1. The total horizontal and diffuse horizontal voltages are measured by the MFRSR instrument. The direct normal voltage is determined within the data logger by subtraction of the diffuse voltage from the total, followed by correction for solar zenith angle. We refer to these voltages as "raw voltages."


2. Nighttime bias corrections are applied only to the diffuse horizontal voltages. This is done by:
   1. determining the time of minimum solar elevation for the set of data currently residing in the database table temp_data_poll (amount of data varies, usually 1-3 days)
   2. averaging the nighttime bias voltages from 1 hour prior to 1 hour after the time of minimum solar elevation
   3. subtracting the average bias from the diffuse voltages, only if the diffuse voltage is greater than 1.

   Note: The direct normal component is effectively bias-corrected during the subtraction in the data logger; the total horizontal is re-calculated as explained below and, therefore, needs no bias correction in this step.

3. Angular corrections (instrument cosine responses) are applied only to the direct normal voltages. The cosine responses are taken from the most recent laboratory determination that was prior to the date of the data being corrected.

   The instrument cosine responses were determined either by Yankee Environmental Systems, Inc. (YES) or by NOAA's Central UV Calibration Facility (CUCF). Older determinations were typically made by YES while more recent ones are from CUCF.

4. Diffuse cosine correction factors, determined using the isotropic sky assumption, are applied to the bias-corrected diffuse horizontal voltages:

        diffuse_bias_corrected_voltage/diffuse_cosine_factor

5. Total horizontal voltages are re-calculated by summing the direct horizontal voltage and the diffuse horizontal voltage:

        total_horizontal =
        (cosine_corrected_direct_normal x cos(zenith_angle x pi/180)) + cosine_corrected_diffuse

6. The voltages, as they are at this point in the procedure, are stored in the database as "cosine-corrected voltages."

   Note: The cosine-corrected direct normal voltages are later input to the Langley Analyzer for the generation of V-naughts for the V-naught time series.

7. Calibrations are applied to the cosine-corrected direct normal, diffuse horizontal, and total horizontal voltages to convert them to irradiances:

        irradiance = cosine_corrected_voltage / calibration factor

   Calibration factors can be laboratory-determined (lamp-calibrated) or calculated from Langley analyses. A lamp calibration factor is the product of head and board gains (head_gain x board_gain). The gain values used are linear interpolations of the two determinations that surround the date of the data being corrected. If there is no closing determination, the most recent determination before the date of the data being corrected is used.

   Head gains are from lamp calibrations performed either by Yankee Environmental Systems, Inc. (YES) or by NOAA's Central UV Calibration Facility (CUCF). Older determinations were typically made by YES while more recent ones are from CUCF. Board gains are recorded by UVB Program personnel. Langley calibration is discussed in the last section of this document.

Back to the top

Source of Information: Review of C code taken from the program "tu" (the unpacker). The program, written by personnel at ASRC, Atmospheric Solar Radiation Group at SUNY-Albany NY, uses methodology described in Harrison et al. (1994)

Instrument cosine responses used in this procedure were determined either by Yankee Environmental Systems, Inc. (YES) or by NOAA's Central UV Calibration Facility (CUCF). Older determinations were typically made by YES while more recent ones are from CUCF.

1. The instrument's most recent cosine responses, determined in the laboratory of the testing agency (YES or CUCF) prior to the date of the data being corrected, are retrieved from the database.

   For each of the 7 channels, there are 2 sets of responses: one from the south to north scan (labelled SN), and one from the west to east scan (WE). Each set is comprised of 181 responses; each response corresponds to 1integer degree. The responses of each set are organized into a list in the following order:
        M90, M89, M88 ... M3, M2, M1, P0, P90, P89, P88 ... P3, P2, P1

   The responses represent the deviations from ideal instrument responses and are unitless. The character M indicates minus; P indicates plus; and the integer indicates the angle of the beam with 0 being the point at which the beam is normal to the top of the diffuser.

   For simplicity, the remainder of this section describes the procedure as it applies to a single channel; all channels are treated in the same manner.

2. The azimuth and solar elevation (both in degrees) at the time the UV-MFRSR voltages were measured in the field are used to determine the angular correction to be applied. Both values must be within certain limits.

   The degrees of azimuth must be in the range 0 - 359. If the azimuth is less than zero, 360 is added to it; if it is greater than 359, 360 is subtracted from it.

   If the elevation is outside the range 0.001 - 89.5, the rest of the procedure is skipped and no correction is made.

