Introduction
As the design of instruments for spectral measurements of solar radiation evolves, and as the interest in and the request for spectral aerosol optical depth (τa,λ) data increases, more and more stations with more and more sophisticated spectral radiometers are established almost all over the world. Even today, however, continuous spectral measurements are much sparser than broadband pyrheliometer measurements. Therefore, it is of great interest to utilize the available pyrheliometer measurements to derive the atmospheric turbidity and, further, to estimate τa,λ. In Sweden, continuous pyrheliometer measurements have been made since 1983 at 12 sites and continuous spectral measurements for τa,λ determination are only made at two sites. One of these sites is at the Swedish Meteorological and Hydrological Institute (SMHI) in Norrköping, Sweden, from which data in this study are taken. The other site is a station within the Aerosol Robotic Network (AERONET; Holben et al. 1998), on the island of Gotland in the Baltic Sea. The question is how good τa,λ estimates from broadband measurements really are.
The original aim was to compare τa,λ estimates and observations at nine wavelengths in the 368–1024-nm range, using operational calibration and optical depth calculation procedures. Observations were to be made with two different spectral instruments, a three-channel sun photometer and simple spectroradiometer (300–1100 nm) and a broadband pyrheliometer. However, it turned out that the performance and calibration accuracy of the spectroradiometer were not good enough to be used as a reference. Therefore, the comparison is restricted to the three wavelengths (368, 500, 778 nm) of the sun photometer.
Measurements and methods
From March of 1999 to March of 2000, manual direct sun measurements with the spectroradiometer were taken when possible. The measuring site was the radiation measurement platform on the roof of SMHI (58.58°N, 16.15°E, 43 m altitude). Altogether, about 300 spectral scans from 32 different days during all seasons were recorded. At the research radiation station of SMHI, 1-min (mean values) radiation data are collected continuously. From this database, data from the sun photometer and the pyrheliometer at the times of the spectroradiometer scans were extracted.
Instruments
The spectroradiometer used was the manually operated LI-COR, Inc., LI-1800 portable spectroradiometer No. 178 [300–1100 nm, single monochromator, 6–7-nm bandwidth full width half maximum (FWHM), silicon photodetector, not temperature stabilized]. To scan the full wavelength range at 1-nm intervals took about 45 s. The instrument was equipped with a collimator to allow measurements of the direct solar radiation with a field of view (FOV) of 2.5° (full angle). The instrument was either operated indoors through an open window, especially in cold weather, or mounted outdoors on a suntracker. The whole instrument had to be moved and pointed toward the sun. The instrument housing was always shaded from direct sun, and the Teflon diffusor (entrance optics) was shaded between the scans. Among others, Adeyefa et al. (1997) have used the LI-1800 in this configuration for τa,λ determination, and, for example, Cachorro et al. (1987), Martínez-Lozano et al. (1998), and Jacovides et al. (2000) used the LI-1800 in a slightly different configuration.
The sun photometer was a three-channel Centre Suisse d'Electronique et de Microtechnique (CSEM) SPM2000, S/N 16 (CSEM2016 in the following), originally developed at the Physikalisch-Meteorologisches Observatorium Davos, Switzerland, World Radiation Center (hereinafter referred to as WRC). This instrument measures at approximately 368, 500, and 778 nm with 5-nm FWHM and 2.8° full-angle FOV. Each channel has a silicon photodiode detector with an integrated interference filter in a sealed housing assembled into a temperature-stabilized enclosure.
The broadband direct solar irradiance was measured with an Eppley Laboratory, Inc., normal incidence pyrheliometer (NIP) (No. 20919, 5.7° FOV).
Calibration
The LI-1800 was calibrated several times against standard lamps, which is the normal way to calibrate spectroradiometers of this type. The lines plotted in Fig. 1 represent the ratio of the spectral calibration factors derived at each calibration to the reference calibration factors, which simply were calculated as the mean of the four calibrations. The two standard lamps labeled SP-6 and SP-9 are 1000-W halogen free electron laser (FEL) lamps that were calibrated by the Swedish National Testing and Research Institute in June-1996, using the same reference that is traceable to the spectral irradiance scale of the National Institute of Standards and Technology. The total uncertainty in the calibration of the lamps is stated to be 2.5%–3.5% in the wavelength range of 300–1100 nm. Investigations by Kiedron et al. (1999) suggest that the uncertainty of the standard lamps could be even higher.
