wrf-lesintherealworld: towardsaseamless ...label real vortex−les 111 m vortex−pbl 3 km 0.00 0.05...

30
17 th WRF Users’ Workshop WRF-LES in the real world: Towards a seamless modeling chain for wind industry applications A. Montorn` es 1 P. Casso 1 B. Kosovic 2 G. Lizcano 1 1 Vortex, 2 NCAR–RAL Montorn` es et. al, [email protected] Vortex WRF-LES in the real world

Upload: others

Post on 06-Feb-2021

0 views

Category:

Documents


0 download

TRANSCRIPT

  • 17th WRF Users’ Workshop

    WRF-LES in the real world: Towards a seamless

    modeling chain for wind industry applications

    A. Montornès1 P. Casso1 B. Kosovic2 G. Lizcano1

    1Vortex, 2NCAR–RAL

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    ◮ Experienced Vortex started its technology development in 2005 byformer Wind Site engineers, atmospheric physicists and computerexperts in a unusual collaborative team of experienced professionalswith active researchers.

    ◮ Wind industry Vortex provides wind resource maps and seriesoriented for wind resources assessment and forecasting purposes.

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    0

    10

    20

    30

    19/12 21/12 23/12 25/12 27/12 29/12 31/12Time (10')

    10

    ' me

    an

    Win

    d s

    pe

    ed

    [m

    /s]

    lab Real

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2000s - 2010s

    1 m 10 m100 m

    1 km10 km

    100 km

    1.000 km

    10.000 km

    1 h

    1 day

    1 week

    1 Month

    1 Year

    10 Years

    100 Years

    1000 Years

    10 min

    1 min

    10 s

    1 s

  • 17th WRF Users’ Workshop

    Mesoscale models 2000s - 2010s

    F = F̄ + F ′

    ◮ ∆x ≥ 500 m

    ◮ Wind resolved at each grid-point of the domain describes the meanstate flow F̄ .

    ◮ Mixing motions F ′ must be simplified and parameterized.

    ◮ Model splits the spatial diffusion

    ◮ Vertical diffusion → PBL schemes.◮ Horizontal diffusion → represented in terms of the

    deformation of the large-scale flow.

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2000s - 2010s

    0

    10

    20

    30

    19/12 21/12 23/12 25/12 27/12 29/12 31/12Time (10')

    10

    ' me

    an

    Win

    d s

    pe

    ed

    [m

    /s]

    lab Real Vortex−PBL 3 km

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2016: Microscale is here

    1 m 10 m100 m

    1 km10 km

    100 km

    1.000 km

    10.000 km

    10 cm1 cm

  • 17th WRF Users’ Workshop

    Large Eddy Simulations

    F′ = Large Eddies (> ∆x) + Small Eddies (< ∆x)

    ◮ Turbulence motions are divided in Large Eddies and Small Eddies.

    ◮ Large Eddies (> ∆x) are solved as a solution of the Navier-StokesEquations.

    ◮ Small Eddies (< ∆x) need to be parameterized in subgrid-scalemodels (SGS) and resolved sub-filter scales (SFS).

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2016: Real or model?

    Serie 1

    Serie 2

    0

    10

    20

    30

    0

    10

    20

    30

    16/07 18/07 20/07 22/07 24/07 26/07 28/07 30/07Time (10')

    10

    ' me

    an

    Win

    d s

    pe

    ed

    [m

    /s]

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2016: Real or model?

    0

    10

    20

    30

    16/07 18/07 20/07 22/07 24/07 26/07 28/07 30/07Time (10')

    10

    ' me

    an

    Win

    d s

    pe

    ed

    [m

    /s]

    lab Real Vortex−LES 111 m

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    2016: Real or model?

    0

    10

    20

    30

    16/07 18/07 20/07 22/07 24/07 26/07 28/07 30/07Time (10')

    10

    ' me

    an

    Win

    d s

    pe

    ed

    [m

    /s]

    lab Real Vortex−LES 111 m Vortex−PBL 3 km

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    Limitations in real simulations

    Mesoscale PBL

    BC

    Microscale LES

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    Limitations in real simulations

    Mesoscale PBL

    BC

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    Limitations in real simulations

    Mesoscale PBL

    BC

    θnew = θold + θ'

    MuñozEsparza (2014)

    +Vortex inhouse R+D

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    Vortex approach

    Reanalysis

    VortexWRFLESVortex

    WRFLES

    Mesoscale PBL

    Microscale LES

    Postprocessing

    4 Hz output 10' averages

    10' standard deviation

    20150 meters above ground

    Wind speed, Wind direction,Temperature, Pressure, RichardsonNumber, PBL Fluxes, Wind Veer,

    Inflow angle, ...

