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Time Constants

Thursday, 26 August 2010 08:45 Rocky
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Question: We have been using the PRR800 at 15hz sampling speed to record the shallow water variability in shallow coral reefs of Israel caused by wave lensing. We experimented in Australia with the PUV2500 at 20 hz and found very tight agreement between the modelled and actually wave lensing intensity measurements in the UV range of the spectrum. When we were working in Israel the fastest we could get the PRR800 in Israel to sample was at 15 hz. At 15 hz we are getting measurements every 66ms, but what would the integration time be for the sampling period as obviously there is some time in there where the data is being written off and not necessarily recording so I am guessing the integration time must be less than 66ms.

Answer: The time constant in our radiometers is defined as the “RC time constant” (  For both the PUV and PRR it is 50mS.  The PRR800 is running slower as it has more channels to sample. The channels are being sampled by an analog to digital converter running a new conversion every 25uS.  Channels are sampled in order within an instrument housing, and are sampled continuously with the result averaged until it is transmitted, and then a new average starts accumulates.  So, an instrument with fewer channels will average more readings into a single report data frame than an instrument with more channels.  There is buffering in the instrument so that when data is being transmitted, it is being sampled in the background for the next data frame to transmit.  The maximum rate that an instrument will run is a function of the number of channels and number of instruments connected.



Immersion Coefficients

Thursday, 26 August 2010 08:44 Rocky
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Question:  The PRR800 we were using has an immersion coefficient so that it can be used for both a surface and aquatic radiometer. The reviewer asked "how is it derived, and does the instrument in fact have a different field of view in or out of the water? If it has a 2π (pi) diffuser how does the FOV of that change?"

Answer:  It is more accurate say that the PRR800 has an immersion coefficient to correct the response of the instrument for the effects of being immersed in water. All of our instruments are calibrated in air, but underwater instruments like the PRR800 will change their response (the amount of light entering the collector is different when the refractive index changes) when immersed. We measure that change in response (the immersion coefficient) and provide that in the calibration data. A reference describing how this is done is found in Hooker and Zibordi, “Advanced Methods for Characterizing the Immersion Factor of Irradiance Sensors,”

The PRR800 is designed to have a very good cosine response in water and the PRR810 is designed to have a very good cosine response in air — each is optimized for the environment for which they are intended to be used. By "very good" I mean ±2% from 0° to 65°, and ±10% from 65° to 85°. Both sensors have a “field of view” of 180°. A good discussion of this cosine response is found here: In your case, I believe you do not have the normal PRR810 or PUV2510 surface (“deck”) versions, so you are using the underwater version without the immersion coefficient. The accuracy of the cosine response will be less than optimum in this case, and the loss of accurate cosine correction will probably not be significant when the Sun is high in the sky. At lower solar angles, you will begin to see the effects of the cosine response error. Typically the measured values will be somewhat higher than should be as the Sun is lower. This effect will be more pronounced in the long wavelengths, and minor in the UV.

In addition, when using the underwater version of the instrument in air, you need to switch calibration data and use calibration without the immersion factor.

Last Updated ( Tuesday, 05 October 2010 14:08 )


Thursday, 26 August 2010 08:41 Rocky
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K(PAR) refers to the diffuse attenutaion coefficient for PAR (Photosynthetically Active [or Available] Radiation). Many researchers commonly use K(xxx), where xxx is a particular wavelength, to describe the rate of attenuation of irradiance in water, for example. If the water mass is uniform, then this attenuation coefficient will be almost constant with depth. Because overlapping groups of researchers commonly use PAR in biological studies (plant growth) the use of K(PAR) has crept into common use. This has a problem.

Because PAR is a spectral integral from 400–700 nm, as opposed to a single wavelength, the attenuation coefficient for perfectly mixed water (ranging from distilled or pure water to highly turbid) will be different at every depth. The reason for this is as light penetrates through water, the spectral distribution changes because the absorption coefficient differs greatly depending on what part of the spectrum you consider.

We see this when we look at a vertical profile to 10 meters as an example. In well-mixed water, K(PAR) is large near the surface and rapidly declines as the red part of the spectrum is filtered out by water absorption, while the blue part is attenuated at a much slower rate. Thus, by 10 m, you have already lost most of the red, and the K that is calculated represents the attenuation of the blue part of the spectrum (lower attenuation coefficient).

