[PPT] - Including the urban canopy layer in a Lagrangian particle dispersion PowerPoint Presentation

SLIDE 1

Including the urban canopy layer in a Lagrangian particle dispersion model

Stefan Stöckl, Mathias W. Rotach, and Natascha Kljun

SLIDE 2

Project Overview

FERUS Footprint Estimation over Rough Urban Surfaces

Figure: This Wikimedia Commons image is

from the user Ramessos and is freely available under the creative commons cc-by-sa 3.0 license.

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 3

Project Overview

FERUS Footprint Estimation over Rough Urban Surfaces dispersion model as “core” for footprint model more accurate dispersion model better footprint model

Figure: This Wikimedia Commons image is

from the user Ramessos and is freely available under the creative commons cc-by-sa 3.0 license.

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 4

Why urban canopy layer

height (log-scale) planetary boundary layer free troposphere

uter or mixed layer

inertial sublayer surface layer zi 0.1 zi

Figure: adapted from Rotach and Calanca (2015)

Rotach et al. (1996)

non-urban
3D in de Haan and

Rotach (1998)

ICUC10, Stöckl et al. 2018-08-06 2

SLIDE 5

Why urban canopy layer

height (log-scale) planetary boundary layer free troposphere

uter or mixed layer

inertial sublayer surface layer zi 0.1 zi d roughness sublayer (RS) z*

Figure: adapted from Rotach and Calanca (2015)

Rotach (2001)

urban
Roughness

Sublayer

significantly

improved performance

has zero-plane

displacement d

ICUC10, Stöckl et al. 2018-08-06 2

SLIDE 6

Why urban canopy layer

height (log-scale) planetary boundary layer free troposphere

uter or mixed layer

inertial sublayer surface layer zi 0.1 zi urban canopy layer (UCL) zt z* roughness sublayer (RS)

Figure: adapted from Rotach and Calanca (2015)

Now

new urban canopy

layer

zero-plane

displacement no longer required

parameterizations
f turbulence

profiles necessary

ICUC10, Stöckl et al. 2018-08-06 2

SLIDE 7

Lagrangian Particle Dispersion Model

distance height

horizontally homogeneous (no topography)
stationary
unstable to neutral/stable
non-Gaussian and Gaussian PDFs
requires vertical profiles of u, u′w′, u′2, v′2, w′2, w′3, ε

ICUC10, Stöckl et al. 2018-08-06 3

SLIDE 8

Roadmap

Goal model down to ground (footprint sources there!)

ICUC10, Stöckl et al. 2018-08-06 4

SLIDE 9

Roadmap

Goal model down to ground (footprint sources there!)

1 find turbulence parameterization in the UCL 2 show model sensitivity to UCL-parameterizations 3 investigate changes in concentration output

ICUC10, Stöckl et al. 2018-08-06 4

SLIDE 10

Problem

Figure: taken from Harman et al. (2016)

spatially heterogeneous
hard to measure
depends strongly on geometry
possible with LES/DNS/CFD:

expensive (e.g. Auvinen et al., 2017)

ICUC10, Stöckl et al. 2018-08-06 5

SLIDE 11

Problem

Figure: taken from Harman et al. (2016)

spatially heterogeneous
hard to measure
depends strongly on geometry
possible with LES/DNS/CFD:

expensive (e.g. Auvinen et al., 2017) Solution? spatial average

ICUC10, Stöckl et al. 2018-08-06 5

SLIDE 12

Data sets so far

part of London(Xie and Castro, 2009)
cubes(Coceal et al., 2007, 2006)

LES/DNS

ICUC10, Stöckl et al. 2018-08-06 6

SLIDE 13

Data sets so far

part of London(Xie and Castro, 2009)
cubes(Coceal et al., 2007, 2006)

LES/DNS

“tombstone” canopy (Harman et al.,

2016)

solid tree shapes (Böhm et al., 2013)
model of part of Nantes (France)

(Kastner-Klein and Rotach, 2004)

model of part of London (Carpentieri

et al., 2009)

