DesertAerosol
ModelingToolkit implementation of the Desert atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Desert distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [726, 114, 0.178] cm^-3, D_g = [0.002, 0.038, 21.60] um, log10 sigma = [0.247, 0.770, 0.438]) — two fine modes plus a coarse mineral-dust mode at 21.6 um. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl DesertAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Desert Table 8.3 mode parameters as defaults.
Description
ModelingToolkit implementation of the Desert atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 (“Properties of the Atmospheric Aerosol”), Table 8.3. The Desert distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [726, 114, 0.178] cm^-3, D_g = [0.002, 0.038, 21.60] um, log10 sigma = [0.247, 0.770, 0.438]) — two fine modes plus a coarse mineral-dust mode at 21.6 um. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl DesertAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Desert Table 8.3 mode parameters as defaults.
Reference
Seinfeld, J. H., and Pandis, S. N. (2006). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd Edition, John Wiley & Sons, Chapter 8, “Properties of the Atmospheric Aerosol”. Multi-modal lognormal size distribution: Eq. 8.54 (number), 8.49/8.50 (surface area), 8.52/8.53 (volume); Hatch-Choate diameters Eq. 8.44/8.50/8.53; total moments Eq. 8.41 with Eq. 8.5/8.7; vertical mass profile Eq. 8.55. Mode parameters are the Desert entry of Table 8.3.
_source_ref: Aerosol.jl@c8c640bb636b22f2425460e9ed5cba50793bfee1:src/size_distribution.jl:282
Upstream DesertAerosol(; name=:DesertAerosol) is a thin preset wrapper that calls AerosolDistribution(3; name, N_vals, D_g_vals, logsigma_vals) with the Desert mode parameters of Seinfeld & Pandis (2006) Table 8.3. It returns a flat MTK System — not a hierarchical composition — identical in structure to the base AerosolDistribution component but with the three array @parameters N / D_g / logsigma defaulted to the Desert values. The migration is therefore a standalone copy of components/aerosol/size/aerosol_distribution.esm with the nine scalarized mode-parameter defaults replaced; the ten observed-output expressions and the empty equations array are unchanged.
Migration form: observed-form, matching aerosol_distribution.esm. The base component carries two @constants (pi_c = pi, ln10 = log(10)), the length-n_modes array @parameters N / D_g / logsigma plus the scalar @parameters D_p, z, H_p, and ten time-indexed @variables (n_N_o, n_S_o, n_V_o, N_t, S_t, V_t, D_s, D_v, D_bar, M_z) each defined by one algebraic lhs ~ rhs equation whose RHS references only parameters and constants. Per the purely-algebraic migration rule each output is encoded as type: observed with its defining relation in the expression field and the equations array is empty.
Array scalarization: as in the base migration the length-3 array parameters N, D_g, logsigma are scalarized into nine scalar parameters N_1..N_3, D_g_1..D_g_3, logsigma_1..logsigma_3 and each sum(... for i in 1:n_modes) is unrolled into an explicit three-term sum. DesertAerosol is a three-mode distribution, so n_modes = 3 is exact (not a default truncation). The .esm array-variable path emits getindex nodes (tracked upstream as gt-p3ep), which is why the scalarized form is used.
Desert defaults (Table 8.3, Seinfeld & Pandis 2006, Chapter 8): N = [726.0, 114.0, 0.178] cm^-3 -> [7.26e8, 1.14e8, 1.78e5] m^-3 (x1e6); D_g = [0.002, 0.038, 21.60] um -> [2.0e-9, 3.8e-8, 2.16e-5] m (x1e-6); logsigma = [0.247, 0.770, 0.438] (log10 of the geometric standard deviation, dimensionless). Modes 1 and 2 are fine modes; mode 3 (D_g = 21.6 um) is the coarse mineral-dust mode characteristic of desert aerosol. D_p defaults to 1.0e-7 m (0.1 um) — the evaluation diameter used by the upstream test suite, consistent with aerosol_distribution.esm; z = 0 and H_p = 1000 m are the upstream scalar defaults.
Constant handling: pi_c and ln10 are upstream @constants. The ESS schema has no constant variable type, so each migrates as a type: parameter with a fixed evaluated numeric default (pi_c = 3.141592653589793, ln10 = 2.302585092994046); the symbols are kept in the expressions. ln10 converts the log10-based logsigma to natural-log form: ln(sigma_g) = logsigma * ln10.
Pruned parameter: the base component’s @parameter rho_p (particle density, default 1500 kg/m^3) appears in none of the ten equations and is omitted per the unused-parameter rule, as in aerosol_distribution.esm.
Tests: desert_default_distribution pins all ten outputs at the Desert defaults (D_p = 1.0e-7 m). The remaining six tests are the preset-independent equation-correctness tests carried over verbatim from aerosol_distribution.esm — they override the mode parameters (a single mode with modes 2 & 3 switched off, the lognormal one-sigma points, the near-monodisperse Hatch-Choate limit) or the vertical-profile parameters, so their expected values do not depend on the Desert defaults and verify the migrated equations directly. The Urban/Marine/Remote-continental preset-override tests of the base file are dropped as off-topic for the Desert preset.
