Journal of Geophysical Research: Atmospheres

Diffuse UV erythemal radiation experimental values



[1] Measurements of diffuse UV erythemal radiation (UVER) using a shadowband have been corrected using the models proposed by Drummond (1956), LeBaron et al. (1990), and Batlles et al. (1995). Two different methods were used to validate these models: intercomparison with an Optronic OL754 spectroradiometer and comparison with the values simulated by two radiative transfer codes, SMARTS and SBDART. For this comparison only clear days have been used. The corrected experimental values were analyzed in order to study the average values of the diffuse UVER fraction in relation to the clearness index kt. These varied between 62%, for kt close to 0.8, and 93% for kt of 0.2–0.3. Finally, a study of the monthly average and extreme values of the UV Index for diffuse radiation is presented, showing a maximum value of 6 in June.

1. Introduction

[2] In 1995 the International Commission on Non-Ionizing Radiation Protection (ICNIRP), in collaboration with the World Health Organization (WHO), the World Meteorological Organization (WMO), and the United Nations Environmental Program, defined the Ultraviolet Index (UV Index) [International Commission on Non-Ionizing Radiation Protection, 1995]. According to WMO guidelines [World Meteorological Organization, 1998] the UV Index is defined as a physical parameter averaged biologically using an action spectrum defined by the Commission Internationale de l'Éclairage [McKinlay and Diffey, 1987; Commission Internationale de l'Éclairage, 2000]. The UV radiation weighted by this curve, which represents the response of human skin to erythema or sunburn, is called the UV erythemal radiation (UVER) or erythemally active radiation. The numerical value of the UV Index is determined from the UVER expressed in W m−2, multiplied by 40 W−1m2. It is rounded to the nearest integer and always refers to a horizontal plane. Some international organizations have proposed calling this index the Global UV Index, but this term is not yet officially recognized. Currently many researchers are working toward the definition of more sophisticated indexes, such as a UV Index for inclined surfaces, or the UV Index for diffuse radiation.

[3] The solar radiation is dimmed by the absorption and scattering through the atmosphere. The scattered or diffuse radiation is an important part of the total since as much as 50% of the UVB irradiance reaching the Earth's surface comes from the scattering of solar radiation by air molecules and other particles in suspension in the atmosphere. The study of the diffuse radiation in the horizontal plane is also important because it is used as an input parameter in many models for the estimation of the irradiance in tilted surfaces.

[4] Furthermore, the UVER will also have a very important diffuse component which has not been evaluated by other authors because of the difficulty in finding suitable devices to measure it. However, the climatology of the UVER in the global component has been adequately established with radiometers YES UVB-1 or similar. An immediate solution has been to put together a radiometer with such characteristics and a shadowband. This method is universally known in other ranges, and in the same way as in the visible range the experimental values have been corrected using existing models proposed by other authors adapted to the UVER range.

[5] This paper presents a first approximation of the measurement of diffuse UVER by applying a shadowband to a standard radiometer. First we describe the experimental set up and then we discuss the correction of the shadowband using three different models. To check the validity of these models two methods were used: (1) comparison with the values provided by a spectroradiometer and (2) comparison with the simulated values from two radiative transfer models, one with single scattering and the other with multiple scattering.

2. Instrumentation and Measurement Setup

[6] The characterization of the diffuse component of radiation is especially important in the UVB range where it can account for over 50% of the global radiation, because of the effects of atmospheric scattering which increase with decreasing wavelength.

[7] The value of the diffuse horizontal irradiance can be calculated indirectly from global and direct irradiance data using the expression:

equation image

where ID is the diffuse irradiance, IG is the global horizontal irradiance, IB is the direct irradiance normal to the incidence angle and θ is the solar zenith angle. The biggest problem with the use of this equation is the high cost of the solar trackers needed for the continuous measurement of the direct irradiance.

[8] An alternative is to use direct measurements of diffuse irradiance, using a pyranometer together with a mechanism that stops the direct component of the irradiance from falling on the measurement instrument's detector. This approach requires correcting the experimental measurements since some of the sky irradiance is reduced by the shadow mechanism. Usually shadowbands or rings are used mounted on an axis parallel to the polar axis [Batlles et al., 1995]. Normally, these are covered in low reflective black paint.

