GaussianPGB
Classic Gaussian plume dispersion model parameterized with Pasquill-Gifford-Briggs (PGB) stability classification and dispersion coefficients. Given the current puff position (lon, lat) and height above ground (z_agl), classifies atmospheric stability from near-surface meteorology (wind speed, solar radiation, cloud fraction, temperature lapse), selects Briggs dispersion-curve coefficients, computes the haversine downwind distance from the source, and evaluates horizontal (sigma_h) and vertical (sigma_z) dispersion widths and the ground-level Gaussian concentration (C_gl). Migrated from EnvironmentalTransport.jl@a48559c4 src/GaussianDispersion.jl:83. When coupled with Puff, lon/lat/z_agl are supplied by the Puff component; in standalone mode they are treated as constant parameters.
Description
Classic Gaussian plume dispersion model parameterized with Pasquill-Gifford-Briggs (PGB) stability classification and dispersion coefficients. Given the current puff position (lon, lat) and height above ground (z_agl), classifies atmospheric stability from near-surface meteorology (wind speed, solar radiation, cloud fraction, temperature lapse), selects Briggs dispersion-curve coefficients, computes the haversine downwind distance from the source, and evaluates horizontal (sigma_h) and vertical (sigma_z) dispersion widths and the ground-level Gaussian concentration (C_gl). Migrated from EnvironmentalTransport.jl@a48559c4 src/GaussianDispersion.jl:83. When coupled with Puff, lon/lat/z_agl are supplied by the Puff component; in standalone mode they are treated as constant parameters.
Reference
_source_ref: EnvironmentalTransport.jl@a48559c4114eb9f06668ecf9f06235aad20f63f0:src/GaussianDispersion.jl:83
Upstream GaussianPGB is an MTK @component returning a purely algebraic System — all three output equations (sigma_h, sigma_z, C_gl) are algebraic assignments (~), not ODEs. There are no D(state)/dt terms. The component has three input variables marked input=true: lon(t), lat(t) (puff position, provided by Puff), and z_agl(t) (hypsometric height above ground, provided by an external data coupling such as GEOSFP or MERRA2). When coupled via EarthSciMLBase.couple(), these become shared symbolic variables with Puff/data connectors. In standalone mode they are held constant as parameters.
Migration approach: purely algebraic ESM. All outputs (sigma_h, sigma_z, C_gl) are type=observed. The lon, lat, z_agl input variables are type=parameter (with physically representative defaults) for standalone simulation. When the Puff ESM and appropriate data connector ESMs are available, a coupling entry will tie these parameters to the corresponding Puff/data outputs.
Intermediate observed variables (wind_speed, dTsurf, stab_cls, ay, az, bz, delta_lon, delta_lat, hav_a, hav_c, x) are exposed as named observed variables so they can be individually inspected and tested. The ESS runner evaluates observed variables in dependency order.
Stability class encoding: stab_cls returns a floating-point integer 1.0-6.0 (A=1, B=2, C=3, D=4, E=5, F=6). Coefficient selectors use threshold comparisons (stab_cls < 1.5, < 2.5 etc.) to avoid exact floating-point equality, which is unreliable for class E/F at SWGDN boundaries.
Briggs sigma_h formula: sigma_h = A_y * x * (1 + B_y * x)^(-0.5). B_y is class-independent (by=1e-4 m^-1) per EPA MMGRMA.
Briggs sigma_z formula: sigma_z = A_z * x * (1 + B_z * x)^(-0.5) for classes A-D (unstable/neutral); sigma_z = A_z * x / (1 + B_z * x) for classes E-F (stable).
Gaussian ground-level concentration: C_gl = exp(-z_agl^2 / (2sigma_z^2)) / ((2pi)^(3/2) * sigma_h^2 * sigma_z). At z_agl=0 this is the maximum surface concentration per unit puff mass.
Haversine downwind distance: The great-circle distance from source (lon0, lat0) to current puff position (lon, lat) is computed via haversine: a = sin((lat-lat0)/2)^2 + cos(lat0)cos(lat)sin((lon-lon0)/2)^2; c = 2atan(sqrt(a)/sqrt(1-a)); x = Rc. R=6.371e6 m (Earth mean radius).
Unicode/Julia symbol normalization: Δz → dz (not used; GaussianPGB is Gaussian plume, not puff-KC), σ_h → sigma_h, σ_z → sigma_z, AY → AY, stab_cls integer 1-6 replaces character A-F.
Tolerance (model-level rel=1e-8, abs=1e-12): for algebraic evaluation the integrator tolerance is not operative; the tolerance is specified for consistency with the ESM contract and future runner versions. Observed expressions are composed of elementary trig/exp functions; accumulated rounding is <5 ULP (<1e-15 relative) well inside rel=1e-8.
