How to Improve Mesoscale How to Improve Mesoscale Atmospheric-Modeling Atmospheric-Modeling

ResultsResultsBob BornsteinBob Bornstein

San Jose State UniversitySan Jose State University

San Jose, CASan Jose, CApblmodel@hotmail.com

Presented atPresented atUNAM Mx City UNAM Mx City 9 March 20079 March 2007

AcknowledgementsAcknowledgements

Dr. H. Taha, Altostratus & SJSUDr. H. Taha, Altostratus & SJSU Dr. F. FreedmanDr. F. Freedman Dr. Erez Weinroth, HUJI & SJSUDr. Erez Weinroth, HUJI & SJSU my M.S. (ex) STUDENTS: Dr. C. Lozej-my M.S. (ex) STUDENTS: Dr. C. Lozej-

Archer, T. Ghidey, K. Craig, R. Archer, T. Ghidey, K. Craig, R. Balmori Balmori

Funded by: NSF, USAID, DHS, LBL, Funded by: NSF, USAID, DHS, LBL, NSF NSF

OUTLINEOUTLINE

IntroductionIntroduction Getting Mesomet models to work betterGetting Mesomet models to work better

SYNOPTIC FORCINGSYNOPTIC FORCING INPUT DATAINPUT DATA SFC/PBL FORCINGSFC/PBL FORCING

uMM5: uMM5: Houston ozoneHouston ozone ConclusionsConclusions (Future) uWRF efforts(Future) uWRF efforts

Basic-Theme 1Basic-Theme 1

e.g., Oe.g., O33-EPISODES OCCUR-EPISODES OCCUR

NOT NOT FROM CHANGING TOPOGRAPHY OR EMISSIONSFROM CHANGING TOPOGRAPHY OR EMISSIONS

BUTBUT DUE TO CHANGING DUE TO CHANGING GC/SYNOPTIC GC/SYNOPTIC PATTERNS, PATTERNS, WHICHWHICH

ENTER MESO-SOLUTIONENTER MESO-SOLUTION FROM FROM CORRECT (we hope) CORRECT (we hope)

LARGER-SCALE MODEL-FIELDS, & WHICH LARGER-SCALE MODEL-FIELDS, & WHICH

THUS ALLOWTHUS ALLOW SCF MESO THERMAL-FORCINGS SCF MESO THERMAL-FORCINGS (i.e., (i.e., UP/DOWN SLOPE, LAND/SEA, URBAN, CLOUDS/FOG) UP/DOWN SLOPE, LAND/SEA, URBAN, CLOUDS/FOG) TO DEVELOP TO DEVELOP CORRECTLY (we hope) CORRECTLY (we hope)

CORRECT-ORDER OF FORCINGS CORRECT-ORDER OF FORCINGS IN A MESO-MET MODEL IS THUSIN A MESO-MET MODEL IS THUS

FIRST:FIRST: UPPER-LEVEL Syn/GC FORCING UPPER-LEVEL Syn/GC FORCINGpressurepressure (the GC/Syn driver) (the GC/Syn driver)

Syn/GC windsSyn/GC winds NEXT:NEXT: TOPOGRAPHY TOPOGRAPHY

grid spacinggrid spacing flow-channeling flow-channeling LAST:LAST: MESO SFC-CONDITIONS MESO SFC-CONDITIONS

temptemp (the meso-driver) & sfc z (the meso-driver) & sfc z0 mesoscale windsmesoscale winds

Case Study 1:Case Study 1: Atlanta Summer Atlanta Summer Thunderstorm (K. Craig)Thunderstorm (K. Craig)

Obs: Obs: weak-cold front N of cityweak-cold front N of city Large-scale IC/BC:Large-scale IC/BC: front S of city front S of city MM5 UHI-induced thunderstorm:MM5 UHI-induced thunderstorm:

5-km deep, w5-km deep, wmaxmax 6-m/s, 8-cm precip 6-m/s, 8-cm precip Should be:Should be: 9-km, 12-m/s, 14-cm 9-km, 12-m/s, 14-cm Source of problem:Source of problem:

Wx model incorrectly put front S of City Wx model incorrectly put front S of City

MM5-storm formed in MM5-storm formed in stable-flow stable-flow from N from N (& not in (& not in unstable-flowunstable-flow from S)from S)

ATLANTA UHI-INITIATED STORM: OBS SAT & PRECIP (UPPER) & MM5 W & PRECIP (LOWER)

Case study 2: Case study 2: SFBA Summer SFBA Summer OO33--episode (T. episode (T.

