Light Attenuation Vertical Profile

Propagate downwelling irradiance through layered Beer–Lambert extinction; supplied coefficients include only modeled optical attenuation and no bottom reflection.

Description

Downwelling light declines with accumulated optical depth.

Downwelling light declines with accumulated optical depth. Layered Beer–Lambert attenuation permits different extinction coefficients along a vertical profile.^[1]

The tool returns boundaryDepthsM, boundaryIrradiances. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Light Attenuation Vertical Profile

Use this for the following task: Propagate downwelling irradiance through layered Beer–Lambert extinction; supplied coefficients include only modeled optical attenuation and no bottom reflection. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Light Attenuation Vertical Profile and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter layerThicknessesM, extinctionCoefficientsPerMeter, surfaceIrradiance according to the field table, then run the tool.
Read boundaryDepthsM, boundaryIrradiances. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
layerThicknessesM	Layer thicknesses m	list of number	Required
extinctionCoefficientsPerMeter	Extinction coefficients per meter	list of number	Required
surfaceIrradiance	Surface irradiance	number	Required

Provide aligned positive layer thicknesses and nonnegative extinction coefficients and surface irradiance. Accumulate depth and optical depth, returning surface and every layer-bottom boundary.

irradiance(z)=surfaceIrradiance×exp(−ΣlayerThickness×extinction)

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
boundaryDepthsM	Boundary depths m	list of number
boundaryIrradiances	Boundary irradiances	list of number

json

{
  "input": {
    "layerThicknessesM": [
      1,
      2
    ],
    "extinctionCoefficientsPerMeter": [
      0.1,
      0.2
    ],
    "surfaceIrradiance": 100
  },
  "output": {
    "boundaryDepthsM": [
      0,
      1,
      3
    ],
    "boundaryIrradiances": [
      100,
      90.48374180359595,
      60.653065971263345
    ]
  }
}

Limitations and assumptions

Coefficients are supplied and constant within each layer. Bottom reflection and unmodeled optical processes are excluded; very long boundary output is rejected.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Compensation Depth Light Level when you need its operation: Invert constant optical extinction for a supplied compensation light threshold; a deeper-than-bottom model value is flagged, not silently clipped or declared biologically valid. Choose Littoral Zone Percent Area for the complementary operation: Classify measured lake-bottom patches by a caller colonization depth and sum area; assumes each representative depth describes its patch and does not infer vegetation presence or map geometry.

Background reference: Quantitative Spectrophotometry and Beer’s Law.

References

Quantitative Spectrophotometry and Beer’s Law — University of California Davis, Chemistry LibreTexts

Similar or alternative tools

Compensation Depth Light Level
Invert constant optical extinction for a supplied compensation light threshold; a deeper-than-bottom model value is flagged, not silently clipped or declared biologically valid.
Littoral Zone Percent Area
Classify measured lake-bottom patches by a caller colonization depth and sum area; assumes each representative depth describes its patch and does not infer vegetation presence or map geometry.