Coupler identity: this model was serialized with the model-level field coupletype: "GaussianPGBCoupler", the EarthSciMLBase CoupleType metadata tag naming the Julia coupler struct that EarthSciMLBase.couple2 dispatches on to find this component’s pairwise coupling rules. The esm schema defined coupletype only before 0.8.0 (“informational label identifying this system’s role in coupling”); 0.8.0 removed it in favour of explicit coupling — coupling entries naming components directly, or coupling_roles + coupling_import in a coupling-library file (esm-spec §10.9–§10.11). esm 1.0.0 has no model-level coupler-identity field, so the tag is recorded here to keep it recoverable._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
lon | rad | 0.0 | Puff longitude (radians). Supplied by Puff.x when coupled; held as constant parameter in standalone mode. |
lat | rad | 0.0 | Puff latitude (radians). Supplied by Puff.y when coupled; held as constant parameter in standalone mode. |
z_agl | m | 25.0 | Puff height above ground level (m). Supplied by an external data coupling (e.g. GEOSFP pressure-to-height) when coupled; held as constant parameter in standalone mode. |
lon0 | rad | 0.0 | Emission source longitude (radians). Fixed for the lifetime of the trajectory. |
lat0 | rad | 0.0 | Emission source latitude (radians). Fixed for the lifetime of the trajectory. |
earth_radius | m | 6371000.0 | Earth mean radius (m). Used in haversine downwind distance computation. |
AY_A | 0.22 | Briggs A_y coefficient for Pasquill stability class A (very unstable). | |
AY_B | 0.16 | Briggs A_y coefficient for class B (unstable). | |
AY_C | 0.11 | Briggs A_y coefficient for class C (slightly unstable). | |
AY_D | 0.08 | Briggs A_y coefficient for class D (neutral). | |
AY_Ep | 0.06 | Briggs A_y coefficient for class E (slightly stable). | |
AY_F | 0.04 | Briggs A_y coefficient for class F (stable). | |
AZ_A | 0.2 | Briggs A_z coefficient for class A. | |
AZ_B | 0.12 | Briggs A_z coefficient for class B. | |
AZ_C | 0.08 | Briggs A_z coefficient for class C. | |
AZ_D | 0.06 | Briggs A_z coefficient for class D. | |
AZ_Ep | 0.03 | Briggs A_z coefficient for class E. | |
AZ_F | 0.016 | Briggs A_z coefficient for class F. | |
by | m^-1 | 0.0001 | Briggs B_y coefficient (class-independent, 1e-4 m^-1). Controls the far-field saturation of horizontal spread. |
BZ_A | m^-1 | 0.0 | Briggs B_z coefficient for class A. |
BZ_B | m^-1 | 0.0 | Briggs B_z coefficient for class B. |
BZ_C | m^-1 | 0.0002 | Briggs B_z coefficient for class C. |
BZ_D | m^-1 | 0.0015 | Briggs B_z coefficient for class D. |
BZ_Ep | m^-1 | 0.0003 | Briggs B_z coefficient for class E. |
BZ_F | m^-1 | 0.0003 | Briggs B_z coefficient for class F. |
v2 | m/s | 2.0 | Wind-speed threshold 2 m/s for Pasquill classification. |
v3 | m/s | 3.0 | Wind-speed threshold 3 m/s. |
v5 | m/s | 5.0 | Wind-speed threshold 5 m/s. |
v6 | m/s | 6.0 | Wind-speed threshold 6 m/s. |
solrad_strong | W/m^2 | 925.0 | Solar radiation threshold for very strong insolation (≥925 W/m^2 → class A/B/C). |
solrad_moder | W/m^2 | 675.0 | Solar radiation threshold for moderate insolation (675-925 W/m^2). |
solrad_slight | W/m^2 | 175.0 | Solar radiation threshold for slight insolation (175-675 W/m^2). |
solrad_night | W/m^2 | 10.0 | Solar radiation threshold for night (<10 W/m^2); 10-175 W/m^2 defaults to neutral class D. |
cloudfrac_clear | 0.5 | Cloud fraction threshold for clear sky (CLDTOT ≤ 0.5 → clear). Used for nighttime stability classification. | |
inversion_thresh | K | 0.0 | Temperature difference threshold (T10M-T2M > 0 K) for surface inversion detection. Inversions drive class E or F at night. |
U10M | m/s | 3.0 | 10 m wind speed U component (eastward, m/s). Used to compute surface wind speed for stability classification. |
V10M | m/s | 0.0 | 10 m wind speed V component (northward, m/s). |
SWGDN | W/m^2 | 700.0 | Surface downwelling shortwave radiation (W/m^2). Drives daytime stability class (A-D) via solar insolation thresholds. |
CLDTOT | 0.3 | Total cloud fraction (0-1). Used for nighttime stability classification: CLDTOT ≤ cloudfrac_clear → clear sky. | |
T2M | K | 293.15 | 2 m air temperature (K). Used with T10M to compute surface temperature lapse dTsurf = T10M - T2M. |
T10M | K | 292.65 | 10 m air temperature (K). dTsurf = T10M - T2M > inversion_thresh indicates surface inversion. |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
wind_speed | m/s | Surface wind speed magnitude sqrt(U10M^2 + V10M^2) (m/s). Used for Pasquill stability classification. | |
dTsurf | K | Surface temperature lapse T10M - T2M (K). Positive values indicate a surface temperature inversion; used for nighttime stability class E/F classification. | |
stab_cls | Pasquill-Gifford stability class as floating-point integer 1.0-6.0 (A=1, B=2, C=3, D=4, E=5, F=6). Determined from SWGDN, CLDTOT, wind_speed, and dTsurf per EPA MMGRMA Table 6-7. | ||
ay | Briggs horizontal dispersion coefficient A_y (dimensionless) for the current stability class. | ||
az | Briggs vertical dispersion coefficient A_z (dimensionless) for the current stability class. | ||
bz | m^-1 | Briggs vertical saturation coefficient B_z (m^-1) for the current stability class. Zero for classes A and B. | |
delta_lon | rad | Longitude difference lon - lon0 (radians). Intermediate for haversine downwind distance. | |
delta_lat | rad | Latitude difference lat - lat0 (radians). Intermediate for haversine downwind distance. | |
hav_a | Haversine intermediate a = sin((lat-lat0)/2)^2 + cos(lat0)*cos(lat)*sin((lon-lon0)/2)^2. In [0,1]; equals sin^2(central_angle/2). | ||
hav_c | rad | Great-circle central angle c = 2*atan(sqrt(hav_a)/sqrt(1-hav_a)) (radians). The arc between source and puff. | |
x | m | Haversine downwind distance x = R * hav_c (m). The great-circle surface distance from the emission source (lon0, lat0) to the current puff position (lon, lat). | |
sigma_h | m | Horizontal Gaussian dispersion coefficient sigma_h (m). Computed from Briggs formula sigma_h = A_y * x * (1 + B_y * x)^(-0.5). | |
sigma_z | m | Vertical Gaussian dispersion coefficient sigma_z (m). Uses sigma_z = A_zx(1+B_zx)^(-0.5) for classes A-D; sigma_z = A_zx/(1+B_z*x) for classes E-F (stable, stronger vertical confinement). | |
C_gl | m^-3 | Ground-level centerline Gaussian concentration per unit puff mass (m^-3). C_gl = exp(-z_agl^2/(2sigma_z^2)) / ((2pi)^(3/2) * sigma_h^2 * sigma_z). Maximum at z_agl=0 (puff at ground level). |
Observed expressions
$$ wind_{speed} = \sqrt{U10M^{2.0} + V10M^{2.0}} $$Surface wind speed magnitude sqrt(U10M^2 + V10M^2) (m/s). Used for Pasquill stability classification.
$$ dTsurf = T10M - T2M $$Surface temperature lapse T10M - T2M (K). Positive values indicate a surface temperature inversion; used for nighttime stability class E/F classification.
