Primal path algorithm for compositional data analysisstat.snu.ac.kr/idea/seminar/20170703/plume...

Primal path algorithm for compositional dataanalysis

Jong-June Jeon1

1University of Seoul

Idea seminar 2017 Summer

Jeon, Jong-June Idea seminar 2017 Summer

Atmospheric air pollutant dispersion

Goal: estimate air pollutant concentrations downwind of emissionpoint sources

Downwind air pollution concentrations are a function of

dispersion from point emission sources

dispersion mixing height

atmospheric stability

dispersion coefficients.

....

Note that there are three types of pollutant emission: point, line, plane.


Atmospheric air pollutant dispersion

dispersiontypes

longitudinal: mixing along direction of flowtransverse: mixing perpendicular to the flow

causesgradient in flow velocitysplitting of flow paths

First we consider a dispersion model with mixing direction of flows


Simplified Steady-State Plume Model

View from below of “Coning” plume under neutral atmosphericconditions

Figure: left: snapshot; right: time average



Figure: h: effective height of plume, x: distance

Concentration of a pollutant is proportional to the number of theparticles in the unit volume.



Assume that all particles lie within the cone.

Figure: Ck is a concentration at k



Consider the number of particles pass through the circle in the coneper unit time.

Mass emission rate is fixed.

The particle move with a fixed wind speed.

Then,

Total number of particles = concentration × wind speed× the area of circle.

Note that the total number of particles per unit time is emissionrate



It is assumed that density of pollutant at x far away from the origin isuniform.



C: concentration

u: wind speed

Q: emission rate

C =Qu× density of circle



Figure: H: effective height; h: actual height of plume



C(x, y, z): concentration at (x, y, z)

u: wind speed

Q: emission rate

C(x, y, z) =Qu× density of plane (y-z)



Figure: dispersion along y axis depends on the distance x



Refection

Figure: dispersion along z axis depends on the distance x



Gaussian dispersion equation

C(x, y, z; H) =Qu

f (y, z; Σ(x),H)

=Qu

12πσy(x)σz(x)

exp(−(z− H)2

2σ2z (x)

) + exp(−(z + H)2

2σ2z (x)

)︸︷︷︸reflection

× exp(− y2

2σ2y

)



The Gaussian dispersion model is theoretically derived by advectiondiffusion equation, which assumes

Steady state conditions: ∂C/∂t = 0

Constant wind speed with height (u does not depend on z).

Diffusion constant in σy and σz does not depend on (y, z).

Mass is conserved:∫ ∫Cdydz = Q for all x > 0



Atmospheric stabilityDry adiabatic lapse rate: 0.976C /100mStability condition by actual lapse rate

super-adiabaticsub-adiabaticinversion



Figure: Stability conditions



Pasquill stability categorycategory: A(very unstable), B(moderately unstable), C(slightlyunstable), D(neutral), E(moderately stable), F(very stable)The category is determined by

day incoming solar radiation (strong, moderate, slight)night cloudiness (cloudy and clear)



Estimation of σy(x) and σz(x)

Figure: left: σy(x); right : σz(x)



EPA’s ISC ModelVertical distribution:

σz = axb

(x: km, σz: m)

Cross-wind distribution:

σy = 465.1168x tan(θ)

where θ = 0.017453293(c− d log(x)). (x: km, σy: m)

Here, the constant c and d is determined by the stability conditions.



Plume rise estimation Required data:

wind speed

stack exit velocity

top inside stack diameter

stack gas temperature

gravity



Gaussian dispersion model

C(x, y, z; H) is computed by

location: (x, y, z);

wind speeddispersion parameter:

stability conditionssolar radiationnight cloudiness

Effective plume height (H)physical plume heightplume rise


AERMOD model

Gaussian dispersion model is used in EPA Industrial SourceComplex - Short Term (ISCST3) dispersion air quality model.ISCST3 assumes

constant wind speed with height (u does not depend on z).diffusion constant in σy and σz does not depend on (y, z).simple topographic model

AERMOD (AMS/ EPA Regularatory model) modify Gaussiandispersion model.


AERMOD model

Wind speed for height


AERMOD model

Terrain effect

Figure: Terrain correction


AERMOD model

Building downwash

Consider downwash of the building within 5 times height of theplume.


AERMOD model

SoftwareAERMOD model (diffusion model)

BPIPPRM (Building downwash pre-processing)AERMET (Meteorological pre-processing: eg wind)AERMAP (Terrain pre-processing)

Surfer 8.0 (visualization)


BPIPPRM

Inputbuilding height

building width

Building length

coordinate distance (x,y) between plume and building


BPIPPRM


AERMET

InputMeteorological file ( date, wind speed, flow vector, temperature,mixing height, stability.)

Mixing data from surface observatory and aerologicalobservatory.


Non gaussian plume


CALPUFF model

CALPUFF model assumes the pollutant consists of puffs.Modeling

the movement of puffs in the 3 dimensional wind field;the contribution of a puff to receptor.

Hence, the model can reflect the change of wind direction andspeed immediately. (Unsteady model)

This model can be used for predicting diffusions of massivepollutant point source near the coastal line


Non gaussian plume

Figure: Comparison of AERMOD and CALPUFF


CALPUFF model

InputMM5 model (3 dimensional wind field model on grid system→location of the center of a puff)

Overwater and coastal interaction effects

Puff formulation

diffusion parameter (σy and σz)

vertical wind shear

plume rise

building downwash

terrain

chemical transformation option


CALPUFF model

Contribution of puffs at ground level (receptor)

C =Q

2πσxσyg exp

(− d2

x

2σ2x

)exp

(−

d2y

2σ2x

)

where

g =2√

2πσz

∞∑n=−∞

exp(−(H + 2nh)2

2σ2z

)

dx: x-coordinate distance between puffs and receptor.

H: height of puff, h: mixing height.


Primal path algorithm for compositional data analysisstat.snu.ac.kr/idea/seminar/20170703/plume...

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