[9] In our case, a semicircular shadowband was designed, in order to adjust it to a YES UVB-1, with arms anchored to a supporting structure with the same inclination as the latitude of the measurement site. When the band was attached perpendicular to the supporting arms it was parallel to the equatorial plane and, in successive adjustments over the length of the year it moved according to the axis parallel to the polar axis [López et al., 2004]. The shadowband was designed following the guidelines of Horowitz [1969], and could be built from low-cost materials. The designed mechanism consisted of two main elements which are illustrated in Figure 1, the structural support and the shadowband itself.

Figure 1.

Experimental setup for measuring diffuse UVER.

[10] The diffuse UVER measurements were obtained using a UVB-1 radiometer by YES (Yankee Environment Systems) which has a spectral range between 280 and 400 nm and a spectral sensitivity close to the erythemal action spectrum. The UVB-1 is designed to be stable over long periods of time and to operate continuously and autonomously in the field. The cosine response is less than 4% for solar zenith angles below 55° [Dichter et al., 1993].

[11] A second YES UVB-1 was used to measure the global irradiance. This instrument was calibrated in the National Institute for Aerospace Technology. This standard calibration consists of a measurement of the spectral response of the radiometer indoor and a comparison with a Brewer MKIII spectroradiometer outdoor. The calibration result is the matrix shown in Figure 2 [Vilaplana et al., 2006]. It can be observed that it is necessary to choose a cut off criterion in order to ensure that the data are not affected by an excessively high error. For a radiometer similar to that used for measuring the diffuse irradiance values, for a constant ozone value of 300 Dobson units, the error given by the calibration matrix is below 9% for zenith angles below 70°, reaching 16% for zenith angles of 75° [Vilaplana et al., 2006]. In order to use a general criterion, easy to reproduce to other similar radiometers, 70° was taken as a cut off point, thus ensuring an error of less than 10% in the experimental values. The YES UVB-1 used to measure the diffuse UVER with the shadowband was calibrated by intercomparison with the one used to measure the global irradiance.

Figure 2.

Calibration matrix for the UVB-1 radiometer.

[12] The two instruments were installed on the terrace of the Physics Faculty (latitude 39.508°, longitude −0.418°, 60 m above sea level), in the Burjassot campus of the University of Valencia. Burjassot is a town of some 35.000 inhabitants located 5 km from Valencia and 10 km from the Mediterranean coast. The measurements were taken between May 2004 and December 2006.

[13] An Optronic OL754 spectroradiometer was used to measure the spectral direct radiation, allowing the diffuse irradiance to be determined by subtracting the direct from the global. The Optronic 754 is equipped with a double monochromator, with a spectral range that extends from 250 nm to 800 nm, with a full width at half maximum of 1.6 nm allowing measurements to be made with a minimum wavelength step of 0.05 nm. The detector is a solid state photomultiplier, temperature stabilized by the Peltier effect. For the calibration of the spectroradiometer the system provided by the manufacturer Optronics is used. The instrument is calibrated twice a year against a NIST-traceable 200 W tungsten-halogen standard lamp (OL-752-10), and its wavelength and gain accuracy are verified using a dual source calibration module (OL-752-150). An OL-56A programmable current source powers the lamp.

[14] The values given by the YES UVB-1 needed to be corrected with respect to those from the OL754 spectroradiometer since the first one is designed to give a response “similar” to that of human skin. The experimental spectroradiometric measurements convolved with respect to the erythemal action spectrum give a physical value and so a more precise measure for the UVER radiation.

[15] This correction must be performed on the global irradiance values. For this purpose this instrument was placed on the terrace of the Physics Faculty of the University of Valencia. Measurements were taken over the length of a week, with basically clear skies on the days 22 to 27 March 2005, with maximum solar zenith angles between 18.8° (27 March) and 19.0° (22 March). Once the values given by the Optronic had been convolved with the erythemal action spectrum and then integrated, Figure 3 was produced. From this:

equation image

In other words, the values obtained with the UVB-1 were greater than those obtained with the OL754. For this reason, the radiometer values have been adjusted (multiplied by 0.87) to provide a proxy for the OL754 Optronics global UV measurements.