$$ stab_{cls} = \mathrm{ifelse}\left(\mathrm{<}\left(SWGDN, solrad_{night}\right), \mathrm{ifelse}\left(\mathrm{<=}\left(CLDTOT, cloudfrac_{clear}\right), \mathrm{ifelse}\left(\mathrm{>}\left(dTsurf, inversion_{thresh}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), 6.0, 5.0\right), 4.0\right), 4.0\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{strong}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v3\right), 1.0, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), 2.0, 3.0\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{moder}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), 1.0, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), 2.0, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v6\right), 3.0, 4.0\right)\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{slight}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), 2.0, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), 3.0, 4.0\right)\right), 4.0\right)\right)\right)\right) $$Pasquill-Gifford stability class as floating-point integer 1.0-6.0 (A=1, B=2, C=3, D=4, E=5, F=6). Determined from SWGDN, CLDTOT, wind_speed, and dTsurf per EPA MMGRMA Table 6-7.
$$ ay = \mathrm{ifelse}\left(\mathrm{<}\left(SWGDN, solrad_{night}\right), \mathrm{ifelse}\left(\mathrm{<=}\left(CLDTOT, cloudfrac_{clear}\right), \mathrm{ifelse}\left(\mathrm{>}\left(dTsurf, inversion_{thresh}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AY_{F}, AY_{Ep}\right), AY_{D}\right), AY_{D}\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{strong}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v3\right), AY_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AY_{B}, AY_{C}\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{moder}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AY_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AY_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v6\right), AY_{C}, AY_{D}\right)\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{slight}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AY_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AY_{C}, AY_{D}\right)\right), AY_{D}\right)\right)\right)\right) $$Briggs horizontal dispersion coefficient A_y (dimensionless) for the current stability class.
$$ az = \mathrm{ifelse}\left(\mathrm{<}\left(SWGDN, solrad_{night}\right), \mathrm{ifelse}\left(\mathrm{<=}\left(CLDTOT, cloudfrac_{clear}\right), \mathrm{ifelse}\left(\mathrm{>}\left(dTsurf, inversion_{thresh}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AZ_{F}, AZ_{Ep}\right), AZ_{D}\right), AZ_{D}\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{strong}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v3\right), AZ_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AZ_{B}, AZ_{C}\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{moder}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AZ_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AZ_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v6\right), AZ_{C}, AZ_{D}\right)\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{slight}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), AZ_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), AZ_{C}, AZ_{D}\right)\right), AZ_{D}\right)\right)\right)\right) $$Briggs vertical dispersion coefficient A_z (dimensionless) for the current stability class.
$$ bz = \mathrm{ifelse}\left(\mathrm{<}\left(SWGDN, solrad_{night}\right), \mathrm{ifelse}\left(\mathrm{<=}\left(CLDTOT, cloudfrac_{clear}\right), \mathrm{ifelse}\left(\mathrm{>}\left(dTsurf, inversion_{thresh}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), BZ_{F}, BZ_{Ep}\right), BZ_{D}\right), BZ_{D}\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{strong}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v3\right), BZ_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), BZ_{B}, BZ_{C}\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{moder}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), BZ_{A}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), BZ_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v6\right), BZ_{C}, BZ_{D}\right)\right)\right), \mathrm{ifelse}\left(\mathrm{>=}\left(SWGDN, solrad_{slight}\right), \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v2\right), BZ_{B}, \mathrm{ifelse}\left(\mathrm{<}\left(wind_{speed}, v5\right), BZ_{C}, BZ_{D}\right)\right), BZ_{D}\right)\right)\right)\right) $$Briggs vertical saturation coefficient B_z (m^-1) for the current stability class. Zero for classes A and B.
$$ delta_{lon} = lon - lon0 $$Longitude difference lon - lon0 (radians). Intermediate for haversine downwind distance.
$$ delta_{lat} = lat - lat0 $$Latitude difference lat - lat0 (radians). Intermediate for haversine downwind distance.
$$ hav_{a} = \sin\left(\frac{delta_{lat}}{2.0}\right)^{2.0} + \cos\left(lat0\right) \cdot \cos\left(lat\right) \cdot \sin\left(\frac{delta_{lon}}{2.0}\right)^{2.0} $$Haversine intermediate a = sin((lat-lat0)/2)^2 + cos(lat0)*cos(lat)*sin((lon-lon0)/2)^2. In [0,1]; equals sin^2(central_angle/2).
$$ hav_{c} = 2.0 \cdot \mathrm{atan}\left(\frac{\sqrt{hav_{a}}}{\sqrt{1.0 - hav_{a}}}\right) $$Great-circle central angle c = 2*atan(sqrt(hav_a)/sqrt(1-hav_a)) (radians). The arc between source and puff.
$$ x = earth_{radius} \cdot hav_{c} $$Haversine downwind distance x = R * hav_c (m). The great-circle surface distance from the emission source (lon0, lat0) to the current puff position (lon, lat).
$$ sigma_{h} = ay \cdot x \cdot \left(1.0 + by \cdot x\right)^{-0.5} $$Horizontal Gaussian dispersion coefficient sigma_h (m). Computed from Briggs formula sigma_h = A_y * x * (1 + B_y * x)^(-0.5).
$$ sigma_{z} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{and}\left(\mathrm{<}\left(SWGDN, solrad_{night}\right), \mathrm{<=}\left(CLDTOT, cloudfrac_{clear}\right)\right), \mathrm{>}\left(dTsurf, inversion_{thresh}\right)\right), \frac{az \cdot x}{1.0 + bz \cdot x}, az \cdot x \cdot \left(1.0 + bz \cdot x\right)^{-0.5}\right) $$Vertical Gaussian dispersion coefficient sigma_z (m). Uses sigma_z = A_zx(1+B_zx)^(-0.5) for classes A-D; sigma_z = A_zx/(1+B_z*x) for classes E-F (stable, stronger vertical confinement).
$$ C_{gl} = \frac{1.0}{15.749609945722419 \cdot sigma_{h}^{2.0} \cdot sigma_{z}} \cdot e^{\frac{\left(-1.0\right) \cdot z_{agl}^{2.0}}{2.0 \cdot sigma_{z}^{2.0}}} $$Ground-level centerline Gaussian concentration per unit puff mass (m^-3). C_gl = exp(-z_agl^2/(2sigma_z^2)) / ((2pi)^(3/2) * sigma_h^2 * sigma_z). Maximum at z_agl=0 (puff at ground level).