The consequence of this is that you may see linear parts of the log profile at specific wavelengths, but you will not normally have a linear part for PAR, because of the changing spectral nature of PAR with depth.

Last Updated ( Friday, 17 May 2019 09:56 )

UVindex from GUV

Thursday, 26 August 2010 08:42 Rocky
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There are two methods to calculate the UV Index from GUV measurements, a simple and a more advanced method. The UV Index discussed here refers to the action for erythema (sunburn) as defined in the CIE norm by McKinlay and Diffey (1987).


1. Simple method

The simple method is described in the BSI Application Note "GUV Diffey Dose Calculations.pdf". In brief, the UV Index is calculated from a linear combination of measurements of the GUV channels at 305, 320, and 340 nm:

UV Index = a1 E305 + a2 E320 + a3 E340

where a1 = 0.8911, a2 = 0.0818, and a3 = 0.007751. These coefficients refer to the "2B. Coefficients for 96 UV INDEX" listed in Table 1 of the aforementioned application note. E305, E320, and E340 are spectral irradiances at 305, 320, and 340 nm, which are calculated by applying offsets and scale factors to the GUV's measurements as described in the instrument's calibration certificate.

If a GUV radiometer is equipped with a channel at 313 nm, the UV Index can also be calculated from a linear combination of measurements of four GUV channels, namely 305, 313, 320, and 340 nm:

UV Index = a1 E305 + a2 E313 + a3 E320 + a4 E340

where a1 = 0.8058, a2 = 0.0887, a3 = 0.0324, and a4= 0.0131. Using measurements of four, rather than three, channels lead to slightly more accurate results, in particular for low-sun conditions.

2. Advanced method

An alternative method of calculating the UV Index from GUV measurements is described by Bernhard et al. (2005). The paper is available at This is the method implemented by the NSF UV Monitoring Network. The method requires measurements of the GUV's spectral response functions plus associated calibration factors.

Bernhard, G., C.R. Booth, and J.C. Ehramjian. (2005). Real-time ultraviolet and column ozone from multichannel ultraviolet radiometers deployed in the National Science Foundation’s ultraviolet monitoring network. Opt. Eng., 44(4), 041011-1 — 041011-12.

McKinlay, A.F., and B.L. Diffey (Eds.). (1987). A reference action spectrum for ultraviolet induced erythema in human skin, CIE Res. Note, 6(1), 17–22.

Last Updated ( Wednesday, 13 October 2010 07:04 )

Spectral Response

Wednesday, 25 August 2010 07:57 Rocky
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Spectral Response refers to the level of response as a function of wavelength of a radiometer.  Most radiometers offered by Biospherical Instruments either have a PAR response or a 10 nm wide narrow-band response which, when combined with an array of similar photodetectors across the spectrum, forms a spectroradiometer.

By default, AMOUR radiometers measure with the spectral response of a silicon photodiode (wide-band response between 250 and 1100 nm).  If the wavelength distribution of the source being measured is known, and the instrument is ordered with a response function calibration, the optical flux can be measured.

Spectral response functions offered for Biospherical Instruments' AMOUR radiometer. The functions were measured with the BSI spectral testerSpectral response functions offered for Biospherical Instruments' AMOUR radiometer. The functions were measured with the BSI spectral tester

The AMOUR radiometer features a selection of different filter assemblies that modify the spectral response of a silicon photodiode. The instruments can also be ordered with a large selection of filters, including narrow-band, and filters that mimic some physiological response function. These include: 

  • Narrow-Band filters (~10 nm bandwidth) are normally used when the source distribution is known and typically confined to a small region, such as a laser, or where it is combined in an ensemble of radiometers spaced through the spectral region of interest, such that the entire spectrum can be reconstructed.
  • PAR (Photosynthetically Active Radiation), which is confined to the 400–700 nm spectral region and is weighted with a quantum response, as opposed to most weighted spectral responses. Calibration units include moles/(cm2 s), einsteins/(cm2 s), and quanta or photons/(cm2 s), and their MKS variants.
  • Blue Light Hazard, which is defined as the potential for a photochemical-induced retinal injury resulting from radiation exposure at wavelengths primarily between 400 nm and 500 nm.
  • Photometric Response, which describes the perceived brightness to the human eye.
  • Erythema, which describes the wavelength-dependent sensitivity of the human skin to sunburn.
Additional response functions, tailored to customer needs, are available.
Last Updated ( Tuesday, 05 October 2010 07:31 )

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