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

a. Basic notions

The direct solar beam irradiance measured by the MFRSR at each time step in ith spectral channel can be represented in the form,

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where μ is the inverse of the airmass (essentially equal to the cosine of the solar zenith angle), τ_i is the atmospheric column extinction optical depth corresponding to the ith channel, and I⁰_i are the top of the atmosphere solar intensities. This means that we take the lamp-calibrated intensities and determine correction factors C_i to the calibration used. The original (lamp) calibration is used only for a rough conversion of counts into watts per meters squared.

The optical depths τ_i can be expressed from (1) as

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Here we introduce the notation

c_iC_i(3)

In the following we use the term “calibration coefficients” for the coefficients c_i.

We will also use the notation τ̃_i for the uncalibrated optical depths:

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In this notation a Langley plot is the plot of τ̃_i/μ versus air mass (1/μ). Examples of such plots are shown in Fig. 2. By assuming stability of τ during the morning and afternoon periods with air masses higher than two and approximating the curves in Fig. 2 with straight lines for these periods, estimates of the calibration coefficient c_i can be obtained as the intercepts of the corresponding lines. However, when aerosol optical depth changes (Fig. 2b), the Langley technique cannot be used to determine the calibration.

The contribution of the Rayleigh scattering is accurately known. We use

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where λ is the wavelength in micrometers, P is atmospheric pressure in millibars, and P₀ = 1013.25 mb is the standard pressure (Hansen and Travis 1974) to remove the Rayleigh contribution from each channel before we begin. This formula has been shown to produce good agreement with exact calculations (Teillet 1990) and be consistent with the results of Bodhaine et al. (1999) for the spectral range of interest. Thus, in the following, τ̃_i refers to optical depths with the Rayleigh contribution subtracted.

Finally, it is necessary to select the data or data interval that is appropriate for analysis. While we have developed several automated cloud-screening procedures, based on the spectral behavior and temporal variability of cloud extinction, we have manually selected the clear intervals on partially cloudy days for this analysis using an interactive program that allows us to edit the data interval to ensure that we are not including thin cirrus.

Once we have selected the data interval for analysis we proceed with the retrieval algorithm, which consists of the following steps: 1) determination of the calibration coefficient and aerosol optical depth in the fifth channel (870 nm), 2) analytical solution of a system of linear (in aerosol optical depth and gas column amounts) equations to retrieve the aerosol size distribution parameters and the aerosol optical depths for all five channels, 3) retrieval of the NO₂ and ozone column amounts (together with the calibration coefficients in the first two channels), and 4) determination of the calibration coefficients in the first five channels.

b. Calibration using direct-to-diffuse ratios and determination of 870-nm channel optical depth

Direct to diffuse ratios present a source of information that is independent of instrumental calibration, provided that both the direct and diffuse intensities are measured with the same detector. The following factors contribute to the diffuse radiation under cloud-free conditions: aerosol optical depth, particle size, and single scattering albedo as well as surface albedo and Rayleigh scattering. In the case of absorbing aerosol, its vertical profile is important as well. Variations of real part of the aerosol refractive index within a typical natural range (1.3–1.6) do not play a significant role (King and Herman 1979). In our algorithm we restrict our use of the diffuse flux measurements to the 870-nm channel since this is the only channel not notably affected by ozone and/or NO₂ absorption, hence the diffuse intensity does not depend on the unknown vertical distribution of these gases.

In a vertically inhomogeneous atmosphere the optical depth derived from the direct beam and diffuse horizontal measurements are not identical since the optical depth determined from the diffuse measurement using a plane-parallel multiple scattering model is an average over all angles. Hence, in comparison with the direct beam optical depth the diffuse optical depth is smoother and changes slower as a function of time than the optical depth derived from the direct beam.