Wind Tunnel

ICUC10, Stöckl et al. 2018-08-06 6

SLIDE 14

Data sets so far

part of London(Xie and Castro, 2009)
cubes(Coceal et al., 2007, 2006)

LES/DNS

“tombstone” canopy (Harman et al.,

2016)

solid tree shapes (Böhm et al., 2013)
model of part of Nantes (France)

(Kastner-Klein and Rotach, 2004)

model of part of London (Carpentieri

et al., 2009)

Wind Tunnel

BUBBLE in Basel (Rotach et al., 2005)

Field study

ICUC10, Stöckl et al. 2018-08-06 6

SLIDE 15

Data sets so far

part of London(Xie and Castro, 2009)
cubes(Coceal et al., 2007, 2006)

LES/DNS

“tombstone” canopy (Harman et al.,

2016)

solid tree shapes (Böhm et al., 2013)
model of part of Nantes (France)

(Kastner-Klein and Rotach, 2004)

model of part of London (Carpentieri

et al., 2009)

Wind Tunnel

BUBBLE in Basel (Rotach et al., 2005)

Field study

ETH Atmospheric Boundary Layer wind tunnel, poster by Christina Tsalicoglou tomorrow

To do Suggestions welcome!

ICUC10, Stöckl et al. 2018-08-06 6

SLIDE 16

Turbulence parameterization in UCL – example

−2.0 −1.5 −1.0 −0.5 0.0 0.5

u′w′/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

Height scaling

established that σh important
z/(zh + bσh)
b = 1.5 for now

ICUC10, Stöckl et al. 2018-08-06 7

SLIDE 17

Turbulence parameterization in UCL – example

−2.0 −1.5 −1.0 −0.5 0.0 0.5

u′w′/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

Old model

stops at zero-plane displacement

ICUC10, Stöckl et al. 2018-08-06 7

SLIDE 18

Turbulence parameterization in UCL – example

−2.0 −1.5 −1.0 −0.5 0.0 0.5

u′w′/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

UCL parameterization

use general function: u′w′UCL = beaz + c
transition in height zt = zh + 1.5σh
continuous to profile from top:

u′w′UCL(zt) = u′w′t

boundary condition: u′w′(0) = u′w′0
free parameter (tuning): a

ICUC10, Stöckl et al. 2018-08-06 7

SLIDE 19

Turbulence parameterization in UCL – example

−2.0 −1.5 −1.0 −0.5 0.0 0.5

u′w′/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

UCL parameterization

use general function: u′w′UCL = beaz + c
transition in height zt = zh + 1.5σh
continuous to profile from top:

u′w′UCL(zt) = u′w′t

boundary condition: u′w′(0) = u′w′0
free parameter (tuning): a

Result (in black)

u′w′UCL = u′w′0 + u′w′t−u′w′0

eazt

(eaz − 1)

ICUC10, Stöckl et al. 2018-08-06 7

SLIDE 20

Turbulence Profiles

2 4

u/uh

1 2 3 4

z/(zh + 1.5σh)

20 40

u′2/u2

∗L 1 2 3 4

z/(zh + 1.5σh)

−2 −1

u′w′/u2

∗IS 20 40

v′2/u2

∗L −1.0 −0.5 0.0

Skw

5 10 15

w′2/u2

∗L Xie and Castro (2009) Harman et al. (2016) B¨

hm et al. (2013)

Coceal et al. (2006), staggered Coceal et al. (2006), aligned Coceal et al. (2006), square Coceal et al. (2007) Kastner-Klein and Rotach (2004) BUBBLE U1 BUBBLE U2 Carpentieri et al. (2009)

ICUC10, Stöckl et al. 2018-08-06 8

SLIDE 21

Turbulence Profiles

2 4

u/uh

1 2 3 4

z/(zh + 1.5σh)

20 40

u′2/u2

∗L 1 2 3 4

z/(zh + 1.5σh)