    3'' gust

    Montornès et. al, [email protected] Vortex

    WRF-LES in the real world

  • 17th WRF Users’ Workshop

    Site 1 Metmast: 60 m

    Vortex-3 km

    Vortex-111 m

    Bias10' RMSE10' R2

    hourly R2

    daily

    1.0 ms-1 1.7 ms-1

    1.0 ms-1 1.7 ms-1

    0.87 0.95

    0.86 0.94

    0.00

    0.03

    0.06

    0.09

    0.12

    0 10 20 3010' mean wind speed [m/s]

    Pro

    babili

    ty D

    ensity

    label Real Vortex−LES 111 m Vortex−PBL 3 km

    ●●

    ●●●

    ● ●

    ● ●●

    ●● ●●● ●

    ● ●

    ●●

    ●●

    ● ●●

    ● ●

    ●●

    ●●●

    ●●●

    ●●●●●

    ●●●●

    ●●

    ●●●

    ● ●●●

    ● ●

    ●●

    ●●●

    ●●

    ●●●

    ●●●●

    ●●●●●●

    ●●●●●

    ●●●●●●●●

    ●●●●

    ●●●●

    ●●

    ●●●●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●●●●●

    ●●●●●

    ●●●

    ●●

    ●●●

    ●●●●

    ●●●

    ●●●●●●●

    ●●●

    ●●

    ●●●

    ●●●●

    ●● ●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●● ●

    ●●

    ●●●●

    ●●

    ●●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●●●

    ●●

    ● ●●●●●●●●

    ●●●●●●

    ●●●●●

    ●●●●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●●●

    ●● ●●●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●●●●

    ●●●

    ●●● ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●●

    ●●●●●●●

    ●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●●

    ●●

    ●●●

    ●●●●●●●

    ●●●●●

    ●● ●

    ●●

    ●●●

    ●●●●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●●

    ● ●

    ●●●●●●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●● ●

    ●●●●

    ●●●●●●

    ●●●● ●●●●

    ● ●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●●

    ●●●

    ●●

    ●●●

    ● ●

    ●●

    ●●●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●●●

    ●●●●

    ●●● ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ● ●

    ●●

    ●●

    ●●●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●●●● ● ●

    ●●●

    ●●

    ●●

    ● ●● ●●●● ●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●●

    ● ●●

    ●●

    ●●●●

    ●●●

    ●●●●

    ●● ●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●● ●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●● ●●●●●● ●

    ●●●●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ● ●●●●

    ● ●

    ●● ●

    ●●●

    ● ●●●

    ●●●

    ●●●

    ● ●●

    ●●●

    ●●●● ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●●

    ●●●●

    ●●●●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●●●

    ●●●

    ●●●

    ●●

    ● ●

    ●●

    ●● ●

    ● ●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●●

    ●●●●●

    ● ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ● ●●

    ●●●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●●

    ● ●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●● ●

    ●●

    ●●●

    ●●●

    ●●●●●●●●

    ●●●●

    ●●●

    ●●●●●●●

    ●●●●●● ●

    ●●●●●●●●●●●

    ●●

    ●●●●●

    ●● ●●

    ●●●●●●●●●

    ●●

    ●●●●

    ● ●

    ●●

    ●●●

    ●●●

    ●●●●

    ●●●●

    ●●●●●●●●●● ●

    ●●

    ●●●●

    ●●●

    ●●●●●●

    ●●

    ●●●●●●●●●●●●

    ●●

    ●●●●●●●●●●

    ●●●●

    ● ●●●●●●

    ●●●

    ●●

    ●●●

    ●●●●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●●●

    ●●●●

    ●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●● ●

    ●●●●●●

    ●●●●

    ●●●●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●●

    ● ●●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ● ●●

    ●●●●

    ●●

    ●●●●

    ●●●

    ●●●●●●●●●●●●●●

    ●●●●

    ●●● ●●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ● ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●●●●

    ●●●

    ●●●

    ●●●

    ●●●●

    ●●●●

    ● ●●

    ●●●

    ●●●●

    ● ●●●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●● ●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ● ●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●