Analyses
sigma_vs_distance_class_d
Horizontal and vertical dispersion coefficients sigma_h and sigma_z vs downwind distance x under neutral stability class D (SWGDN=50 W/m^2, U10M=3 m/s). lat varies from ~100 m to ~50 km north of source (lon0=lat0=0). Class D Briggs coefficients AY_D=0.08, AZ_D=0.06, BZ_D=0.0015 produce moderate spread. sigma_h grows as x*(1+1e-4x)^(-0.5), sigma_z as x(1+0.0015*x)^(-0.5) — sigma_z saturates faster than sigma_h due to larger BZ_D.
Time span: 0.0 → 0.0
Swept over: lat
stability_effect_on_concentration
Effect of solar radiation (and thus stability class) on ground-level concentration C_gl at a fixed downwind distance of ~1000 m (lat=1.5696e-4 rad). As SWGDN increases from night (0) to strong sun (1000 W/m^2), stability shifts from stable (F/E) to unstable (A/B/C), increasing both sigma_h and sigma_z and reducing C_gl. Wind speed fixed at U10M=3 m/s (class boundary E/D at night; A/B/C during day).
Time span: 0.0 → 0.0
Swept over: SWGDN
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: EnvironmentalTransport.jl@a48559c4114eb9f06668ecf9f06235aad20f63f0:src/GaussianDispersion.jl:83\n\nUpstream GaussianPGB is an MTK @component returning a purely algebraic System — all three output equations (sigma_h, sigma_z, C_gl) are algebraic assignments (~), not ODEs. There are no D(state)/dt terms. The component has three input variables marked input=true: lon(t), lat(t) (puff position, provided by Puff), and z_agl(t) (hypsometric height above ground, provided by an external data coupling such as GEOSFP or MERRA2). When coupled via EarthSciMLBase.couple(), these become shared symbolic variables with Puff/data connectors. In standalone mode they are held constant as parameters.\n\nMigration approach: purely algebraic ESM. All outputs (sigma_h, sigma_z, C_gl) are type=observed. The lon, lat, z_agl input variables are type=parameter (with physically representative defaults) for standalone simulation. When the Puff ESM and appropriate data connector ESMs are available, a coupling entry will tie these parameters to the corresponding Puff/data outputs.\n\nIntermediate observed variables (wind_speed, dTsurf, stab_cls, ay, az, bz, delta_lon, delta_lat, hav_a, hav_c, x) are exposed as named observed variables so they can be individually inspected and tested. The ESS runner evaluates observed variables in dependency order.\n\nStability class encoding: stab_cls returns a floating-point integer 1.0-6.0 (A=1, B=2, C=3, D=4, E=5, F=6). Coefficient selectors use threshold comparisons (stab_cls < 1.5, < 2.5 etc.) to avoid exact floating-point equality, which is unreliable for class E/F at SWGDN boundaries.\n\nBriggs sigma_h formula: sigma_h = A_y * x * (1 + B_y * x)^(-0.5). B_y is class-independent (by=1e-4 m^-1) per EPA MMGRMA.\n\nBriggs sigma_z formula: sigma_z = A_z * x * (1 + B_z * x)^(-0.5) for classes A-D (unstable/neutral); sigma_z = A_z * x / (1 + B_z * x) for classes E-F (stable).\n\nGaussian ground-level concentration: C_gl = exp(-z_agl^2 / (2*sigma_z^2)) / ((2*pi)^(3/2) * sigma_h^2 * sigma_z). At z_agl=0 this is the maximum surface concentration per unit puff mass.\n\nHaversine downwind distance: The great-circle distance from source (lon0, lat0) to current puff position (lon, lat) is computed via haversine: a = sin((lat-lat0)/2)^2 + cos(lat0)*cos(lat)*sin((lon-lon0)/2)^2; c = 2*atan(sqrt(a)/sqrt(1-a)); x = R*c. R=6.371e6 m (Earth mean radius).\n\nUnicode/Julia symbol normalization: Δz → dz (not used; GaussianPGB is Gaussian plume, not puff-KC), σ_h → sigma_h, σ_z → sigma_z, AY → AY, stab_cls integer 1-6 replaces character A-F.\n\nTolerance (model-level rel=1e-8, abs=1e-12): for algebraic evaluation the integrator tolerance is not operative; the tolerance is specified for consistency with the ESM contract and future runner versions. Observed expressions are composed of elementary trig/exp functions; accumulated rounding is <5 ULP (<1e-15 relative) well inside rel=1e-8.\n\nCoupler identity: this model was serialized with the model-level field `coupletype: \"GaussianPGBCoupler\"`, the EarthSciMLBase `CoupleType` metadata tag naming the Julia coupler struct that `EarthSciMLBase.couple2` dispatches on to find this component's pairwise coupling rules. The esm schema defined `coupletype` only before 0.8.0 (\"informational label identifying this system's role in coupling\"); 0.8.0 removed it in favour of explicit coupling — `coupling` entries naming components directly, or `coupling_roles` + `coupling_import` in a coupling-library file (esm-spec §10.9–§10.11). esm 1.0.0 has no model-level coupler-identity field, so the tag is recorded here to keep it recoverable."
},
"tolerance": {
"rel": 1e-08,
"abs": 1e-12
},
"variables": {
"lon": {
"type": "parameter",
"units": "rad",
"default": 0.0,
"description": "Puff longitude (radians). Supplied by Puff.x when coupled; held as constant parameter in standalone mode."
},
"lat": {
"type": "parameter",
"units": "rad",
"default": 0.0,
"description": "Puff latitude (radians). Supplied by Puff.y when coupled; held as constant parameter in standalone mode."
},
"z_agl": {
"type": "parameter",
"units": "m",
"default": 25.0,
"description": "Puff height above ground level (m). Supplied by an external data coupling (e.g. GEOSFP pressure-to-height) when coupled; held as constant parameter in standalone mode."
},
"lon0": {
"type": "parameter",
"units": "rad",
"default": 0.0,
"description": "Emission source longitude (radians). Fixed for the lifetime of the trajectory."
},
"lat0": {
"type": "parameter",
"units": "rad",
"default": 0.0,
"description": "Emission source latitude (radians). Fixed for the lifetime of the trajectory."