−2 −1

u′w′/u2

∗IS 20 40

v′2/u2

∗L −1.0 −0.5 0.0

Skw

5 10 15

w′2/u2

∗L v1 v2 v3 v4 default

ICUC10, Stöckl et al. 2018-08-06 8

SLIDE 22

Example comparison original model – model with UCL

10−4 10−3 10−2 10−1 100 101 102 103 104 105

concentration (ng m−3) of original model

10−4 10−3 10−2 10−1 100 101 102 103 104 105

concentration (ng m−3) of model with UCL

grid positions measurement positions

change in concentration due to UCL: point moves up or down

ICUC10, Stöckl et al. 2018-08-06 9

SLIDE 23

Sensitivity of UCL parameterizations

v1

u

v2 v3 v4

u′w ′ u′2 v ′2 w ′2 w ′3

log concentration, default run log concentration, sensitivity run

hardly any

sensitivity for u′w′ and w′3

variances u′2, v′2,

w′2 intermediate

highest or u

ICUC10, Stöckl et al. 2018-08-06 10

SLIDE 24

Comparison with tracer experiments

compare measured and simulated concentrations (point to point)
all BUBBLE (Basel Urban Boundary Layer Experiment) field studies
selected MUST (Mock Urban Setting Test) field studies (Yee and Biltoft, 2004)

ICUC10, Stöckl et al. 2018-08-06 11

SLIDE 25

Comparison with tracer experiments

compare measured and simulated concentrations (point to point)
all BUBBLE (Basel Urban Boundary Layer Experiment) field studies
selected MUST (Mock Urban Setting Test) field studies (Yee and Biltoft, 2004)

Experiment FB NMSE CORR F2

riginal model

0.32 6.62 0.81 0.31 UCL included 0.30 6.67 0.80 0.27 better values in bold FB ..........................fractional bias NMSE ....normalized mean square error CORR ............. correlation coefficient F2 ............................factor of two

ICUC10, Stöckl et al. 2018-08-06 11

SLIDE 26

Comparison with tracer experiments

compare measured and simulated concentrations (point to point)
all BUBBLE (Basel Urban Boundary Layer Experiment) field studies
selected MUST (Mock Urban Setting Test) field studies (Yee and Biltoft, 2004)

Experiment FB NMSE CORR F2

riginal model

0.32 6.62 0.81 0.31 UCL included 0.30 6.67 0.80 0.27

significance by bootstrapping
significantly better or worse at 95% level

ICUC10, Stöckl et al. 2018-08-06 11

SLIDE 27

Summary

Conclusion

turbulence parameterization found by fitting general functions to spatially

averaged profiles

UCL-model is most sensitive to changes in u
increased complexity (including UCL) does not deteriorate model

performance significantly Outlook

find more profile data → improve UCL parameterization, especially u
validate with more dispersion experiments
footprint model

ICUC10, Stöckl et al. 2018-08-06 12

SLIDE 28

References I

Auvinen, M., L. Järvi, A. Hellsten, U. Rannik, and T. Vesala, 2017: Numerical framework for the computation of urban flux footprints employing large-eddy simulation and Lagrangian stochastic modeling. Geosci. Model. Dev., 10, 4187–4205, doi:10.5194/gmd-10-4187-2017. Böhm, M., J. J. Finnigan, M. R. Raupach, and D. Hughes, 2013: Turbulence structure within and above a canopy

f bluff elements. Boundary-Layer Meteor., 146, 393–419, doi:10.1007/s10546-012-9770-1.

Carpentieri, M., A. G. Robins, and S. Baldi, 2009: Three-dimensional mapping of air flow at an urban canyon

intersection. Boundary-Layer Meteor., 133, 277–296, doi:10.1007/s10546-009-9425-z.

