# Working Limits of Particle Concentrations

#### What is the measurable concentration range of LISST instruments?

In Brief:  The range of concentrations that LISST instruments can measure depends on particle size. For laser-diffraction LISST instruments, the recommended upper limit of concentrations is:

Cmax = 375 x D/P μliter/liter

where D is mean grain size in μm, and P is laser path-length in mm. Similarly,

Cmin ≈ Cmax/120.

These limits are, however, not absolute. The following briefly describes how they are derived. For a more detailed technical description, see here.

#### Range for different particle size distributions

The figure below presents the expected limits for various log-normal particle size distributions (PSD). The working limits are shown for log-normal PSD centered at the grain size on x-axis, and of width indicated as number of size bins of a LISST instrument.

#### Rationale

The upper limit is defined by the concentration at which transmission across the optical path drops to 30%. This is not an absolute limit. It is approximately where multiple-scattering starts to become significant. Measurements can be made in more turbid environment, but with some degradation of PSD at the small sizes.

The lower limit is defined by the concentration where signals are likely to be adequate. We have chosen 99% transmission of laser as this lower concentration limit. Working in lower concentrations can cause problems of signal to noise, producing noisy PSD’s.

#### Convenient Rules

The upper limit for 10 micron mean size (and any width) is ~75 μl/liter. This is due to the convenient crossing of all lines around this point. The lowest limit of concentration are about 120 times lower. [this is based on ratio of log of optical transmissions, 30% and 99%; i.e. log(0.3)/log(0.99)].

#### Effect of Optical Path Length

The limits are shown for an optical path in water of 50mm, i.e. for the LISST-100X and LISST-DEEP. For other instruments with shorter paths, the limits increase proportionately; e.g. 10X shorter path (5mm) would have a 10X higher working limit. Consequently,

• For LISST-SL, (3mm path) the maximum limits are 17 times higher.
• For LISST-200X (25mm path) the maximum limits are 2 times higher.
• For LISST-Hydro, LISST-Infinite, LISST-StreamSide, and a LISST-200X with 80% PRM, (all with 5mm path) the limits are 10 times higher.

The upper limit is set by the mean diameter of particles and their size spread. The lines above are for widths of 1,2,4,6, and 8 size bins of LISSTs. Log-normal PSD’s of these widths, centered on bin 12, are shown in top-left inset.

If you must work outside these limits

Too Clear Water: Since clear water means weak signals, averaging of multiple scans helps smooth the results. This can be done even after data collection, so relax! But when signals are weak, you must be especially careful with cleaning and background measurements.

Too Turbid Water: When the particle concentration is too high (i.e. likely to create multiple scattering), we recommend installing a Path Reduction Module (PRM) in the optics. For the LISST-200X, this reduces the optical path by 80%, i.e. from 25mm to 5mm. It results in a 5X increase in upper working limit. For details on the PRM, click here. How would you know if a PRM is needed before a field experiment? If you think concentration is likely to be high (say ~200 micro-l/l), then be safe, use it. You only give up the low-end of measurable concentrations.

Revised 17 Sept. 2018