Diffuse flux measurements provide information on both aerosol absorption and the instrument's calibration. Differences in the solar zenith angle dependence of these two effects suggests that they should be separable provided that the aerosol composition is stable over the day and sufficient clear periods exist in the datasets. However, determination of the aerosol single scattering albedo from comparisons between direct and diffuse measurements is problematic (at least for low-altitude sites), because of a clear-sky direct to diffuse discrepancy issue. This discrepancy is an overestimation of diffuse irradiance by radiative transfer models that use as inputs the optical parameters obtained from the direct beam measurements (Kato et al. 1997; Halthore et al. 1998; Halthore and Schwartz 2000). Our modeling of the diffuse beam (assuming conservative scattering) shows that the optical depths inverted from direct to diffuse ratios cannot match the uncalibrated direct beam optical depths solely through the addition of a calibration term. Some additional opacity, with an average optical depth of 0.02, seems to be missing from the diffuse measurements. This discrepancy can be resolved by assuming an unphysical aerosol single scattering albedo of about 0.5. This complicates the retrieval of a physically plausible aerosol single scattering albedo, since real aerosol absorption cannot be separated from the “anomalous” one. In the present work we do not attempt to solve the direct to diffuse discrepancy, instead we use the observed stability of the missing opacity (it appears to be nearly constant not only during the day but also for periods of several months) to improve the direct–diffuse calibration procedure. The stability of the missing opacity allows us to apply Langley-like regressions to the difference between direct beam and direct–diffuse ratio optical depths to obtain the instrument's calibration constant. The validity of this approach has been tested on an exceptionally clear dataset from Davis, California. As described in section 3a, our calibrations agree with those from reliable Langley regressions, while our regression technique is shown to be more conclusive than the ordinary Langley approach for the most of the days studied.

To model the diffuse flux, we perform multiple scattering calculations using the doubling and adding method (Hansen and Travis 1974) with a Henyey–Greenstein phase function. The spectral dependence of aerosol extinction is calculated using Mie theory assuming nonabsorbing aerosol (n_r = 1.4, n_i = 0). King et al. (1978) have shown that aerosol spectral extinction does not significantly vary with aerosol absorption for n_i ≤ 0.03. We investigated the sensitivity to phase function by comparing the Henyey–Greenstein results with those obtained using a full Mie phase function, confirming the fact that retrieval results are not sensitive to the particular functional shape of the phase function. Finally, we run the direct–diffuse calibration procedure in two iterations. As a first guess, we assume an asymmetry parameter of 0.75 then determine the actual particle size by the method described below, and then rerun the calibration routine with the new asymmetry parameter thereby iteratively correcting the calibration coefficient determined in the first step. The effect of aerosol absorption is to alter the direct–diffuse ratio resulting in overestimation of the calibration coefficient and underestimation of aerosol optical depth.

The retrievals are substantially simplified by using the analytical relationship between the direct to diffuse ratio Φ = I_dir/I_dif and the surface albedo (King and Herman 1979):

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where A is the surface albedo; Φ is the direct to diffuse ratio corresponding to this albedo; and Φ₀ to zero surface reflectivity, respectively; and where R = R(τ) is the reflection function integrated over all scattering angles; and θ is the solar zenith angle. It is important to note that I_dir and I_dif are measured using the same spectral filter and detector, thus the calibration constant is cancelled in the ratio Φ.

Figure 3 shows that this calibration procedure works even for days with highly variable optical depth. For many of these days the retrieval of other parameters is impossible, but the optical depth in the 870-nm channel can be estimated. Although the surface albedo is an unknown quantity, the retrieved aerosol optical depth depends only weakly on its assumed value: a reasonable assumption of 0 < A < 50% results in the uncertainty of ±0.01 (shown by shaded area in Fig. 3) in the optical depth inverted from (6). Analytical estimates of the errors caused by the uncertainty in surface albedo were also performed by O'Neill et al. (1989). The method is certainly not applicable in the presence of strong side reflections from clouds and/or bright objects affecting the diffuse irradiance measurements. However, periods with these conditions can be easily detected from the data and removed from the analysis.

c. Regression method for determination of aerosol extinction

The conventional Langley technique does not yield accurate results when aerosol optical depth is changing systematically during the day. However, as shown below, in such cases aerosol spectral extinction properties (determined by composition and particle size distribution) appear to be more stable. Here we describe a new regression technique that is similar to the Langley approach but relies on the spectral stability of aerosol extinction instead of optical depth stability. Philosophically similar methods were introduced by Forgan (1994) and Soufflet et al. (1992) in order to reduce uncertainties in calibration. However the present method is somewhat different both conceptually and in its practical applications.

The a priori reason for assuming stability in aerosol extinction rather than optical depth is that most of the optical depth variability stems from transport. An aerosol “cloud” consisting of particles having the same origin, composition, and size distribution may have a complicated horizontal distribution, which induces high optical depth variability when this cloud passes over a sun photometer. Support for the greater stability of aerosol extinction is found in the regression plots shown in Figs. 4a and 4b that appear to be much closer to a straight line (i.e., the same for the whole day) than the Langley plot for the same day (previously shown in Fig. 2b). Note that these plots are linear when the spectral shape of aerosol extinction does not change, while the optical depth may arbitrarily vary.