},
"earth_radius": {
"type": "parameter",
"units": "m",
"default": 6371000.0,
"description": "Earth mean radius (m). Used in haversine downwind distance computation."
},
"AY_A": {
"type": "parameter",
"default": 0.22,
"description": "Briggs A_y coefficient for Pasquill stability class A (very unstable)."
},
"AY_B": {
"type": "parameter",
"default": 0.16,
"description": "Briggs A_y coefficient for class B (unstable)."
},
"AY_C": {
"type": "parameter",
"default": 0.11,
"description": "Briggs A_y coefficient for class C (slightly unstable)."
},
"AY_D": {
"type": "parameter",
"default": 0.08,
"description": "Briggs A_y coefficient for class D (neutral)."
},
"AY_Ep": {
"type": "parameter",
"default": 0.06,
"description": "Briggs A_y coefficient for class E (slightly stable)."
},
"AY_F": {
"type": "parameter",
"default": 0.04,
"description": "Briggs A_y coefficient for class F (stable)."
},
"AZ_A": {
"type": "parameter",
"default": 0.2,
"description": "Briggs A_z coefficient for class A."
},
"AZ_B": {
"type": "parameter",
"default": 0.12,
"description": "Briggs A_z coefficient for class B."
},
"AZ_C": {
"type": "parameter",
"default": 0.08,
"description": "Briggs A_z coefficient for class C."
},
"AZ_D": {
"type": "parameter",
"default": 0.06,
"description": "Briggs A_z coefficient for class D."
},
"AZ_Ep": {
"type": "parameter",
"default": 0.03,
"description": "Briggs A_z coefficient for class E."
},
"AZ_F": {
"type": "parameter",
"default": 0.016,
"description": "Briggs A_z coefficient for class F."
},
"by": {
"type": "parameter",
"units": "m^-1",
"default": 0.0001,
"description": "Briggs B_y coefficient (class-independent, 1e-4 m^-1). Controls the far-field saturation of horizontal spread."
},
"BZ_A": {
"type": "parameter",
"units": "m^-1",
"default": 0.0,
"description": "Briggs B_z coefficient for class A."
},
"BZ_B": {
"type": "parameter",
"units": "m^-1",
"default": 0.0,
"description": "Briggs B_z coefficient for class B."
},
"BZ_C": {
"type": "parameter",
"units": "m^-1",
"default": 0.0002,
"description": "Briggs B_z coefficient for class C."
},
"BZ_D": {
"type": "parameter",
"units": "m^-1",
"default": 0.0015,
"description": "Briggs B_z coefficient for class D."
},
"BZ_Ep": {
"type": "parameter",
"units": "m^-1",
"default": 0.0003,
"description": "Briggs B_z coefficient for class E."
},
"BZ_F": {
"type": "parameter",
"units": "m^-1",
"default": 0.0003,
"description": "Briggs B_z coefficient for class F."
},
"v2": {
"type": "parameter",
"units": "m/s",
"default": 2.0,
"description": "Wind-speed threshold 2 m/s for Pasquill classification."
},
"v3": {
"type": "parameter",
"units": "m/s",
"default": 3.0,
"description": "Wind-speed threshold 3 m/s."
},
"v5": {
"type": "parameter",
"units": "m/s",
"default": 5.0,
"description": "Wind-speed threshold 5 m/s."
},
"v6": {
"type": "parameter",
"units": "m/s",
"default": 6.0,
"description": "Wind-speed threshold 6 m/s."
},
"solrad_strong": {
"type": "parameter",
"units": "W/m^2",
"default": 925.0,
"description": "Solar radiation threshold for very strong insolation (≥925 W/m^2 → class A/B/C)."
},
"solrad_moder": {
"type": "parameter",
"units": "W/m^2",
"default": 675.0,
"description": "Solar radiation threshold for moderate insolation (675-925 W/m^2)."
},
"solrad_slight": {
"type": "parameter",
"units": "W/m^2",
"default": 175.0,
"description": "Solar radiation threshold for slight insolation (175-675 W/m^2)."
},
"solrad_night": {
"type": "parameter",
"units": "W/m^2",
"default": 10.0,
"description": "Solar radiation threshold for night (<10 W/m^2); 10-175 W/m^2 defaults to neutral class D."
},
"cloudfrac_clear": {
"type": "parameter",
"default": 0.5,
"description": "Cloud fraction threshold for clear sky (CLDTOT ≤ 0.5 → clear). Used for nighttime stability classification."
},
"inversion_thresh": {
"type": "parameter",
"units": "K",
"default": 0.0,
"description": "Temperature difference threshold (T10M-T2M > 0 K) for surface inversion detection. Inversions drive class E or F at night."
},
"U10M": {
"type": "parameter",
"units": "m/s",
"default": 3.0,
"description": "10 m wind speed U component (eastward, m/s). Used to compute surface wind speed for stability classification."
},
"V10M": {
"type": "parameter",
"units": "m/s",
"default": 0.0,
"description": "10 m wind speed V component (northward, m/s)."
},
"SWGDN": {
"type": "parameter",
"units": "W/m^2",
"default": 700.0,
"description": "Surface downwelling shortwave radiation (W/m^2). Drives daytime stability class (A-D) via solar insolation thresholds."
},
"CLDTOT": {
"type": "parameter",
"default": 0.3,
"description": "Total cloud fraction (0-1). Used for nighttime stability classification: CLDTOT ≤ cloudfrac_clear → clear sky."
},
"T2M": {
"type": "parameter",
"units": "K",
"default": 293.15,
"description": "2 m air temperature (K). Used with T10M to compute surface temperature lapse dTsurf = T10M - T2M."
},
"T10M": {
"type": "parameter",
"units": "K",
"default": 292.65,
"description": "10 m air temperature (K). dTsurf = T10M - T2M > inversion_thresh indicates surface inversion."
},
"wind_speed": {
"type": "unknown",
"units": "m/s",
"description": "Surface wind speed magnitude sqrt(U10M^2 + V10M^2) (m/s). Used for Pasquill stability classification."
},
"dTsurf": {
"type": "unknown",
"units": "K",
"description": "Surface temperature lapse T10M - T2M (K). Positive values indicate a surface temperature inversion; used for nighttime stability class E/F classification."