Figure 3.

Representation of the average global horizontal UVER measured by the OL-754 against the horizontal irradiance measured by the UVB-1.

3. Models for the Correction of the Shadowband

[16] The shadowband does not only remove the direct irradiance from the Sun but also, because of its size, stops part of the sky radiance and so part of the diffuse UVER from reaching the sensor. Thus it was necessary to correct the values of erythemal diffuse irradiance. To do this we applied three models, described in the bibliography and developed for measurement of diffuse irradiance in the whole of the solar spectral range: (1) the isotropic model, or Drummond model [Drummond, 1956]; (2) the LeBaron model [LeBaron et al., 1990], which considers diffuse radiation anisotropy by including two parameters (the clearness index for the diffuse irradiance and the quotient between the diffuse irradiance and the sum of the direct normal and diffuse irradiances); and (3) the Batlles model [Batlles et al., 1995], which considers the same parameters as the LeBaron model but proposes an analytic function rather than a tabulation.

3.1. Drummond Model

[17] This is based on a purely geometric analysis, assuming isotropic sky conditions. Thus the fraction of the horizontal diffuse irradiance, X, that is hidden by the shadowband, with the axis parallel to the polar axis, supposing that the width of the band is small relative to its radius, that the size of the sensor is negligible and that there are no reflections from the inside of the band, can be expressed as [Drummond, 1956]:

equation image

where b is the width of the shadowband, r is its radius, t is the time angle, t0 the time angle at sunset, ϕ the latitude, δ the declination and L the sky radiance.

[18] If we consider that the radiance is distributed isotropically, that is to say that it is distributed in a homogeneous way in every direction, then the fraction X of the diffuse irradiance with respect to the total radiance received in the hemisphere T, can be written as:

equation image

The diffuse UVER is corrected by multiplying by a correction factor, Ci, given by the equation:

equation image

3.2. LeBaron Model

[19] This model uses four parameters to describe the isotropic and anisotropic contributions of the sky radiance. The first parameter, Ci, is the same isotropic correction factor from the Drummond model and is given in equation (5) above. The three other parameters provide the correction for anisotropy and depend on the sky conditions. These parameters are: the zenith angle θ the parameter ɛ, which is the sky clearness index, being primarily a function of the cloud condition, and the parameter Δ, which is the brightness index, being primarily a function of the cloud thickness or aerosol loading. These two parameters ɛ and Δ are given by:

equation image
equation image

where I0 is the extraterrestrial irradiance obtained from the Solar Ultraviolet Spectral Irradiance Monitor Atlas3 (, ID the horizontal diffuse irradiance and IB the direct irradiance in the normal direction.

[20] The parameters ɛ and Δ are tabulated for total irradiance. In order to apply them to the range of the erythemal irradiance it was necessary to recalculate the intervals of the Δ parameter for a much smaller order of magnitude. Bearing in mind the maximum experimental value of diffuse UVER the new intervals proposed for Δ are given in Table 1. The maximum value of interval 3 is here of 0.0130 instead of 0.300. The maximum values of intervals 1 and 2 have been normalized to that one.

Table 1. Proposed New Intervals for the Parameter Δ in the UVER Range
Δ (LeBaron model)0.0–0.1200.120–0.2000.200–0.3000.300–
Δ (proposed)0–0.00520.0052–0.00870.0087–0.01300.0130–

[21] The combination of intervals considered for the four parameters (θ, Ci, ɛ and Δ) gave rise to 256 categories describing the geometry and sky conditions, such that for each combination a diffuse irradiance correction factor was obtained, as shown in Table 2.

Table 2. Correction Factors for Diffuse Irradiance for the LeBaron Modela
Value of IValue of j
  • a

    The symbols are the zenith angle, θ; the isotropic shadowband correction factor, Ci; the sky clearness index, ɛ, being primarily a function of the cloud condition; and the brightness index, Δ, being primarily a function of the cloud thickness or aerosol loading. i = θ, j = Ci, k = ɛ, and l = Δ.