In the problem at hand (after the Rayleigh terms are removed), the measured quantities and the quantities to be determined satisfy the following system of five equations:

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Here, τ̃_i is the measured optical depth in the ith channel [Eq. (4)]; q_i = Qⁱ_ext/Q⁵_ext is the Mie-scattering extinction ratio normalized to the fifth (870 nm) channel (by definition q₅ = 1); β_i and γ_i are the effective spectral absorption coefficients for NO₂ and O₃, respectively, weighted by the solar flux and filter response function of each respective MFRSR channel (the coefficients β₅, γ₁, and γ₅ are effectively equal to zero); x_NO2 and x_O3 are respective column amounts of NO₂ and ozone; τ_a is the aerosol optical depth in MRFSR channel 5 (at 870 nm), and c_i are the calibration coefficients [Eq. (3)].

In modeling gaseous absorption we use the room temperature absorption cross-sections for NO₂ measured by Merienne et al. (1995) for wavelengths below 500 nm and by Schneider et al. (1987) for wavelengths above 500 nm. The absorption cross sections for ozone (a reference temperature of 220 K is used) were obtained from E. P. Shettle (1997, personal communication), they are based on the measurements of Anderson and Mauersberger (1992) and Burkholder and Talukdar (1994). The absorption cross-sections for NO₂ and ozone have recently been reviewed and compared with those obtained using the Global Ozone Monitoring Experiment (GOME) flight model (FM) spectrometer. Burrows et al. (1998) find that the average difference between the Merienne et al. (1995) cross sections and the GOME results is smaller than 2%. The cross-sections measured by Schneider et al. (1987) are on average 1%–4% smaller than those measured by the GOME spectrometer. Given the uncertainty in our NO₂ retrievals introduced by ambiguities in the aerosol size distribution (described below), this level of accuracy is more than sufficient for our retrievals. In the 540–640-nm spectral range, our ozone coefficients are 2%–3% higher than those determined using the GOME FM spectrometer (Burrows et al. 1999).

In the above set of equations the explicit dependence on x_NO2, and then on x_O3 can be eliminated. Then by substituting τ_a = τ₅ − c₅μ, and dividing the expressions by μ, the following two equations can be obtained:

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where we use the following notations:

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and i = 3, 4. In the above, b_ij = β_i/β_j and g_ij = γ_i/γ_j are the spectrally weighted NO₂ and O₃ absorption coefficient ratios, respectively. Note that the left-hand side F_i of the Eqs. (12) and (13) contain only measured parameters as expressed by (15) and can therefore be calculated directly from the observed data at each measurement time step (i.e., without any modeling assumptions). Meanwhile, the right-hand sides are linear functions of the argument x = τ̃₅/μ over any time interval where the aerosol extinction parameters q_i do not change (note also that so far no assumptions have been made with respect to the aerosol size distribution).

It is seen from the system of Eqs. (12) and (13) that F_i = A_i when extrapolated to the point x = c₅ for any value of B_i (here and below, i = 3, 4). Accordingly, the A_i represent combinations of calibration coefficients, and are expected to remain constant during the day. The B_i being combinations of aerosol extinction ratios, may change in response to changes that may take place in aerosol spectral extinction due to variations in aerosol size or composition. Representative plots of F_i versus x for a typical clear day are shown in Figs. 4a and 4b. It follows from the above that all points on the plot F_i(x) corresponding to the same aerosol size distribution belong to a straight line with slope B_i passing through the “calibration point” with the coordinates (c₅, A_i). This point, strictly speaking, must be located to the left of the plotted data, since otherwise the aerosol optical depth at 870 nm would have to be negative. Since we actually do not know which points belong to the same size mode, the calibration point cannot be found as the intersection of all such lines. Nevertheless, the general shape of the resulting plots F₃(x) and F₄(x) is such that knowing the x-coordinate c₅ of the calibration point (see the previous section), the values of its y-coordinate A_i can be determined from the condition of the minimal mean deviation of the corresponding functions B_i(x) = [F_i(x) − A_i]/(x − c₅) from their mean values. This minimum is usually well pronounced; that is, the curves in Fig. 4 “point” to the calibration point.

