NOCTURNAL DRAINAGE FLOW
Scientific Manuscript
OBSERVATIONS OF NOCTURNAL DRAINAGE FLOW IN A SHALLOW
GULLY
M.R.Soler, C.Infante and P.Buenestado
Department of Astronomy and Meteorology
University of Barcelona,
Avinguda Diagonal 647
08028 Barcelona Spain
Larry Mahrt
College of Oceanic & Atmospheric Sciences
Oregon State University
Corvallis, OR 97331 USA
Adrdess for correspondence:
M.R. Soler, Department of Astronomy and Meteorology,
University of Barcelona, Avinguda Diagonal 647, 08028 Barcelona , Spain, Telephone:
0034 93 402 11 24, Fax: 00 34 93 402 11 33, e-mail: rosa@am.ub.es
Abstract. The formation of cold air drainage flow in a shallow gully is studied during
CASES-99 (Cooperative Atmosphere-Surface Exchange Study).
Fast and slow response wind and temperature measurements were obtained on an
instrumented 10m tower located in the gully and from a network of thermistors and 2-D
sonic anemometers, situated across the gully.
Gully flow formed on clear nights even with significant synoptic flow.
Large variations in surface temperature developed within an hour after sunset and in situ
cooling was the dominant factor in wind sheltered locations. The depth of the drainage
flow and the height of the down-gully wind speed maximum were found to be largest
when the external wind speed above the gully flow is less than 2 m /s. The shallow
drainage current is restricted to a depth of few meters. The drainage flow is deeper
when the stratification is stronger and the external flow is weaker.
During the night the drainage flow breaks down, sometimes on several occasions, due to
intermittent turbulence and downward flux of heat and momentum. The near surface
temperature may increase by 6 C in less than 30 minutes due to vertical convergence of
downward heat flux. These mixing events are related to acceleration of the flow above
the gully flow and decreased Richardson number. These warming events lead to
warming of the near surface soil and reduction of the upward soil heat flux. To examine
the relative importance of different physical mechanisms that could contribute to
produce this increase of temperature, the sensible heat budget will be analyzed.
Keywords: Drainage flows, Katabatic winds, Stable Boundary Layer
1. Introduction
Nocturnal drainage winds begin when air adjacent to a sloping surface cools and
becomes more dense than the free air at the same elevation. Common drainage flows
dictate local transport and determine the spatial distribution of nocturnal minimum
temperatures.
Previous experimental and theoretical studies on the climatology of drainage flows,
their formation mechanisms, their interaction with large scale winds systems and their
response to specific terrain configurations include Horst and Doran, (1986), Blumen
(1984), van der Avoird and Duynkerke (1999), and Papadoulos and Helmis (1999) and
references therein. However most of these measurements and analyses have addressed
mountain slopes and deeper valleys or larger scale slopes and only a few studies have
concentrated on weak or small scale slopes (Mahrt , 1982). This paper studies shallow
drainage flows generated in a shallow gully during CASES99, in south-east Kansas,
USA, (LeMone et al., 2000). We will examine the vertical structure of the drainage
flow, its interaction with the overlying ambient flow and its horizontal structure within
the shallow gully.
2. Site and Instrumentation
The observational field campaign took place in a shallow gully within the Walnut River
Watershed, east of Wichita, Kansas, USA. The surface vegetation was grass with a
typical height of 25 cm and there were no trees within one kilometre of the sight. The
map of the gully and the location of the different instruments are presented in Figure 1.
We instrumented a 10-m tower with slow response measurements of temperature, wind
speed and direction, and humidity at 1.06, 3.07 and 9 m. Sonic anemometers were
deployed at 1.7 and 7.4 m. The measurements also include net radiation at 1.06 m,
ground heat flux at 8 cm, four soil temperature sensors at 2, 6, 14, 28 cm, and two
moisture sensors at 14 and 28 cm.
Wind speed and direction were measured with a propeller anemometer (RM young
05103) with a sampling frequency of 5 Hz . The wind vane threshold is 1.0 m/s at 10º
displacement and 1.5 m/s at 5º with an accuracy of 3º. The cup anemometer threshold
is 0.4 m/s with an accuracy of 0.2 m/s.
Temperature and humidity were measured with precision thermistors and a capacitive
relative humidity sensors mnufactured by Vaisäla (Campbell HMP35AC), with a
sample frequency of 1Hz. The accuracy of the temperature sensors is  0.01 ºC from
(-23 to 48)ºC and the accuracy of the humidity sensors is 1% RH from 0-90% and
3% from 90-100%.
Net radiation was measured with a (Campbell Q7) net radiometer with a sampling rate
of 1 Hz and accuracy of 5% to 10 %
Soil Temperature was measured with a Campbell 107 temperature probe with a
sampling rate of 1 Hz and accuracy of  0.1 ºC from (-23 to 48)ºC
Soil heat flux was measured with a soil water content reflectometer (Campbell CS615),
with a sampling rate of 1 Hz and accuracy of  1% to  5%.
Ground heat flux was measured with a Campbell RECS HFT-3 heat flux plate with a
sampling rate of 1 Hz , the resolution is 10-6 m3/m3 and the accuracy is 2%.
These instruments were calibrated prior to the campaign at the Campbell headquarters
in England.
Low frequency measurements were averaged every five minutes.
The sonic anemometers located at 1.7 and 7.4 m were a Campbell CSAT3, and a Solent
1012-R2, respectively, both with a sampling rate of 20 Hz.
