Back to Odor Forecast

1. Model Overview

1.1 What This Model Is

This is a real-time odor scoring heuristic that runs entirely in a web browser. It ingests publicly available weather observations and forecasts, combines them with emissions data from LDEQ air permits, and produces a 0–100 odor intensity score for each point on a map, updated every 30 minutes across a 48-hour forecast horizon.

1.2 What This Model Is Not

This is not a regulatory dispersion model. It does not replace AERMOD, CALPUFF, or any EPA-approved model. Key differences:

• It does not compute actual pollutant concentrations in mass/volume units
• It has no upper-air sounding data and cannot directly determine mixing heights or Monin-Obukhov stability parameters
• Its output is a dimensionless 0–100 score calibrated against subjective odor reports, not measured concentrations
• It uses a single surface weather station (KAEX ASOS), not a spatial meteorological field

The model borrows specific physics formulations from AERMOD (EPA’s regulatory Gaussian plume model, version 24142) where possible and documents every deviation where simplification was necessary.

1.3 Scoring Architecture

The core prediction is a product of seven dimensionless factors:

$$\text{Score} = E \times T \times I \times D \times H \times G \times M \times 100$$

Symbol	Factor	Range	What it captures
$E$	Emission	0–1	Source strength: temperature-driven volatilization, source category weighting
$T$	Transport	0–1	Wind direction, distance decay, meander
$I$	Inversion	1.0–1.8	Multi-hour accumulation under persistent trapping
$D$	Diurnal	0.5–1.0	Time-of-day atmospheric mixing regime
$H$	Humidity	0.6–1.3	Moisture effects on odor perception and droplet absorption
$G$	Terrain	0.5–1.6	Elevation-based drainage, valley channeling
$M$	Mixing height	0.6–1.0	Boundary layer depth from AERMOD-inspired vertical physics

2. Meteorological Inputs

2.1 Data Sources

Source	Parameters	Update frequency	Role
KAEX ASOS	Temperature, dewpoint, humidity, wind speed/direction, pressure, visibility, ceiling, cloud cover	~30 min (METAR)	Ground truth for current hour; blended into forecast
NWS hourly forecast (LCH gridpoint 88,143)	Temperature, dewpoint, humidity, wind speed/direction, cloud cover, short forecast text	~1 hr	Primary forecast source (0–48h)
Open-Meteo (ECMWF)	Temperature, dewpoint, humidity, wind speed/direction, cloud cover, surface pressure	~6 hr (model runs)	Secondary forecast; sole source of forecast pressure
NWS Area Forecast Discussion (LCH)	Free-text meteorological analysis	~2×/day	Scanned for inversion/stagnation keywords

2.2 Forecast Blending

NWS and Open-Meteo forecasts are blended with time-dependent weights. Near-term forecasts favor NWS (local forecaster skill); extended forecasts favor Open-Meteo (ECMWF global model). Wind direction is blended using vector averaging to handle the 360°/0° wraparound.

$$w_{\text{NWS}} = \begin{cases} 0.70 & \text{lead} \leq 6\text{h} \\ 0.70 - \frac{0.40}{42}(\text{lead} - 6) & 6\text{h} < \text{lead} < 48\text{h} \\ 0.30 & \text{lead} \geq 48\text{h} \end{cases}$$

2.3 What We Do Not Have

The following standard AERMOD/AERMET inputs are unavailable to this model:

• Upper-air soundings — no radiosonde data for mixing height or temperature profiles
• Surface energy balance — no net radiation, soil heat flux, or sensible heat flux measurements
• Monin-Obukhov length ($L$) — cannot be computed without the above
• Friction velocity ($u_*$) with stability correction — we estimate from neutral log-law only
• Turbulence measurements — no direct $\sigma_v$, $\sigma_w$ observations
• Spatial wind field — single station observation applied uniformly