Tolerance rationale (model-level rel=1e-9): the component is purely algebraic with no ODE integration. Each output is a finite composition of +, *, /, ^, sqrt, exp and log10 in float64 (round-off ~1e-16 relative); rel=1e-9 leaves seven orders of magnitude of headroom and absorbs any associativity difference in the n-ary sums. The desert_default_distribution expected values were generated with the canonical ESS Python runner (earthsci_ast.simulate) — the same pathway as the inline-test gate.
Units: descriptive only; the ESS runners do no dimensional analysis. Units are copied from the upstream unit metadata verbatim (n_S_o / S_t in m^-1, n_V_o / V_t / M_z dimensionless)._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
π_c | 1 | 3.141592653589793 | Pi (mathematical constant). Upstream MTK @constants entry pi_c = pi; the ESS schema has no constant variable type, so it migrates as a fixed-default parameter with the evaluated numeric value. |
ln10 | 1 | 2.302585092994046 | Natural logarithm of 10. Upstream MTK @constants entry ln10 = log(10.0); migrated as a fixed-default parameter. Converts the log10-based geometric standard deviations logsigma to natural-log form, ln(sigma_g) = logsigma * ln10. |
N_1 | m^-3 | 726000000.0 | Total number concentration of mode 1 (fine mode). Upstream array @parameter N[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (726 cm^-3 converted to m^-3 by x1e6). |
N_2 | m^-3 | 114000000.0 | Total number concentration of mode 2 (fine mode). Upstream array @parameter N[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (114 cm^-3 converted to m^-3 by x1e6). |
N_3 | m^-3 | 178000.0 | Total number concentration of mode 3 (coarse mineral-dust mode). Upstream array @parameter N[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.178 cm^-3 converted to m^-3 by x1e6). |
D_g_1 | m | 2e-09 | Geometric median diameter of mode 1 (fine mode). Upstream array @parameter D_g[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.002 um converted to m by x1e-6). |
D_g_2 | m | 3.8e-08 | Geometric median diameter of mode 2 (fine mode). Upstream array @parameter D_g[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.038 um converted to m by x1e-6). |
D_g_3 | m | 2.16e-05 | Geometric median diameter of mode 3 (coarse mineral-dust mode). Upstream array @parameter D_g[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (21.60 um converted to m by x1e-6). |
logσ_1 | 1 | 0.247 | Log10 of the geometric standard deviation of mode 1 (fine mode) (dimensionless). Upstream array @parameter logσ[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3. |
logσ_2 | 1 | 0.77 | Log10 of the geometric standard deviation of mode 2 (fine mode) (dimensionless). Upstream array @parameter logσ[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3. |
logσ_3 | 1 | 0.438 | Log10 of the geometric standard deviation of mode 3 (coarse mineral-dust mode) (dimensionless). Upstream array @parameter logσ[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3. |
D_p | m | 1e-07 | Particle diameter at which the number, surface-area and volume distribution densities n_N_o/n_S_o/n_V_o are evaluated. The upstream base AerosolDistribution declares D_p with no default; 1.0e-7 m (0.1 um) is adopted here — the diameter the upstream test suite evaluates the distributions at, consistent with components/aerosol/size/aerosol_distribution.esm. |
z | m | 0.0 | Altitude above the surface, used by the vertical mass profile M_z. Default 0 m (surface). Upstream @parameter z = 0.0. |
H_p | m | 1000.0 | Aerosol mass scale height in the vertical profile M_z = exp(-z/H_p). Default 1000 m. Upstream @parameter H_p = 1000.0. |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
n_N_o | m^-3 | Number distribution density dN/d(log D_p) at the evaluation diameter D_p — the sum of n_modes lognormal modes (Seinfeld & Pandis 2006, Eq. 8.54). | |
n_S_o | m^-1 | Surface-area distribution density dS/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.49/8.50). | |
n_V_o | 1 | Volume distribution density dV/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.52/8.53). | |
N_t | m^-3 | Total number concentration — the sum of the per-mode number concentrations N_i. | |
S_t | m^-1 | Total surface-area concentration — Seinfeld & Pandis (2006) Eq. 8.5 evaluated with the k=2 lognormal moment Eq. 8.41. | |
V_t | 1 | Total volume concentration — Seinfeld & Pandis (2006) Eq. 8.7 evaluated with the k=3 lognormal moment Eq. 8.41. | |
D_s | m | Surface-area median diameter of mode 1 — the Hatch-Choate relation D_s = D_g * exp(2*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.50). | |
D_v | m | Volume median diameter of mode 1 — the Hatch-Choate relation D_v = D_g * exp(3*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.53). | |
D_bar | m | Mean diameter of mode 1 — the Hatch-Choate relation D_bar = D_g * exp(0.5*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.44). | |
M_z | 1 | Vertical aerosol mass profile ratio M(z)/M(0) = exp(-z/H_p) (Seinfeld & Pandis 2006, Eq. 8.55), dimensionless. |
Observed expressions
$$ n_{N\,o} = \frac{N_{1}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{1}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,1}}\right)^{2}}{2 \cdot logσ_{1}^{2}}} + \frac{N_{2}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{2}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,2}}\right)^{2}}{2 \cdot logσ_{2}^{2}}} + \frac{N_{3}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{3}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,3}}\right)^{2}}{2 \cdot logσ_{3}^{2}}} $$Number distribution density dN/d(log D_p) at the evaluation diameter D_p — the sum of n_modes lognormal modes (Seinfeld & Pandis 2006, Eq. 8.54).
