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"## Notebook S06. Size Distribution Inversion of Ambient Data \n",
"\n",
" Notebook Version 2: This notebook has been updated to reflect changes made to the package DifferentialMobilityAnalyzers.jl to work with the Julia v1 series (tested with Julia 1.1.0). To read the original supplement published with the paper please switch to v1.0.0 of the package DifferentialMobilityAnalyzers.jl and/or download the virtual machine on zenodo.org which contains a complete installation that works with Julia 0.6.4 \n",
"\n",
"This notebook demonstrates how to use JDL to invert size distribution data obtained from the TSI Aerosol Instrument Manager (AIM) software. The notebook also demonstrates that the software produces comparable results to the TSI software. This notebook is a supplement to the manuscript A language to simplify computation of differential mobility analyzer response functions , Aerosol Science & Technology. loadtsidata Loads txt file exported from TSI Aerosol Instrument Manager (20130618_1410_SMPS3_BP.txt). The file was edited to remove a unicode character in line 154 that results in a load error. The load function will need to be adapted for files with different scan length and export parameters. The data corresponds to ambient data collected by Dr. Grieshop and Saha during the SOAS campaign (alse see Acknowledgements). It contains a total of 160 spectra. The instrument was operated at 4 L min-1 sheath flow and 1 L min-1 sample flow with a TSI 3081 long column DMA and TSI 3010 CPC. The data were exported with multiple charge correction turned on and diffusion correction turned off. $N_a = \\frac{-W(-N_m Q_{cpc}\\tau)}{Q_{cpc}\\tau}$ \n",
"\n",
"where $N_a$ is the coincidence corrected concentration, $N_m$ is the measured raw concentration, $Q_{cpc}$ is the volumetric CPC flow rate, $\\tau$ is the beam transit time, and $W$ is the zero branch of the LambertW function. Here $\\tau = 0.4\\mu s$, where the value is for the TSI 3010 CPC and obtained from the manufacturer manual."
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"## Block 4. Inversion using regularization\n",
"Theory of the inversion is presented in detail in Notebook S3. Here, the same routines are applied to actual data. The block makes use of the wrapper function rinv(), which computes the inverse of a response function and returns a size distribution\n",
"```julia\n",
"function rinv(R, δ;λ₁= 1e-2, λ₂=1e1)\n",
" eyeM = Matrix{Float64}(I, length(R), length(R))\n",
" setupRegularization(δ.𝐀,eyeM,R,inv(δ.𝐒)*R) # setup the system\n",
" λopt = lcorner(λ₁,λ₂;n=10,r=3) # compute the optimal λ\n",
" N = clean((reginv(λopt, r = :Nλ))[1]) # find the inverted size\n",
" return SizeDistribution([],δ.De,δ.Dp,δ.ΔlnD,N./δ.ΔlnD,N,:regularized)\n",
"end\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32mInverting TSI SMPS ...100%|█████████████████████████████| Time: 0:03:52\u001b[39m\n"
]
}
],
"source": [
"λ₁,λ₂ = 1e-2, 1e1 # bounds [λ₁,λ₂] within which the optimal distribution lies\n",
"\n",
"𝕟ᵢₙᵥ = SizeDistribution[]\n",
"@showprogress 1 \"Inverting TSI SMPS ...\" for i = 1:b\n",
" push!(𝕟ᵢₙᵥ, rinv(𝕣[i].N, δ,λ₁=λ₁,λ₂=λ₂))\n",
"end\n",
"\n",
"# Compute size distribution statistics.\n",
"Nt, Ninv = Float64[],Float64[]\n",
"At, Ainv = Float64[],Float64[]\n",
"Vt, Vinv = Float64[],Float64[]\n",
"for i = 1:b\n",
" push!(Nt, sum(𝕟[i].N))\n",
" push!(Ninv,sum(𝕟ᵢₙᵥ[i].N))\n",
" push!(At, sum(π/4.0.*(𝕟[i].Dp./1000.0).^2 .* 𝕟[i].N))\n",
" push!(Ainv,sum(π/4.0.*(𝕟ᵢₙᵥ[i].Dp./1000.0).^2 .* 𝕟ᵢₙᵥ[i].N))\n",
" push!(Vt, sum(π/6.0.*(𝕟[i].Dp./1000.0).^3 .* 𝕟[i].N))\n",
" push!(Vinv,sum(π/6.0.*(𝕟ᵢₙᵥ[i].Dp./1000.0).^3 .* 𝕟ᵢₙᵥ[i].N))\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Block 5. Visualization"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (a) Example size distribution comparison"
]
},
{
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"0 1000 2000 0 10 20 0 50 100 150 0 2 4 TSI AIM TSI AIM TSI AIM This work This work This work Scan number N (cm⁻³) A (μm² cm⁻³) V (μm³ cm⁻³) Figure 3. Top to bottom: integrated number concentration, surface area, and volume concentration from TSI AIM software provided dn/dlnD distribution and from the inversion of this work. Note that for scan 54, the agreement is poor. The spectrum can be visualized using the block above if desired. The disagreement is due to failed convergence of the L-curve algorithm. This can be fixed by changing the bounds $\\lambda_1$ and $\\lambda_2$ in the lcorner() call or perhaps a more robust L-curve algorithm. It is left in place here to alert potential users of this issue. It is apparent from graphing the inverted spectra from scan 54 that inversion failed."
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"### (c) Comparison of relative error"
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"## Summary and Conclusions\n",
"Figures 2-4 demonstrate that the code can be used to invert size distribution data. Figure 2 shows that the inverted spectra is in good qualitative agreement with the inverted spectra from the TSI software. The error of the regularization routine here appears to be similar to that of the TSI algorithm. Number surface area, and volume concentration agree within ~2%, 2%, and 4% for the entire dataset. This agreement is comparable to the range given by Wiedensohler et al. (2012), who compared the performance of several commercial and non-commercial inversion routines. "
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"## Acknowlegements and References\n",
"\n",
"The data were collected by Drs. Andrew Grieshop and Provat Saha during the 2013 SOAS campaign (Saha et al., 2017). I thank Andrew Grieshop for sharing the datafile.