3. Stability Estimation

3.1 Our Approach

Atmospheric stability is represented as a single value from 0 (strongly unstable/convective) to 1 (strongly stable/inversion). This proxy is derived from a weighted combination of nine surface observation signals processed by the inversion detection module. The inversion score (0–1) is then mapped to stability:

$$\text{stability} = 0.5 + \text{inversionScore} \times 0.45$$

With overrides:

• Nighttime floor: $\text{stability} \geq 0.55$
• Peak daytime with $T > 85$°F: $\text{stability} \leq 0.25$
• Peak daytime with $T > 70$°F: $\text{stability} \leq 0.4$
• Wind $\geq 15$ mph: $\text{stability} \leq 0.35$
• Wind $\geq 10$ mph: $\text{stability} \leq 0.45$

3.2 Inversion Detection Signals

The inversion score is a weighted sum of nine proxy signals. Weights depend on whether KAEX observation data is blended into the current period:

Signal	What it measures	Obs weight	Fcst weight
Dewpoint spread	$|T - T_d|$; tight spread suggests fog/saturation	0.10	0.10
Temperature trend	Overnight temp rising/flat = inversion; cooling = normal	0.10	0.10
Wind speed	Calm wind allows stratification to persist	0.15	0.20
Time-of-day prior	Bayesian prior for radiation inversions (peak 3–8 AM)	0.05	0.05
AFD text keywords	NWS Area Forecast Discussion scanned for “inversion,” “fog,” “stagnation,” “high pressure,” “ridge”	0.10	0.15
Visibility	KAEX ASOS visibility; low = trapping confirmed	0.15	—
Pressure trend	Steady/rising = stagnation; falling = frontal mixing	0.10	—
Sky condition	Clear night sky + Brutsaert radiative cooling estimate	0.10	0.20
Persistence	Exponential carryover from overnight formation (half-life ~2h)	0.15	0.20

Wind veto: When wind speed $\geq 8$ mph, the inversion score is floored to $\min(0.2,\; \text{AFD} \times 0.2)$ regardless of other signals.

3.3 Subsidence Floor

When surface pressure is $\geq 1025$ mb, wind $\leq 8$ mph, and it is evening/nighttime (18:00–09:00), a floor is applied to the inversion score:

Pressure (mb)	Inversion score floor
$\geq 1030$	0.65
$\geq 1025$	0.50
$\geq 1020$	0.35

3.4 AERMOD’s Approach (for comparison)

AERMOD classifies stability solely from the Monin-Obukhov length $L$:

• $L > 0$: stable
• $L < 0$: unstable

$L$ is computed from friction velocity $u_*$, sensible heat flux $H_0$, and surface temperature via the surface energy balance in AERMET. This requires net radiation measurements or cloud cover with a radiation model, plus surface roughness and Bowen ratio — none of which we have.

4. Mixing Height Estimation

4.1 Our Approach

The boundary layer depth $z_i$ (meters) is estimated from three mechanisms, taking the minimum of applicable constraints:

Mechanical mixing depth (Zilitinkevich 1972 form)

$$z_{i,\text{mech}} = \frac{2300 \cdot u_*^{3/2}}{\sqrt{\text{stability}}}$$

where $u_*$ is estimated from neutral log-law:

$$u_* = \frac{\kappa \cdot U_{10}}{\ln(z_{\text{ref}} / z_0)}$$

with $\kappa = 0.4$, $z_{\text{ref}} = 10$ m, $z_0 = 0.5$ m (suburban/light industrial).

Convective mixing depth (daytime only)

$$z_{i,\text{conv}} = (400 + 1200 \cdot I_{\text{solar}}) \times f_T$$

where $I_{\text{solar}}$ is the normalized solar intensity (0 at horizon, 1 at solar noon) from Spencer (1971) solar position equations, and $f_T$ is a temperature boost (1.0 below 70°F, 1.1 at 70–85°F, 1.3 above 85°F).