},
"stab_cls": {
"type": "unknown",
"description": "Pasquill-Gifford stability class as floating-point integer 1.0-6.0 (A=1, B=2, C=3, D=4, E=5, F=6). Determined from SWGDN, CLDTOT, wind_speed, and dTsurf per EPA MMGRMA Table 6-7."
},
"ay": {
"type": "unknown",
"description": "Briggs horizontal dispersion coefficient A_y (dimensionless) for the current stability class."
},
"az": {
"type": "unknown",
"description": "Briggs vertical dispersion coefficient A_z (dimensionless) for the current stability class."
},
"bz": {
"type": "unknown",
"units": "m^-1",
"description": "Briggs vertical saturation coefficient B_z (m^-1) for the current stability class. Zero for classes A and B."
},
"delta_lon": {
"type": "unknown",
"units": "rad",
"description": "Longitude difference lon - lon0 (radians). Intermediate for haversine downwind distance."
},
"delta_lat": {
"type": "unknown",
"units": "rad",
"description": "Latitude difference lat - lat0 (radians). Intermediate for haversine downwind distance."
},
"hav_a": {
"type": "unknown",
"description": "Haversine intermediate a = sin((lat-lat0)/2)^2 + cos(lat0)*cos(lat)*sin((lon-lon0)/2)^2. In [0,1]; equals sin^2(central_angle/2)."
},
"hav_c": {
"type": "unknown",
"units": "rad",
"description": "Great-circle central angle c = 2*atan(sqrt(hav_a)/sqrt(1-hav_a)) (radians). The arc between source and puff."
},
"x": {
"type": "unknown",
"units": "m",
"description": "Haversine downwind distance x = R * hav_c (m). The great-circle surface distance from the emission source (lon0, lat0) to the current puff position (lon, lat)."
},
"sigma_h": {
"type": "unknown",
"units": "m",
"description": "Horizontal Gaussian dispersion coefficient sigma_h (m). Computed from Briggs formula sigma_h = A_y * x * (1 + B_y * x)^(-0.5)."
},
"sigma_z": {
"type": "unknown",
"units": "m",
"description": "Vertical Gaussian dispersion coefficient sigma_z (m). Uses sigma_z = A_z*x*(1+B_z*x)^(-0.5) for classes A-D; sigma_z = A_z*x/(1+B_z*x) for classes E-F (stable, stronger vertical confinement)."
},
"C_gl": {
"type": "unknown",
"units": "m^-3",
"description": "Ground-level centerline Gaussian concentration per unit puff mass (m^-3). C_gl = exp(-z_agl^2/(2*sigma_z^2)) / ((2*pi)^(3/2) * sigma_h^2 * sigma_z). Maximum at z_agl=0 (puff at ground level)."
}
},
"tests": [
{
"id": "class_a_unstable",
"description": "Stability class A (very unstable): strong sun (SWGDN=950 >= 925 W/m^2) and low wind (U10M=1 m/s < v3=3 m/s) → class A. Puff at 1000 m north of source (lat=1.5696e-4 rad, lon=lon0=lat0=0). z_agl=0. Expected: stab_cls=1, sigma_h = AY_A*1000*(1+by*1000)^(-0.5) = 0.22*1000*(1.1)^(-0.5) = 209.7618 m; sigma_z = AZ_A*1000*(1+0)^(-0.5) = 200 m (BZ_A=0 → denominator 1); C_gl = exp(0)/((2pi)^(3/2)*sigma_h^2*sigma_z). Verifies class A selection, zero-BZ_A sigma_z, and C_gl formula at ground level.",
"parameter_overrides": {
"lon": 0.0,
"lat": 0.0001569612305760477,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 1.0,
"V10M": 0.0,
"SWGDN": 950.0,
"CLDTOT": 0.3,
"T2M": 293.15,
"T10M": 292.65,
"z_agl": 0.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "stab_cls",
"time": 0,
"expected": 1.0,
"tolerance": {
"abs": 0.01
}
},
{
"variable": "x",
"time": 0,
"expected": 1000.0,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_h",
"time": 0,
"expected": 209.76176963403023,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_z",
"time": 0,
"expected": 200.0,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "C_gl",
"time": 0,
"expected": 7.215185901618299e-09,
"tolerance": {
"rel": 1e-05
}
}
]
},
{
"id": "class_d_neutral",
"description": "Stability class D (neutral): low solar radiation (SWGDN=50 < 175 W/m^2 → default neutral), any wind → class D. Puff at 5000 m north (lat=7.848e-4 rad). z_agl=50 m. U10M=4, V10M=3 → wind_speed=5 m/s. Expected: stab_cls=4, sigma_h = 0.08*5000*(1+1e-4*5000)^(-0.5) = 326.6 m; sigma_z = 0.06*5000*(1+0.0015*5000)^(-0.5) = 60*(8.5)^(-0.5) = 102.9 m; C_gl includes exp(-50^2/(2*102.9^2)). Verifies class D selection, non-zero BZ_D sigma_z, and concentration at elevated height.",
"parameter_overrides": {
"lon": 0.0,
"lat": 0.0007848061528802386,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 4.0,
"V10M": 3.0,
"SWGDN": 50.0,
"CLDTOT": 0.3,
"T2M": 293.15,
"T10M": 292.65,
"z_agl": 50.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "stab_cls",
"time": 0,
"expected": 4.0,
"tolerance": {
"abs": 0.01
}
},
{
"variable": "x",
"time": 0,
"expected": 5000.0,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_h",
"time": 0,
"expected": 326.5986323710904,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_z",
"time": 0,
"expected": 102.89915108550531,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "C_gl",
"time": 0,
"expected": 5.140659109986362e-09,
"tolerance": {
"rel": 1e-05
}
}
]
},
{
"id": "class_f_stable",
"description": "Stability class F (stable): night (SWGDN=5 < 10 W/m^2), clear sky (CLDTOT=0.3 ≤ 0.5), surface inversion (T10M=294.0 > T2M=293.15 → dTsurf=0.85>0), low wind (U10M=1 < v2=2) → class F. Puff at 500 m north (lat=7.848e-5 rad). z_agl=0. Expected: stab_cls=6; sigma_z = AZ_F*x/(1+BZ_F*x) (stable formula, >=5): 0.016*500/(1+0.0003*500) = 8/1.15 = 6.957 m; sigma_h = AY_F*x*(1+by*x)^(-0.5) = 0.04*500*(1.05)^(-0.5) = 19.52 m. Verifies nighttime class F selection and stable sigma_z formula.",
"parameter_overrides": {
"lon": 0.0,
"lat": 7.848061528802385e-05,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 1.0,
"V10M": 0.0,
"SWGDN": 5.0,
"CLDTOT": 0.3,
"T2M": 293.15,
"T10M": 294.0,
"z_agl": 0.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "stab_cls",
"time": 0,
"expected": 6.0,
"tolerance": {
"abs": 0.01
}
},
{
"variable": "x",
"time": 0,
