Implementation of L inear - PowerPoint Presentation

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Implementation of Linear Sensitivity Approximate Method

Pedram Falsafi, Amir HakamiCarleton University, Canada

CMAS 2015, Chapel Hill

for Sensitivity Advection in CMAQSlide2

OverviewHorizontal advection in CTMsIssues with current advection schemes – CMAQ and PPMLinear Sensitivity Approximate MethodPreliminary resultsFuture steps and conclusions

2Slide3

Horizontal advection in CTMsMain transport processInherently linear process3

Negative values

s

uppressed peak

d

iffused signalSlide4

Solves continuity equation for each species in two separate directions

Piecewise Parabolic Method (PPM) (with

Yamo)Monotonic and Mass conservative Therefore, Nonlinear schemeHorizontal advection in CMAQ

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Sensitivity in AdvectionPerturbation at a single grid cellImpact at a few cells downwind

(finite-difference sensitivity) 5

?Slide6

Sensitivity in Advection

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Negative

values

, physically

meaningless

Depend on profile (species)

There

is no “nonlinear term

” in

PPM

discontinuous operations Slide7

Sensitivity in Advection

7Slide8

Does artificial nonlinearity matter?Can we trust advection process when …There are large gradients in concentration field?

Sensitivity analysis?Derivative of an advection is not the same for nonlinear scheme (DDM and adjoint analysis)Taking differences in concentrations?We often calculate sensitivities (differences) even if we don’t call it sensitivity!

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9 Why do we solve the continuity equation for each species?After all, it is air that is advected

; everything else is advected within the air.Linear Sensitivity Approximate M

ethodSlide10

1-D advection of

air

density fieldApply same coefficients (Jacobian

) to other species

L

inear

S

ensitivity

A

pproximate

M

ethod

10

i

jSlide11

Trace air mass of only 1 cell at a timeIndependent of concentration profile (only wind field)No negative coefficientsApproximate solutionIs it computationally efficient ?

PPM advection scheme: only 5 cells contribute11

Linear Sensitivity Approximate Method0

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0

1

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J

i-2

J

i-1

J

i

J

i

+1

J

i+2

0Slide12

How good is the approximation?

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Using LSAM [

ppmv

]

Ozone: LSAM – PPM (8-day simulations)Slide13

Daily Maximum O313

4-day simulation8-day simulation

Using PPM [ppmv]

Using LSAM [

ppmv

]

How good is the approximation?

R-squared = 0.946

R-squared = 0.965Slide14

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Daily Maximum CO

How good is the approximation?

Using PPM [

ppmv

]

Using LSAM [

ppmv

]

4-day simulation

8

-day simulation

R-squared

= 0.969

R-squared = 0.948Slide15

Sensitivity Tests - DDM

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DDM Using

LSAM

DDM Using PPM

10 Time steps

120 Time steps (1 day)Slide16

ConsApproximateProspositive definite and mass conservativeTruly linear method, independent of profileSensitivities will be “exact”

Computationally less expensive Use of more expensive but more accurate scheme is feasible16Linear Sensitivity

Approximate MethodSlide17

Where to use LSAMIntended for sensitivity calculationsNot for using instead of PPM (for now!)

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ConclusionsModeling linear advection process with a nonlinear/discontinuous scheme can entail problemsWith sensitivity calculations With concentration calculations used to estimate differencesAdvected air densities provide an approximate operator to apply on all species

More efficientMore accurate/expensive schemes are feasible 18Slide19

Future stepsPropose a reliable benchmark for validationTry less diffusive and more accurate schemesFind a smoother base profiles for estimations of the contribution matrix

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AcknowledgementThanks to Talat Odman and Ted Russell (Georgia Tech)

for insightful discussionsSlide21

Thank You!Slide22
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