For wavelengths λ shorter than about 500 nm, the results of the calibration of the LI-1800 indicate a strong degradation in responsivity with time. For example, between the calibrations on 2 June 1999 and 22 October 1999, the responsivity at 368 nm decreased by almost 3.6%. For wavelengths in the range 369 ≤ λ < 550 nm, the change was smaller. For λ < 368 nm, the responsivity change was even larger. In the latter wavelength interval, the influence of noise is strong. To account for the change in responsivity of the LI-1800, the responsivity degradation for λ < 550 nm was modeled as a linear function of time and as a third-degree polynomial function of λ. Comparison with the CSEM2016 sun photometer 368-nm channel also supported the significant responsivity degradation with time of the LI-1800. For the same period (142 days), the degradation was estimated to be 2.4%, using CSEM2016 as reference.
Also, for wavelengths longer than 950 nm, the calibration results varied considerably. However, there was not a continuous change over time. As already shown by Riordan et al. (1989), the LI-1800 has a very strong temperature dependence, especially in the IR region. Because neither the instrument nor the calibration room was temperature stabilized, the responsivity variations for λ > 950 nm are thought to be caused mainly by different detector temperatures. Because neither the LI-1800 was temperature stabilized nor was the detector temperature measured, the dependence on temperature was something for which one could not compensate. For determination of τa,λ at λ > 950 nm this drawback is serious. As a final calibration for λ > 550 nm, the average of the four lamp calibrations was applied to all LI-1800 measurements during the study. The uncertainty of LI-1800 irradiance measurements has been studied earlier (Myers 1989; Riordan et al. 1989).
For a sun photometer channel, the expected output voltage V0 for a measurement outside the atmosphere at mean Sun–Earth distance is used as calibration constant. The CSEM2016 sun photometer has been calibrated several times at WRC, both against lamps and by comparison with τa results from WRC's sun photometers at the wavelengths of CSEM2016. The difference between lamp and sun calibration results at WRC for CSEM2016 is 0%–4%. At wavelengths free from strong gaseous absorption, the so-called Langley calibrations of the WRC sun photometers are considered to be more accurate than lamp calibrations (Schmid and Wehrli 1995). To derive sun photometer V0 from calibrations against the lamp requires knowledge about the extraterrestrial solar irradiance. Among others, the accuracy of calibrations against the lamp, therefore, depends on both the accuracy of the lamp and the accuracy of the extraterrestrial solar irradiance data used. Hence, the sun calibrations of the CSEM2016, using the Langley-calibrated WRC sun photometers as reference, are considered to be more accurate than the lamp calibrations. The CSEM2016 was compared with WRC's sun photometers in both February of 1998 and March of 1999. For some unknown reason, the resulting V0 were 3%–4% higher in 1998 than in 1999 for all three channels.
The common way to calibrate reference sun photometers is through some type of Langley calibration method; see, for example, Schmid and Wehrli (1995). Through the use of a Langley calibration method, the exact knowledge of the extraterrestrial solar irradiance is not needed for the calculation of aerosol optical depth. Langley calibrations are preferably based on measurement data from a high-altitude site with very clean and stable atmospheric conditions, and this is how the WRC sun photometers are calibrated. However, as part of the quality control of the CSEM2016 measurements, analysis of classical Langley plots has also been made on data from the low-altitude site in Norrköping. In a classical Langley-plot calibration of one sun photometer channel, linear regression of the (natural) logarithm of the sun photometer signal, corrected to mean Sun–Earth distance, versus optical air mass is made. The point at which the regression line intercepts the ordinate yields the logarithm of V0 for that particular channel. It is assumed that the optical depth is constant over the whole airmass range. There are several criteria defining a measurement period that is suitable for Langley-plot analysis. First, 1-min data from the sun photometer and collocated pyrheliometer were inspected manually to find candidate periods for Langley-plot analysis. Then, the basic objective criteria used here were as follows: approximate τa,368 < 0.10 (derived using V0,368 from the latest calibration at WRC), optical air mass ≤7, range in optical air mass ≥3, and the difference between the regression line and accepted points of ln(V368) < 0.2% of ln(V368) at the highest accepted airmass value. The 368-nm channel is most sensitive to nonstable atmospheric (aerosol) conditions. After more than 30 V0 values for each channel had been achieved in this way, outliers that were more than 5% off from the mean were discarded. In the end, about 80 occasions with accepted Langley-plot results were found during 1995–2001. The Norrköping Langley results indicate that the changes in sensitivity have been small in time for all of the CSEM2016 channels. The standard deviation of all accepted V0 values were 2.0%, 1.4%, and 1.1% for the 368-, 500-, and 778-nm channels, respectively.