"expected": 500.0,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_h",
"time": 0,
"expected": 19.518001458970662,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_z",
"time": 0,
"expected": 6.956521739130435,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "C_gl",
"time": 0,
"expected": 2.395892668456125e-05,
"tolerance": {
"rel": 1e-05
}
}
]
},
{
"id": "class_e_slightly_stable",
"description": "Stability class E (slightly stable): night (SWGDN=5 < 10), clear sky, inversion (T10M=294.5 > T2M=294.0 → dTsurf=0.5>0), moderate wind (U10M=3 ≥ v2=2) → class E (not F). Puff at 2000 m north (lat=3.139e-4 rad). z_agl=0. Expected: stab_cls=5; sigma_z = AZ_Ep*x/(1+BZ_Ep*x) = 0.03*2000/(1+0.0003*2000) = 60/1.6 = 37.5 m exactly. sigma_h = AY_Ep*x*(1+by*x)^(-0.5) = 0.06*2000*(1.2)^(-0.5) = 120/sqrt(1.2) = 109.545 m. Verifies class E selection (vs F at same conditions with lower wind), stable sigma_z formula, and exact BZ_Ep arithmetic.",
"parameter_overrides": {
"lon": 0.0,
"lat": 0.0003139224611520954,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 3.0,
"V10M": 0.0,
"SWGDN": 5.0,
"CLDTOT": 0.3,
"T2M": 294.0,
"T10M": 294.5,
"z_agl": 0.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "stab_cls",
"time": 0,
"expected": 5.0,
"tolerance": {
"abs": 0.01
}
},
{
"variable": "x",
"time": 0,
"expected": 2000.0,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_h",
"time": 0,
"expected": 109.54451150103321,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "sigma_z",
"time": 0,
"expected": 37.5,
"tolerance": {
"rel": 1e-06
}
},
{
"variable": "C_gl",
"time": 0,
"expected": 1.410969687427577e-07,
"tolerance": {
"rel": 1e-05
}
}
]
}
],
"equations": [
{
"lhs": "wind_speed",
"rhs": {
"op": "sqrt",
"args": [
{
"op": "+",
"args": [
{
"op": "^",
"args": [
"U10M",
2.0
]
},
{
"op": "^",
"args": [
"V10M",
2.0
]
}
]
}
]
}
},
{
"lhs": "dTsurf",
"rhs": {
"op": "-",
"args": [
"T10M",
"T2M"
]
}
},
{
"lhs": "stab_cls",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"SWGDN",
"solrad_night"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<=",
"args": [
"CLDTOT",
"cloudfrac_clear"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">",
"args": [
"dTsurf",
"inversion_thresh"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
6.0,
5.0
]
},
4.0
]
},
4.0
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_strong"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v3"
]
},
1.0,
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
2.0,
3.0
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_moder"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
1.0,
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
2.0,
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v6"
]
},
3.0,
4.0
]
}
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_slight"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
2.0,
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
3.0,
4.0
]
}
]
},
4.0
]
}
]
}
]
}
]
}
},
{
"lhs": "ay",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"SWGDN",
"solrad_night"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<=",
"args": [
"CLDTOT",
"cloudfrac_clear"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">",
"args": [
"dTsurf",
"inversion_thresh"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AY_F",
"AY_Ep"
]
},
"AY_D"
]
},
"AY_D"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_strong"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v3"
]
},
"AY_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AY_B",
"AY_C"
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_moder"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AY_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AY_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v6"
]
},
"AY_C",
"AY_D"
]
}
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_slight"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AY_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AY_C",
"AY_D"
]
}
]
},
"AY_D"
]
}
]
}
]
}
]
}
},
{
"lhs": "az",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"SWGDN",
"solrad_night"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<=",
"args": [
"CLDTOT",
"cloudfrac_clear"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">",
"args": [
"dTsurf",
"inversion_thresh"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AZ_F",
"AZ_Ep"
]
},
"AZ_D"
]
},
"AZ_D"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_strong"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v3"
]
},
"AZ_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AZ_B",
"AZ_C"
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_moder"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AZ_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AZ_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v6"
]
},
"AZ_C",
"AZ_D"
]
}
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_slight"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"AZ_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"AZ_C",
"AZ_D"
]
}
]
},
"AZ_D"
]
}
]
}
]
}
]
}
},
{
"lhs": "bz",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"SWGDN",
"solrad_night"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<=",
"args": [
"CLDTOT",
"cloudfrac_clear"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">",
"args": [
"dTsurf",
"inversion_thresh"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"BZ_F",
"BZ_Ep"
]
},
"BZ_D"
]
},
"BZ_D"
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_strong"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v3"
]
},
"BZ_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"BZ_B",
"BZ_C"
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_moder"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"BZ_A",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"BZ_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v6"
