Numerical integration errors in calculated tropospheric photodissociation rate coefficients

Abstract

Tropospheric photodissociation rate coefficients (J values) were calculated for NO2, O3, HNO2, CH2O, and CH3CHO using high spectral resolution (0.1 mm wavelength increments), and compared to the J values obtained with numerically degraded resolution (Δλ=1, 2, 4, 6, 8, and 10 nm, and several commonly used nonuniform grids). Depending on the molecule, substantial errors can be introduced by the larger increments. Thus for Δλ=10 nm, errors are less than 1% for NO2, less than 2% for HNO2, +6.5% to -16% for CH2O, -6.9% to +24% for CH3CHO, and -24% to +110% for O3. The errors for CH2O arise from the fine structure of its absorption spectrum, and are prevalently negative (underestimate of J). The errors for O3, and to a lesser extent for CH3CHO, arise mainly from under-resolving the overlap of the molecular action spectrum and the tropospheric actinic flux in the wavelength region of stratospheric ozone attenuation. The sign of those errors depends on whether the actinic flux is averaged onto the grid before or after the radiative transfer calculation. In all cases studied, grids with Δλ≤2 nm produced errors no larger than 5%.

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Madronich, S., Weller, G. Numerical integration errors in calculated tropospheric photodissociation rate coefficients. J Atmos Chem 10, 289–300 (1990). https://doi.org/10.1007/BF00053864

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Key words

  • Atmospheric chemistry
  • tropospheric chemistry
  • photodissociation
  • photolysis
  • J values
  • molecular action spectrum
  • spectral integration
  • errors