Linear regression of the V0 results from Norrköping versus time agrees within 0.8% (778 nm) or better with the WRC sun calibration results of 1999, and they are about 3% lower than the WRC calibration of 1998. For this reason, the results of the 1999 WRC calibration were applied on all sun photometer data in this study. During September–October of 2000, the CSEM2016 also participated in the first filter radiometer comparison (FRC-I) held at WRC. The results of FRC-I indicate that 6–7 months after the last measurements of the current study were taken, the V0 were 0.3%–1.3% higher than the ones used in this study. From this change, it is estimated that the uncertainty of the CSEM2016 V0 is 2% at a level of confidence of 95% for all three channels.
The NIP 20919 is regularly calibrated against the two reference pyrheliometers of SMHI, PMO-6 absolute radiometer No. 811108 and Ångström pyrheliometer No. 171. The reference pyrheliometers participated in the three international pyrheliometer comparisons held between 1990 and 2000 at WRC and are directly traceable to the World Radiometric Reference. NIP 20919 has been found to be very stable over time, and a single calibration factor (111.0 W m−2 mV−1) was adopted for the whole study. Every year several hundred calibration points are determined. The standard deviation of the individual NIP calibration results from one year is approximately 0.4% for all data and 0.3% for the cases in which the solar elevation was 35° or higher. The total uncertainty in the mean calibration constant originates mainly from the bias uncertainty of the reference pyrheliometers and is estimated to be 0.3% (1 standard deviation σ).
Calculation of aerosol optical depth
For the sun photometer, values of τa,λ was calculated in the same way as for the LI-1800, except that E0,λ and Eλ in Eq. (1) were replaced by V0,λ and Vλ (=measured output voltage from λ-nm channel). The 500- and 778-nm channels were corrected for ozone absorption. No correction for nitrogen dioxide (NO2) absorption was made.
In many cases, using α = 1.3 appears to be a good approximation. For the sun photometer data investigated in this study, the average α was found to be close to 1.3. This finding also holds for all data collected with the CSEM2016 between 1995 and 2001 at the same site. In these data (to be presented elsewhere), an annual cycle of monthly mean α, ranging from about 1.0 in winter to 1.6 in summer, is found. For the closest AERONET station on the island of Gotland in the Baltic Sea, 180 km from Norrköping, very similar results on α are found for level-2.0 data for March–November during 1999–2002. (These data are available online on the AERONET Web site at http://aeronet.gsfc.nasa.gov/.) Adeyefa et al. (1997) reported values on α of about 1.2 in conditions not affected by volcanic aerosol for the Abisko site in northernmost Sweden. Gonzi et al. (2002) investigated level-1.5 data from all available European AERONET stations. For most remote, urban, and coastal sites, the annual average α was between 1.0 and 1.6. Michalsky et al. (2001) report aerosol optical depth results from three sites in the United States. Also at these stations there is a typical annual cycle in α, with lower values in winter and higher values during summer. In conditions not influenced by volcanic aerosols, the mean annual variation is between approximately 1.0 and 1.6. Holben et al. (2001) also report monthly and yearly mean α values of between 1.0 and 1.6 at some AERONET stations, for example, in North and South America and in Europe. However, it is also clear that, for example, in pronounced oceanic and desert dust environments, α normally deviates considerably from 1.3.
One must keep in mind that the uncertainty in α determined from spectral aerosol optical depth data is significant. It is especially large in low-aerosol-optical-depth conditions. The resulting α is heavily dependent on calibration accuracy and the wavelength range that is used for its determination. In normal conditions, the smaller the wavelength range is, the higher the uncertainty becomes. Nevertheless, α is still commonly used to present a simple measure of the relative size distribution of the observed aerosol.
With the Gueymard model, it is also possible to compensate for the circumsolar radiation received by ordinary, relatively large FOV, pyrheliometers, such as the Eppley NIP. The circumsolar correction slightly increases the calculated β values. The solar elevation–corrected model, the original model, and the circumsolar-corrected original model were used to estimate spectral τa,λ.