    ●●●

    ●●●●●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●● ●

    ●●●●●●●●●●●

    ●●●●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●●

    ●●●

    ●● ●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●

    ●●● ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●●●●●

    ● ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●● ●

    ●●

    ● ●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●● ●●

    ●●

    ●●●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●●●●●

    ●●●

    ●●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ● ●●●●

    ●●

    ●●● ●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ● ●

    ●● ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ● ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●●●●●

    ●●

    ●●

    ●●● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●●

    ●●

    ●●● ●

    ●●●

    ●●

    ●●

    ●●●●●●●●

    ● ●●

    ●●●

    ●● ●

    ●●●●●●●●●●●

    ●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●

    ●● ●

    ●●●

    ●●●●

    ●●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●●●●

    ●●

    ●●

    ●●●●

    ●● ●

    ● ● ●●●●

    ●●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●●●

    ● ●

    ●●

    ●●

    ●●

    ● ●

    ●●●●

    ●●●●

    ●●

    ●●● ●

    ●●

    ●●

    ●●●●●

    ●●●●

    ●●●●●

    ●●

    ●●●

    ●● ●●

    ●●●

    ●●

    ●●

    ● ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●●●

    ●●●●●●●●

    ●●●●

    ●●●●●●

    ●●

    ●●●●●●●●● ●●

    ●● ●●●●

    ●●

    ●●●●●●●●●●

    ●●●

    ●●

    ● ●●

    ●●●●●

    ●●●●

    ●●●●●

    ●●●

    ●●●●●●● ●●

    ●●

    ●●

    ●● ●●●●●

    ●●● ●

    ●●

    ●●

    ● ●●

    ●●●

    ●●

    ●●●●●●

    ●●●●●●●●●●●●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●●●●

    ●●●●●●●

    ●●● ●●●●●

    ● ●●●

    ●●

    ●●●●●●●●●●●

    ●●●●●●●●●●●●

    ●●

    ●●● ●

    ●●●

    ●●●●

    ●● ●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●

    ● ● ●●

    ●●●●●

    ● ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●●●

    ● ●●

    ●●

    ●●●●●

    ● ● ●●

    ● ● ● ●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ● ●●●

    ● ●

    ●●●

    ● ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ● ●

    ●●●

    ●● ●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●●

    ●●

    ● ●

    ●●

    ● ●

    ●●

    ●●●

    ●●●

    ● ●●●●

    ●●

    ●●

    ●●●●

    ●●●●●●

    ●●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ● ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●● ●

    ●●●

    ●●●●●●

    ●●●●●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●●●

    ●●●● ●●

    ●●

    ●●

    ●●

    ●●●●●●●●●

    ●●●

    ●● ●●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●●●●●●

    ●●●●

    ● ● ●●●

    ●●●● ●●●●

    ●●●

    ●●

    ●●

    ●● ●●●

    ●●

    ●●●

    ●● ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●● ●●● ●●

    ●●●●●●●●

    ●● ●●●●

    ●●●●●

    ●●

    ●●

    ●●●●

    ●●

    ●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●●

    ●●● ●

    ●● ●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ● ●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●●

    ● ●

    ●●●●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ● ●

    ● ●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ● ●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●●

    ●●

    ● ●●●

    ●● ●

    ●●

    ●●

    ● ●

    ● ●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ● ● ●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●● ●

    ●●

    ●●● ●● ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●● ●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●

    ● ●

    ●●●●

    ● ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ● ●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●●●●●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ● ● ●

    ●●

    ●●

    ●●

    ●●

    ●●● ●

    ●●

    ●●●●●

    ●●●●

    ●●●●

    ●●●●●●●●●●●●●●●●●

    ●●●●

    ●●●●

    ●●●●

    ●●●

    ●●

    ●●●●●●●●

    ●●●●●●●●●●●●●●●

    ●●●●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●

    ● ●●

    ●●●

    ●●●

    ●●

    ●●●●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●●●●●●●●

    ●●●●●

    ● ●

    ●●●

    ●●●●●●●●●

    ●●

    ●●●●●●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●● ●

    ●●●●

    ●●

    ●● ●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ● ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●

    ● ●

    ●●

    ●●

    ●●●●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ● ●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ● ●

    ●●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●● ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●● ●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●●●●●

