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®See section 3.3. bSee section 3.4. °Means and standard deviations of the parameters are given over the whole ranges of solar elevations (10° - 90°) anc ozone colums (250 - 400 DU). Table 2. Parameters to Calculate Errors Caused by Finite Resolution of a Spectroradiometer* and Wavelength Shifts® on Dependence of Solar Elevation (Sh) and Total Ozone (Oz)

Table 2 ®See section 3.3. bSee section 3.4. °Means and standard deviations of the parameters are given over the whole ranges of solar elevations (10° - 90°) anc ozone colums (250 - 400 DU). Table 2. Parameters to Calculate Errors Caused by Finite Resolution of a Spectroradiometer* and Wavelength Shifts® on Dependence of Solar Elevation (Sh) and Total Ozone (Oz)

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Table 1. Expanded Uncertainties (Coverage Factor k = 2) of Reference Standards From Different Stan- dards Laboratories According to Calibration Certifi- cates
Table 1. Expanded Uncertainties (Coverage Factor k = 2) of Reference Standards From Different Stan- dards Laboratories According to Calibration Certifi- cates
where tug, uc and wp are the standard uncertainties of g(A), C(A, Ysun, Ysun), and D(A), respectively. The magnitudes of these uncertainties depend very much on the instrument specifications and the prevailing atmo- spheric conditions, as discussed below. UV measurements can be corrected for the cosine error by multiplying the measurement result with the correction factor Kc(A) = 1/Rce(A). Because of the uncertainties in q(A), C(A, Ysun, sun), and D(A), the accuracy of the correction is limited. The standard un- certainty ur, (A) of Rc(A) is expressed by
where tug, uc and wp are the standard uncertainties of g(A), C(A, Ysun, Ysun), and D(A), respectively. The magnitudes of these uncertainties depend very much on the instrument specifications and the prevailing atmo- spheric conditions, as discussed below. UV measurements can be corrected for the cosine error by multiplying the measurement result with the correction factor Kc(A) = 1/Rce(A). Because of the uncertainties in q(A), C(A, Ysun, sun), and D(A), the accuracy of the correction is limited. The standard un- certainty ur, (A) of Rc(A) is expressed by
Figure 1. Ratio g(\) between direct and global spec- tral irradiance in dependence of wavelengths for dif- ferent zenith angles Jsy, and aerosol optical depths T(A). The values are based on UVSPEC model cal- culations assuming a total ozone column of 320 Dobson units (DU). Aerosol optical depths at 300 nm are (top) 7(300 nm) = 0.0; (middle) 7(300 nm) = 0.5; and (bot- tom) 7(300 nm) = 1.0.
Figure 1. Ratio g(\) between direct and global spec- tral irradiance in dependence of wavelengths for dif- ferent zenith angles Jsy, and aerosol optical depths T(A). The values are based on UVSPEC model cal- culations assuming a total ozone column of 320 Dobson units (DU). Aerosol optical depths at 300 nm are (top) 7(300 nm) = 0.0; (middle) 7(300 nm) = 0.5; and (bot- tom) 7(300 nm) = 1.0.
Figure 2. High-resolution solar spectrum in the region of the calcium doublet obtained with the Fourier trans- form spectrometer at the McMath/Pierce Solar Tele- scope situated on Kitt Peak, Arizona. The thin line represents the spectrum in original resolution, while the thick line denotes the spectrum convolved with the slit function of the mobile Fraunhofer Institute for Atmo- spheric Environmental Research (IFU) spectroradiome- ter of 0.574 nm full width at half maximum (FWHM).
Figure 2. High-resolution solar spectrum in the region of the calcium doublet obtained with the Fourier trans- form spectrometer at the McMath/Pierce Solar Tele- scope situated on Kitt Peak, Arizona. The thin line represents the spectrum in original resolution, while the thick line denotes the spectrum convolved with the slit function of the mobile Fraunhofer Institute for Atmo- spheric Environmental Research (IFU) spectroradiome- ter of 0.574 nm full width at half maximum (FWHM).
Figure 3. Effect of resolution on DNA weighted irra- diance. Shown are ratios Rr,pna(B) of measured and “true” DNA weighted irradiance as a function of solar elevation and total ozone for four different bandwidths between 0.3 and 2.0 nm. For each solar elevation a subset of seven data points is drawn, referring to the ozone values of (left to right) 250, 280, 300, 320, 340, 370, and 400 DU. The ratios RR pna(2nm) approxi- mate Rr pna(2nm) according to equation (20).
Figure 3. Effect of resolution on DNA weighted irra- diance. Shown are ratios Rr,pna(B) of measured and “true” DNA weighted irradiance as a function of solar elevation and total ozone for four different bandwidths between 0.3 and 2.0 nm. For each solar elevation a subset of seven data points is drawn, referring to the ozone values of (left to right) 250, 280, 300, 320, 340, 370, and 400 DU. The ratios RR pna(2nm) approxi- mate Rr pna(2nm) according to equation (20).