Pressure-based subsidence cap (removed)

An earlier version of this model included a pressure-based subsidence cap: $z_{i,\text{sub}} = \max(80,\; 800 - 20 \cdot (P - 1013))$. This was removed after analysis of KSHV (Shreveport) radiosonde soundings from March 21–29, 2026, which showed no reliable relationship between surface pressure and inversion height:

Date/Time (CDT)	Sfc P (mb)	Inversion base (m AGL)	Strength
Mar 21, 1 PM	1005	~830	Strong (+3.6°C)
Mar 24, 7 PM	1007	~1700	Weak
Mar 25, 7 PM	1007	~1900	Strong (+2.4°C)
Mar 26, 7 PM	1005	~1500	Very strong (+4.2°C)
Mar 27, 7 PM	1011	None	Unstable (pre-frontal)
Mar 28, 7 PM	1017 (SHV) / 1026 (KAEX)	~830	Moderate (+1.8°C)

The coefficient 20 m/mb had no literature basis, and the data show that inversions at ~830 m can occur at both 1005 mb and 1017 mb, while no inversion exists at 1011 mb. The synoptic pattern (ridge position, frontal timing, warm advection) determines inversion structure, not surface pressure alone. Mixing height estimation without upper-air soundings remains the model’s weakest link.

Inversion compression

When inversion score $> 0.5$:

$$z_i \leq 300 \times (1.5 - \text{inversionScore})$$

At score 1.0, this caps $z_i$ at 150 m. At score 0.85 (strong fog inversion), $z_i \leq 195$ m.

Final mixing height

$$z_i = \max\!\big(30,\; \min(z_{i,\text{mech}},\; z_{i,\text{conv}},\; z_{i,\text{inv}})\big)$$

5. Transport Model

5.1 Lateral Spread: Empirical Angular Model

The transport factor uses an empirical angular-sigma approach rather than Gaussian lateral dispersion ($\sigma_y$). For a receptor at distance $d$ (km) and bearing offset $\theta$ from the downwind direction:

Angular Gaussian falloff

$$F_{\theta} = \exp\!\left(-\frac{1}{2}\left(\frac{\theta}{\sigma_{\theta}}\right)^2\right)$$

Wind speed	$\sigma_{\theta}$ (degrees)	Base max distance (km)
$\leq 8$ mph	50°	5
8–15 mph	30°	7
$> 15$ mph	20°	10

Distance decay

$$F_d = \left(1 - \frac{d}{d_{\max}}\right)^{\alpha}$$

where the decay exponent $\alpha$ and max distance $d_{\max}$ are stability-dependent:

$$\alpha = 2.2 - 1.2 \times \text{stability}$$ $$d_{\max} = d_{\text{base}} \times (0.85 + 0.75 \times \text{stability})$$

Under strong stability ($s = 0.9$): $\alpha = 1.12$ (slow decay), $d_{\max} = 5 \times 1.525 = 7.6$ km.
Under instability ($s = 0.2$): $\alpha = 1.96$ (fast decay), $d_{\max} = 5 \times 1.0 = 5.0$ km.

Meander transition (AERMOD MEANDR)

Under calm winds, the plume meanders in all directions rather than maintaining a coherent fan. The meander fraction $m$ determines the blend between circular (pooling) and directional (fan) modes. The FRAN equation follows AERMOD’s MEANDR subroutine in calc2.f:

$$\text{FRAN} = \frac{2\sigma_v^2 + \overline{U}^2_{\text{mean}}(1 - e^{-t_{\text{trav}}/T})}{U^2}$$ $$m = 1 - \text{FRAN}$$

where $\overline{U}^2_{\text{mean}} = \max(0.01,\; U^2 - 2\sigma_v^2)$, $T = 86400$ s (24-hour meander timescale), and $t_{\text{trav}} = d/U$ is the travel time.

Directional transport score

$$T_{\text{dir}} = F_{\theta} \times F_d \times F_{\text{dilution}}$$

where $F_{\text{dilution}}$ accounts for wind dilution at wind speeds above 5 mph.