The column amount of water vapor w is a critical input for a good estimate of β. Here, two ways to calculate w have been tried. One way is to calculate w from the 6–12-h forecast fields of the operational weather-forecast High-Resolution Limited Area Model (HIRLAM). In a comparison of w calculated from upper-air sounding data and HIRLAM fields from April and July of 1997, it was found that, on average, w(HIRLAM) was higher than w(soundings). The difference was slightly less than 1 mm (=kg m−2). It is not known how much water vapor there was above the highest points reached by the sounding balloons. The other way is to estimate w from the 2-m temperature and relative humidity according to the method by Gueymard (1994), hereinafter referred to as w(T, RH).
Uncertainty of τa,λ derived from sun photometer measurements
Not taking NO2 absorption and diffuse radiation into account introduces biases in the derived τa,λ values. However, these biases are of different sign and therefore cancel out each other to some extent, at least at the wavelengths of 368 and 500 nm.
The magnitude of the estimated total uncertainty (expanded uncertainty with coverage factor k = 2) of τa,λ, as well as the contributions from the individual sources of uncertainty considered here, is plotted versus aerosol optical air mass in Fig. 3. To show their contribution to the total uncertainty, the individual standard uncertainties are multiplied by k = 2. The individual uncertainties are here assumed to be symmetrically distributed around zero. It is evident that for ma ≤ 3 the accuracy of the calibration of the sun photometer is the most important source of uncertainty at all wavelengths. At higher air masses, especially for relatively high τa,λ, the uncertainty in ma is the largest source of uncertainty. It is hoped that the uncertainty in ma is here somewhat overestimated. In situations without any significant amount of volcanic aerosol particles in the stratosphere, the uncertainty could probably be reduced by not taking ma = mR and instead using ma(SMARTS2), for example.
So far it has been assumed that the probability functions of the individual uncertainties are normally or rectangularly distributed around zero. However, this is not the case in reality for some of the sources of uncertainty. The diffuse radiation seen by a direct sun radiometer only tends to reduce the derived aerosol optical depths. On the other hand, neglecting NO2 absorption results in overestimated values of τa,λ. The same holds for using a too-small value of ma, which is the case if ma really is more close to ma(SMARTS2) than to mR. For these reasons, the positive and negative uncertainty limits are calculated separately. In the estimated positive (upper) uncertainty limits (see Fig. 6), no u(τN,λ) was taken into account and only 1/3 of u(ma) was considered. It was simply considered very unlikely that ma was actually lower than mR by more than 2 × 0.75 [ma(SMARTS2) − mR]/3 (95% level of confidence) under the measuring conditions during this study, with no, or only very small, amounts of volcanic aerosol particles in the stratosphere. In the estimated negative (lower) uncertainty limits, no u(Vdif,λ) was taken into account. The asymmetry of the uncertainty estimates is, however, only visible at high values of ma (see Fig. 6).
According to the International Organization of Standardization (1995), a standard uncertainty is classified as either being obtained from statistical analysis, a type-A evaluation of standard uncertainty, or being obtained by means other than statistical analysis, a type-B evaluation of standard uncertainty. In this study, only two of the individual standard uncertainties, u(Vλ)DVM and u(Vλ)mi, are obtained by statistical analysis (type A). All of the other uncertainties were instead obtained by means other than statistical analysis (type B). In all cases, the type-B uncertainty evaluations were assumed to have infinite degrees of freedom. [See the International Organization of Standardization (1995) for details on evaluation and expression of uncertainty in measurements.]
Results
The measuring and aerosol conditions during this study (March 1999–March 2000), as determined by CSEM2016, are listed in Table 1. Statistics of the τa,λ comparison are summarized in Tables 2 and 3. As is clear from Table 1, the atmospheric turbidity and τa,λ were mostly low during the study, with no occasions of really high turbidity (β ≥ 0.200).
Examples of instantaneous spectral τa,λ derived using the three different instruments are plotted versus wavelength in log–log diagrams in Fig. 4. The τa,λ values are from one very clear day (29 April 1999) and from a more turbid day (14 September 1999). For the more turbid case, the Ångström relation is a very good approximation of the spectral distribution of τa,λ (α = 1.7, β = 0.025), according to both the spectroradiometer and the sun photometer. Using single α and β in the clear case still appears to be a good approximation for the CSEM2016 τa,λ values (α = 1.2, β = 0.015). However, this is not the case for the LI-1800 results. The log–log plot could be misleading, but, nevertheless, the disagreement between LI-1800 and CSEM2016 τa,λ for λ < 450 nm and λ > 950 nm is much higher in the clear case. The LI-1800 τa,λ data at these wavelengths are most probably influenced by measurement errors.
