soot aerosol are the largest and smallest, respectively, at all times over all 3 days. The thick line represents the absolute and fractional differences of the measured irradiances. The aerosol size distribution in the model calculations was changed at times that are indicated by a "v" on the abscissa. The absolute and fractional difference of the Monte Carlo modeled diffuse field irradiances are shown by asterisks. rect beam irradiance and can easily be accounted for by errors in the aerosol extinction optical thicknesses and the column amounts of water vapor and ozone (Ta- ble 4). The discrepancy of 30.3 W m -2 in the diffuse field, however, amounts to -40% of the measured diffuse field irradiances and cannot be accounted for by errors in the model inputs. The errors in the 52-stream model calculations of 6.6 W m -2 (Table 4) reduce but do not eliminate the model bias. Estimating the errors in the model diffuse field irradiances due to aerosols is difficult, because the compositions and sizes of the aerosol particles are unknown. The soot-based model diffuse field irradiances on two of the days are in good agreement with the measured diffuse field irradiances. The single-scattering albedo that we used for the soot, however, is not appropriate for the DOE ARM central facility. For example, a study of the Kuwait oil fires [Weiss and Hobbs, 1992] shows that the single-scattering albedos of particles from black oilfire plumes are 0.35 to 0.40 near the plumes and they quickly increase with distance from the plumes. A further constraint on the aerosol composition is that it must have physically realistic particle sizes and number densities. For example, consider the inversion of the Sun photometer optical thicknesses on October 14 to obtain the aerosol size distribution. The retrieval produced a size distribution with a mode radius of 0.03 / m and a standard deviation of 1.77 for soot particles, while it produced a size distribution with a mode radius of 0.64 / m and a standard deviation of 1.37 for mineral aerosol. The single-scattering albedos calculated by Mie theory for these two sets of aerosol size distribution were 0.40 and 0.90 for soot and mineral aerosol, respectively, at a wavelength of um. Since the absorption cross section for an absorbing particle small compared with the incident radiation wavelength is proportional to its volume, while the scattering cross section of the same particle is proportional to the square of its volume [Bohren and Huffman, 1983], the single-scattering albedos of absorbing particles decrease rapidly as their sizes become small compared with the incident radiation wavelength. Therefore the extinction due to an absorbing particle small compared with the incident radiation wavelength is dominated by absorption. In addition, the overall extinction cross section of any particle small compared with the wavelength decreases with decreasing particle size. Therefore, if we were to use aerosol distribution parameters for mineral

15 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25, (a) 415 nm (b) 499 nm (c) 664 nm (d) 860 nm o ß o _o_ lo Figure 10. Narrow-band diffuse-total ratios, i.e., the ratio of the downward diffuse field irradiance to the downward total irradiance, on October 14 derived from MFRSR measurements (thick solid line) and 52-stream model calculations that incorporate sulfate, mineral and soot aerosols (thin solid lines). The MFRSR channels are 10 nm wide and they are centered at (a) 415 nm, (b) 499 nm, (c) 644 nm, and (d) 860 nm. The largest model diffuse-total ratios are for sulfate, while the smallest model ratios are for soot. The fractional differences are for the model diffuse-total ratios relative to the corresponding MFRSR ratios. aerosol that corresponded more closely to or smaller than those for soot, e.g., a mode radius of 0.01/ m, the single-scattering albedo for this mineral aerosol would be on the order of 0.09 for a wavelength of 0.545/ m, which is much less than the soot single-scattering albedos derived above. If we assume that these particles are distributed in the planetary boundary layer, the concentration of these small particles would have to be on the order of 108 cm -3 to produce the measured aerosol optical thickness. A mineral aerosol with such a small mode radius and high concentration, however, is completely unrealistic [Twomey, 1977]. Without such physical constraints on the aerosol properties, any kind of an error analysis becomes untenable. The measured diffuse field irradiances on 2 of the 3 days are comparable to what would be expected from a molecular atmosphere alone. Incorporating the properties of a weakly absorbing aerosol with realistic singlescattering albedos