Circular transport score

$$T_{\text{circ}} = \left(1 - \frac{d}{d_{\text{calm}}}\right)^{\alpha_c}$$

where $d_{\text{calm}} = 4.0 \times (0.85 + 0.75 \times s)$ km and $\alpha_c = \max(0.8, \alpha - 0.4)$.

Final transport factor

$$T = m \cdot T_{\text{circ}} + (1 - m) \cdot T_{\text{dir}}$$

6. Vertical Dispersion Physics

6.1 Vertical turbulence ($\sigma_w$)

Estimated from friction velocity with stability reduction (AERMOD siggrid.f form):

$$\sigma_w = \max\!\big(0.08,\; 1.3 \cdot u_* \cdot (1 - 0.6 \cdot s)\big)$$

The factor 1.3 is the AERMOD mechanical $\sigma_w$ coefficient near the surface. The $(1 - 0.6s)$ term reduces vertical turbulence under stable conditions.

6.2 Vertical dispersion parameter ($\sigma_z$) with BVF capping

This is the AERMOD formula from sigmas.f for stable conditions:

$$\sigma_z = \frac{\sigma_w \cdot t}{\sqrt{1 + \sigma_w \cdot t \cdot \left(\frac{1}{0.72\,z_i} + \frac{N}{0.54\,\sigma_w}\right)}}$$

where $t = x / U$ is travel time and $N$ is the Brunt-Väisälä frequency:

$$N = 0.005 + 0.035 \times s$$

Asymptotic behavior: As $x \to \infty$, $\sigma_z$ saturates at $\sqrt{0.54 \cdot \sigma_w / N}$. For strong stability ($s = 0.9$, $N = 0.037$ s$^{-1}$), this cap is approximately 5–8 m. This is the key mechanism that extends plume range under stable conditions: vertical spread stops growing, so concentration decays only as $1/\sigma_y$ (one dimension) instead of $1/(\sigma_y \cdot \sigma_z)$ (two dimensions).

$\sigma_z$ is additionally capped at $0.8 \times z_i$ (cannot exceed mixing layer depth).

6.3 Vertical concentration term ($F_z$) with reflections

Ground-level concentration from an elevated source requires accounting for reflections off the ground ($z = 0$) and the mixing height lid ($z = z_i$). Following AERMOD calc2.f, the vertical term uses an image-source sum:

$$F_z = \frac{1}{\sqrt{2\pi}\,\sigma_z} \sum_{n=-2}^{2} \left[ \exp\!\left(-\frac{(H_e + 2nz_i)^2}{2\sigma_z^2}\right) + \exp\!\left(-\frac{(-H_e + 2nz_i)^2}{2\sigma_z^2}\right) \right]$$

where $H_e$ is the effective release height. For the transport scoring, $H_e = 2$ m (ground-level sources dominate community odor). The sum uses 5 image pairs ($n = -2$ to $2$), which is sufficient when $\sigma_z < z_i$.

Well-mixed limit: When $\sigma_z \to z_i$, the image sum converges to $1/z_i$. This is the classic box-model result: concentration is inversely proportional to mixing height. Under subsidence (low $z_i$), $F_z$ is large, naturally producing higher concentrations without a separate multiplier.

6.4 Mixing Height Factor ($M$)

The mixing height factor compares the vertical concentration under current conditions to a neutral reference at 2 km downwind:

$$M = \frac{F_z(z_i, \sigma_z, U_{\text{eff}})}{F_z(z_{i,\text{ref}}, \sigma_{z,\text{ref}}, U_{\text{ref}})}$$

Reference conditions: $z_{i,\text{ref}} = 500$ m, stability $= 0.4$, $U_{\text{ref}} = 3.0$ m/s. The ratio is clamped to [0.6, 1.0] — the factor can reduce scores during strong daytime mixing but does not amplify above 1.0 because the morning inversion model was already calibrated without it.