In addition to the temperature dependence for λ > 950 nm and the presumed responsivity degradation with time (or exposure?) for λ < 500 nm in the LI-1800, an airmass dependence at shorter wavelengths is indicated by comparison with the CSEM2016 at 368 nm. Using the sun photometer as reference, calibration constants for the LI-1800 at 368 nm, which would give the same τa,λ as the CSEM2016, were calculated. LI-1800 calibration factors for λ = 368 nm appear to be very dependent on air mass (Fig. 5). Possible explanations for this result could be nonlinearity, temperature dependence, and tilting of the instrument. Of course, an erroneous V0,368 applied on the CSEM2016 signals could also lead to such a result. However, it is strongly believed that the error in V0,368 (plus nonlinearity in V368) is much less than the 10% that at least is needed to give results similar to those in Fig. 5. If such a large change had occurred after the calibration of CSEM2016 in 1999 at WRC, it would have shown up at FRC-I or even in the Langley plots of sun photometer data from Norrköping. After the calibration in Davos, 35 accepted Langley plots have been made. The maximum deviation from the average V0,368 is about ±4%, but the deviation of the mean from the WRC V0,368 is only +0.3%.
The τa,λ-weighted averages of U95(τa,λ) estimated for each value of τa,λ(CSEM2016) were only 0.014, 0.011, and 0.011. There are no significant deviations from these values when looking at the positive and negative uncertainty limits separately at 500 and 778 nm. At 368 nm, the positive and negative uncertainty limits were calculated to +0.012 and −0.013. These low uncertainties are partly due to the mostly low τa,λ values and the large number of measurements with ma in the range between 2 and 5 during the study. By taking the average uncertainty as the uncertainty of the average or median aerosol optical depth, it is assumed that all individual standard uncertainties u(xi) are made up of bias uncertainty only. Indeed, the major part of many of the standard uncertainties, such as u(V0,λ), for example, is really bias uncertainty. However, among others, depending on the considered timescale, minor or major parts of all standard uncertainties are of random nature. Ignoring this fact does at least not lead to an underestimation of the uncertainty of the average τa,λ results.
The differences in aerosol optical depth derived from sun photometer measurements and the two other methods for the three investigated wavelengths are plotted vs optical air mass in Fig. 6. Also, the uncertainty in sun photometer τa,λ, at an approximate level of confidence of 95% is shown. The uncertainty is calculated for 0.33, 0.22, and 0.11 aerosol optical depth for 368-, 500-, and 778-nm wavelengths, respectively. In at least 95% of the cases, τa,λ were equal to or lower than these limits. These limits are significantly higher than the average and median values of τa,λ for the whole study (see Table 1). The total number of cases is 279, originating from 32 days spread over 1 yr. For ma > 2, the agreement between the LI-1800 and the CSEM2016 τa,λ determinations is good, normally within 0.01, at 500 and 778 nm (Fig. 6). At 368 nm the difference is larger, especially for ma < 3, and the dependence on optical air mass is also clear. Because of the problems of the LI-1800 at shorter wavelengths, the mean and rms differences in aerosol optical depth at 368 nm are actually larger between the two spectral instruments than between the pyrheliometer [τa,λ(NIP)] and the sun photometer retrievals (Fig. 6 and Table 2).
In most cases, the broadband methods slightly overestimate τa,λ at all three wavelengths. For the best broadband method in this comparison, the solar elevation–corrected [Eq. (3)] Gueymard model without circumsolar compensation, and using w(HIRLAM) as precipitable water input, the τa,λ(NIP) estimates were on average 0.014, 0.014, and 0.013 higher than the sun photometer τa,λ values at 368, 500, and 778 nm, respectively. This result is close to, but just above, the average uncertainty of the sun photometer τa,λ values. Considering the uncertainties involved with the broadband method, the agreement in average aerosol optical depth between sun photometer and the pyrheliometer method is surprisingly good. Using the original model by Gueymard, but still without the circumsolar compensation, increased the mean differences to 0.034, 0.027, and 0.020, respectively. Because these results are already too high, also adding the proposed circumsolar correction to the original model increased the mean differences even further, to 0.040, 0.031, and 0.022 for the same wavelengths (Table 2). When considering these latter differences, it must be kept in mind that the sun photometer optical depths were not corrected for circumsolar radiation. The circumsolar contribution was only included in the uncertainty analysis. The quality of the circumsolar correction of β by Gueymard cannot be evaluated from the results of this study.