After the calibration point is determined, the time series of the coefficients B₃ and B₄ [Eq. (16)] can be obtained. Note that B_i, being the slopes of the curves in Figs. 4a and 4b, can be estimated, without knowing c₅ by means of a Langley-like regression. This means that the retrievals of the aerosol spectral extinction properties cannot be significantly affected by calibration uncertainties in the aerosol optical depth determination of the previous step of the retrieval algorithm.

d. Retrieval of aerosol size and optical depth in all channels

In our case, the coefficients B₃ and B₄ being the combinations of the (unknown) aerosol extinction ratios q_i are the only available source of information about the aerosol size distribution. This means that one can generally determine no more than two parameters of the aerosol size distribution from this data. Thus, the direct inversion of the aerosol size distribution from the spectral data (King et al. 1978; Shaw 1979b, 1979c; Schmid et al. 1997; Dubovik and King 2000) is not appropriate for our purposes. We note however that our algorithm does not rely on external data sources, while in the cited papers the gas column amounts are either determined from other measurements or estimated from climatology.

It is formally possible to use the coefficients B₃ and B₄ to determine the effective radius r_eff and effective variance υ_eff (cf. Hansen and Travis 1974) of an assumed aerosol size distribution. However, in practical applications, such retrievals are ambiguous because the measured optical depths cannot be uniquely explained with a combination of aerosol, ozone, and NO₂ contributions within the measurement accuracy of the MFRSR. This results in an interplay between aerosol size distribution parameters and NO₂ column amount such that one can simultaneously change the NO₂ column amount and the aerosol size distribution in such a way that the total optical depths in all channels remain unchanged. Fortunately, despite this ambiguity, both aerosols and atmospheric gases still can be characterized, but an accurate determination of the retrieval error bars is necessary for the retrieval products to be useful.

The formal procedure for determining the parameters of the assumed aerosol size distribution can be described as follows. First, Mie theory is used (specifying aerosol complex refractive index) to calculate the extinction ratios q_i for each pair of size distribution parameters. Then, the formulas [Eq. (16)] are applied to create lookup tables for B₃ and B₄ as functions of r_eff and υ_eff. For each observed data point, these tables are used to construct level curves in the (r_eff, υ_eff)-plane corresponding to the values of B₃ and B₄ measured at this point. If these curves intersect, the coordinates of their intersection point are the r_eff and υ_eff of the assumed aerosol size distribution at the time of the measurement. However, for real data no intersection or multiple intersections may occur. Typically, the level curves for B₃ and B₄ intersect only for a small fraction of measurements made during the day. The retrieved effective radii and variances exhibit high point-to-point variability, however, when plotted on the (r_eff, υ_eff)-plane they group tightly along the lines described above (Figs. 5b–d). This suggests a random character of the level curve intersections and their sensitivity to small errors in the measurements and calibrations which requires a modification to the retrieval approach.

We characterize the curve in Fig. 5a by the function r_eff(υ_eff). This function can always be restored given the value of r_eff corresponding to the point of the curve where υ_eff = 0 (actually, we take variance 0.01 to average out the Mie size parameter oscillations). We refer to this r_eff as to “monodistribution radius” since it is calculated under the assumption that all aerosol particles are effectively the same size. To quantify the dependence of our retrievals on the position of the (r_eff, υ_eff)-point on the curve, we perform all retrievals for five such points corresponding to υ_eff = 0.01, 0.1, 0.2, 0.3, and 0.4. We use the difference between the retrievals for different υ_eff to define the error bars due to uncertainties in the size distribution. These errors are typically negligible for ozone column amounts and long-wavelength aerosol optical depths. They are larger for NO₂ column amounts and short-wavelength aerosol optical depths due to the trade-offs between small particle and NO₂ extinction.

The time series of the monodistribution radius can be obtained either from B₃ or B₄ as functions of time (Fig. 6a). The values obtained from B₄ generally coincide with the ones derived from B₃, but are usually noisier, thus we use them primarily as a consistency check.

Once the aerosol size has been determined the aerosol optical depth, at any wavelength, can be calculated from the Mie spectral extinction and the previously determined aerosol optical thickness in the 870-nm channel. Figure 6b shows the aerosol optical depth at 550 nm. In this particular case, it changes during the day violating the conditions for Langley analysis.

e. Retrieval of nitrogen dioxide column amounts

The aerosol optical depths calculated in the previous step are then subtracted from the observed total optical depths in all six channels. The remaining optical depth in the first channel (415 nm) is due to NO₂ absorption, while in the second channel (500 nm), both NO₂ and ozone absorption is present. Calibration uncertainties affect both channels, but NO₂ absorption is separated from calibration effects in the 415-nm channel by means of a Langley-like regression (Fig. 7a). The calibration coefficient c₁ is determined by this procedure together with the NO₂ column amount (Fig. 7b). We use Dobson units (1 DU = 10⁻³ atm-cm = 2.687 × 10¹⁶ molecules cm⁻²) to describe the NO₂ column amount as well as the ozone column amount.