7. Briggs Plume Rise

Elevated stack emissions (Pineville kilns, 25–32 ft / ~9 m stacks) undergo buoyancy-driven plume rise. The formulas follow Briggs (1975, 1984) as implemented in AERMOD prise.f:

Buoyancy flux

$$F_b = g \cdot v_s \cdot \left(\frac{d_s}{2}\right)^2 \cdot \frac{T_s - T_a}{T_s}$$

Stable rise

$$\Delta H_{\text{stable}} = 2.66 \cdot \left(\frac{F_b}{U \cdot N^2}\right)^{1/3}$$

Unstable/neutral rise

$$\Delta H_{\text{unstable}} = 1.6 \cdot F_b^{1/3} \cdot x_f^{2/3} / U$$

where $x_f = 49 \cdot F_b^{5/8}$ when $F_b < 55$ m$^4$/s$^3$.

Blended rise

$$\Delta H = s \cdot \Delta H_{\text{stable}} + (1 - s) \cdot \Delta H_{\text{unstable}}$$ $$H_e = H_{\text{stack}} + \min(\Delta H, 50)$$

Note: Plume rise is used in the chemical overlay visualization and the groundLevelFraction calculation, but the transport scoring uses $H_e = 2$ m for all plants because ground-level sources (cylinder operations, storage yards, fugitives) dominate the odor signal at community distances.

8. Wind Profile

KAEX ASOS measures wind at 10 m. Wind at other heights uses neutral log-law (AERMOD windgrid.f):

$$U(z) = U_{\text{ref}} \cdot \frac{\ln(z / z_0)}{\ln(z_{\text{ref}} / z_0)}$$

with $z_0 = 0.5$ m and $z_{\text{ref}} = 10$ m. The ratio is capped at 2.0 to prevent extreme extrapolation.

9. Emission Modeling

9.1 Temperature-Driven Volatilization

VOC emission rates from open-air storage yards follow the Clausius-Clapeyron relation for vapor pressure. For naphthalene (the dominant odor compound at the Alexandria facility):

$$\text{VP ratio} = 2^{(T_{\text{eff}} - 77) / 15}$$

where 77°F is the reference temperature and the vapor pressure doubles every 15°F. For cresol (dominant at Pineville): the doubling interval is 18°F. The effective temperature $T_{\text{eff}}$ includes a solar heating boost for dark creosote surfaces during daytime, scaled by astronomical solar elevation angle (Spencer 1971).

9.2 Source Categories and Diurnal Weighting

Each facility’s emissions are split into source categories with time-of-day-dependent weights. Source characterization is derived from LDEQ air permits and production data.

Category	Release height	Day weight	Night weight	Driver
Alexandria: tie yard (area)	Ground	0.65	0.40	Solar-heated surfaces
Alexandria: cylinders (point)	Ground	0.35	0.60	Process at 140°F, 24/7
Pineville: pole yard (area)	Ground	0.30	0.10	Solar-heated surfaces
Pineville: ground process	Ground	0.25	0.35	Cylinders, tanks, fugitives
Pineville: kiln stacks	9 m	0.45	0.55	Batch process, 65% duty cycle

10. Terrain

Terrain elevation is interpolated from 60+ USGS 1/3 arc-second DEM control points using inverse-distance-weighted (IDW) interpolation with $w = 1/d^2$.

During calm/inversion conditions, terrain modifies the score:

• Point >10 ft below plant: boost up to 1.4 (pollutants drain into low areas)
• Pineville-specific: point >20 ft below the 103 ft bluff: boost up to 1.6 (heavy compound drainage)
• Point >15 ft above plant: factor 0.5 (partially shielded)
• With light wind (<10 mph) aligned to the N–S Red River valley axis: 1.15× channeling boost

11. Brutsaert Radiative Cooling (Inversion Signal)

The sky condition signal in the inversion detector uses the Brutsaert (1975) clear-sky atmospheric emissivity to estimate net radiative cooling rate:

$$\varepsilon_{\text{clear}} = 1.24 \cdot \left(\frac{e_a}{T_K}\right)^{1/7}$$

with the Li et al. (2017) nighttime correction ($+0.035$) and Crawford & Duchon (1999) cloud modification ($\varepsilon_{\text{all}} = \varepsilon_{\text{clear}} \times (1 + 0.22 \cdot CF^{2.75})$). Net cooling: $R = \sigma T^4 (1 - \varepsilon)$, normalized to a 0–1 signal over the range 20–70 W/m².