$$ n_{S\,o} = \frac{π_{c} \cdot N_{1} \cdot \left(D_{g\,1} \cdot e^{2 \cdot \left(logσ_{1} \cdot ln10\right)^{2}}\right)^{2}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{1}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,1} \cdot e^{2 \cdot \left(logσ_{1} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{1}^{2}}} + \frac{π_{c} \cdot N_{2} \cdot \left(D_{g\,2} \cdot e^{2 \cdot \left(logσ_{2} \cdot ln10\right)^{2}}\right)^{2}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{2}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,2} \cdot e^{2 \cdot \left(logσ_{2} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{2}^{2}}} + \frac{π_{c} \cdot N_{3} \cdot \left(D_{g\,3} \cdot e^{2 \cdot \left(logσ_{3} \cdot ln10\right)^{2}}\right)^{2}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{3}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,3} \cdot e^{2 \cdot \left(logσ_{3} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{3}^{2}}} $$Surface-area distribution density dS/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.49/8.50).
$$ n_{V\,o} = \frac{\frac{π_{c}}{6} \cdot N_{1} \cdot \left(D_{g\,1} \cdot e^{3 \cdot \left(logσ_{1} \cdot ln10\right)^{2}}\right)^{3}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{1}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,1} \cdot e^{3 \cdot \left(logσ_{1} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{1}^{2}}} + \frac{\frac{π_{c}}{6} \cdot N_{2} \cdot \left(D_{g\,2} \cdot e^{3 \cdot \left(logσ_{2} \cdot ln10\right)^{2}}\right)^{3}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{2}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,2} \cdot e^{3 \cdot \left(logσ_{2} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{2}^{2}}} + \frac{\frac{π_{c}}{6} \cdot N_{3} \cdot \left(D_{g\,3} \cdot e^{3 \cdot \left(logσ_{3} \cdot ln10\right)^{2}}\right)^{3}}{\sqrt{2 \cdot π_{c}} \cdot logσ_{3}} \cdot e^{\frac{-\log_{10}\left(\frac{D_{p}}{D_{g\,3} \cdot e^{3 \cdot \left(logσ_{3} \cdot ln10\right)^{2}}}\right)^{2}}{2 \cdot logσ_{3}^{2}}} $$Volume distribution density dV/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.52/8.53).
$$ N_{t} = N_{1} + N_{2} + N_{3} $$Total number concentration — the sum of the per-mode number concentrations N_i.
$$ S_{t} = π_{c} \cdot N_{1} \cdot D_{g\,1}^{2} \cdot e^{2 \cdot \left(logσ_{1} \cdot ln10\right)^{2}} + π_{c} \cdot N_{2} \cdot D_{g\,2}^{2} \cdot e^{2 \cdot \left(logσ_{2} \cdot ln10\right)^{2}} + π_{c} \cdot N_{3} \cdot D_{g\,3}^{2} \cdot e^{2 \cdot \left(logσ_{3} \cdot ln10\right)^{2}} $$Total surface-area concentration — Seinfeld & Pandis (2006) Eq. 8.5 evaluated with the k=2 lognormal moment Eq. 8.41.
$$ V_{t} = \frac{π_{c}}{6} \cdot N_{1} \cdot D_{g\,1}^{3} \cdot e^{4.5 \cdot \left(logσ_{1} \cdot ln10\right)^{2}} + \frac{π_{c}}{6} \cdot N_{2} \cdot D_{g\,2}^{3} \cdot e^{4.5 \cdot \left(logσ_{2} \cdot ln10\right)^{2}} + \frac{π_{c}}{6} \cdot N_{3} \cdot D_{g\,3}^{3} \cdot e^{4.5 \cdot \left(logσ_{3} \cdot ln10\right)^{2}} $$Total volume concentration — Seinfeld & Pandis (2006) Eq. 8.7 evaluated with the k=3 lognormal moment Eq. 8.41.
$$ D_{s} = D_{g\,1} \cdot e^{2 \cdot \left(logσ_{1} \cdot ln10\right)^{2}} $$Surface-area median diameter of mode 1 — the Hatch-Choate relation D_s = D_g * exp(2*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.50).
$$ D_{v} = D_{g\,1} \cdot e^{3 \cdot \left(logσ_{1} \cdot ln10\right)^{2}} $$Volume median diameter of mode 1 — the Hatch-Choate relation D_v = D_g * exp(3*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.53).
$$ D_{bar} = D_{g\,1} \cdot e^{0.5 \cdot \left(logσ_{1} \cdot ln10\right)^{2}} $$Mean diameter of mode 1 — the Hatch-Choate relation D_bar = D_g * exp(0.5*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.44).
$$ M_{z} = e^{-\frac{z}{H_{p}}} $$Vertical aerosol mass profile ratio M(z)/M(0) = exp(-z/H_p) (Seinfeld & Pandis 2006, Eq. 8.55), dimensionless.