Figures 7a and 7b show that urban [New York City (NYC)] nitrogen dioxide does not exhibit strong diurnal changes that are seen in stratospheric NO₂. Thus, the regression analysis is applicable; but unfortunately, this approach is not very accurate because of the strong interplay between the NO₂ column amount and the aerosol spectral extinction described above and the high variability of NO₂ in the urban New York environment. An uncertainty in the retrieved NO₂ column amount of 30%–50% is caused by our inability to uniquely constrain the variance υ_eff of the aerosol size distribution evident in Fig. 7b. On physical grounds, larger effective variances are likely to be more realistic than υ_eff = 0. Also, neglect of aerosol absorption in the presence of absorbing aerosol also leads to some overestimation of the NO₂ column amount, while not significantly affecting the accuracy of other retrievals.

f. Retrieval of ozone column amounts

The standard approach to retrieve atmospheric ozone column amounts is to use the UV spectral region (Dobson and Brewer spectrometers). Nevertheless, the visible (Chappuis) absorption band has also been widely used to retrieve ozone column amounts (King and Byrne 1976; Shaw 1979a; Flittner et al. 1993; Michalsky et al. 1995). With aerosol removed, in our retrieval method the (uncalibrated) NO₂ absorption contributions are first analytically removed from the 500-nm channel measured optical depth. Then a Langley-like regression technique (Fig. 8a) is applied to obtain both the ozone column amount as function of time (Fig. 8b) and the calibration coefficient c₂. Here we emphasize that the retrieval of the ozone column amount has its own calibration procedure, making ozone retrievals almost independent of the retrievals of aerosol parameters and NO₂. If aerosol particle size does not dramatically change during the day (a condition met for most sites) then the contribution from errors in aerosol optical depth due to calibration errors has the form const. μ, which is corrected during the ozone calibration procedure. (The same is also true for errors in NO₂ calibration, even without any conditions on aerosol particle size.)

This procedure appears to be robust since the retrieved ozone column amount shows little change through the day. The small changes that are seen are mostly due to variations in surface ozone (Kerr and McElroy 1995). Despite large high-frequency variations due to instantaneous instrumental noise shown in Fig. 8b (the data have not been averaged), the mean ozone column amount is a well determined quantity, and column ozone can be retrieved with much better accuracy than NO₂. Moreover, by having filter channels on both the long- and short-wavelength sides of the ozone absorption, it is possible to more effectively separate the ozone and aerosol contributions, unlike the situation for NO₂.

g. Calibration histories and calibration averaging

The method described in this paper provides for the simultaneous determination of the instrument's calibration together with the retrieval of physical quantities. In addition to the calibration coefficients determined in the previous steps, values of c₃ and c₄ can be obtained from A₃, A₄, c₁, and c₂, or directly by subtracting the retrieved optical depths from the measured ones. This information allows us to monitor any changes in the instrument's calibration.

The calibration history of the Goddard Institute for Space Studies (GISS) MFRSR during the period from 1 September 1995 to 27 November 1996 is shown in Fig. 9a (smoothed trends in Fig. 9b). The results show a loss of filter transmittance, approximately by a factor of 3 (assuming detector–electronics stability), for 615-nm and 670-nm channels during the first 200 days of operation, followed by a gradual stabilization. (This poor filter performance led to the replacement of these filters with ion assisted deposition filters in subsequent MFRSRs.) The transmission loss in the 415-nm and 500-nm channels was roughly 20% and 40%, respectively, while the 870-nm channel remained essentially stable. Subsequent laboratory recalibration of the instrument by the manufacturer (Yankee Environmental Systems, Inc.) confirmed these observed trends in filter transmittance. Since filter transmission can change rapidly (over the course of days), determining the calibration from the data on a daily basis allows us to catch these changes as they occur and correct them without compromising retrieval accuracy.