These formulas are applied as published with no modification.

12. Summary of Deviations from AERMOD

Component	AERMOD approach	Our approach	Rationale
Stability	Monin-Obukhov length $L$ from energy balance	0–1 proxy from 9 surface signals	No flux measurements available
Mixing height	AERMET with upper-air soundings	Estimated from $u_*$, solar heating, inversion score (pressure proxy tested and removed)	No radiosonde data; pressure-to-zi relationship not supported by KSHV sounding analysis
Lateral dispersion	$\sigma_y$ from M-O similarity	Angular sigma (20–50°) with empirical decay	Sub-hourly wind variability; validated against field obs
Vertical dispersion	$\sigma_z$ from M-O with measured $N$	$\sigma_z$ from AERMOD formula with estimated $N$	Formula is standard; $N$ input is heuristic
BVF ($N$)	$\sqrt{g \cdot d\theta/dz \;/\; T}$ from soundings	$0.005 + 0.035 \times s$ (linear mapping)	No temperature profile data
Wind profile	M-O similarity with $\psi_M$ correction	Neutral log-law only	$L$ not available for stability correction
Concentration output	$\mu$g/m³	Dimensionless 0–100 score	No $Q$ in g/s; calibrated to odor perception
Emission rates	Direct input ($Q$ in g/s)	Relative intensity from permits + temperature	Real-time emission data not available
Terrain	AERMAP with dividing streamline	Elevation-difference heuristic	Simplified for browser computation
Subsidence detection	Not needed (receives $z_i$ from AERMET)	Inversion score floor when P $\geq$ 1025 mb (stability proxy, not $z_i$ estimate)	Surface pressure indicates stable conditions but does not reliably predict $z_i$

13. Known Limitations

1. No upper-air data: Mixing height, BVF, and stability are all estimated from surface observations. This is the model’s single largest source of uncertainty.
2. Hourly resolution: The model cannot resolve sub-hourly plume passage events. A transient 15-minute odor puff receives the same score as a persistent 60-minute event.
3. Single wind observation: KAEX ASOS is applied uniformly across the domain. Local terrain-induced wind variations (valley channeling, slope flows) are not resolved.
4. Empirical calibration: Scores are calibrated against subjective odor reports from a small number of observers. Olfactory sensitivity varies between individuals.
5. Multiplicative structure: If any single factor is severely wrong, it multiplicatively corrupts the entire score. There is no additive fallback.
6. No building downwash: AERMOD’s PRIME algorithm for wake effects behind structures is not implemented. Near-field concentrations from stacks near buildings may be underestimated.
7. No reactive chemistry: VOC compounds are treated as inert tracers. Photochemical transformation and deposition are not modeled.
8. Emission uncertainty: Actual real-time emission rates are unknown. Permit data represents maximum allowable, not actual, emissions.
9. Meander parameterization is uncalibrated: The $\sigma_v$ input to the FRAN meander equation (Section 5.1) is a heuristic approximation that produces more circular spread than AERMOD would compute. Field-validated plume boundaries suggest the current parameterization produces reasonable results, but the agreement may be coincidental — the “too high” $\sigma_v$ may compensate for other simplifications in the angular-sigma lateral model. This is the highest-priority candidate for empirical recalibration once sufficient geo-tagged odor observations have been collected. A regression of model residuals (predicted score minus reported intensity) against wind speed, receptor distance, and angle from the downwind axis would reveal whether the meander fraction is systematically over- or under-spreading the plume, and allow data-driven tuning of $\sigma_v$ and the meander timescale $T$.