]
},
"BZ_C",
"BZ_D"
]
}
]
}
]
},
{
"op": "ifelse",
"args": [
{
"op": ">=",
"args": [
"SWGDN",
"solrad_slight"
]
},
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v2"
]
},
"BZ_B",
{
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"wind_speed",
"v5"
]
},
"BZ_C",
"BZ_D"
]
}
]
},
"BZ_D"
]
}
]
}
]
}
]
}
},
{
"lhs": "delta_lon",
"rhs": {
"op": "-",
"args": [
"lon",
"lon0"
]
}
},
{
"lhs": "delta_lat",
"rhs": {
"op": "-",
"args": [
"lat",
"lat0"
]
}
},
{
"lhs": "hav_a",
"rhs": {
"op": "+",
"args": [
{
"op": "^",
"args": [
{
"op": "sin",
"args": [
{
"op": "/",
"args": [
"delta_lat",
2.0
]
}
]
},
2.0
]
},
{
"op": "*",
"args": [
{
"op": "cos",
"args": [
"lat0"
]
},
{
"op": "cos",
"args": [
"lat"
]
},
{
"op": "^",
"args": [
{
"op": "sin",
"args": [
{
"op": "/",
"args": [
"delta_lon",
2.0
]
}
]
},
2.0
]
}
]
}
]
}
},
{
"lhs": "hav_c",
"rhs": {
"op": "*",
"args": [
2.0,
{
"op": "atan",
"args": [
{
"op": "/",
"args": [
{
"op": "sqrt",
"args": [
"hav_a"
]
},
{
"op": "sqrt",
"args": [
{
"op": "-",
"args": [
1.0,
"hav_a"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "x",
"rhs": {
"op": "*",
"args": [
"earth_radius",
"hav_c"
]
}
},
{
"lhs": "sigma_h",
"rhs": {
"op": "*",
"args": [
"ay",
"x",
{
"op": "^",
"args": [
{
"op": "+",
"args": [
1.0,
{
"op": "*",
"args": [
"by",
"x"
]
}
]
},
-0.5
]
}
]
}
},
{
"lhs": "sigma_z",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "and",
"args": [
{
"op": "and",
"args": [
{
"op": "<",
"args": [
"SWGDN",
"solrad_night"
]
},
{
"op": "<=",
"args": [
"CLDTOT",
"cloudfrac_clear"
]
}
]
},
{
"op": ">",
"args": [
"dTsurf",
"inversion_thresh"
]
}
]
},
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"az",
"x"
]
},
{
"op": "+",
"args": [
1.0,
{
"op": "*",
"args": [
"bz",
"x"
]
}
]
}
]
},
{
"op": "*",
"args": [
"az",
"x",
{
"op": "^",
"args": [
{
"op": "+",
"args": [
1.0,
{
"op": "*",
"args": [
"bz",
"x"
]
}
]
},
-0.5
]
}
]
}
]
}
},
{
"lhs": "C_gl",
"rhs": {
"op": "*",
"args": [
{
"op": "/",
"args": [
1.0,
{
"op": "*",
"args": [
15.749609945722419,
{
"op": "^",
"args": [
"sigma_h",
2.0
]
},
"sigma_z"
]
}
]
},
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
-1.0,
{
"op": "^",
"args": [
"z_agl",
2.0
]
}
]
},
{
"op": "*",
"args": [
2.0,
{
"op": "^",
"args": [
"sigma_z",
2.0
]
}
]
}
]
}
]
}
]
}
}
],
"analyses": [
{
"id": "sigma_vs_distance_class_d",
"description": "Horizontal and vertical dispersion coefficients sigma_h and sigma_z vs downwind distance x under neutral stability class D (SWGDN=50 W/m^2, U10M=3 m/s). lat varies from ~100 m to ~50 km north of source (lon0=lat0=0). Class D Briggs coefficients AY_D=0.08, AZ_D=0.06, BZ_D=0.0015 produce moderate spread. sigma_h grows as x*(1+1e-4*x)^(-0.5), sigma_z as x*(1+0.0015*x)^(-0.5) — sigma_z saturates faster than sigma_h due to larger BZ_D.",
"initial_state": {},
"parameters": {
"lon": 0.0,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 3.0,
"V10M": 0.0,
"SWGDN": 50.0,
"CLDTOT": 0.3,
"T2M": 293.15,
"T10M": 292.65,
"z_agl": 0.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "lat",
"range": {
"start": 1.569612e-05,
"stop": 0.007848062,
"count": 50,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "sigma_h_vs_x",
"type": "line",
"description": "Horizontal dispersion coefficient sigma_h (m) vs downwind distance x (m) for neutral stability class D.",
"x": {
"variable": "x",
"label": "Downwind distance x (m)"
},
"y": {
"variable": "sigma_h",
"label": "sigma_h (m)"
}
},
{
"id": "sigma_z_vs_x",
"type": "line",
"description": "Vertical dispersion coefficient sigma_z (m) vs downwind distance x (m). sigma_z saturates more quickly than sigma_h due to larger B_z for class D.",
"x": {
"variable": "x",
"label": "Downwind distance x (m)"
},
"y": {
"variable": "sigma_z",
"label": "sigma_z (m)"
}
},
{
"id": "C_gl_vs_x",
"type": "line",
"description": "Ground-level concentration C_gl (m^-3 per unit mass) vs downwind distance x under class D stability, z_agl=0. Monotonically decreasing as puff spreads.",
"x": {
"variable": "x",
"label": "Downwind distance x (m)"
},
"y": {
"variable": "C_gl",
"label": "C_gl (m^-3)"
}
}
]
},
{
"id": "stability_effect_on_concentration",
"description": "Effect of solar radiation (and thus stability class) on ground-level concentration C_gl at a fixed downwind distance of ~1000 m (lat=1.5696e-4 rad). As SWGDN increases from night (0) to strong sun (1000 W/m^2), stability shifts from stable (F/E) to unstable (A/B/C), increasing both sigma_h and sigma_z and reducing C_gl. Wind speed fixed at U10M=3 m/s (class boundary E/D at night; A/B/C during day).",
"initial_state": {},
"parameters": {
"lon": 0.0,
"lat": 0.0001569612305760477,
"lon0": 0.0,
"lat0": 0.0,
"U10M": 3.0,
"V10M": 0.0,
"CLDTOT": 0.3,
"T2M": 293.15,
"T10M": 294.0,
"z_agl": 0.0
},
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "SWGDN",
"range": {
"start": 0.0,
"stop": 1000.0,
"count": 50,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "stab_cls_vs_SWGDN",
"type": "line",
"description": "Stability class (1=A very unstable ... 6=F stable) vs SWGDN solar radiation. Shows discrete class transitions as SWGDN crosses thresholds.",
"x": {
"variable": "SWGDN",
"label": "SWGDN (W/m^2)"
},
"y": {
"variable": "stab_cls",
"label": "Stability class (1=A ... 6=F)"
}
},
{
"id": "C_gl_vs_SWGDN",
"type": "line",
"description": "Ground-level concentration C_gl (m^-3) vs SWGDN. Daytime (SWGDN > 10): more unstable conditions (higher SWGDN) increase dispersion and decrease C_gl. Night (SWGDN < 10): stable conditions concentrate the plume.",
"x": {
"variable": "SWGDN",
"label": "SWGDN (W/m^2)"
},
"y": {
"variable": "C_gl",
"label": "C_gl (m^-3)"
}
}
]
}
]
}