Ghidey)) Obs: daily Obs: daily max- Omax- O33 sequentially moved sequentially moved

from Livermore to Sacramento to SJVfrom Livermore to Sacramento to SJV Large scale IC/BC:Large scale IC/BC:

shifting shifting meos-700 hPameos-700 hPa high high

shifting shifting meos-sfc lowmeos-sfc low changing sfc- changing sfc-flow flow

max-Omax-O33 changed location changed location Results: Results: good good analysis-nudginganalysis-nudging in MM5 in MM5

good mesoscale winds good mesoscale winds

H

H

L

SAC episode day:SAC episode day: D-1 700 hPa Syn H moved to Utah with coastal “bulge” & L D-1 700 hPa Syn H moved to Utah with coastal “bulge” & L in S-Calin S-Calcorrect SW correct SW flow from SFBA to Sacflow from SFBA to Sac

L

H

SJV episode day:SJV episode day: D-3 700 hPa Fresno eddy moved N & H moves D-3 700 hPa Fresno eddy moved N & H moves inlandinland flow around eddy blocks SFBA flow to SAC, but forces it S into SJVflow around eddy blocks SFBA flow to SAC, but forces it S into SJV

Theme 2: Theme 2: MM5 MM5 Non-urbanNon-urban Sfc-IC/BC Issues Sfc-IC/BC Issues

Deep-soil temp: BCDeep-soil temp: BC Controls nighttime min-TControls nighttime min-T Values unknown & MM5 estimation-method is Values unknown & MM5 estimation-method is

flawedflawed Soil-moisture: ICSoil-moisture: IC

Controls daytime max-TControls daytime max-T Values unknown & MM5-table values are Values unknown & MM5-table values are too too

specificspecific SST: IC/BCSST: IC/BC

Horiz coastal T-Horiz coastal T-gradgrad controls sea-breeze flow controls sea-breeze flow But we usually focus only on But we usually focus only on land-sfcland-sfc tempstemps IC/BC-SST values from IC/BC-SST values from large-scale model large-scale model are are

too too coarse & not f(t) coarse & not f(t)

Theme 2A: MM5Theme 2A: MM5 deep-soil deep-soil temptemp

Calculated as Calculated as average large-scale model-average large-scale model-inputinput surface-Tsurface-T during simulation-period during simulation-period

But this assumes But this assumes zero time-lagzero time-lag b/t sfc & b/t sfc & lower-level (about 1 m) soil-tempslower-level (about 1 m) soil-temps

But obs show But obs show 2-3 month time-lag b/t these two temps2-3 month time-lag b/t these two temps Larger-lag in low-conductivity dry-soilsLarger-lag in low-conductivity dry-soils

Thus MM5 min-temps always are too-high Thus MM5 min-temps always are too-high in in summer & summer & too-low in too-low in winterwinter

Need to Need to develop techdevelop tech (beyond current trial (beyond current trial & error) to account for lag & error) to account for lag

Case Study 3: Mid-east 2-m air tempCase Study 3: Mid-east 2-m air temp (S. (S. Kasakech)Kasakech)

July 29 August 1 August 2

July 31 Aug 1 Aug2

Standard-MM5 summer night-time min-T,

But lower input deep-soil temp better 2-m T results better winds better O3

obs

Run 1

MM5:Run 4

Obs

Run 4:ReducedSeep-soil T

First 2 days show GC/Syn trend not in MM5, as MM5-runs had no analysis nudging

Case study 4: SCOS96Case study 4: SCOS96 2-m Temps 2-m Temps

(D. Boucouvual)(D. Boucouvual)RUN 1: hasNo GC warming trendWrong max and min T

3-Aug 4-Aug 5-Aug 6-Aug

RUN 5: corrected, as it used> Analysis nudging > Reduced deep-soil T

Theme 2B: Theme 2B: MM5 input-table MM5 input-table zz0 problemsproblems

WaterWater z z0 = 0.01 cm = 0.01 cm Only IC Only IC updatedupdated internally by Charnak eq = f(MM5 internally by Charnak eq = f(MM5

uu*)) But Eq only valid for But Eq only valid for open-sea,open-sea, smooth-swell, smooth-swell,

conditionsconditions Obs for rough-sea Obs for rough-sea coastal-areascoastal-areas ~ 1 cm ~ 1 cm