14. Known Unknowns

This section lists every place where the model bridges a gap between published physics and available data with an invented coefficient. These are known unknowns — we know exactly what we don’t know, we know what measurement would answer it, and we are using a placeholder until that data is available. Each constant is extracted by name at the top of prediction.js so it can be found, questioned, and replaced.

14.1 Mechanical Mixing Height

Constant: ZI_MECH_COEFF = 2300

$$z_{i,\text{mech}} = 2300 \cdot \frac{u_*^{3/2}}{\sqrt{s}}$$

What we know	The Zilitinkevich (1972) formula relates stable mixing height to $u_*$, Monin-Obukhov length $L$, and the Coriolis parameter: $z_i = 0.4\sqrt{u_* L / f}$. This is published, peer-reviewed physics.
What we don’t know	The Monin-Obukhov length $L$. Computing $L$ requires sensible heat flux, which requires net radiation measurements we do not have. We substituted our 0–1 stability proxy for $L$ and absorbed the dimensional mismatch into the coefficient.
What the coefficient is	The number 2300 has no literature basis. It was chosen to produce $z_i \approx 150$ m at $u_* = 0.3$ m/s, stability $= 0.7$ (a typical stable night). It has not been validated against sounding data.
What would replace it	Regression of KSHV radiosonde mixing heights against concurrent KAEX surface observations. The nearest sounding station (Shreveport, 190 km NW) launches at 00Z and 12Z daily. A dataset of $z_i$ vs. ($u_*$, stability, season) would yield a real coefficient — or reveal that the functional form $u_*^{3/2}/\sqrt{s}$ is itself wrong.

14.2 Convective Mixing Height

Constants: ZI_CONV_BASE = 400, ZI_CONV_SOLAR = 1200

$$z_{i,\text{conv}} = (400 + 1200 \cdot I_{\text{solar}}) \times f_T$$

What we know	Daytime mixing height is driven by surface sensible heat flux, which is driven by solar radiation. $z_i$ grows through the morning and peaks in the early afternoon. Typical values for central Louisiana: 500–2000 m depending on season and cloud cover.
What we don’t know	The actual surface heat flux. Computing it requires net radiation (measured or parameterized from cloud cover + albedo + soil moisture), none of which we have. We substituted solar elevation angle as a proxy for heat flux.
What the coefficients are	400 and 1200 are invented. They were chosen to produce $z_i \approx 500$ m at sunrise and $\sim$1600 m at solar noon, which seemed reasonable. There is no published formula of this form.
What would replace them	KSHV 12Z (7 AM) and 00Z (7 PM) soundings paired with KAEX surface conditions. Published alternatives exist: Betts (1992) and Stull (1988) provide convective scaling diagnostics, but they still require heat flux estimates. A simpler approach: build a $z_i$ climatology for KSHV binned by month, hour, and cloud cover.

14.3 Brunt-Väisälä Frequency Mapping

Constants: BVF_BASE = 0.005, BVF_SLOPE = 0.035

$$N = 0.005 + 0.035 \times s$$

What we know	The Brunt-Väisälä frequency is $N = \sqrt{g \cdot (\partial\theta/\partial z) / T}$. This is fundamental atmospheric physics. Typical values: 0.005–0.01 s$^{-1}$ (neutral/weakly stable), 0.02–0.04 s$^{-1}$ (strongly stable nocturnal inversion). The BVF controls the asymptotic cap on $\sigma_z$ in the AERMOD formula.
What we don’t know	The potential temperature gradient $\partial\theta/\partial z$. This requires a vertical temperature profile from a radiosonde. We have no vertical measurements of any kind.
What the coefficients are	0.005 and 0.035 define a linear mapping from our 0–1 stability proxy to the BVF range. We assumed the relationship is linear. It may not be — inversions can form abruptly (a step change in $N$) rather than scaling smoothly with surface signals.
What would replace them	Compute $N$ from KSHV soundings at multiple levels (surface to 1000 m AGL), then plot observed $N$ against our stability proxy for the same hour. This would reveal the actual functional form — linear, exponential, step function, or something else entirely.

