#### What are the concentration limits for a LISST instrument?

There are really 2 answers to this question: The short one and the more elaborate one. The short one follows here, the elaborate one a bit further down this webpage. At the bottom is a table you can use if you are really in a hurry and don’t have time to read all this! You can also find a simpler explanation here.

#### The Short Answer

The maximum working concentration for an instrument depends on the particle size and optical path of the laser in instrument optics. The cut-off can be estimated as d/L where d is grain size in µm, and L is laser path-length in water in meters. This limit is in mg/L with an assumed mass density of 2.65g/mL.

As an example, the LISST-100 with its path length of 0.05 m, and for particles of 10 µm in diameter, the upper limit would be 200 mg/L (10/0.05). The limit changes to 1,000mg/L if an 80% path reduction module (PRM) (0.01 m path length) is employed. For other instruments, the same 10 µm grains can be measured at concentrations up to 2,000 mg/L with the LISST-StreamSide (0.005 m path length), and up to 3,300mg/L with the LISST-Infinite and LISST-HYDRO (0.003 m path length) before dilution.

Note that the instruments do not suddenly stop functioning at these upper limits. These limits define an actually fuzzy boundary beyond which accuracy of measurement degrades due to multiple scattering of light (i.e. re-scattering of once scattered light). Measurements can continue with loss of accuracy (less than ~20%) down to optical transmission of 10%.

When considering a distribution of sizes, the limits should be calculated by substituting the diameter above with the Sauter Mean Diameter (total volume/total area).

#### The Elaborate Answer

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 is

c= 1.13*SSC/dor

SSC=c*d/1.13

where* c* is the beam attenuation coefficient (m-1), *SSC *is suspended sediment concentration (mg l -1 ) and *d *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

whereLis 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.

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.

#### Tables

The table below shows the **maximum theoretical mass concentration in mg/l (equivalent to PPM by MASS)** that the LISST would be able to measure, as a function of mean particle size in µm and optical path length varying from 50 mm (standard LISST-100X) to 3 mm (standard LISST-Infinite). Note that the LISST-Portable|XR has a different transmission limit (75% instead of 30%) from other LISST instruments, so this figures in this table do not apply to it. See the LISST-Portable|XR Specifications for details.

Mean particle diameter |
Wentworth grades |
LISST Optical Pathlength in mm | |||||
---|---|---|---|---|---|---|---|

µm | Phi | 50 | 25 | 10 | 5 | 3 | |

1.95 | 9.00 | Clay | 42 | 83 | 208 | 416 | 693 |

3.9 | 8.00 | Very Fine Silt | 83 | 166 | 416 | 831 | 1385 |

7.8 | 7.00 | Fine Silt | 166 | 332 | 831 | 1662 | 2770 |

15.6 | 6.00 | Medium Silt | 332 | 665 | 1662 | 3324 | 5540 |

31.25 | 5.00 | Coarse Silt | 666 | 1332 | 3330 | 6659 | 11099 |

62.5 | 4.00 | Very fine sand | 1364 | 2728 | 6819 | 13638 | 22730 |

125 | 3.00 | Fine sand | 2664 | 5327 | 13318 | 26637 | 44394 |

250 | 2.00 | Medium sand | 5327 | 10655 | 26637 | 53273 | 88789 |

The table below shows the** maximum theoretical volume concentration in µl/l (equivalent to PPM by VOLUME)** that the LISST would be able to measure, as a function of mean particle size in µm and optical path length varying from 50 mm (standard LISST-100X) to 3 mm (standard LISST-Infinite).It is assumed that the particles have a density of 2.65 g/cm3.

Mean particle diameter |
Wentworth grades |
LISST Optical Pathlength in mm | |||||
---|---|---|---|---|---|---|---|

µm | Phi | 50 | 25 | 10 | 5 | 3 | |

1.95 | 9.00 | Clay | 16 | 31 | 79 | 157 | 262 |

3.9 | 8.00 | Very Fine Silt | 31 | 63 | 157 | 314 | 523 |

7.8 | 7.00 | Fine Silt | 63 | 125 | 314 | 627 | 1045 |

15.6 | 6.00 | Medium Silt | 126 | 251 | 627 | 1254 | 2091 |

31.25 | 5.00 | Coarse Silt | 251 | 502 | 1256 | 2512 | 4188 |

62.5 | 4.00 | Very fine sand | 515 | 1029 | 2573 | 5146 | 8577 |

125 | 3.00 | Fine sand | 1005 | 2010 | 5025 | 10051 | 16752 |

250 | 2.00 | Medium sand | 2010 | 4020 | 10051 | 20103 | 33505 |

#### Path lengths for LISST models

50 mm: Standard LISST-100X and LISST-STX

25 mm: Standard LISST-200X, LISST-25X. With 50% PRM installed: LISST-100X and LISST-STX.

10 mm: LISST-100X with 80% PRM installed.

5 mm: Standard LISST-StreamSide, LISST-Portable, LISST-Portable|XR and custom LISST-HYDRO. With 80% PRM installed: LISST-200X. With 90% PRM installed: LISST-100X

3 mm: Standard LISST-Infinite, LISST-HYDRO and LISST-SL (LISST-SL actual path length 3.2 mm).

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* Updated Dec 5, 2014 *