MM5 coastal-winds are MM5 coastal-winds are over-estimatedover-estimated

UrbanUrban z z0 = 80 cm = 80 cm too low for tall cities: obs up to too low for tall cities: obs up to 3-4 m3-4 m Urban-winds: Urban-winds: too fasttoo fast Must Must adjustadjust input-value input-value oror use GIS/RS input as f(x,y) use GIS/RS input as f(x,y)

Case study 5: Case study 5: Houston GIS/RS zHouston GIS/RS zoo (S. Stetson) (S. Stetson)

Values up 3 m

Values too large, Values too large, as they were as they were f(h) f(h) and not f(ơand not f(ơhh))

Theme 2C: Theme 2C: MM5 SST-problemsMM5 SST-problems

Current Wx Model SSTs Current Wx Model SSTs MM5 MM5 Only every 6 or 12 hoursOnly every 6 or 12 hours Lack small scale SST-variationsLack small scale SST-variations Thus produces poor land-sea T-gradients Thus produces poor land-sea T-gradients

poor sea-breeze flows poor sea-breeze flows Solution: satellite-derived SSTsSolution: satellite-derived SSTs

More frequent More frequent More detailedMore detailed

Case Study 6: NYC SST+currents Case Study 6: NYC SST+currents (J. (J. Pullen)Pullen)

COAMPS input satellite: SST + sfc COAMPS input satellite: SST + sfc currents currents

LL

Theme 3: Model-Urbanization Theme 3: Model-Urbanization HistoryHistory

Need to urbanizeNeed to urbanize momentum, thermo , & TKE Eqs momentum, thermo , & TKE Eqs At surface & in SBL: diagnostic EqsAt surface & in SBL: diagnostic Eqs In PBL: prognostic Eqs In PBL: prognostic Eqs

Newest from Newest from veg-veg-canopycanopy model of Yamada (1982) model of Yamada (1982) But Veg-param’s But Veg-param’s replacedreplaced with GIS/RS urban param’s with GIS/RS urban param’s

Brown and Williams (1998)Brown and Williams (1998) Masson (2000)Masson (2000) Martilli et al. (2001) in Martilli et al. (2001) in TVM/URBMETTVM/URBMET Dupont, Ching,Dupont, Ching, et al. (2003) in et al. (2003) in EPA/MM5EPA/MM5 Taha et al. (2005), Balmori et al. (2006b) in Taha et al. (2005), Balmori et al. (2006b) in uMM5uMM5

Input: detailed urban-parameters as f(x,y)

T int

Q wall

Ts roof

Drainage outside the system

Sensible heat flux

Latent heat flux

Net radiation

Storage heat flux

Anthropogenic heat flux

Precipitation

Roughness approach

Root zone layer

Infiltration

Diffusion

Deep soil layer

Drainage

Drainage network

natural soil

roof

water

Paved surface

bare soil

Surface layer

Drag-Force approach

Rn pav Hsens pav LEpav

Gs pav Ts pav

From EPA uMM5:

Mason + Martilli (by Dupont)

Within Gayno-

Seaman

PBL/TKE scheme

Advanced urbanization

scheme from Masson (2000)

____________

_________

3 new termsin each progequation

New GIS/RS inputs for uMM5 as f (x, y, z)

land use (38 categories) roughness elements anthropogenic heat as f (t) vegetation and building heights paved-surface fractions drag-force coefficients for buildings & vegetation building height-to-width, wall-plan, & impervious-

area ratios building frontal, plan, & and rooftop area densities wall and roof: ε, cρ, α, etc. vegetation: canopies, root zones, stomatal resistances

Performance for 18 hour prediction using 12 to 96 cpus

0

2

4

6

8

10

12

14

16

18

20

22

24

12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

CPU

t (h

)

MM5x

uMM5x

Performance for 18 hour prediction using 12 to 96 cpus

0

2

4

6

8

10

12

14

12 24 36 48 60 72 84 96

CPUP

(%

)

MM5x

uMM5x

Performance for 18 hour prediction

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80 90 100

CPU

t (h

)