and asymmetry parameters into the model will produce model diffuse field irradiances that are high compared to the measurements. The only way to reduce the diffuse field irradiance, while not altering the direct beam irradiance, is to reduce the total singlescattering albedo and asymmetry parameter of some, or all, atmospheric layers used in the model. Using a soot aerosol or a mineral aerosol with a high density of small particles can lead to single-scattering albedos and asymmetry parameters that produce model results in agreement with the measurements; however, based on previou studies of Southern Great Plains aerosol, these types of aerosols are not appropriate for the atmosphere above the DOE ARM central facility in north central Oklahoma. Also, the MFRSR results at 415 nm (Figure 10a), where the diffuse field produced by assuming soot aerosol is still greater than the observed diffuse field, lead us to conclude that no aerosol that is plausible at the site can reproduce the MFRSR-derived diffuse-total ratios. These results suggest that the discrepancy between the modeled and measured diffuse field irradiances is due to a gaseous absorption not included in the 52- stream model. The wavelength dependent differences between the model and MFRSR diffuse-total ratios dis- cussed in section 5.4 suggest that the absorption cross section of this gas increases from midvisible to shorter wavelengths. If we postulate the existence of such a gaseous absorption process, the Sun photometer derived optical thickness now has two components: r xt - r + ra, (10) where text is the extinction optical thickness inferred

16 25,896 KATO ET AL.: CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE from the Sun photometer measurements after subtracting the Rayleigh optical thickness, -a is the aerosol optical thickness, and -g is the absorption optical thickness due to the hypothetical gas. Since the extinction optical thickness -ext is fixed by the Sun photometer measurements, the direct beam irradiance is not altered by introducing the absorbing gas. Rather, the aerosol optical thickness decreases. If errors in the model and the uncertainties in the measurements are taken into ac- count, this gas must absorb 14 to 34 W m -2 in order to eliminate the discrepancy. To absorb 14 to 34 W m -2 from the shortwave spectrum, however, any potential gas, or gases, must have relatively large values of the absorption cross section and high concentrations. 7. Conclusions A comparison of the downward shortwave irradiances at the surface measured by three independently calibrated unshaded pyranometers and two reconstructed irradiances from two sets of corrected direct beam and diffuse field measurements reveals that they vary over a 5% range, where the variation is due to differences in the calibration coei cients. Importantly, the two sets of reconstructed irradiances, whose absolute calibration is based on two cavity radiometers, are consistent with each other and the BR unshaded pyranometer measurements to within instrument accuracies of -1.5%. A comparison of the computed downward shortwave irradiance at the surface from the 52-stream model to polated extinction optical thickness of the atmosphere, that are input to the model are accurate. In contrast to the close agreement between the mod- eled and measured direct beam irradiances, the 52- stream model diffuse field irradiances based on aerosols with realistic single-scattering albedos are significantly higher (30.3 W m -2) than the BR and SIROS shaded pyranometer measurements. Since scattering in the near-iniyared spectral region is negligible in a clearsky atmosphere, this discrepancy in the diffuse fields indicates that the source of the discrepancy between the modeled and measured downward shortwave irradi- ances is in the visible spectral region. Assessing possible sources of error in the 52-stream model diffuse fields, we conclude that the two-stream approximation and the neglect of the spectral-dependence of the surface albedo leads to biases of 2.7 and 3.9 W m -, respectively, when the errors are averaged between 1600 and 2000 UT over the three days. Neglecting the state of polarization introduces a negligible error in the downward shortwave irradiance at the surface. The effect of aerosol composition on the computed downward shortwave irradiance at the surface is large even when aerosol extinction optical thicknesses are fixed by Sun photometer measurements. Modeled downward shortwave diffuse field irradiances computed by using any physically reasonable aerosol optical properties and number concentrations, however, fail to match the measured irradiances when the aerosol loading is not large because the measured