Analyses
aerosol_size_distribution_curves
The Seinfeld & Pandis Chapter 8 size-distribution figure for the Desert aerosol (Table 8.3). Sweeps the evaluation diameter D_p logarithmically from 1 nm to 100 um — the upper bound is extended past the usual 10 um so the coarse mineral-dust mode at D_g = 21.6 um is captured — and plots the number (n_N_o, Eq. 8.54), surface-area (n_S_o, Eq. 8.49/8.50) and volume (n_V_o, Eq. 8.52/8.53) distribution densities. The characteristic shift of the distribution peak toward larger diameters going from number to surface to volume, and the dominance of the coarse dust mode in the volume distribution, are the headline results.
Time span: 0.0 → 1.0
Swept over: D_p
vertical_mass_profile
Vertical aerosol mass profile of Seinfeld & Pandis Eq. 8.55. Sweeps altitude z from the surface to 5 km and plots the mass concentration ratio M_z = M(z)/M(0) = exp(-z/H_p) with the default scale height H_p = 1000 m. The profile decays exponentially, reaching 1/e of the surface value at z = H_p.
Time span: 0.0 → 1.0
Swept over: z
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"citation": "Seinfeld, J. H., and Pandis, S. N. (2006). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd Edition, John Wiley & Sons, Chapter 8, \"Properties of the Atmospheric Aerosol\". Multi-modal lognormal size distribution: Eq. 8.54 (number), 8.49/8.50 (surface area), 8.52/8.53 (volume); Hatch-Choate diameters Eq. 8.44/8.50/8.53; total moments Eq. 8.41 with Eq. 8.5/8.7; vertical mass profile Eq. 8.55. Mode parameters are the Desert entry of Table 8.3.",
"notes": "source_ref: Aerosol.jl@c8c640bb636b22f2425460e9ed5cba50793bfee1:src/size_distribution.jl:282\n\nUpstream `DesertAerosol(; name=:DesertAerosol)` is a thin preset wrapper that calls `AerosolDistribution(3; name, N_vals, D_g_vals, logsigma_vals)` with the Desert mode parameters of Seinfeld & Pandis (2006) Table 8.3. It returns a flat MTK `System` — not a hierarchical composition — identical in structure to the base `AerosolDistribution` component but with the three array `@parameters` N / D_g / logsigma defaulted to the Desert values. The migration is therefore a standalone copy of `components/aerosol/size/aerosol_distribution.esm` with the nine scalarized mode-parameter defaults replaced; the ten observed-output expressions and the empty equations array are unchanged.\n\nMigration form: observed-form, matching `aerosol_distribution.esm`. The base component carries two `@constants` (pi_c = pi, ln10 = log(10)), the length-n_modes array `@parameters` N / D_g / logsigma plus the scalar `@parameters` D_p, z, H_p, and ten time-indexed `@variables` (n_N_o, n_S_o, n_V_o, N_t, S_t, V_t, D_s, D_v, D_bar, M_z) each defined by one algebraic `lhs ~ rhs` equation whose RHS references only parameters and constants. Per the purely-algebraic migration rule each output is encoded as `type: observed` with its defining relation in the `expression` field and the `equations` array is empty.\n\nArray scalarization: as in the base migration the length-3 array parameters N, D_g, logsigma are scalarized into nine scalar parameters N_1..N_3, D_g_1..D_g_3, logsigma_1..logsigma_3 and each `sum(... for i in 1:n_modes)` is unrolled into an explicit three-term sum. DesertAerosol is a three-mode distribution, so n_modes = 3 is exact (not a default truncation). The `.esm` array-variable path emits `getindex` nodes (tracked upstream as gt-p3ep), which is why the scalarized form is used.\n\nDesert defaults (Table 8.3, Seinfeld & Pandis 2006, Chapter 8): N = [726.0, 114.0, 0.178] cm^-3 -> [7.26e8, 1.14e8, 1.78e5] m^-3 (x1e6); D_g = [0.002, 0.038, 21.60] um -> [2.0e-9, 3.8e-8, 2.16e-5] m (x1e-6); logsigma = [0.247, 0.770, 0.438] (log10 of the geometric standard deviation, dimensionless). Modes 1 and 2 are fine modes; mode 3 (D_g = 21.6 um) is the coarse mineral-dust mode characteristic of desert aerosol. D_p defaults to 1.0e-7 m (0.1 um) — the evaluation diameter used by the upstream test suite, consistent with `aerosol_distribution.esm`; z = 0 and H_p = 1000 m are the upstream scalar defaults.\n\nConstant handling: pi_c and ln10 are upstream `@constants`. The ESS schema has no constant variable type, so each migrates as a `type: parameter` with a fixed evaluated numeric default (pi_c = 3.141592653589793, ln10 = 2.302585092994046); the symbols are kept in the expressions. ln10 converts the log10-based logsigma to natural-log form: ln(sigma_g) = logsigma * ln10.\n\nPruned parameter: the base component's `@parameter rho_p` (particle density, default 1500 kg/m^3) appears in none of the ten equations and is omitted per the unused-parameter rule, as in `aerosol_distribution.esm`.\n\nTests: desert_default_distribution pins all ten outputs at the Desert defaults (D_p = 1.0e-7 m). The remaining six tests are the preset-independent equation-correctness tests carried over verbatim from `aerosol_distribution.esm` — they override the mode parameters (a single mode with modes 2 & 3 switched off, the lognormal one-sigma points, the near-monodisperse Hatch-Choate limit) or the vertical-profile parameters, so their expected values do not depend on the Desert defaults and verify the migrated equations directly. The Urban/Marine/Remote-continental preset-override tests of the base file are dropped as off-topic for the Desert preset.\n\nTolerance rationale (model-level rel=1e-9): the component is purely algebraic with no ODE integration. Each output is a finite composition of +, *, /, ^, sqrt, exp and log10 in float64 (round-off ~1e-16 relative); rel=1e-9 leaves seven orders of magnitude of headroom and absorbs any associativity difference in the n-ary sums. The desert_default_distribution expected values were generated with the canonical ESS Python runner (earthsci_ast.simulate) — the same pathway as the inline-test gate.\n\nUnits: descriptive only; the ESS runners do no dimensional analysis. Units are copied from the upstream `unit` metadata verbatim (n_S_o / S_t in m^-1, n_V_o / V_t / M_z dimensionless)."