As mentioned above, ma = mR in the calculations of τa,λ(CSEM2016) and τa,λ(LI-1800). This is not the case in the broadband method, where ma is calculated as proposed by Gueymard (1998). If the same values on ma had been used in both the spectral and broadband methods, the τa,λ differences would have been slightly larger, especially for high ma.
For the same water vapor amount, w(HIRLAM), τa,λ(NIP) estimated from the β model by Grenier et al. (1994) are on average slightly higher than those of the original Gueymard model at 368 and 500 nm. At 778 nm it is slightly lower but still exceeds the sun photometer τa,λ values (Table 3). There are only minor differences in the scatter between the two broadband methods (standard deviation in Tables 2 and 3).
There is naturally a larger scatter in the difference between τa,λ derived from pyrheliometer and spectral (sun photometer) measurements (Fig. 6). This scatter is mainly due to erroneous values of α and w used in the broadband method. The scatter in τa,λ differences appears to decrease with increasing air mass. The errors introduced in β by using incorrect values of w and total ozone decrease marginally with increasing air mass. It is thought that the main reason why the scatter in τa,λ differences in Fig. 6 decreases with increasing air mass is simply the fact that the range in atmospheric conditions was small for the measurements when ma was high. For example, the values of α for the 10 cases with ma > 5 only varied between 1.2 and 1.5.
The importance of a good estimate of w to be used when estimating β is illustrated in Table 3. On average, w(T, RH) was found to be lower by 0.17 cm than w(HIRLAM), resulting in higher values of β and τa,λ. However, the w(T, RH) − w(HIRLAM) difference ranges from largely positive (0.86 cm) to largely negative (−1.28 cm). According to the τa,λ difference statistics in Table 3, using w(HIRLAM) significantly improves the τa,λ(NIP) estimates.
Conclusions and discussion
From this study, the following conclusions are drawn:
According to the CSEM2016 sun photometer, an average α = 1.38 (in the wavelength range of 368–778 nm) was found during the period of the study at the inland site in southern Sweden. Hence, using α = 1.3 in the τa,λ determinations from broadband measurements is fairly well supported.
In general, estimates of spectral τa,λ(λ < 1000 nm) from pyrheliometer measurements of the direct irradiance using the β models by Grenier et al. (1994) and Gueymard (1998) were found to exceed τa,λ as determined from accurate sun photometer measurements. Average results of the β model by Gueymard without circumsolar compensation but corrected according to Eq. (3) are closest to the reference values but still slightly exceed the estimated measurement uncertainty of the sun photometer τa,λ values.
Taking precipitable water amount from an atmospheric model results in significantly better turbidity estimates than if w is calculated from measured 2-m temperature and relative humidity.
The two largest sources of uncertainty in aerosol optical depth derived from sun photometer measurements are uncertainties of calibration and aerosol optical air mass.
Especially because of its low accuracy and instability at λ < 500 nm and λ > 950 nm, the LI-1800, in its current configuration, is not suited well for determination of τa,λ and its spectral dependence in the form of Ångström's wavelength exponent α. In particular, it is not suited for long-term monitoring and/or at locations where the turbidity normally is low.
As long as there are no major errors in the WRC calibration of the CSEM2016 or in the NIP calibration, it appears certain that τa,λ(λ < 1000 nm) is overestimated with the broadband methods. Considering the uncertainties involved with the broadband method, however, the agreement in average aerosol optical depth between sun photometer and the closest pyrheliometer method is considered to be very good. Molineaux et al. (1998) compared aerosol optical depth at 700 nm derived from spectral and broadband measurements. For a 9-month period in Geneva, Switzerland, they found mean differences ranging from −0.09 to 0.033 in aerosol optical depth at 700 nm between broadband and spectral methods. In the majority of cases, the broadband methods gave higher optical depths. The differences depended on the aerosol model used, the calibration of the spectral instrument, and how the columnar water vapor was derived. The standard deviations were about the same as or slightly higher than what was found for the 500-nm wavelength in this study.