Cionco, R. M., 1965: A mathematical model for air flow in a vegetative canopy. J. Appl. Meteor., 4, 517–522, doi:10.1175/1520-0450(1965)004<0517:AMMFAF>2.0.CO;2. Coceal, O., A. Dobre, T. G. Thomas, and S. E. Belcher, 2007: Structure of turbulent flow over regular arrays of cubical roughness. J. Fluid Mech., 589, 375–409, doi:10.1017/S002211200700794X. Coceal, O., T. G. Thomas, I. P . Castro, and S. E. Belcher, 2006: Mean flow and turbulence statistics over groups

f urban-like cubical obstacles. Boundary-Layer Meteor., 121, 491–519, doi:10.1007/s10546-006-9076-2.

de Haan, P ., and M. W. Rotach, 1998: A novel approach to atmospheric dispersion modelling: The Puff-Particle

Model. Q. J. Roy. Meteor. Soc., 124, 2771–2792, doi:10.1002/qj.49712455212.

Hanna, S. R., 1989: Confidence limits for air quality model evaluations, as estimated by bootstrap and jackknife resampling methods. Atmos. Environ. (1967), 23, 1385–1398, doi:10.1016/0004-6981(89)90161-3.

ICUC10, Stöckl et al. 2018-08-06 13

SLIDE 29

References II

Harman, I. N., M. Böhm, J. J. Finnigan, and D. Hughes, 2016: Spatial variability of the flow and turbulence within a model canopy. Boundary-Layer Meteor., 160, 375–396, doi:10.1007/s10546-016-0150-0. Kastner-Klein, P ., and M. W. Rotach, 2004: Mean flow and turbulence characteristics in an urban roughness

sublayer. Boundary-Layer Meteor., 111, 55–84, doi:10.1023/B:BOUN.0000010994.32240.b1.

Rotach, M. W., 2001: Simulation of urban-scale dispersion using a Lagrangian stochastic dispersion model. Boundary-Layer Meteor., 99, 379–410, doi:10.1023/A:1018973813500. Rotach, M. W., and P . Calanca, 2015: Microclimate. Encyclopedia of Atmospheric Sciences, G. R. North, J. Pyle, and F . Zhang, Eds., 2nd ed., Academic Press, Oxford, 258–264, doi:10.1016/B978-0-12-382225-3.00225-5. Rotach, M. W., S.-E. Gryning, and C. Tassone, 1996: A two-dimensional Lagrangian stochastic dispersion model for daytime conditions. Q. J. Roy. Meteor. Soc., 122, 367–389, doi:10.1002/qj.49712253004. Rotach, M. W., and Coauthors, 2005: BUBBLE – an urban boundary layer meteorology project. Theor. Appl. Climatol., 81, 231–261, doi:10.1007/s00704-004-0117-9. Xie, Z.-T., and I. P . Castro, 2009: Large-eddy simulation for flow and dispersion in urban streets. Atmos. Environ., 43, 2174–2185, doi:10.1016/j.atmosenv.2009.01.016. Yee, E., and C. A. Biltoft, 2004: Concentration fluctuation measurements in a plume dispersing through a regular array of obstacles. Boundary-Layer Meteor., 111, 363–415, doi:10.1023/B:BOUN.0000016496.83909.ee.

ICUC10, Stöckl et al. 2018-08-06 14

SLIDE 30

Scaling

Traditional canopy scaling

not all peaks at z/zh = 1
non-uniform heights: higher buildings more

influence

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 31

Scaling

New canopy height scaling

established that σh important
use that: z/(zh + aσh)
uniform not affected
non-uniform brought down
a = 1.5 for now

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 32

Scaling

New canopy height scaling

established that σh important
use that: z/(zh + aσh)
uniform not affected
non-uniform brought down
a = 1.5 for now

BUT shape of profiles not right

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 33

Scaling

New canopy scaling

in roughness sublayer and canopy layer:

local u∗L relevant

before: u∗ = u∗IS
now: u∗L =

4

u′w′2 + v′w′2
profiles L-shaped

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 34

Scaling

New canopy scaling

in roughness sublayer and canopy layer:

local u∗L relevant

before: u∗ = u∗IS
now: u∗L =

4

u′w′2 + v′w′2
profiles L-shaped

BUT

most datasets have no v′w′
some datasets have low values of u′w′ →

runaway values

ICUC10, Stöckl et al. 2018-08-06 1

SLIDE 35

Turbulence parameterization in UCL – u

1 2 3 4 5

u/uh

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function (Cionco, 1965):

uUCL = bea(z/zt−1)

transition in height zt = zh + 1.5σh
continuous to profile from top:

uUCL(zt) = ut

free parameter (tuning): a

Solution

uUCL = utea(z/zt−1)