MM5x

uMM5x

Case study 7: SJSUCase study 7: SJSUuMM5 performance by CPUuMM5 performance by CPU

With 1 CPU: MM5 is With 1 CPU: MM5 is 10x10x faster than uMM5 faster than uMM5

With 96 CPU: MM5 is onlyWith 96 CPU: MM5 is only3x 3x faster than uMM5 faster than uMM5 (< 12 CPU not shown)(< 12 CPU not shown)

With With 9696 CPU: MM5 is still gaining, but CPU: MM5 is still gaining, but MM5 has ceased to gain at MM5 has ceased to gain at 4848 CPU & CPU & then it starts to loosethen it starts to loose

Performance by physicsPerformance by physics

Performance by category

0

5

10

15

20

25

30

35

40

45

50

Sound Solve Convection SBL Radiation PBL Domain Microphysics Other

Category

P(%

)

MM5

uMM5

Performance (real time) by category

0

2

4

6

8

10

12

14

16

18

Sound Solve Convection SBL Radiation PBL Domain Microphysics Other

Category

t (h

)

MM5

uMM5

sound waves & PBLsound waves & PBL schemes schemes take most CPU in bothtake most CPU in both

urban/PBL scheme in urban/PBL scheme in uMM5 takes almost uMM5 takes almost 50%50% of all timeof all time

Urbanization day& nite on same line stability effects not important mechanical effects are important

Is it worth it?:Is it worth it?: Case study 7 (A. Martilli) Case study 7 (A. Martilli)

MM5:MM5:

uMM5uMM5

(Last) Case Study 8:(Last) Case Study 8: uMM5 for uMM5 for Houston: Balmori (2006)Houston: Balmori (2006)

Goal:Goal: Accurate uMM5 Houston urban/rural temps & Accurate uMM5 Houston urban/rural temps &

winds for Aug 2000 Owinds for Aug 2000 O33-episode via-episode via Texas2000 field-study dataTexas2000 field-study data Taha/SJSUTaha/SJSU modification of LU/LC & urban modification of LU/LC & urban

morphology parameters bymorphology parameters by processing processing BurianBurian parameters parameters modifying uMM5 to accept themmodifying uMM5 to accept them

USFS USFS urban-reforestation scenariosurban-reforestation scenarios lower daytime max-lower daytime max-UHI-intensityUHI-intensity & O & O3 EPA emission-reduction credits EPA emission-reduction credits $’s saved$’s saved

GCGC influences are small influences are small Early-AM along-shore flow Early-AM along-shore flow (from east) from (from east) from

N-edge of N-edge of off-shore cold-core Loff-shore cold-core L Flow is then sequentially:Flow is then sequentially:

from Ship Channel to Houston by from Ship Channel to Houston by Bay BreezeBay Breeze into Houston by into Houston by UHI-convergenceUHI-convergence (time of O (time of O33--

max)max) and finally beyond Houston and finally beyond Houston to NW by Gulf to NW by Gulf

BreezeBreeze

Domain-5, episode-day, obs ODomain-5, episode-day, obs O33-transport: -transport: sea breeze + UHI-convergence influencessea breeze + UHI-convergence influences

L

H

CC

Urban min + UHI Conv

H

Start of N-flow

HL H

L over-Houston: due to titration

HNear-max O3

uMM5 simulation for uMM5 simulation for 22-26 August22-26 August case case Model configurationModel configuration

5 domains, with 5 domains, with ΔΔx =x = 108, 36, 12, 4, and 108, 36, 12, 4, and 1 km1 km (x, y) grid-pts: 43x53, 55x55, 100x100, 136x151, 133x141(x, y) grid-pts: 43x53, 55x55, 100x100, 136x151, 133x141 full-full- levels: 29 (Domains 1-4) & 49 (Domain 5) levels: 29 (Domains 1-4) & 49 (Domain 5) lowest ½ lowest ½ level= 7 mlevel= 7 m 2-way feedback in Domians 1-42-way feedback in Domians 1-4

Parameterizations/physics optionsParameterizations/physics options > Grell cumulus (D 1-2) > ETA or MRF PBL (D 1-4) > Grell cumulus (D 1-2) > ETA or MRF PBL (D 1-4) > > Gayno-Seaman PBLGayno-Seaman PBL (D 5) > Simple ice moisture (D 5) > Simple ice moisture > > Urbanization module Urbanization module > NOAH LSM> NOAH LSM