},
"tolerance": {
"rel": 1e-09
},
"variables": {
"π_c": {
"type": "parameter",
"units": "1",
"default": 3.141592653589793,
"description": "Pi (mathematical constant). Upstream MTK @constants entry pi_c = pi; the ESS schema has no constant variable type, so it migrates as a fixed-default parameter with the evaluated numeric value."
},
"ln10": {
"type": "parameter",
"units": "1",
"default": 2.302585092994046,
"description": "Natural logarithm of 10. Upstream MTK @constants entry ln10 = log(10.0); migrated as a fixed-default parameter. Converts the log10-based geometric standard deviations logsigma to natural-log form, ln(sigma_g) = logsigma * ln10."
},
"N_1": {
"type": "parameter",
"units": "m^-3",
"default": 726000000.0,
"description": "Total number concentration of mode 1 (fine mode). Upstream array @parameter N[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (726 cm^-3 converted to m^-3 by x1e6)."
},
"N_2": {
"type": "parameter",
"units": "m^-3",
"default": 114000000.0,
"description": "Total number concentration of mode 2 (fine mode). Upstream array @parameter N[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (114 cm^-3 converted to m^-3 by x1e6)."
},
"N_3": {
"type": "parameter",
"units": "m^-3",
"default": 178000.0,
"description": "Total number concentration of mode 3 (coarse mineral-dust mode). Upstream array @parameter N[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.178 cm^-3 converted to m^-3 by x1e6)."
},
"D_g_1": {
"type": "parameter",
"units": "m",
"default": 2e-09,
"description": "Geometric median diameter of mode 1 (fine mode). Upstream array @parameter D_g[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.002 um converted to m by x1e-6)."
},
"D_g_2": {
"type": "parameter",
"units": "m",
"default": 3.8e-08,
"description": "Geometric median diameter of mode 2 (fine mode). Upstream array @parameter D_g[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (0.038 um converted to m by x1e-6)."
},
"D_g_3": {
"type": "parameter",
"units": "m",
"default": 2.16e-05,
"description": "Geometric median diameter of mode 3 (coarse mineral-dust mode). Upstream array @parameter D_g[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3 (21.60 um converted to m by x1e-6)."
},
"logσ_1": {
"type": "parameter",
"units": "1",
"default": 0.247,
"description": "Log10 of the geometric standard deviation of mode 1 (fine mode) (dimensionless). Upstream array @parameter logσ[1] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3."
},
"logσ_2": {
"type": "parameter",
"units": "1",
"default": 0.77,
"description": "Log10 of the geometric standard deviation of mode 2 (fine mode) (dimensionless). Upstream array @parameter logσ[2] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3."
},
"logσ_3": {
"type": "parameter",
"units": "1",
"default": 0.438,
"description": "Log10 of the geometric standard deviation of mode 3 (coarse mineral-dust mode) (dimensionless). Upstream array @parameter logσ[3] of AerosolDistribution. Default: Desert distribution, Seinfeld & Pandis (2006) Table 8.3."
},
"D_p": {
"type": "parameter",
"units": "m",
"default": 1e-07,
"description": "Particle diameter at which the number, surface-area and volume distribution densities n_N_o/n_S_o/n_V_o are evaluated. The upstream base AerosolDistribution declares D_p with no default; 1.0e-7 m (0.1 um) is adopted here — the diameter the upstream test suite evaluates the distributions at, consistent with components/aerosol/size/aerosol_distribution.esm."
},
"z": {
"type": "parameter",
"units": "m",
"default": 0.0,
"description": "Altitude above the surface, used by the vertical mass profile M_z. Default 0 m (surface). Upstream @parameter z = 0.0."
},
"H_p": {
"type": "parameter",
"units": "m",
"default": 1000.0,
"description": "Aerosol mass scale height in the vertical profile M_z = exp(-z/H_p). Default 1000 m. Upstream @parameter H_p = 1000.0."
},
"n_N_o": {
"type": "unknown",
"units": "m^-3",
"description": "Number distribution density dN/d(log D_p) at the evaluation diameter D_p — the sum of n_modes lognormal modes (Seinfeld & Pandis 2006, Eq. 8.54)."