diffuse field is already as small as the model diffuse field for a the measured irradiance reveals that the model overestimates the downward irradiance by 5%. The aver- molecular atmosphere. In addition, comparison beage difference between modeled and measured irradi- tween model- and MFRSR-derived narrow-band ratios ance between 1600 and 2000 UT over the three clear- of the diffuse field irradiance to the total irradiance insky days is 34 W m -2 for an aerosol with a realistic dicates both that the measured diffuse field irradiance single-scattering albedo. Since the measurements were taken in a rural area, mineral aerosol is the most likely aerosol present at the site and we included its properties in the 52-stream model calculations. The current analysis demonstrates that errors in the water vapor and ozone amounts, as well as the extinction optical thicknesses, are not the source of the 34 W m -2 discrepancy. Comparing reis smaller than the computed diffuse field irradiance and that this difference has a spectral signature. A solution to these problems in the model diffuse fields, without requiring the presence of aerosol with a single-scattering albedo as low as 0.3, is to postulate the existence of some gaseous absorption processes at visible wavelengths that we have yet to incorporate into the model calculations. This conclusion, of course, sults of MODTRAN3 simulations that we performed relies on the accuracy of the data that we used in this with and without trace gas absorption, we conclude study. These data were obtained by two cavity radiomethat the impact of trace gases on the downward surface irradiance is negligible. Close agreement between ters, two shaded pyranometers and one unshaded pyranometer, as well as ratios of irradiances measured by a MODTRAN3 and two-stream model direct beam irra- MFRSR. We cannot find any logical reasons to suspect diances indicates that our treatment of gaseous absorption using k distribution and correlated-k techniques is accurate. In addition, the small differences between the these data beyond the range of uncertainties that we discussed in this paper. There is a growing body of evidence that our untwo-stream model direct beam irradiances and direct derstanding of shortwave clear-sky radiative transfer is beam measurements by the BR and SIROS pyrheliome- incomplete [Charlock and Alberta, 1996; Wild et al., ters (3.4 W m-2), as well as the ASTI (1.6 W m-2), 1995]. Our current results, indicating that the model provide strong evidence that our treatment of gaseous diffuse field irradiances overestimate the measurements, absorption is accurate. Accurate two-stream model direct beam irradiances also indicate that the water vapor and ozone profiles, as well as the measured and intersupport this view. Even though the current study is based on only 3 days of data, we have confidence in the analysis because we attempted to accurately model

17 KATO ET AL.' CLEAR-SKY SURFACE SHORTWAVE IRRADIANCE 25,897 the irradiance for each day using an aerosol with reasonable properties, and for each day we found that the model diffuse fields were too large. Introducing a new gaseous absorption process into the model, we were able to significantly reduce the model bias. Although the multiple instruments at the DOE ARM central facility are what allowed us to carry out this detailed assessment, it is evident that additional observations are required to completely resolve the issues raised here. Spectrally resolved solar irradiance measurements would be extremely helpful. Recently, some measurements of this type were made at the DOE ARM central facility and we hope that they begin to provide additional insight into the source of our current model biases. Finally, aerosol size distribution and composition measurements are necessary to constrain the effects of aerosol composition; such measurements are promised for the DOE ARM central facility. Acknowledgments. We thank C. Whitlock and G. Schuster of NASA Langley for supplying their data for our study. We also thank S. Clough and E. Mlawer of AER Boston for useful suggestions related to the correlated-k assumption, G. Anderson of Phillips Laboratory for guidance for using the MODTRAN3 radiative transfer code, C. Pavloski of Penn State for helping with using King's algorithm, J. Barnard of PNL for useful information about the MFRSR data, and L. Ramsey and R. Wade of Penn State for advice regarding limb darkening. W. Wiscombe of NASA GSFC, B. Forgan of the Australian Bureau of Mete- orology, A. Vogelmann of Scripps, and two anonymous reviewers provided helpful comments on the manuscript and we are grateful for their contributions. 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