14.4 Vertical Turbulence Stability Damping

Constants: SW_COEFF = 1.3 (AERMOD, published), SW_STAB_DAMP = 0.6 (invented)

$$\sigma_w = \max\!\big(0.08,\; 1.3 \cdot u_* \cdot (1 - 0.6 \cdot s)\big)$$

What we know	AERMOD computes mechanical $\sigma_w = 1.3\,u_* \cdot \sqrt{1 - z/z_i}$ near the surface (from siggrid.f). The 1.3 coefficient is published and standard. Under stable conditions, vertical turbulence is suppressed by stratification.
What we don’t know	How much stability suppresses $\sigma_w$ in our model. AERMOD uses the full Monin-Obukhov similarity profile with height dependence. We evaluate only at the surface and need a single reduction factor.
What the coefficient is	The 0.6 stability damping factor is invented. It reduces $\sigma_w$ to 40% of neutral under strong stability ($s = 1.0$). We do not know if this is correct. It could be 0.4 or 0.8 — we have no direct measurement to constrain it.
What would replace it	Indirectly, through the odor observation dataset. If the model systematically under-predicts at long range under stable conditions, the damping may be too strong ($\sigma_w$ too small, $\sigma_z$ capped too low, concentration too near-source). If it over-predicts at long range, the damping is too weak. The regression residuals from geo-tagged odor reports, binned by stability class and distance, would constrain this.

14.5 Inversion Score Compression of Mixing Height

Constants: INV_CAP_BASE = 300, INV_CAP_OFFSET = 1.5, INV_CAP_THRESHOLD = 0.5

$$z_i \leq 300 \times (1.5 - \text{inversionScore}) \quad \text{when score} > 0.5$$

What we know	Strong surface inversions compress the mixing height. A fog event with strong radiation cooling can produce $z_i$ as low as 50–200 m. Our inversion detection score (Section 3) correlates with these conditions.
What we don’t know	The actual mapping between our inversion score and $z_i$. Is a score of 0.85 really associated with $z_i = 195$ m? Or is it 100 m? Or 400 m?
What the coefficients are	300, 1.5, and 0.5 are invented. They were chosen because the resulting scores (60–65 near Pineville under fog) matched one validated morning event (March 25, 2026). One data point is not a calibration.
What would replace them	Pair our inversion scores with the concurrent KSHV 12Z sounding $z_i$. If the sounding shows $z_i = 200$ m when our score is 0.85, the formula is close. If it shows 400 m, we are over-compressing. A scatter plot of (inversion score, observed $z_i$) from 30+ sounding pairs would determine these constants — or show that a linear formula is the wrong shape.

14.6 Meander Parameters

The $\sigma_v$ input to the FRAN equation (Section 5.1) and the meander timescale $T$ are the highest-priority known unknowns. See Section 5.1 for the full deviation analysis. These will be the first targets for the odor observation regression described in Section 13.

What we know	The FRAN equation structure is from AERMOD. Hanna (1990) showed $\sigma_v$ maintains ~0.5 m/s in calm conditions. EPA’s 2021 low-wind white paper recommended a 12-hour meander timescale.
What we don’t know	The correct $\sigma_v$ for our angular-sigma lateral model (which differs from AERMOD’s $\sigma_y$-based model). The current value may be compensating for other simplifications.
What the values are	$\sigma_v = 0.5 \times \min(U, 2.0)$ and $T = 86400$ s (24 hours). Neither is derived from local data.
What would replace them	Regression of model residuals (predicted − observed intensity) against wind speed, distance, and angle from downwind. Systematic over-prediction at off-axis points means too much meander. Systematic under-prediction means too little.

15. References

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