> RRTM radiative cooling> RRTM radiative cooling InputsInputs

> NNRP Reanalysis fields > ADP observational data > NNRP Reanalysis fields > ADP observational data > > S. Burian urban-morphologyS. Burian urban-morphology LIDAR building-data (D-5) LIDAR building-data (D-5)

> LU/LC modifications (from D. Byun )> LU/LC modifications (from D. Byun )

Episode-day Episode-day Synoptics:Synoptics: 8/25, 12 UTC (08 8/25, 12 UTC (08 DST)DST)

HH HH

700 hPa 700 hPa Surface Surface

700 hPa & sfc GC H’s: at their weakest (no gradient 700 hPa & sfc GC H’s: at their weakest (no gradient over Texas) over Texas) meso-scale forcing (sea breeze & UHI convergence) meso-scale forcing (sea breeze & UHI convergence) will dominate will dominate

Concurrent NNRP fields at 700 hPa & Concurrent NNRP fields at 700 hPa & sfcsfc

HH

NNRPNNRP-input to -input to MM5MM5 (as IC/BC) captured (as IC/BC) captured GC/synoptic features, as location & strength of GC/synoptic features, as location & strength of H were similar to H were similar to NWS chartsNWS charts (previous slide) (previous slide)

p=2 hPa

MM5: episode day, 3 MM5: episode day, 3 PM PM > D–1> D–1: reproduces : reproduces weak GC p-grad & flowweak GC p-grad & flow> D-2:> D-2: weak coastal-L weak coastal-L > D-3: > D-3: well-formed L well-formed L produces produces along-shore Valong-shore V

LL

D-1 D-2

D-3

Domain 4Domain 4 (3 PM) :(3 PM) : L is off of Houston only on O L is off of Houston only on O33 day day (25(25thth))

LL LL

EpisodeEpisode dayday

Urbanized Urbanized Domain 5:Domain 5: near-sfc 3-PM V, 4-days near-sfc 3-PM V, 4-days

EpisodeEpisode dayday

Cold-LCold-L

HotHot

CoolCool

Along-shore flow, 8/25 (episode day): obs at 15-UTC Along-shore flow, 8/25 (episode day): obs at 15-UTC vs uMM5 (Domain-5) at 20-UTCvs uMM5 (Domain-5) at 20-UTC

Tx2000

HGA

uMM5 (D-5, red box) cap-tured along-shore V

HGA

uMM5

1-km 1-km uMM5 uMM5 Houston UHI: 8 PM, 21 Houston UHI: 8 PM, 21 AugAug

Upper, L:Upper, L: MM5MM5 UHI (2.0 UHI (2.0 K)K)

Upper,R: Upper,R: uMM5 uMM5 UHI (3.5 UHI (3.5 K)K)

Lower L: Lower L: (uMM5-MM5)(uMM5-MM5) UHIUHI

LU/LC errorLU/LC error

8/23 Daytime 2-m UHI: obs vs uMM5 (D-5)8/23 Daytime 2-m UHI: obs vs uMM5 (D-5)

H

OBS: 1 PMOBS: 1 PMuMM5: 3 PMuMM5: 3 PM

Cold

UHI

UHI

Along –shore V: due to Along –shore V: due to Cold-Core L :Cold-Core L : D-3 MM5 vs. Obs-TD-3 MM5 vs. Obs-T

MM5: produces coastal MM5: produces coastal cold-core lowcold-core low

Obs (18 UTC): Obs (18 UTC):

> Cold-core L (only 1 ob) > Cold-core L (only 1 ob)

> Urban area (blue-dot clump) > Urban area (blue-dot clump) retards cold-air penetrationretards cold-air penetration

C

H

H

UHI-Induced Convergence: UHI-Induced Convergence: obs vs. uMM5obs vs. uMM5

OBSERVEDOBSERVED uMM5uMM5

C

C

Obs speeds (D-5): Obs speeds (D-5): large zlarge z0 speed-decrease over city speed-decrease over city

---+

+

+

+

V

Current base-case Veg-cover (in 0.1’s), with an urban min of 0.2-0.3

Future case (from USFS)Increases in veg-cover (in 0.01’s), with max increases (in urban areas) of about 0.1

uMM5 urban reforestation& rural deforestation

simulations

Soil moisture increaseSoil moisture increase for: for: Run 12 (entire area, left) and Run 12 (entire area, left) and Run 13 (urban area only, right)Run 13 (urban area only, right)