3. The quadrant corresponding to the location of the sun determines the starting locations of pointers into the sets of angular responses. The quadrant is defined as the integer portion of:
        azimuth degrees/90.0

   The degree of elevation (el_deg) is defined as the integer portion of the degrees of solar elevation at the time of the field measurement.

   The pointers are set as shown in the table below, depending upon the quadrant. These are the starting points for Step 5.

   	Quadrant index	azimuth	pointer #1	pointer #2
   	--------------	-----------	----------	----------
   	0	0 - 89	SN P90	WE P90
   	1	90 - 179	WE P90	SN M90
   	2	180 - 269	SN M90	WE M90
   	3	270 - 359	WE M90	SN P90

4. Weighting factors are determined for each direction and for both the degree of elevation (el_deg) and the next highest degree of elevation.

   Azimuthal Weighting Factors:
       awt2 = weight of the second direction = the fractional portion of azimuth degrees/90.0
       awt1 = weight of the first direction = 1.0 - awt2
   Elevational Weighting Factors:
       ewt2 = weight of next highest degree = the fractional portion of the degrees of solar elevation
       ewt1 = weight of this degree = 1.0 - ewt2
   

5. Four values are needed from the lists of angular responses: 2 from SN and 2 from WE. Advance the pointers 1 value for each degree of el_deg. For example, if el_deg is 25 and the quadrant index is 0, advance pointer #1 from SN P90 to SN P65 and pointer #2 from WE P90 to WE P65. After saving the angular responses at those locations (r1deg, r2deg), advance each pointer to the next location in each list to get the responses for the next highest degree (r1next, r2next).
6. The angular correction is then calculated as follows:

   c1 (for 1st direction) = (r1deg x ewt1) + (r1next x ewt2)
   c2 (for 2nd direction) = (r2deg x ewt1) + (r2next x ewt2)
   final correction factor = (c1 x awt1) + ( c2 x awt2)
   

7. If the raw direct component voltage is greater than 0.00009, divide it by the correction factor. Otherwise, no correction is made.

Back to the top

The methodology for this algorithm is from: Leszscynski et al., Erythemal weighted radiometers . . . Photochem. and Photobiology, 67(2), 212-221, 1998. Eqn 1.

This explanation is for one channel for simplicity. All channels are processed in the same manner.

1. Retrieve from the database the instrument's most recent angular responses that were determined in the laboratory of the testing agency (YES or CUCF) prior to the date of the data being corrected.

2. Organize the angular responses in a 2-dimensional array with 4 rows and 91 columns. Each row will contain angular responses from 0 through 90 degrees for one direction in the order shown below. The angles 0 - 90 are referred to as theta.

        P0, M1, M2, M3, M4 ... M90
        P0, P1, P2, P3, P4 ... P90
        P0, M1, M2, M3, M4 ... M90
        P0, P1, P2, P3, P4 ... P90

   The first two rows contain responses from the south to north scan; The last two rows contain responses from the west to east scan. Note that the SN P0 and WE P0 values are duplicated one time each.

3. For the first row, compute a product for each value in the row:

        product = angular response x cos(theta) x sin(theta) x pi²/360

   For example, if we were doing the 5th value in the row, theta would be 4^o (product = M4 x cos(4^o) x sin(4^o) x pi²/360).

   Sum the 91 products for the row. Repeat for the other 3 rows. This will result in 4 sums of products.

4. Add the 4 sums of products together and divide the total by pi. The result is the diffuse angular correction factor for the channel. The correction is applied by dividing the bias-corrected diffuse voltages by the correction factor.

Back to the top

During the first week of each month new V-naught data are generated by submitting QC-screened data, collected over the previous month, to a program named "la" (Langley Analyzer). The program originated at ASRC, Atmospheric Solar Radiation Group at SUNY-Albany NY, and uses the methodology described in Harrison and Michalsky (1994). In short, the method performs regressions of bias- and cosine-corrected direct normal voltages, expressed as ln(mV), on airmass and subjects them to a sequence of statistical tests. A Langley analysis is attempted for each morning and afternoon period corresponding to the time of a selected airmass range. From each successful final regression, comprised of points that pass all of the tests, a V-naught value (V₀) is taken as the intercept of the line at airmass 0; the slope of the line is the average optical depth.

The program has parameters that can be set by the user. These are defined as:

LSfitSD	Limit of the standard deviation of the final regression
LowAM	Lower limit of the airmass range
HighAM	Upper limit of the airmass range
OutLimit	Number of standard deviations allowed in each least squares test
CloudSlop	Flexibility in the cloud passage test
FracPts	Fraction of points in the airmass range that must remain after other tests have completed
Key	If a key channel is specified, all tests are performed only on that channel. If enough points remain for a Langley plot to be produced, those same points are used to derive plots for the other channels.