(i, j, 1, 1)
(i, j, 2, 1)
(i, j, 3, 1)
(i, j, 4, 1)
(i, j, 1, 2)
(i, j, 2, 2)
(i, j, 3, 2)
(i, j, 4, 2)
(i, j, 1, 3)
(i, j, 2, 3)
(i, j, 3, 3)
(i, j, 4, 3)
(i, j, 1, 4)
(i, j, 2, 4)
(i, j, 3, 4)
(i, j, 4, 4)

3.3. Batlles Model

[22] This model uses a correction factor for the diffuse irradiance obtained from an analytical approximation from the parameters of the LeBaron model:

equation image

Using the same criterion as for the LeBaron model, the values of the parameter Δ were modified, taking an average value given by:

equation image

With which the correction factor becomes:

equation image

An alternative to this correction consists in modifying the parameter ɛ, as well as the parameter Δ, such that the coefficient of the term that depends on ɛ is obtained from the equation:

equation image

leaving the final analytical expression (Batlles2 model) in the following form:

equation image

where the coefficients of logΔ and logɛ have been fitted by equations (9) and (11).

4. Results

[23] Two different methods have been used to determine the validity of the results given by the models described above: (1) comparison with values from a spectroradiometer and (2) comparison with values simulated by radiative transfer models.

4.1. Comparison With the Values Derived From an Optronic OL-754 and a YES UVB-1

[24] To obtain the values of direct radiation, days between January and August 2005 were selected for their optimal clear sky conditions. From these measurements the diffuse UVER was calculated by:

equation image

where UVERD is the diffuse horizontal UVER, UVERG is the global horizontal UVER measured with the radiometer and transformed using the previous expression, UVERB is the direct normal UVER measured with the Optronic OL754 spectroradiometer. As before, to apply this equation to the values obtained by the Optronic, it is necessary to integrate them convolving them with the erythemal action spectrum at ground level. The error affecting these measurements depend on the error of the UVERB, measured by the Optronic (3%) and the error of the UVERG, obtained by the radiometer for zenith angles lower than 55° (5%). So the total error may be estimated as an 8%.

[25] These values corresponded to the erythemal diffuse radiation derived from the OL754 and the UVB-1. If we wanted to study the UVER measured with the UVB-1, supposing that the same relation existed between the global and the diffuse values, we would have to divide by 0.87.

4.2. Comparison With the Simulated Values From Radiative Transfer Codes

[26] The single scattering code SMARTS2.9 [Gueymard, 2001] and the multiple scattering code SBDART2.4 [Ricchiazzi et al., 1998] were used. In both cases the entry parameters were the total stratospheric ozone content provided by the TOMS satellite and the aerosol optical depth (at 500 nm in the case of SMARTS and at 550 nm for SBDART, which relate to the aerosol optical depth at the UV band by the use of the Ångström wavelength exponent (α) that is an experimental (or modeled) parameter that describes the spectral behavior of the aerosol extinction through a potential function) determined using a CIMEL CE318 photometer, located on the terrace of the Faculty of Physics [Estellés et al., 2007].

[27] Values simulated every 5 min in the period between June 2004 and April 2006 (a total of over 25000 values) were used. Only those values for which aerosol optical depth values were available were considered.

[28] Previously, as occurred with the Optronic, the global horizontal UVER values had been simulated, and these were compared with the experimental UVER obtained using the UVB-1 radiometer. The results, which can be seen in Figure 4, can be summarized as:

equation image
equation image

The SMARTS reproduced the experimental data with a discrepancy of 2% considering all data available. The SBDART overestimated the experimental values from the UVB-1 and we need to multiply the experimental values by 1.144 (or add 14%) for them to be comparable. This behavior of the multiple scattering models has been noted already by other authors [De Backer et al., 2001; De Cabo et al., 2004]. However, the SBDART performs the same way for all seasons thought the year meanwhile the fast spectral model is less stable and overvalues in spring and summer and underestimates in autumn and winter.

Figure 4.

Representation of the global horizontal UVER as simulated by the SMARTS and SBDART codes against the horizontal irradiance measured by the UVB-1. (a) SMARTS and (b) SBDART.