},
"n_S_o": {
"type": "unknown",
"units": "m^-1",
"description": "Surface-area distribution density dS/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.49/8.50)."
},
"n_V_o": {
"type": "unknown",
"units": "1",
"description": "Volume distribution density dV/d(log D_p) at D_p (Seinfeld & Pandis 2006, Eq. 8.52/8.53)."
},
"N_t": {
"type": "unknown",
"units": "m^-3",
"description": "Total number concentration — the sum of the per-mode number concentrations N_i."
},
"S_t": {
"type": "unknown",
"units": "m^-1",
"description": "Total surface-area concentration — Seinfeld & Pandis (2006) Eq. 8.5 evaluated with the k=2 lognormal moment Eq. 8.41."
},
"V_t": {
"type": "unknown",
"units": "1",
"description": "Total volume concentration — Seinfeld & Pandis (2006) Eq. 8.7 evaluated with the k=3 lognormal moment Eq. 8.41."
},
"D_s": {
"type": "unknown",
"units": "m",
"description": "Surface-area median diameter of mode 1 — the Hatch-Choate relation D_s = D_g * exp(2*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.50)."
},
"D_v": {
"type": "unknown",
"units": "m",
"description": "Volume median diameter of mode 1 — the Hatch-Choate relation D_v = D_g * exp(3*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.53)."
},
"D_bar": {
"type": "unknown",
"units": "m",
"description": "Mean diameter of mode 1 — the Hatch-Choate relation D_bar = D_g * exp(0.5*ln^2 sigma_g) (Seinfeld & Pandis 2006, Eq. 8.44)."
},
"M_z": {
"type": "unknown",
"units": "1",
"description": "Vertical aerosol mass profile ratio M(z)/M(0) = exp(-z/H_p) (Seinfeld & Pandis 2006, Eq. 8.55), dimensionless."
}
},
"equations": [
{
"lhs": "n_N_o",
"rhs": {
"op": "+",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"N_1",
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_1"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
"D_g_1"
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_1",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"N_2",
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_2"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
"D_g_2"
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_2",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"N_3",
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_3"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
"D_g_3"
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_3",
2
]
}
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "n_S_o",
"rhs": {
"op": "+",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"π_c",
"N_1",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_1"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_1",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"π_c",
"N_2",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_2",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_2"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_2",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_2",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"π_c",
"N_3",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_3",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_3"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_3",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_3",
2
]
}
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "n_V_o",
"rhs": {
"op": "+",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_1",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
3
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_1"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_1",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_2",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_2",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
3
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_2"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_2",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_2",
2
]
}
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_3",
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"D_g_3",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
3
]
}
]
},
{
"op": "*",
"args": [
{
"op": "sqrt",
"args": [
{
"op": "*",
"args": [
2,
"π_c"
]
}
]
},
"logσ_3"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
{
"op": "^",
"args": [
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"D_p",
{
"op": "*",
"args": [
"D_g_3",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
]
},
2
]
}
]
},
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
"logσ_3",
2
]
}
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "N_t",
"rhs": {
"op": "+",
"args": [
"N_1",
"N_2",
"N_3"
]
}
},
{
"lhs": "S_t",
"rhs": {
"op": "+",
"args": [
{
"op": "*",
"args": [
"π_c",
"N_1",
{
"op": "^",
"args": [
"D_g_1",
2
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
"π_c",
"N_2",
{
"op": "^",
"args": [
"D_g_2",
2
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
"π_c",
"N_3",
{
"op": "^",
"args": [
"D_g_3",
2
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "V_t",
"rhs": {
"op": "+",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_1",
{
"op": "^",
"args": [
"D_g_1",
3
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