Figure 4. Effect of bandwidth on spectral irradiance. Shown are ratios of measured and true spectral irra- diance approximated by the exponential fit functions RRA, B), which are given in equation (21). The ratios were calculated with a triangular slit function of 1 nm FWHM and are shown for three different solar eleva- tions and ozone columns. The shaded areas refer to solar elevations of 10°, 30°, and 90°. The left bound- ary of each area refers to 250 DU; the right boundary refers to 400 DU. For 10° and 30° the shortwave ends of the shaded areas refer to a spectral irradiance E(A) of 0.01 mW/(m? nm); for 90° solar elevation the boundary spectral irradiance is 0.1 mW/(m? nm).
Figure 4. Effect of bandwidth on spectral irradiance. Shown are ratios of measured and true spectral irra- diance approximated by the exponential fit functions RRA, B), which are given in equation (21). The ratios were calculated with a triangular slit function of 1 nm FWHM and are shown for three different solar eleva- tions and ozone columns. The shaded areas refer to solar elevations of 10°, 30°, and 90°. The left bound- ary of each area refers to 250 DU; the right boundary refers to 400 DU. For 10° and 30° the shortwave ends of the shaded areas refer to a spectral irradiance E(A) of 0.01 mW/(m? nm); for 90° solar elevation the boundary spectral irradiance is 0.1 mW/(m? nm).
Figure 5. Effect of wavelength misalignment on mea- surements of biologically weighted irradiance. The top curve shows the error ratio Rw,pna(0.1nm) of mea- sured and true DNA weighted irradiance as a function of solar elevation and total ozone for 0.1 nm wavelength shift. The bottom curve is the ratio for erythemal irra- diance. For each solar elevation a subset of seven data points is drawn, referring to the ozone values of (left to right) 250, 280, 300, 320, 340, 370, and 400 DU.
Figure 5. Effect of wavelength misalignment on mea- surements of biologically weighted irradiance. The top curve shows the error ratio Rw,pna(0.1nm) of mea- sured and true DNA weighted irradiance as a function of solar elevation and total ozone for 0.1 nm wavelength shift. The bottom curve is the ratio for erythemal irra- diance. For each solar elevation a subset of seven data points is drawn, referring to the ozone values of (left to right) 250, 280, 300, 320, 340, 370, and 400 DU.
Figure 6. Ratio of wavelength-shifted and -unshifted spectral irradiance approximated by the exponential fit functions Rj p(A, AA) given in (26). The ratios were calculated for a wavelength shift of 0.1 nm and a band- width of 1.0 nm FWHM and are shown for three differ- ent solar elevations and different ozone columns. The shaded areas refer to solar elevations of 10°, 30°, and 90°. The left boundary of each area refers to 250 DU; the right boundary refer to 400 DU. For 10° and 30° the shortwave ends of the shaded areas refer to a spectral irradiance E(A) of 0.01 mW/(m? nm); for 90° solar ele- vation the boundary spectral irradiance is 0.1 mW/(m? nm).
Figure 6. Ratio of wavelength-shifted and -unshifted spectral irradiance approximated by the exponential fit functions Rj p(A, AA) given in (26). The ratios were calculated for a wavelength shift of 0.1 nm and a band- width of 1.0 nm FWHM and are shown for three differ- ent solar elevations and different ozone columns. The shaded areas refer to solar elevations of 10°, 30°, and 90°. The left boundary of each area refers to 250 DU; the right boundary refer to 400 DU. For 10° and 30° the shortwave ends of the shaded areas refer to a spectral irradiance E(A) of 0.01 mW/(m? nm); for 90° solar ele- vation the boundary spectral irradiance is 0.1 mW/(m? nm).
Figure 7. Effect of time shifts on spectral measurements. Shown are ratios Rr(\,t,30s) of shifted/unshifted spectral irradiance at 300 and 400 nm. The shift applied was 30 s. The solid lines are based on measurements conducted on July 22, 1996, in Garmisch-Partenkirchen. The dotted lines represent the corresponding modeled ratio.
Figure 7. Effect of time shifts on spectral measurements. Shown are ratios Rr(\,t,30s) of shifted/unshifted spectral irradiance at 300 and 400 nm. The shift applied was 30 s. The solid lines are based on measurements conducted on July 22, 1996, in Garmisch-Partenkirchen. The dotted lines represent the corresponding modeled ratio.
Table 3. Standard Uncertainties (k = 1) in Radiomet- ric Calibration of the Mobile IFU Spectroradiometer The combined uncertainty of references 1-16 is 1.0%.