Run 12 (urban-max reforestation) minus Run 10 (base case): Run 12 (urban-max reforestation) minus Run 10 (base case): near-sfc ∆T at 4 PMnear-sfc ∆T at 4 PM

reforested central urban-area reforested central urban-area coolscools & &surrounding deforested rural-areas surrounding deforested rural-areas warmwarm

UHI(t) for Base-case minus Runs 15-UHI(t) for Base-case minus Runs 15-1818

U1

sea

Ru

U2

• UHI UHI = = TempTemp in Box-Urban minus Temp in in Box-Urban minus Temp in Box-Rural Box-Rural • Runs 15-18:Runs 15-18: different urban re-forestation different urban re-forestation scenariosscenarios• UHI=UHI=Run-17 UHI –Run-13 UHI (max effect, Run-17 UHI –Run-13 UHI (max effect, green line) green line) • Reduced UHIReduced UHI lower max-Olower max-O33 (not shown) (not shown)

EPA emission-reduction creditsEPA emission-reduction credits

Urban temp difference between runs at location 1 (3-pt smoothing)

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

20 0 4 8 12 16 20 0 4 8 12 16

LST

Tdi

ff (K

)

run14-run13s

run15-run13s

run16-run13s

run17-run13s

run18-run13s

Max-impact of –0.9 K ofMax-impact of –0.9 K of a a 3.5 K Noon3.5 K Noon-UHI, of which-UHI, of which1.5 K was from uMM51.5 K was from uMM5

Overall LessonsOverall Lessons

Models can’t be assumed to be Models can’t be assumed to be perfectperfect black boxesblack boxes

If obs not available If obs not available OK to make OK to make reasonable reasonable educated educated estimates, e.g., forestimates, e.g., for Deep-soil tempDeep-soil temp Soil moisture Soil moisture

Need Need datadata for comparisons with simulated for comparisons with simulated fieldsfields

Need good Need good urbanization,urbanization, e.g., e.g., uMM5uMM5 Need to develop better PBLNeed to develop better PBL

parameterizationsparameterizations

FUTURE WORK: uWRFFUTURE WORK: uWRF uWRF with NCAR (F. Chen) for DTRAuWRF with NCAR (F. Chen) for DTRA

Martilli-Dupont-Taha urbanizationMartilli-Dupont-Taha urbanization Freedman turbulenceFreedman turbulence

Applications (current + will propose*)Applications (current + will propose*) Urban canyon dispersion for DTRAUrban canyon dispersion for DTRA Urban climate (with UNAM)Urban climate (with UNAM) *NYC ozone for EPA*NYC ozone for EPA *Calif ozone for CARB*Calif ozone for CARB *Urban thunderstorms for NSF*Urban thunderstorms for NSF *Urban wx forecasting for NWS*Urban wx forecasting for NWS

PROG* APPROACH FOR LENGTH SCALEFreedman & Jacobson (2002 & 2003, BLM) + Freedman at SJSU

*2 prog Eqs.: TKE & DISSIPATION RATE ε

z

Kz

1

/E

c

/E

NKSK)Ri(c)(adv

t m2

2H

2m

1

z

EK

z

1

l

EcNKSK)E(adv

t

Em

E

2/32

H2

m

• Where ℓ = cεE3/2/ε• Values of σε & σE are reversed in Mellor & Yamada

reversed in all atm models K & TKE in upper PBL were wrong!

__

__

CALIBRATION TO NEUTRAL ABL: ℓ vs. z

Lines: various values of κ = cε2σε/σE

• x = COLEMAN (‘99) DNS

• New (R-panel) best-fit κ = 1.3 (dashed line), w/ better results (ℓ↓) in upper PBL

• Standard approach (left panel) best fit with κ = 2.5, w/ poor results in upper PBL newold

Same, but for K (z)

x = COLEMAN (‘99) DNS

New (R-panel) best-fit κ = 1.3 (dashed line), w/ better results in lower PBL & K↓ aloft

Standard approach (left panel) best fit with κ = 2.5, w/ poor results in lower PBL

new

old

ThanksThanksAny questions?Any questions?