4.5,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_2",
{
"op": "^",
"args": [
"D_g_2",
3
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
4.5,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_2",
"ln10"
]
},
2
]
}
]
}
]
}
]
},
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"π_c",
6
]
},
"N_3",
{
"op": "^",
"args": [
"D_g_3",
3
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
4.5,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_3",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "D_s",
"rhs": {
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
2,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
},
{
"lhs": "D_v",
"rhs": {
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
3,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
},
{
"lhs": "D_bar",
"rhs": {
"op": "*",
"args": [
"D_g_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
0.5,
{
"op": "^",
"args": [
{
"op": "*",
"args": [
"logσ_1",
"ln10"
]
},
2
]
}
]
}
]
}
]
}
},
{
"lhs": "M_z",
"rhs": {
"op": "exp",
"args": [
{
"op": "-",
"args": [
{
"op": "/",
"args": [
"z",
"H_p"
]
}
]
}
]
}
}
],
"tests": [
{
"id": "desert_default_distribution",
"description": "All parameters at their declared defaults — the Desert size distribution of Seinfeld & Pandis (2006) Table 8.3 (three lognormal modes: N = [726, 114, 0.178] cm^-3, D_g = [0.002, 0.038, 21.60] um, log10 sigma = [0.247, 0.770, 0.438]; modes 1-2 fine, mode 3 a coarse mineral-dust mode), evaluated at D_p = 1.0e-7 m (0.1 um). Pins every one of the ten outputs: the number/surface/volume distribution densities n_N_o/n_S_o/n_V_o (Eq. 8.54/8.49/8.52), the total concentrations N_t/S_t/V_t, the mode-1 Hatch-Choate diameters D_s/D_v/D_bar, and the surface vertical mass ratio M_z. N_t = N_1+N_2+N_3 = (726+114+0.178)e6 = 8.40178e8 m^-3; M_z = exp(-z/H_p) = 1 at the surface (z = 0). All outputs are algebraic and time-independent, so N_t and M_z are also asserted at t = 1 to confirm time-invariance.",
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "n_N_o",
"time": 0.0,
"expected": 50892268.50614858
},
{
"variable": "n_S_o",
"time": 0.0,
"expected": 0.0008594232220223416
},
{
"variable": "n_V_o",
"time": 0.0,
"expected": 3.707341460208051e-08
},
{
"variable": "N_t",
"time": 0.0,
"expected": 840178000.0
},
{
"variable": "S_t",
"time": 0.0,
"expected": 0.0022730464146852366
},
{
"variable": "V_t",
"time": 0.0,
"expected": 9.588340339545995e-08
},
{
"variable": "D_s",
"time": 0.0,
"expected": 3.819326828578887e-09
},
{
"variable": "D_v",
"time": 0.0,
"expected": 5.277949584496307e-09
},
{
"variable": "D_bar",
"time": 0.0,
"expected": 2.3510897203696405e-09
},
{
"variable": "M_z",
"time": 0.0,
"expected": 1.0
},
{
"variable": "N_t",
"time": 1.0,
"expected": 840178000.0
},
{
"variable": "M_z",
"time": 1.0,
"expected": 1.0
}
]
},
{
"id": "single_mode_moments_and_diameters",
"description": "A single lognormal mode: N_1 = 1.0e11 m^-3, D_g_1 = 1.0e-7 m, logsigma_1 = 0.3, with modes 2 and 3 switched off (N_2 = N_3 = 0), evaluated at D_p = D_g_1 = 1.0e-7 m. This is the upstream AerosolDistribution(1) single-mode test case. At D_p = D_g the exponential in Eq. 8.54 is unity, so n_N_o reaches its peak N_1/(sqrt(2*pi)*logsigma_1). N_t = 1.0e11 m^-3. S_t and V_t reduce to the single-mode moment forms S_t = pi*N*D_g^2*exp(2*ln^2 sigma) and V_t = (pi/6)*N*D_g^3*exp(4.5*ln^2 sigma) (Eq. 8.41). The Hatch-Choate diameters satisfy D_g < D_bar < D_s < D_v (Eq. 8.44/8.50/8.53). Pins all nine.",
"parameter_overrides": {
"N_1": 100000000000.0,
"N_2": 0.0,
"N_3": 0.0,
"D_g_1": 1e-07,
"logσ_1": 0.3,
"D_p": 1e-07
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "N_t",
"time": 0.0,
"expected": 100000000000.0
},
{
"variable": "S_t",
"time": 0.0,
"expected": 0.008158591515929528
},
{
"variable": "V_t",
"time": 0.0,
"expected": 4.482761000568854e-10
},
{
"variable": "n_N_o",
"time": 0.0,
"expected": 132980760133.81091
},
{
"variable": "n_S_o",
"time": 0.0,
"expected": 0.01084935701409569
},
{
"variable": "n_V_o",
"time": 0.0,
"expected": 5.961209653538489e-10
},
{
"variable": "D_s",
"time": 0.0,
"expected": 2.596960336855569e-07
},
{
"variable": "D_v",
"time": 0.0,
"expected": 4.1850242140101953e-07
},
{
"variable": "D_bar",
"time": 0.0,
"expected": 1.2694521316234356e-07
}
]
},
{
"id": "lognormal_one_sigma_above",
"description": "Single mode (N_1 = 1.0e11, D_g_1 = 1.0e-7, logsigma_1 = 0.3, modes 2 & 3 off), evaluated one geometric standard deviation ABOVE the median diameter: D_p = D_g_1 * 10^logsigma_1. One sigma from the peak the lognormal in log-space drops by a factor exp(-0.5), so n_N_o = [N_1/(sqrt(2*pi)*logsigma_1)] * exp(-0.5) (Eq. 8.54).",
"parameter_overrides": {
"N_1": 100000000000.0,
"N_2": 0.0,
"N_3": 0.0,
"D_g_1": 1e-07,
"logσ_1": 0.3,
"D_p": 1.9952623149688795e-07
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "n_N_o",
"time": 0.0,
"expected": 80656908173.0478
}
]
},
{
"id": "lognormal_one_sigma_below",