While our retrieval algorithm is designed to rely as little as possible on the values of the calibration coefficients, long-term smoothing allows us to improve the retrieval accuracy by reducing calibration noise that arises by including those days with short clear periods. Long-term smoothing of the calibration is reasonable since the instrument's calibration is not expected to vary significantly on a day-to-day basis. Some temperature-related fluctuations in filter transmission may occur, especially if the instrument head is not properly temperature stabilized. However, based on our comparisons with other measurements [e.g., CIMEL Total Ozone Mapping Spectrometer (TOMS), Brewer spectrometer] we have found that most day-to-day variations in the instantaneous MFRSR calibrations derived from the data are correlated with differences in the retrieval products. This suggests that the variability in the instantaneous calibration coefficients is attributable to uncertainties in the calibration technique, rather than actual instrumental effects, in particular, effects due to changes in the diffuse horizontal measurement due to clouds outside the MFRSR field of view on partially cloudy days.

To control for these situations, the data are reprocessed using smooth approximations of the calibration time series. Figure 9b shows such approximations (made by 5 degree polynomial fits) of the calibration coefficients from Fig. 9a. The method used to average the calibration coefficients must preserve the spectral dependence of the measured optical depths. Otherwise, the averaging will affect the retrievals that rely on spectral differences in optical depths (such as particle size and ozone).

To achieve spectral consistency, we perform calibration averaging and data reprocessing using a procedure that follows the steps of the instantaneous retrieval algorithm. This averaging–reprocessing procedure requires that we repeat the retrievals four times for all days during the selected data period. On the first step, we smooth the 870-nm calibration coefficient c₅ over the time period. Then we rerun the retrievals with the smoothed c₅ to obtain the adjusted values of A₃. These values are then also smoothed over the selected time period, and the retrievals are repeated providing corrections to the value of c₁ that is determined from the calibration of the NO₂ column amount. Next, we reprocess the data (with smoothed values of c₅, A₃, and c₁) to produce adjusted ozone calibration coefficients that are then smoothed before the final reprocessing is performed.

We note that the results of reprocessing, with smoothed calibration coefficients depend on the specific method of smoothing. This dependence is most pronounced for the ozone retrievals. Since we prefer a technique that is less sensitive to the algorithmic details, we apply a weighted average of the instantaneous and smoothed ozone calibration coefficients where the weighting factors are determined from the quality of the instantaneous regression plot.

a. Comparison with instantaneous Langley regressions

We compared our retrieved calibration coefficients and optical depths with those determined by Langley regressions using a particularly clear dataset obtained from the U.S. Department of Agriculture (USDA) ultra-violet B (UVB) Radiation Program (Bigelow et al. 1998) for Davis, California (January–July 1996). Only completely cloud-free days are used in this comparison (Alexandrov et al. 1999b). Comparison between the calibration coefficients for the 870-nm channel derived using our direct–diffuse technique and those determined from Langley regression are shown in Fig. 10a. Both approaches yield similar calibration coefficients and follow the same general trend, but, the instantaneous calibration coefficients determined using our direct–diffuse technique show less variability (due in part to a better agreement between the morning and afternoon regressions) and are therefore more stable. The results of comparisons for the other channels are similar, with the exception of the first channel (415 nm) where the advantages of the direct–diffuse approach are less pronounced due to variations in the NO₂ column amount.

The overall difference between the instantaneous daily mean optical depths obtained by the two methods is relatively small as shown in Fig. 10b. Differences are typically less than 0.01 and do not exceed 0.04 during this period. Since optical depth differences of 0.04 are larger than would be expected from well-calibrated data, we performed additional comparisons. Figure 11 compares the Langley regression to our method for a day (2 June 1996) with good agreement. As can be seen, when both methods are applicable, they yield the same result. However, on two other days, shown in Fig. 12, we see that our method produces stable regressions while the Langley method yields morning and afternoon differences that would most likely exclude the data for 9 May shown in Fig. 12a from further analysis, while Langley analysis of the data for 8 June shown in Fig. 12b converges to yield a calibration coefficient not very different from our result. Thus, our regression algorithm provides an objective test of the accuracy of the Langley regression and allows us to retrieve aerosol and gas column amounts from data that would have otherwise have to be excluded.

b. Comparison with AERONET optical depth retrievals

We also compared our calibrations and optical depth retrievals with the optical depths derived from measurements by the Aerosol Robotic Network (AERONET; Holben et al. 1998) CIMEL sun–sky radiometer collocated with MFRSR at the Atmospheric Radiation Measurement (ARM) Cloud and Radiation Testbed (CART) site central facility. Level 2.0 AERONET data are used. These measurements have been cloud-screened and quality-controlled according to Smirnov et al. (2000). We sampled the MFRSR data to match the measurement times of the CIMEL measurements (they are less frequent in time) and selected for this comparison data collected during the period from January to June 1999. During this time period there were 58 clear or partially clear days with data available from both instruments (total 1342 data points). This period contains a variety of atmospheric conditions with aerosol optical depths ranging from 0.03 to 0.4 (at 500-nm wavelength). The MFRSR calibrations and retrievals are performed according to the algorithm described in this paper, including smoothing of the calibration coefficients.