Some of the settings we use vary by wavelength range:

Four other parameters are set as follows for all wavelengths:

FracPts	=	0.33333
CloudSlop	=	0.0
OutLimit	=	1.5
Key Channel	=	none

The results of analyses with 12 or more points remaining in the final regression are entered into a database table. The following values are stored:

•   Raw V₀
•   Normalized V₀ (normalized to remove variation due to Earth-Sun distance)
•   Optical depth
•   Standard deviation of the final regression
•   Number of points in the period (morning or afternoon)
•   Number of points in the selected airmass range
•   Number of points used in the final regression
•   Start and end times (site local standard time) of the airmass range

Back to the top

V-naughts are needed to convert measured voltages from a given MFRSR instrument to irradiances using the Langley calibration method and to compute aerosol optical depths and column ozone. Ideally, Langley analysis of the MFRSR data would produce two V-naught values (one for morning, another for afternoon) for each channel for each day of instrument operation. Also ideally, since it represents the voltage that would be measured by the instrument if it were placed at the top of the atmosphere, V-naught would be constant. In reality neither of these ideals is met. The density of V-naught points varies greatly from site to site, being quite sparse at the more turbid sites; and changes in both atmospheric conditions and instrument function can result in significant variation and drift.

Since V-naught values are needed for every day, and since variability must be considered, estimated daily V-naught values are predicted from a timeseries of Langley-generated V-naughts, accumulated over the entire deployment period of a given instrument at a given site. To be included in the timeseries, we require that V-naughts be:

•   normalized (to remove variation due to Earth-Sun distance)
•   from a morning period
•   from a successful Langley analysis comprised of at least 12 points that passed all of the Langley tests

To accomplish this for the entire history of the network, the period of operation of each site is subdivided according to the deployment periods of the various MFRSR units used. When necessary a given deployment period is further subdivided upon significant changes in board gains. Then to each time period a suitable prediction method is assigned. Currently, the default method is linear regression.

To predict V-naughts using linear regression, a sequence of two Least Squares tests is performed. Points that fall outside two standard deviations from the first regression are omitted; then a second Least Squares fit is applied to the remaining points. The resulting linear equation is used to predict a V-naught value for each day. No predictions are made in cases where there are fewer than four points in a timeseries.

Each month after the Langley Analyzer program (la) has produced a new set of V-naughts from the previous month's data, the predicted daily V-naughts for all instruments currently operating are recomputed with the additional Langley points included.

Note: Before they are used for calibration or computational purposes, the daily predicted V-naught values are converted back to the raw form (as opposed to normalized for Earth-Sun distance).

Back to the top

The Langley calibration method can be used to convert bias- and cosine- corrected MFRSR voltages to irradiances (watts m^-2 nm^-1) by:

     irradiance = mV measured x ET/V₀

ET (extra-terrestrial irradiance) is calculated for each channel of the instrument for each deployment period by weighting the Susim 3 spectrum by the most recent filter function determined by the calibration facility (YES or CUCF) prior to the deployment.

For more information about the Langley calibration method, see Slusser, J.R., J.H. Gibson, D.S. Bigelow, D. Kolinski, P. Disterhoft, K. Lantz and A. Beaubien, 2000, Langley Method of Calibrating UV Filter Radiometers, J. Geophys. Res. 105, 4841-4849.

Back to the top

For most time periods, data calibrated by the Langley method are now available. Whereas lamp-calibrated data typically become available the next day after collection, you can expect a 1 to 5 week delay for Langley-calibrated data. Langley calibrations are updated monthly, usually after the first week of each month. During the time immediately following an instrument rotation, the lag time may be greater than 5 weeks if sufficient calibration information has not yet been collected. This will affect the relatively turbid sites more frequently than sites that are typically dry and sunny.

If Langley-calibrated data are available for a site and time period in which you are interested, please use the following guidelines in deciding which calibration method provides the more accurate information.

• Vis-MFRSR (415 - 940 nm):

  Due to lack of funds for calibrating the Vis-MFRSR instruments, their lamp-calibration information is very outdated. Given that situation, the Langley-calibrated data from those instruments should always be considered more accurate than the lamp-calibrated data. There may, however, be periods for some sites when Langley calibration is not possible due to very short instrument residence times and/or too few clear days during the time a given instrument was operating.