ICUC10, Stöckl et al. 2018-08-06 2

SLIDE 36

Turbulence parameterization in UCL – u′2

2 4 6 8 10

u′2/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function: u′2UCL = bea(z/zt−1)
transition in height zt = zh + 1.5σh
continuous to profile from top:

u′2UCL(zt) = u′2t

free parameter (tuning): a

Solution

u′2UCL = u′2tea(z/zt−1)

ICUC10, Stöckl et al. 2018-08-06 3

SLIDE 37

Turbulence parameterization in UCL – v′2

2 4 6

v′2/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function: v′2UCL = bea(z/zt−1)
transition in height zt = zh + 1.5σh
continuous to profile from top:

v′2UCL(zt) = v′2t

free parameter (tuning): a

Solution

v′2UCL = v′2tea(z/zt−1)

ICUC10, Stöckl et al. 2018-08-06 4

SLIDE 38

Turbulence parameterization in UCL – w′2

1 2 3 4 5

w′2/u2

∗ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function: w′2UCL =

a

√ bz

transition in height zt = zh + 1.5σh
continuous to profile from top:

w′2UCL(zt) = w′2t

free parameter (tuning): a

Solution

w′2UCL = w′2t a

z

zt

ICUC10, Stöckl et al. 2018-08-06 5

SLIDE 39

Turbulence parameterization in UCL – w′3

−0.75 −0.50 −0.25 0.00 0.25

Skw

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function for skewness:

SKw = b(z + c)2 + d

model uses w′3 = SKww′2−3/2
transition in height zt = zh + 1.5σh
continuous to profile from top:

w′3UCL(zt) = w′3t

becomes zero near ground: SKw(z0) = 0
free parameter as peak: SKw(zt/2) = −a

w′3UCL = 4a + 2w′3t(zt−2z0)

w′23/2

t

(zt−z0)

z2

t − 2ztz0

z2 − z(zt + z0) + ztz0
+

w′3t(z − z0 w′23/2

t

(z − z0)

w′23/2

UCL

ICUC10, Stöckl et al. 2018-08-06 6

SLIDE 40

Turbulence parameterization in UCL – ε

0.00 0.02 0.04 0.06

ε

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/(zh + 1.5σh)

use general function: εUCL = bea(z/zt−1)
transition in height zt = zh + 1.5σh
continuous to profile from top: εUCL(zt) = εt
free parameter (tuning): a

Solution

εUCL = εtea(z/zt−1)

ICUC10, Stöckl et al. 2018-08-06 7

SLIDE 41

Other Scaling Idea

Idea

also relevant bulk-descriptors:
frontal area fraction λf
plan area fraction λp
plot peaks of profiles as function of λf, λp
no clear signal → so far unsuccessful

ICUC10, Stöckl et al. 2018-08-06 8

SLIDE 42

Error measures

FB = 2(o − s)

+ s

NMSE = 1 nos

n

i=1

(oi − si)2 CORR = 1 σoσs

n

i=1

(oi − o)(si − s) F2 = 1 n

n

i=1
1

if

0.5 ≤ si

i ≤ 2

else

o . . . observed values, n many
s . . . simulated values, n many
o = 1

n

i=1 oi

s = 1

n

i=1 si

σo =
1

n

i=1(oi − o)2

σs =
1

n

i=1(si − s)2

exclude values where o = 0

from RD and F2 (division by 0)

ICUC10, Stöckl et al. 2018-08-06 9

SLIDE 43

Significance by bootstrapping

“blocked” by experiment (BUBBLE or MUST)
bootstrapping not the values of the error statistics themselves, but their

difference (Hanna, 1989)

Studentized moments for confidence intervals
significantly different if confidence interval of difference does not contain 0

ICUC10, Stöckl et al. 2018-08-06 10