The temperature gradient and transition timescales as a function of topography in

complex terrain

Chad Higgins, Kellie Vache, Chadi Sayde, Sebastian Hoch, and Eric Pardyjak

200 400 600 800 1000 1200 1400 1600 1800 2000

1350

1400

Range [m]

Ele

vatio

n [m

]

• 1.5mm white multimode fiber optic cable

• Oryx DTS unit, 1m, 2 minute resolution

• 4km sample range• Double ended

measurement, 2 calibration baths

• ~100m total elevation gain

• Wild horses dragged the experiment away, twice!

1m

0.5m

Experiment specifics

Channel 1

Channel 215s later

Thank you CTEMPS.org

Oct 9 2012, z=0.5m

Calibrated data, distance time slice at one height

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

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Range [m]

[o C

]

Night 0.5mNight 1mDay 0.5mDay 1m

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1350

1400

Range [m]

Ele

vatio

n [m

]

Prandtl 1942 theory

10-1

10-0.3

10-0.2

10-0.1

100

slope [deg]

dT/d

z [o C

/m]

T 𝑙=4√ 4 𝑘𝑡 𝜇𝑇𝜌𝑔sin2𝛼𝜕𝑇𝜕 𝑧 (sin𝛼)

12

− Δ𝑇

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

sin(slope) [deg]

dT/d

z [o C

/m]

1320 1340 1360 1380 1400 1420 1440 1460-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

elevation [m]

dT/d

z [o C

/m]

1340 1360 1380 1400 1420 1440

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

elevation [m]

dT/d

z [o C

/m]

10-1

10-0.3

10-0.2

10-0.1

100

slope [deg]

dT/d

z [o C

/m]

day night

Search for explanatory variables

• Slope• Elevation• Relative positioning?• Contributing area?

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

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Range [m]

[o C

]

Night 0.5mNight 1mDay 0.5mDay 1m

DEM not sufficient, but we can look at Google earth Photos and on-the-ground photos

200 400 600 800 1000 1200 1400 1600 1800 2000-1

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1

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range [m]

T [o C

]

0.5m1m

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0

1

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range [m]

T [o C

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0.5m1m

Micro-topography has a dramatic influence on drainage flows, all of these features are not visible on a 10m DEM

200 400 600 800 1000 1200 1400 1600 1800 2000-1

0

1

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range [m]

T [o C

]

0.5m1m

200 400 600 800 1000 1200 1400 1600 1800 2000-1

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1

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9

range [m]

T [o C

]

0.5m1m

ES3

Contributing area, and thus the relative spatial positioning is a major factor in these flows

Search for explanatory variables

• Slope• Elevation• Relative positioning?• Contributing area?

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

10

15

20

25

30

Range [m]

[o C

]

Night 0.5mNight 1mDay 0.5mDay 1m

Hypothesis stage at this point, can verify if u* is a function of range during the day, need higher resolution DEM to compute drainage areas at night

23:10 23:20 23:30 23:40 23:50 00:00 00:100

500

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Time [min]

Ran

ge [m

]

G

A𝜌𝑐𝑝 𝜕𝑇𝜕𝑡

RnH

Assume a functional form

12:00 18:00 00:00 06:00 12:00 18:00-5

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Time UTM

T [o C

]

Range=100mRange=2000m

0 50 100 150 200 250 300 3505

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Time [min]

T[o C

]

Range=2000mFit R=2000Range=100mFit R=100

𝑇 (𝑡 )=𝐴𝑒−𝜆 𝑡−𝐵𝑡+𝑐

Fit with nonlinear least squares

Use shadow front as starting time

1320 1340 1360 1380 1400 1420 1440 1460-55

-50

-45

-40

-35

-30

-25

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-10

elevation [m]

dT/d

t [o C

/day

]

1320 1340 1360 1380 1400 1420 1440 146040

60

80

100

120

140

160

180

200

elevation [m]

[d

ay-1

]Fast timescale Cooling rate

1 2 3 4 5 6 7 8 9-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

slope [deg]

dT/d

t [o C

/day

]

1 2 3 4 5 6 7 8 940

60

80

100

120

140

160

180

200

slope [deg]

[d

ay-1

]

0 500 1000 15000

100

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Time [min]S

W D

own

[W/m

2 ]

Oct 9 2012, z=0.5m Clear sky conditions

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Time [min]S

W D

own

[W/m

2 ]

Oct 14 2012, z=0.5m Clear sky conditions

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Time [min]S

W D

own

[W/m

2 ]

Oct 15 2012, z=0.5mClouds, but apparent shadow front

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Time [min]S

W D

own

[W/m

2 ]

Oct 14 2012, z=0.5m

Clouds, but apparent shadow front

0 500 1000 15000

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Time [min]S

W D

own

[W/m

2 ]

Oct 11 2012, z=0.5m

Clouds, but no apparent shadow front

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Time [min]S

W D

own

[W/m

2 ]

Oct 13 2012, z=0.5m

Hypothesis: energy balance closure is better on this day.

Clouds, but no apparent shadow front

Conclusions• Micro-topography has high impact on nighttime temperature and

air drainage and temperature gradient• Slope has a greater impact on daytime temperature gradients, but

spatial disposition plays a equally important role• The daytime temperature gradient begins to vanish ad we go

farther up the hill• The onset timescale of the temperature transition is impacted

heavily by local slope• The cooling rate is more impacted by the spatial positioning• Advection always has the proper sign in complex topography for

the thermal driven flows• If there is no observable shadow front, the evening transition

occurs in the opposite direction