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
10
15
20
25
30
Range [m]
[o C
]
Night 0.5mNight 1mDay 0.5mDay 1m
200 400 600 800 1000 1200 1400 1600 1800 2000
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
10
15
20
25
30
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
0
1
2
3
4
5
6
7
8
9
range [m]
T [o C
]
0.5m1m
200 400 600 800 1000 1200 1400 1600 1800 2000-1
0
1
2
3
4
5
6
7
8
9
range [m]
T [o C
]
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
2
3
4
5
6
7
8
9
range [m]
T [o C
]
0.5m1m
200 400 600 800 1000 1200 1400 1600 1800 2000-1
0
1
2
3
4
5
6
7
8
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
1000
1500
2000
2500
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
0
5
10
15
20
25
30
Time UTM
T [o C
]
Range=100mRange=2000m
0 50 100 150 200 250 300 3505
10
15
20
25
30
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
-20
-15
-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
200
300
400
500
600
700
800
900
Time [min]S
W D
own
[W/m
2 ]
Oct 9 2012, z=0.5m Clear sky conditions
0 500 1000 15000
100
200
300
400
500
600
700
800
900
Time [min]S
W D
own
[W/m
2 ]
Oct 14 2012, z=0.5m Clear sky conditions
0 500 1000 15000
100
200
300
400
500
600
700
800
900
Time [min]S
W D
own
[W/m
2 ]
Oct 15 2012, z=0.5mClouds, but apparent shadow front
0 500 1000 15000
100
200
300
400
500
600
700
800
900
Time [min]S
W D
own
[W/m
2 ]
Oct 14 2012, z=0.5m
Clouds, but apparent shadow front
0 500 1000 15000
100
200
300
400
500
600
700
800
900
Time [min]S
W D
own
[W/m
2 ]
Oct 11 2012, z=0.5m
Clouds, but no apparent shadow front
0 200 400 600 800 1000 1200 1400 16000
100
200
300
400
500
600
700
800
900
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