The 500-, 670-, and 870-nm channels are common to both the CIMEL and MFRSR. For comparison with the 440-nm CIMEL channel, we interpolated between our retrieved optical depths at 415 and 500 nm to obtain an MFRSR-derived estimate of the optical depths at 440 nm.

The AERONET retrieval algorithm neglects the contribution of NO₂ absorption to the retrieved optical depths. Therefore, in this comparison, we have added the NO₂ optical depths to our aerosol optical depths; that is, the comparison is between the total optical depths measured by the two instruments with ozone contribution subtracted. Differences between the climatological ozone column amounts (used by AERONET) and the values retrieved using our algorithm, appear to have a negligible effect on this comparison.

Figure 13 presents scatterplots comparing MFRSR and CIMEL optical depths at 440-, 500-, 670-, and 870-nm wavelengths. Mean differences between our MFRSR retrievals and the AERONET ones do not exceed 0.005 for 440-, 500-, and 870-nm channels with standard deviation of 0.01 or less for all channels. This agreement is similar to that obtained by Halthore et al. (1997) who compared MFRSR- and CIMEL-derived optical depths at the same site for April 1994 (where the agreement was within ±0.01) and April 1996 (where the agreement was within ±0.02). Similarly, Schmid et al. (1999) found that CIMEL–MFRSR differences do not exceed 0.01 for all wavelengths on 29 September and 2 October 1997 using collocated measurements at the Southern Great Plains (SGP) Central Facility. The MFRSR calibration in both of these studies is based on the robust estimate made using the 20 nearest successful Langley plots. While the CIMEL calibration is based on periodic high altitude Langley recalibrations.

We find that small systematic differences exist for the 670-nm channel. Here the MFRSR optical depths are biased compared with those derived from the CIMEL by 0.01. This bias, while not exceeding the commonly accepted calibration accuracy, reflects a difference in spectral slopes between 670- and 870-nm optical depths measured by these two instruments. The aerosol optical depths are expected to monotonically decrease with increasing wavelength in this spectral region (note that NO₂ absorption does not influence this behavior: it is absent at 870 nm and is only about 10⁻⁴ per DU at 670 nm). This behavior is observed in all MFRSR retrievals and in the most of the CIMEL results. However, the CIMEL-determined slope between the two channels is systematically smaller. The difference is more pronounced during winter when the aerosol particles are larger and therefore generally exhibit smaller spectral slopes. On some days, the CIMEL-determined slope becomes negative, which while possible, in these particular cases seems to be inconsistent with spectral behavior of optical depths at other wavelengths. For these days, the CIMEL-derived aerosol optical depth at 670 nm is smaller than that at 870 nm and sometimes even smaller than that determined at 1020 nm. Further, we note that the original (level 1.0) AERONET data for these days are spectrally monotonic, while exhibiting certain calibration artifacts. Calibration changes made in level 2.0 processing might be responsible for these differences. While our algorithm precludes a behavior that is inconsistent with Mie theory, the residuals in our retrieval of the 670-nm optical depths are typically of order 10⁻⁴ and do not exceed 10⁻³ for the dataset considered. Thus, our residuals cannot explain the observed bias.

c. Validation of nitrogen dioxide retrievals: Comparison with Brewer spectrometer data

Our MFRSR-retrieved ozone and NO₂ column amounts are compared with those derived from Brewer spectrophotometer measurements. The Brewer data are taken from Environmental Protection Agency (EPA) UV Monitoring Program (http://www.epa.gov/uvnet/) site at Big Bend National Park, Texas. This site is located at 29.305° latitude and 103.177° longitude, and the site elevation is 1052 m above sea level. The nearest MFRSR site belongs to the USDA UVB Radiation Program and is about 35 km southwest (29.133° latitude and 103.517° longitude) and at a lower altitude (670 m). Because the two instruments are not exactly collocated, precise agreement is not expected since polluted air masses of the same origin may reach the two sites at different times and, due to transport processes, may have different concentrations. Since, ozone is mostly stratospheric, its measurements are not affected significantly by local atmospheric transport, and better agreement between the instruments should be observed.