• UV-MFRSR (300 - 368 nm):

  In the ultraviolet, the question of whether lamp calibration or Langley calibration is better is not so straightforward. For instance, at sites west of the Mississippi River, which are usually sunny and dry, Langley calibration is probably more accurate because of better signal-to-noise ratios. Even so, at the shortest wavelengths (300 - 311 nm), variations in ozone during the Langley calibration period of two to three hours make these calibrations less accurate. At turbid sites which have few Langley events, it is difficult to say which is more accurate.

Back to the top

We wish to acknowledge Kathleen O. Lantz, Cooperative Institute for Research in Environmental Sciences, University of Colorado; and NOAA/SRRB/ARL, Boulder, CO., for her assistance in preparing this section.

The network's UVB-1 Broadband Radiometers are calibrated against a triad of "standard" UVB instruments that are maintained by SRRB's Central UV Calibration Facility (CUCF). The standard instruments are periodically calibrated in the sun by comparing their broadband measurements to the integrated output of UV spectroradiometers. These calibrations are transferred to the field instruments just before they are deployed in the network by operating them side-by-side for a few days. To accomplish this transfer, a scale factor, which is simply a ratio of the test instrument's daily integral to that of the mean of the standards, is computed for each day that the test UVB instrument is run alongside the standards. The mean of the daily scale factors (scale_factor) is used to transfer the standards' well maintained calibrations to the test instruments when they are deployed in the field.

The UVB-1 broadband data are given as erythemal UV irradiance, the total measured surface UVB flux convoluted with the erythemal action spectrum, i.e., that part of the UVB spectrum responsible for sunburn on human skin (erythema) and DNA damage. The broadband instruments are calibrated assuming that the total ozone overhead at the site is 300 Dobson units (DU). This assumption can result in significant error if the true ozone value is either much higher or much lower than 300 DU. For example, if total ozone at the site is 200 DU, the erythemally-weighted irradiance at a solar zenith angle of 20 degrees will give erythema too low by approximately 15% unless a correction for the true ozone is applied. You may wish to view plots illustrating the percent error in daily UV dose for a range of ozone levels at two site locations.

The procedure used to convert raw voltage from the UVB-1 broadband instruments to erythemal UV irradiance, as shown on plots and given in data files from this website, is described below.

For data users requiring a higher level of accuracy, calibration files are available for them to compute ozone-corrected erythemal UV irradiances themselves. If you wish to receive these files, you may contact the UVB directorJim Slusser. Please be aware that these computations will require: a) downloading the raw UVB-1 sensor voltages; b) downloading the total ozone either from TOMS or as calculated by UV-B Monitoring and Research Program from the UV-MFRSR data; and c) obtaining the scale_factor(s) for each broadband instrument involved.

For more information regarding the calibration of UVB broadband radiometers, please refer to Lantz et al., 1999.

Back to the top

The Licor Inc. (LI), Photosynthetically Active Radiation or PAR sensor consists of a high stability silicon photovoltaic detector mounted in a weatherproof aluminum case beneath an acrylic cosine correction diffuser. A visible bandpass interference filter is used in combination with colored glass filters to limit the spectral response to between 400 and 700 nanometers. The azimuthal response accuracy is listed by the manufacturer at better than 1% over 360° at 45° elevation angle. The instrument is calibrated against a National Bureau of Standards lamp, and the manufacturer states the uncertainty in the calibration is ± 5%. The instrument is cosine corrected up to 80° zenith angle. LI recommends recalibration at least every two years and states that the instrument is stable to within 2% / year.

The signal of the LI PAR Sensor is processed according to the procedure recommended in the LI-COR Radiation Sensors Instruction Manual. The instrument is connected to the Yankee Environmental System’s (YES's) Data Acquisition System (DAS) using a millivolt (mV) adapter provided by LI. The purpose of the mV adaptor is to convert the direct output of the detector from units of μ amperes / (1000 μ mol s-1 m-2) to a signal with units of mV/(1000 μ mol s-1 m-2) by insertion of a 604 ohm resistor. LI provides a calibration constant (k) for each sensor given in units of μ amperes / (1000 μ mol s-1 m-2). Additionally, there is a board gain introduced by the amplifier in the YES DAS with a value of 1 / 340 that multiplies the output of the signal. Thus the final formula for processing the LI PAR sensor is:

PAR (μ moles / m2 s) = (mV / 340) * (1000 / (k * 0.604)), where k is the calibration constant.

Back to the top