|It is easy to compute what the concentration limit for your LISST instrument is. What you need is knowledge of the pathlength of the instrument and the mean size of the particles you’re measuring. The basic equation that we need to use isc = 1.13* SSC / d => SSC = c * d /1.13
wherec is the beam attenuation coefficient (m-1),SSC is suspended sediment concentration (mg l -1 ) andd is (mean) particle size in µm.
We see that for a fixed value of c , the concentration limit scales linearly with particle diameter. (For more information about how this equation arises, read this paper by Agrawal et al.).How do we find the beam attenuation coefficient that is associated with the concentration limit? We must first compute the optical transmission, t, associated with the concentration limit. It is usually recommended that the lower value for the optical transmission is 30% (or 0.3; for the LISST-Portable|XR, the minimum recommended is 75% or 0.75). Fortunately, the relationship between t and c is given by Beer’s Law:
t = exp(- c * L ) => c = -ln(t)/ L
where L is the pathlength in m.
Now, for a standard LISST-100X with a path length of 5 cm (0.05m) we can compute the beam attenuation coefficient for tau=0.3:
c = -ln(0.3)/0.05 = 24,
and thus we find that for a an optical transmission of 0.3 the beam attenuation coefficient will be 24 m -1 .
This value then becomes our c in equation 1 above, and if the particle size is 100 µm we have the following:
24 = 1.13* SSC /100 => SSC = 24*100/1.13 = 2124 mg/l
For a particle size of 33 µm we find SSC = 24*33/1.13 =700 mg/l – as expected since the maximum concentration scales linearly with diameter.
The LISST-100X can be equipped with a path reduction module that decreases the optical path to 1 cm instead of 5 cm and we can now compute what the maximum concentration is in this case. Tau is still 0.3, so in order to find the associated c we have c = -ln(tau)/ L = -ln(0.3)/0.01 = 120 m -1 and for a 100 µm particle we find the concentration to be
SSC = c * d /1.13 = 120*100/1.13 = 10,600 mg l -1 .
The LISST-StreamSide has a path length of 5 mm (0.005 m), which means that c = -ln(0.3)/0.005 = 241 m -1 . For a particle size of 33 µm we find that the concentration limit is SSC = c * d /1.13 = 241*33/1.13 = 7038 mg/l.
What about the lower concentration limit? It is generally recommended that the optical transmission does not exceed 98% (0.98). For this value of tau, c = -ln(0.98)/0.005 = 4 m -1 for the LISST-StreamSide. For 33 µm particles, the minimum concentration is therefore = c * d /1.13 = 4*33/1.13 = 116 mg/l; for 10 µm particles the minimum concentration is 35 mg/l.