It was indicated that w(HIRLAM) values used on average could be a little too high. Giving lower w as input, higher β [and higher τa,λ(λ < 1000 nm)] will be returned by the turbidity models, as was the case with w(T, RH). From sensitivity calculations with SMARTS2, it turned out that 10%–15% higher w(HIRLAM) values would be needed to remove fully the average differences between CSEM2016 τa,λ and τa,λ from the corrected Gueymard method. It can not be excluded that w(HIRLAM) actually was negatively biased by this amount. More validation of w from 6–12-h forecast fields of HIRLAM needs to be done to assess better this source of uncertainty. It is not known how large an impact the errors in the calculated water vapor coefficients and their parameterization in the broadband turbidity models could have on the derived β and aerosol optical depths.
If a higher α of 1.38 had been used in the development of the β models, this would have led to even higher τa,λ at 368 and 500 nm and negligibly lower τa,λ at 778 nm in the end. If the CSEM2016 wavelength pairs 368/500 nm and 500/778 nm were considered separately, the average value of α would be determined to 1.54 and 1.25, respectively. If these α values had been used in the Gueymard model in the wavelength ranges <500 nm and >500 nm, respectively, which is possible with the SMARTS2 model, the broadband method τa,λ would have increased by approximately 0.010 at 368 nm and decreased by approximately 0.003 at 500 nm for the data used in the study. The 778-nm mean τa,λ would have been practically unaffected.
Broadband measurements certainly cannot replace spectral measurements for determination of aerosol optical depth. This study suggests that at locations at which only direct solar irradiance measurements are made, one can still get fairly good estimates of the average aerosol optical depth conditions by applying a broadband turbidity model on the direct irradiance data. If the direct irradiance measurements cannot be made close to an upper-air station, the needed columnar water vapor input should be derived from a numerical weather analysis or prediction model.
In pronounced oceanic environments (e.g., Wilson and Forgan 2002) or in places commonly affected by desert dust or biomass-burning aerosols (e.g., Eck et al. 1999; Holben et al. 2001), as well as after major volcanic eruptions (e.g., Dutton et al. 1994; Kaufman et al. 1994; Michalsky et al. 2001), the spectral dependence of aerosol optical depth is known to deviate significantly from the simple Ångström relation with α = 1.3, as assumed in the published broadband turbidity methods. The turbidity models should, for these places and/or times, be modified to represent more closely the aerosol optical depth dependence on wavelength.
The atmospheric conditions during the study were mostly very clear and dry in a global perspective. This fact has to be accounted for when considering the representativity of the aerosol optical depth comparison.
Acknowledgments
The authors are grateful to C. Gueymard for providing the SMARTS2 code. The work has been carried out with financial support from the Swedish National Space Board, which is gratefully acknowledged.
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Lamp calibrations of LI-1800: ratios of individual calibration results (spectral calibration factors) to the average of the results (Cref). The lamps are SP-6 and SP-9
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
The difference between β derived from minimization of SMARTS2 and β derived with the model by Gueymard (1998). The dashed line represents the linear correction function
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
Expanded uncertainty (k = 2) of aerosol optical depth U95(τa) and the effects of individual sources of uncertainty on the uncertainty of τa,λ derived from CSEM2016 sun photometer measurements at 368, 500, and 778 nm
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
Examples of spectral τa derived from measurements with LI-1800 (dots), CSEM2016 (circle-line), and NIP with corrected β model by Gueymard (full line)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
Calibration factors for LI-1800 at 368 nm using CSEM2016 as reference, 27–29 Apr 1999
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
Differences in derived τa,λ at 368, 500, and 778 nm, and uncertainty limits for τa,λ(SPM): LI = LI-1800 spectroradiometer, NIP = pyrheliometer, SPM = CSEM2016 sun photometer
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1598:CAUOAO>2.0.CO;2
Measuring conditions during the study: τ a,λ , α, and β are calculated from the sun photometer CSEM2016 data, and w is calculated from HIRLAM
Difference in τ a,λ between LI-1800 spectroradiometer and CSEM2016 sun photometer, and between broadband method (NIP) and CSEM2016. Comparison statistics are based on 279 cases. SEC = solar elevation correction of β according to Eq. (3). Orig = original model of β by Gueymard. OrigCS = original model of β with correction for circumsolar irradiance by Gueymard
Differences in aerosol optical depth derived from pyrheliometer measurements according to Grenier et al. and from sun photometer measurements. Two different water vapor inputs to the broadband method were used