4.3. Results of the Validation

[29] The correlations obtained by representing the UVER values, corrected using the Drummond model, against the values derived from the Optronic and the UVB-1, corrected for UVER, and those given by the SMARTS and SBDARTS codes corrected with respect to the horizontal plane, are:

equation image
equation image
equation image

The isotropic model underestimated the diffuse erythemal irradiance by approximately 9% in comparison with the values from the OL754 and the UVB-1 and SBDART, and by 5% in comparison with the values from SMARTS.

[30] Employing for the three fittings only the data with direct measurements by the Optronic (1200), the following results are obtained:

equation image
equation image

The correlations obtained by representing the UVER values, corrected using the LeBaron model, against the values given by the Optronic and the UVB-1, corrected for UVER, and those from the SMARTS and SBDART codes, corrected with respect to the horizontal plane, are:

equation image
equation image
equation image

This model underestimated the diffuse UVER by somewhere between 4% and 5% in comparison with the spectroradiometer and with the SBDART code, respectively. The comparison with the SMARTS code showed deviations of only 0.6%. These results represented a substantial improvement compared to those from the isotropic model.

[31] Considering only days with measurements taken by the spectroradiometer, we obtain:

equation image
equation image

Repeating the same process but using the formulation of the Batlles model given in equation (10), the correlations were:

equation image
equation image
equation image

Once again the results were similar in comparison with the values given by the spectroradiometer and the SBDART code, with a deviation of 5%. This model underestimated the diffuse UVER simulated with SMARTS by only 1.5%.

[32] With the 1200 data compatible with the Optronic:

equation image
equation image

Finally the correlations for the UVER irradiances corrected using the second modified Batlles model, given in equation (12), against the values from the Optronic OL-754 and the UVB-1 and the SMARTS and SBDART codes, were:

equation image
equation image
equation image

As can be seen, in this case, the experimental values corrected by the model reproduced quite faithfully the values considered to be exact, since they only differed by 1% in the case of the OL-754 and the SBDART code. This model overestimated the SMARTS values by 2%.

[33] Finally, with the 1200 data compatible with the Optronic:

equation image
equation image

Table 3 summarizes the differences between the corrected diffuse UVER and the three models. It should be noted that all the models proposed for correcting for the shadowband gave acceptable results since none of them had deviations with respect to the Optronic OL-754 and the UVB-1, the SBDART and the SMARTS codes greater than 9%. The high degree of correlation between the results from the Optronic spectroradiometer and the SBDART code was particularly noteworthy.

Table 3. Deviations of the Diffuse UVER Corrected Using the Three Models Analyzed
equation image9%4%5.5%1.1%
equation image4.8%0.6%1.5%−2.4%
equation image9.3%4.6%5.1%1.2%

[34] From here on we will use the Batlles2 correction model for the shadowband since it was the model that gave the best results in comparison with the spectroradiometer and the multiple scattering model.

5. Average Diffuse UVER Values and UV Index for Diffuse

[35] A high percentage of the irradiance in the UVB range reaches the ground in the form of diffuse irradiance due to the importance of molecular dispersion at short wavelengths (∝λ−4). This percentage has been determined in relation to the UVER, making use of the clearness index and the diffuse fraction (equations (36) and (37) respectively).

[36] The clearness index provides the transmission of the incident global irradiance, passing through the atmosphere and, therefore, indicates the degree of availability of the solar irradiance at ground level. It is defined for the whole solar radiation spectral range as [Liu and Jordan, 1960]:

equation image

where IG is the global irradiance and I0 the extraterrestrial irradiance, both on a horizontal plane.

[37] The diffuse fraction, also known as cloudiness index, is defined as the quotient of the diffuse component over the global radiation [Liu and Jordan, 1960]:

equation image

In this work we have determined the diffuse fraction for the UVER range:

equation image

where UVERD and UVERG are the diffuse erythemal radiation and the global radiation respectively.

[38] Figure 5 shows a histogram of the 5-min values corresponding to the fraction of the diffuse UVER corrected by shadowband, using the Batlles2 method, for solar elevations greater than 20 degrees. Analyzing these data in relation to the clearness index, the average values given in Table 4 were obtained. From Table 4 it is possible to say that in very clear sky conditions (0.7 < kt < 0.8), the average value to the diffuse component of UVER reached 62%, with a higher value for all other atmospheric conditions.