Table 3. Standard Uncertainties (k = 1) in Radiomet- ric Calibration of the Mobile IFU Spectroradiometer The combined uncertainty of references 1-16 is 1.0%.
Table 4. Parameters to Quantify the Effect of the Cosine Error on Spectral Measurements of the IFU Radiometer for Wavelengths 300, 350, and 400 nm and for solar zenith angles (SZA) 30° and 60° The parameter Rco(A) expresses the deviation of measurements with the IFU radiometer from the true irradiance due to the cosine error of this instrument. See text for additional parameter definitions. The aerosol optical depth 7(300) used for the calculation of g(A) was set as 0.140.1. All uncertainties are based on a coverage factor of k = 1.
Table 4. Parameters to Quantify the Effect of the Cosine Error on Spectral Measurements of the IFU Radiometer for Wavelengths 300, 350, and 400 nm and for solar zenith angles (SZA) 30° and 60° The parameter Rco(A) expresses the deviation of measurements with the IFU radiometer from the true irradiance due to the cosine error of this instrument. See text for additional parameter definitions. The aerosol optical depth 7(300) used for the calculation of g(A) was set as 0.140.1. All uncertainties are based on a coverage factor of k = 1.
Figure 8. Uncertainty of the IFU radiometer, caused by wavelength shifts and the Sun’s Fraunhofer lines. The thin line (left axis) is the ratio Rw,r(A, AA) of a model spectrum, which was deliberately shifted by 0.04 nm to longer wavelengths, to the unshifted spec- trum. The applied wavelength shift of 0.04 nm is the wavelengh uncertainty of the IFU radiometer. The thick line (right axis) is the relative standard uncer- tainty up /E(A) caused by this wavelength shift accord- ing to (25).
Figure 8. Uncertainty of the IFU radiometer, caused by wavelength shifts and the Sun’s Fraunhofer lines. The thin line (left axis) is the ratio Rw,r(A, AA) of a model spectrum, which was deliberately shifted by 0.04 nm to longer wavelengths, to the unshifted spec- trum. The applied wavelength shift of 0.04 nm is the wavelengh uncertainty of the IFU radiometer. The thick line (right axis) is the relative standard uncer- tainty up /E(A) caused by this wavelength shift accord- ing to (25).
Figure 9. Nonlinearity of the mobile IFU spectrora- diometer. The curves show the ratio Rv (365 nm, S) of measurements of the IFU instrument to the true irra- diance, which would be measured by a perfectly linear radiometer. Ry is displayed as a function of the signal S of the IFU radiometer. The different symbols refer to measurements at different amplifier stages (see legend).
Figure 9. Nonlinearity of the mobile IFU spectrora- diometer. The curves show the ratio Rv (365 nm, S) of measurements of the IFU instrument to the true irra- diance, which would be measured by a perfectly linear radiometer. Ry is displayed as a function of the signal S of the IFU radiometer. The different symbols refer to measurements at different amplifier stages (see legend).
The uncertainties in erythemally weighted irradiance (Ery) and DNA weighted irradiance (DNA) are shown as well for both zenith angles. The uncertainties refer to measurements under cloudless sky with an aerosol optical depth of 0.1 and a ozone column of 320 DU. Calibrations are performed weekly. The two last rows give the combined and expanded (k = 2) uncertainties, calculated with Equation (8). Table 5. Uncertainties of the Mobile IFU Spectroradiometer for Wavelengths 300, 350, and 400 nm and solaz zenith angles (SZA) 30° and 60°
The uncertainties in erythemally weighted irradiance (Ery) and DNA weighted irradiance (DNA) are shown as well for both zenith angles. The uncertainties refer to measurements under cloudless sky with an aerosol optical depth of 0.1 and a ozone column of 320 DU. Calibrations are performed weekly. The two last rows give the combined and expanded (k = 2) uncertainties, calculated with Equation (8). Table 5. Uncertainties of the Mobile IFU Spectroradiometer for Wavelengths 300, 350, and 400 nm and solaz zenith angles (SZA) 30° and 60°
Figure 10. Percentage change in global spectral irra- diance caused by a 1% and 3% change of total ozone compared with the expanded (k = 2) uncertainty of the IFU radiometer. The change in irradiance was cal- culated for 30° solar zenith angle and 300 DU (right axis). The uncertainty of the instrument (left axis) is given for the three scenarios A, B, and C described in the text.
Figure 10. Percentage change in global spectral irra- diance caused by a 1% and 3% change of total ozone compared with the expanded (k = 2) uncertainty of the IFU radiometer. The change in irradiance was cal- culated for 30° solar zenith angle and 300 DU (right axis). The uncertainty of the instrument (left axis) is given for the three scenarios A, B, and C described in the text.
Related topics:
Environmental ScienceGeologyRemote SensingRadiometric CalibrationUncertainty of MeasurementTrend detectionSolar Irradiance
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