The period from February to May 1999 with good quality data available from both instruments was selected for this comparison. Brewer retrievals are made from direct sun measurements. Figure 14 shows the Brewer-retrieved (diamonds with error bars) and MFRSR-retrieved (shaded rectangles) NO₂ column amounts for this period. The mean difference between the minimal and maximal limits of the MFRSR NO₂ retrievals is 3 DU. Most of the Brewer points have uncertainties of about ±0.5 DU. As can be seen, most of the retrieved NO₂ column amounts agree within these uncertainties.

The NO₂ column amounts derived from both the MFRSR and Brewer data are generally considered to be too high for a national park; however, it is likely that they can be attributed to air quality problems at this particular location. According to the National Parks Service (http://www.nps.gov/bibe/aqvis.htm), the air quality in the Big Bend National Park experienced noticeable changes during the 1970s. The air monitoring program, begun in 1978, has allowed park managers to interpret the transport and transformation of pollutants that contribute to air quality problems within their park. Among the major sources that contribute to Big Bend's pollution are North–Central Mexico, including the urban and industrial region of Monterrey and Monclova; East–Central Texas and the Gulf Coast, including the urban and industrial areas of Houston and Galveston; and Mexico City and its surrounding urban area. There are no high-ground concentrations of NO₂ measured within the park since pollutants that are transported to the park from remote sources are likely to be concentrated at a higher altitude.

d. Validation of ozone retrievals: Comparison with Brewer and TOMS data

Figure 15 presents the comparison between the MFRSR-derived ozone column amounts and those derived from Brewer (20 data points) and TOMS (70 data points) measurements as well as a comparison between the Brewer- and TOMS-derived ozone column amounts (21 data points; the TOMS values are referenced to the MFRSR site). The MFRSR ozone retrievals appear to be practically unbiased when compared with the TOMS values (the mean difference is −0.35 DU, i.e., about 0.1% of a typical ozone column amount). The standard deviation is 18 DU and may represent both uncertainties of the measurements and difference in averaging/sampling between satellite- and ground-based measurements. The Brewer retrievals (provide fewer data points for comparison) show some 7–10 DU bias (overestimation) compared to both MFRSR and TOMS with the standard deviation of the same order (14–20 DU) as for the MFRSR–TOMS comparison.

Previously comparisons with EPA Brewer-derived ozone column values and those obtained from shadowband radiometer measurements (in UV) were performed by Slusser et al. (1999) who found that the ultraviolet rotating shadowband radiometer-retrieved ozone column amounts overestimate those derived from the Brewer measurements by 1% (3 DU, relative to the typical value of 300 DU) on average with standard deviation of 2% (6 DU). This accuracy is better than what we obtain with the visible MFRSR, which is to be expected based on the strength of the ozone absorption in the UV. Comparisons between TOMS ozone retrievals and those obtained from direct sun measurements at 29 Brewer stations worldwide were reported by Fioletov et al. (1999). They found results that vary with location with biases ranging from 0.1% to 6.6% (corresponding to 0.3–20 DU) and standard deviations ranging from 0.9% to 5.2% (3–15 DU). Kerr and McElroy (1995) report 4.6% (13.7 DU) bias with TOMS for their direct sun measurements at Table Mountain Observatory. In our case the differences are of the same order: 10 DU bias and 14.4 DU standard deviation.

Figures 16–18 present the comparison of MFRSR-derived ozone column amounts with TOMS measurements for three additional sites: Albany, New York, [Atmospheric Sciences Research Center (ASRC)], New York City (GISS), and Department of Energy (DOE) ARM CART site central facility (Southern Great Plains, Oklahoma). For the latter site, we use the same data previously used in our comparison with the AERONET optical depth measurements described above. All three plots show data from periods containing 40–60 clear days. As described above, the calibration smoothing procedure has been applied to all of these datasets. Calibration smoothing results in a reduction of the standard deviation of the differences by up to 30% when compared with the instantaneous retrievals. The accuracy of MFRSR ozone retrievals depends on both the atmospheric conditions at the instrument location and probably on some instrumental characteristics. We have found that some MFRSRs tend to systematically underestimate the column ozone amounts (compared to TOMS). Among these three datasets, the Albany instrument shows the largest bias (29 DU) when compared with TOMS measurements. The other two instruments exhibit smaller biases that are comparable to those observed in Brewer and Dobson spectrometer comparison (Fioletov et al. 1999), while the standard deviations in MFRSR comparisons with TOMS are generally larger than those for the spectrometric measurements.