    ●●●

    ●● ●●

    ●●●

    ●●●●●

    ●●

    ●●

    ● ●

    ● ●●●

    ●●●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ● ●●

    ●●●

    ● ●●●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●● ●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●● ●

    ●●●

    ●●●●●

    ●●●

    ●●●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ● ●

    ●●●●

    ●●

    ● ●

    ●●

    ●●●

    ●●●●

    ●●●●

    ●●

    ●●●●

    ● ●●●

    ●●

    ●●●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●●● ●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●●

    ● ●●

    ●●

    ●●

    ●●

    ● ●

    ●●● ●

    ●●

    ● ●●

    ●●●●●●●●

    ●●● ●

    ●●●

    ●●●●

    ●● ●●●

    ● ●●●●

    ●● ●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ● ●●●

    ●●

    ●●●●

    ●●●●●●

    ● ●

    ●●●

    ●●

    ● ●

    ●●

    ●●

    ●●●●●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●

    ●●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ● ●

    ●●

    ●●●

    ●●

    ●●

    ●●●●●

    ●●●●

    ●●●●●● ●

    ●●

    ●●●●●●

    ●●

    ●●●●●●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●●●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●●●

    ●● ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●●●

    ●●●●

    ●●●●●●●

    ●●●●

    ●●●●●●●●

    ●●●●

    ●● ●●●

    ●●●

    ●●●

    ●●●●●

    ●●

    ● ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●● ●●●●●

    ●●●

    ●●

    ●●●●

    ●●

    ●● ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●● ●

    ●●●●●●

    ●●

    ●●●●

    ●●

    ●●●●●●

    ●●●●●● ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●● ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●

    ● ●●● ●●

    ●●●

    ●●● ●

    ● ●●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●●●●●●

    ● ●●●●●●

    ●●●●●

    ●●●● ● ●

    ●●

    ● ●●

    ● ●●●●

    ●●●

    ● ●

    ●●

    ●●●● ●

    ●●● ●●

    ●●●●●●●

    ●●

    ●●●●

    ●●●

    ● ●

    ●●

    ●●

    ●● ●

    ● ●

    ●●

    ●●

    ●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ● ●

    ●●●

    ● ● ●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●● ●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ● ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●●

    ●●

    ●●●●●●

    ●●●●●●

    ●●●●

    ●●●●

    ●●●

    ●●●●

    ●●

    ●●

    ●● ●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ● ●

    ●●

    ●●●

    ●●

    ●●

    ● ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●●●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ● ●●

    ●●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●●●

    ●●

    ●●

    ●● ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●● ●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ● ●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●●●

    ●●

    ●●

    ● ●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●

    ●●●●

    ●●●●

    ●●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●●●●

    ●●●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●●●●●●●●●●

    ● ●●●

    ●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●●●

    ●●●●

    ●●●●

    ●● ●●●●●●

    ●●●●●●●

    ●●● ●●

    ●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●

    ●●

    ●● ●

    ●●●

    ●●●●●●●●

    ●●

    ●●

    ●●● ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●●

    ●●●●●●●●●

    ●●● ●

    ●●● ●●●

    ●●●●●

    ●●●●●●

    ●●●●●●●●●●●●

    ●●●●●

    ●●

    ●●●●

    ●●●

    ●●●●●

    ●●●

    ●●●

    ●●●● ●●●

    ●●

    ●●●

    ●●

    ●●●●●

    ●●

    ●●●●●●

    ●●●●●●●●●

    ●●

    ●●●●

    ●●

    ●●●●

    ●●●

    ● ●

    ●●

    ●●

    ●●●

    ●●

    ●●●●●● ●●

    ●●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●●●

    ●●●●

    ●●●

    ●●●

    ● ●●●

    ●●

    ●●●●

    ●●●●

    ●●

    ●●●●●●

    ●●●●

    ●●

    ●● ●

    ●●●

    ●●●●

    ●●●●●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ● ●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ●●

    ●●●

    ●●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ● ●●●

    ●●●●●●

    ●●

    ●●●

    ●●

    ●●

    ●●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●●●

    ●●

    ●●

    ●●

    ●●

    ● ●

    ●●

    ● ●

    ●●

    ● ●

    ●●

    ●●

    ●●●

    ●●

    ●●

    ●●

    ●●●●●

    ●●●●●●●●●●●●

    ●●●

    ●●

    ●●

    ●●●

    ●●●

    ●●

    ●●●

    ●●

    ●●