"description": "Mirror image of lognormal_one_sigma_above: the same single mode evaluated one geometric standard deviation BELOW the median, D_p = D_g_1 * 10^-logsigma_1. The lognormal number distribution is symmetric in log(D_p) about log(D_g_1), so n_N_o here equals the one-sigma-above value to within float round-off (~13 significant figures); the pinned expected value is the exact formula output below the median, and its near-equality to lognormal_one_sigma_above verifies that log-space symmetry.",
"parameter_overrides": {
"N_1": 100000000000.0,
"N_2": 0.0,
"N_3": 0.0,
"D_g_1": 1e-07,
"logσ_1": 0.3,
"D_p": 5.011872336272722e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "n_N_o",
"time": 0.0,
"expected": 80656908173.04778
}
]
},
{
"id": "vertical_profile_one_scale_height",
"description": "Vertical aerosol mass profile (Eq. 8.55), M_z = exp(-z/H_p), evaluated one scale height above the surface: z = H_p = 1000 m. M_z = exp(-1) ~ 0.3679 — the mass concentration has fallen to 1/e of its surface value.",
"parameter_overrides": {
"z": 1000.0,
"H_p": 1000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "M_z",
"time": 0.0,
"expected": 0.36787944117144233
}
]
},
{
"id": "vertical_profile_two_scale_heights",
"description": "Vertical aerosol mass profile (Eq. 8.55) two scale heights up: z = 2*H_p = 2000 m with H_p = 1000 m. M_z = exp(-2) ~ 0.1353. Together with vertical_profile_one_scale_height this confirms the exponential decay M_z = exp(-z/H_p).",
"parameter_overrides": {
"z": 2000.0,
"H_p": 1000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "M_z",
"time": 0.0,
"expected": 0.1353352832366127
}
]
},
{
"id": "near_monodisperse_diameters",
"description": "Near-monodisperse limit: a single mode with logsigma_1 driven to 1.0e-6 (geometric standard deviation sigma_g ~ 1). As logsigma -> 0 the Hatch-Choate corrections exp(k*ln^2 sigma) all collapse to 1, so the surface, volume and mean diameters D_s, D_v, D_bar each converge to the geometric median diameter D_g_1 = 1.0e-7 m. The pinned values are the exact formula outputs (each differs from D_g_1 by < 1.1e-11 relative). N_t = 1.0e11 m^-3.",
"parameter_overrides": {
"N_1": 100000000000.0,
"N_2": 0.0,
"N_3": 0.0,
"D_g_1": 1e-07,
"logσ_1": 1e-06,
"D_p": 1e-07
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "D_s",
"time": 0.0,
"expected": 1.0000000000106037e-07
},
{
"variable": "D_v",
"time": 0.0,
"expected": 1.0000000000159056e-07
},
{
"variable": "D_bar",
"time": 0.0,
"expected": 1.0000000000026509e-07
},
{
"variable": "N_t",
"time": 0.0,
"expected": 100000000000.0
}
]
}
],
"analyses": [
{
"id": "aerosol_size_distribution_curves",
"description": "The Seinfeld & Pandis Chapter 8 size-distribution figure for the Desert aerosol (Table 8.3). Sweeps the evaluation diameter D_p logarithmically from 1 nm to 100 um — the upper bound is extended past the usual 10 um so the coarse mineral-dust mode at D_g = 21.6 um is captured — and plots the number (n_N_o, Eq. 8.54), surface-area (n_S_o, Eq. 8.49/8.50) and volume (n_V_o, Eq. 8.52/8.53) distribution densities. The characteristic shift of the distribution peak toward larger diameters going from number to surface to volume, and the dominance of the coarse dust mode in the volume distribution, are the headline results.",
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "D_p",
"range": {
"start": 1e-09,
"stop": 0.0001,
"count": 100,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "number_distribution",
"type": "line",
"description": "Number distribution density dN/d(log D_p) versus particle diameter on a logarithmic D_p axis — the Desert multi-modal lognormal of Eq. 8.54.",
"x": {
"variable": "D_p",
"label": "particle diameter D_p (m)"
},
"y": {
"variable": "n_N_o",
"label": "number distribution dN/d(log D_p) (m^-3)"
}
},
{
"id": "surface_distribution",
"type": "line",
"description": "Surface-area distribution density dS/d(log D_p) versus particle diameter (Eq. 8.49/8.50) — the peak sits at a larger D_p than the number distribution.",
"x": {
"variable": "D_p",
"label": "particle diameter D_p (m)"
},
"y": {
"variable": "n_S_o",
"label": "surface distribution dS/d(log D_p) (m^-1)"
}
},
{
"id": "volume_distribution",
"type": "line",
"description": "Volume distribution density dV/d(log D_p) versus particle diameter (Eq. 8.52/8.53) — the peak sits at the largest D_p of the three moments.",
"x": {
"variable": "D_p",
"label": "particle diameter D_p (m)"
},
"y": {
"variable": "n_V_o",
"label": "volume distribution dV/d(log D_p) (-)"
}
}
]
},
{
"id": "vertical_mass_profile",
"description": "Vertical aerosol mass profile of Seinfeld & Pandis Eq. 8.55. Sweeps altitude z from the surface to 5 km and plots the mass concentration ratio M_z = M(z)/M(0) = exp(-z/H_p) with the default scale height H_p = 1000 m. The profile decays exponentially, reaching 1/e of the surface value at z = H_p.",
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "z",
"range": {
"start": 0.0,
"stop": 5000.0,
"count": 51,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "mass_ratio_vs_altitude",
"type": "line",
"description": "Aerosol mass concentration ratio M(z)/M(0) versus altitude — the exponential vertical profile of Eq. 8.55.",
"x": {
"variable": "z",
"label": "altitude z (m)"
},
"y": {
"variable": "M_z",
"label": "mass ratio M(z)/M(0) (-)"
}
}
]
}
]
}