## Synthetic Spectrum Data

The UV-MFRSR instrument, described in Section 8.2.2, makes measurements every three minutes in seven spectral regions, each with a nominal bandwidth of 2 nm. The centers of the bandwidth regions are located at 300, 305, 311, 317, 325, 332 and 368 nm. The measurements are useful in assessing damage to plants and human health, particularly when considered in conjunction with specific Biological Spectral Weighting Functions (BSWFs); see for example Caldwell et al. (1986). The calculation of an index is usually required to indicate the overall magnitude of the effects of the UV-B radiation. The indices are almost always obtained by an integration of the downwelling UV-B total horizontal irradiances, spectrally weighted by the BSWF. Because the UV-B irradiances are measured in discrete spectral regions, some means of interpolating the irradiances at wavelengths appropriate for performing the integrations is required. The estimates of the downwelling UV-B irradiances at each nanometer are currently made using curve fitting techniques, and have come to be known as "synthetic spectra." The synthetic spectra algorithm provides a functional form which may be used to approximate the spectral, downwelling UV-B irradiances at any wavelength within the wavelength range of the measurements. The current synthetic spectra algorithm, described in

Min and Harrison (1998) with updates by Davis and Slusser (2005), begins with a form of Beer's Law:

It= I01 exp {-(mX (2) + C^"1 + C2r2 + C3A~3 + C41~4)}, (8.11)

where I0 and I are the extraterrestrial and surface spectral irradiance, respectively, at a wavelength A, m is the atmospheric path, X is the optical depth due to ozone, and the constants C are determined by the fitting algorithm. When considering the method to determine the coefficients C, one of the first considerations is if the functional form is linear in the undetermined coefficients. In this case, the form requires a non-linear approach; in particular, the non-linear least squares approach of Levenberg and Marquardt is basically used as described in Press et al. (1992). Although taking the natural logarithm of the equation puts it in a form amenable to a linear fitting technique, it has been found through extensive testing at UVMRP, using many different functional representations of the term within the exponential, that the original non-linear form results in superior performance, particularly at the shorter wavelengths where much of the interest lies for agricultural research. Figure 8.8 shows an example of a synthetic spectrum obtained from combined UV and visible MFRSR measurements, and two important BSWFs: (1) the photosynthetically active region (PAR), and (2) the Flint BSWF region.

-Synthesized spectrum

• Measurements

-Synthesized spectrum

• Measurements 200 300 400 500 600 700 800 900 1000

Wavelength (nmj

Figure 8.8 An example of a synthetic spectrum, along with the measurements from which it was derived, and the Flint and PAR BSWF regions over which the synthetic spectrum is integrated to produce agriculturally important indices. See Caldwell et al. (1986) for a discussion of the Flint BSWF

200 300 400 500 600 700 800 900 1000

Wavelength (nmj

Figure 8.8 An example of a synthetic spectrum, along with the measurements from which it was derived, and the Flint and PAR BSWF regions over which the synthetic spectrum is integrated to produce agriculturally important indices. See Caldwell et al. (1986) for a discussion of the Flint BSWF

The synthetic spectrum has been applied to the data collected by UV-MFRSR instruments deployed at all US UVMRP climatological sites since 2000 to construct a database of daily sums of unweighted UV-A, unweighted UV-B, erythemal, vitamin D, and Flint and Caldwell indices. Figure 8.9 shows the annual average of the daily sum of unweighted UV-A irradiance for 2001 which was derived from the database. The UVMRP website allows access to the daily sum database to the extent that the user is allowed to find averages of the daily sums over a user specified interval for any of the U.S. UVMRP sites. Figure 8.9 Contour map of 2001 annual accumulation of unweighted UV-A irradiance over the continental U.S. in MJ/m2. The UVMRP station locations are identified by the red asterisks in the figure