Figure 5.

Histogram of the 5-min values corresponding to the fraction of diffuse UVER for solar elevations greater than 20° in Burjassot (Valencia).

Table 4. Values of kUVER in Each kt Interval for 1 Year in Burjassot (Valencia)
Points, %MeanMedian
0.1 < kt <
0.2 < kt <
0.3 < kt <
0.4 < kt <
0.5 < kt <
0.6 < kt < 0.728.60.730.73
0.7 < kt < 0.837.20.620.62
0.8 < kt <

[39] The maximum values reached by the diffuse UVER were significantly lower than those obtained for global UVER. However, the daily pattern was similar with a maximum at 1200 UT.

[40] The daily values of the UV Index were determined using two different criteria: (1) the value corresponding to solar noon and (2) the maximum daily value, which is the criterion currently recommended by all the international organizations.

[41] To establish the differences between the results given by using the two criteria for determining UVI we carried out an elementary statistical analysis. The results of this analysis are summarized in Tables 5 and 6. It should be remembered however, that, independently of the criterion used, because of the rounding needed to express the UV Index as a whole number, differences of just 0.0025 W/m2 in the UVER values can lead to differences of 1 in the Index.

Table 5. Values of the UV Index for Diffuse UVER Measured With the Shadowband From May 2004 to April 2006
MonthPointsUV Index
Table 6. UV Index Data at 1200 UT for Diffuse UVER Measured With the Shadowband From May 2004 to April 2006
MonthPointsUV Index

[42] From these results it could be deduced that in 80% of cases, the maximum value and the 1200 UT value of the UV Index were equal, despite the different number of data considered in each case. If differences of less than one unit are considered equal, then the percentage rose to 97%. Given that a difference of one unit may be due to a difference of 0.0025 W/m2 in the value of UVER, it may be reasonable to consider that estimating the UV Index based on the value at solar midday is acceptable.

6. Conclusion

[43] The design and correction of a shadowband for measuring diffuse UVER has been carried out. The correction was performed using the models proposed by Drummond, LeBaron and Batlles. The first model, which considers an isotropic distribution of the diffuse radiation, is based on a purely geometric correction factor, valid for all irradiance ranges. The other two models, which consider sky anisotropy by including other radiation range-dependent parameters, were modified in order to be applied to the UVER. A modified LeBaron model has been proposed as well as two alternative modifications of the Batlles model.

[44] To validate the results two different methods were used: intercomparison with the Optronic OL754 spectroradiometer and comparison with simulated values from two radiative transfer codes, SMARTS and SBDART. The results showed that the Drummond model underestimated the diffuse UVER by 9% according to the OL-754 validation and by 5% relative to the SMARTS. In turn, the LeBaron, Batlles and Batlles2 models underestimated the diffuse UVER in all cases by percentages that oscillated between 5 and 1%, with the lowest value corresponding to the Batlles2 model. In general the correction models reproduced the diffuse UVER well, with the Batlles2 model giving the best fit. In view of these results the experimental values of diffuse UVER were corrected using this model.

[45] Once the experimental values had been corrected we analyzed the diffuse irradiance values in the UVER range. These varied between 62%, for a kt close to 0.8, and 93% for a kt value of 0.2–0.3. Given the interest that the UV Index has as an indicator of UVER at ground level and as a simple parameter for public information, we performed a study of the monthly average and extreme values of said index. The maximum monthly value was produced in July and corresponded to a UV Index of 6, classified as “high” according to the World Health Organization [2002] classification. The global UV Index for that month was 9 [Marín et al., 2005].


[46] This work is the result of the collaboration between the Valencian Autonomous Government and the Solar Radiation Group of the University of Valencia. A. R. Esteve received a grant subsidized for this collaboration. The collaboration of M. J. Marín was possible thanks to grant CTBPRB/2003/93. This work was also financed by the Spanish Commission of Science and Technology through project REN2002-00749 and the Valencian Autonomous Government through project CTIDIB/2002/113.