Data from these two sonic anemometers were despiked using a procedure described in
Vickers and Mahrt (1997). To remove noise, these time series have been filtered using a
wavelet technique (Daubechies, 1992). The tilt correction method described in Kaimal
et al., 1994 was applied.
Five 2-D sonic anemometer at 1-m height and nine
thermistors, at approximately 0.5-m height were positioned across the gully, and eight
thermistors were located on the tower at 20 cm, 30 cm, 50 cm, and 1, 2.5, 4.2, 6.4, and
9.7 meters respectively. The thermistors are described in Mahrt et al., (2001).
3. Drainage flow observations
For this study, we have selected the nights where the temperature at the 9.7 m level on
the gully tower averages 4ºC warmer than the temperature at the 0.3 m level between
2000 and 0400 local standard time (LST). This criteria assures that the nights will
correspond to relatively stable nights with strong stratification. The nocturnal
circulations in the gully region potentially consists of five different components (Mahrt
et al., 2001): 1) synoptic flow, typically southerly: 2) easterly drainage flow responding
to a 0.5% slope extending upward 10 km east of the site to the Flint Hills; 3) northerly
flow down the local gully; 4) flow down the side slopes of the gully, which have a slope
of about 4% on the east side and a little steeper on the west side if we include a small
escarpment of 2 m just west of the gully bottom, and 5) transient mesoscale motions.
We concentrate on two case studies where the southerly synoptic flow opposed flow
down the gully, 20-21 and 26-27 October.
3.1.- Mean analysis
The sonic anemometers at 1.7 and 7.4 m (Figure 2 a-b) show evidence of intermittent
nocturnal slope flow between approximately 1900 to 0800 (LST). At the lower level,
the wind is often downslope (down the gully) with a nearly northerly direction, while at
the upper level, the wind is from the south sector corresponding to the synoptic flow.
This indicates that the top of the drainage flow is between 1.7 and 7.4 m. During these
nights, the drainage flow breaks down several times when the southerly wind at 7.4 m
increases to about, or exceeds, 2 m/s. During the breakdown, 1) The wind at the lower
level (1.7 m) changes its direction from northerly (drainage flow) to southerly (synoptic
flow) and 2) the temperature near the surface increase, sometimes by more than 6 C.
With northerly flow down the gully, the stratification between 0.2 m and 9.7 m is much
larger than during these mixing events when the gully flow is replaced with southerly
flow; (Figure 3).
Figure 4 presents an example for night 20-21 October of the cross gully flow structure
based on the nine thermistors positioned across the gully and the wind vectors given by
the 2-D sonic anemometers, H3, H1 and H4 . The “x”-axis represents the distances from
the gully tower to the different thermistors, taking the tower as the origin. The “y”-axis
represents time.
The temperature decreases dramatically immediately after sunset, particularly inside the
gully (Figure 4). The wind inside the gully (sonic H1), is from the north sector (drainage
wind), except for a short period when the drainage flow is eliminated by mixing. This
warming event occurs within and on both sides of the gully indicating that it is
associated with processes larger than the gully itself. The wind over the weak slope on
the east side of the gully (H4, Figure 4) follows the local slope toward the west if the
flow at 7 m is weak. Otherwise it comes from the south sector (synoptic flow). The
flow on the west side of the gully shows similar behavior (H3).
3.2. Turbulence analysis
Figure 5a-b shows the fast response data for periods when the gully flow is being
eliminated for the two case study nights. The elimination of the cold gully flow (the
wind direction changes from north to south) is accompanied by substantial warming in
the gully bottom. The elimination of the gully flow is due to increased turbulence
(Figure 5) and downward transport of heat (Figure 6) and momentum (Figure 7).
The onset of turbulence seems to start at the upper level first, as is indicated by time
evolution of the friction velocity and turbulence kinetic energy (Figure 8), and by the
downward vertical transport of vertical velocity variance, w' 3 . During drainage flow,
w' 3 is negative but very small, on the order of 10-4 and 10-5 m3s-3, while during the
breakdown of the drainage flow, its value increases by one or two orders of magnitude,
indicating that the vertical velocity variance is transported downward. Observations
from the nearby 60-m tower indicates that the turbulence events in the gully usually
correspond to enhanced turbulence over a deep layer and originate from near the top of
tower or above.
With the downward heat flux, the cooling of the soil ceases and in fact warms by 0.3
degrees at the 2-cm level, which in turn increases the outward long wave radiation. The
time evolution of subsoil temperature for four nights is presented in Figure 9. Nights 1920 and 23-24 October, are characterized by drainage flow in the gully with weak winds
from the east sector at the upper sonic level. No breakdown or turbulence events are
observed therefore the temperature of both the air and soil decrease continuously
throughout the night. In contrast, for the nights analyzed in this study, 20-21 and 26-27,
both the air and soil temperature temporarily increase during mixing events.
4.- Thermodynamic balance.
In this section, we analyze the relative importance of physical processes that could
contribute to the local change of temperature, observed during the breakdowns of the
gully drainage flow. We therefore analyze the conservation equation for potential
temperature (Stull, 1988: Chapter 3), expressed as:







 (u
v
w
 (u ')  (v  ')  ( w '))  FR  Fc
t
x
y
z x
y
z
(1)
where  is the potential temperature, (u,v, w) are the horizontal and vertical components
of velocity, t is the time and the Cartesian coordinates (x,y,z) are directed to east, north
and anti-parallel to gravity. The terms containing primed quantities describe horizontal
and vertical flux divergence of the turbulent heat flux. All these terms were averaged
every five minutes.
The quantities FR and Fc represent infrared radiative flux divergence and cooling or
warming from evaporation or condensation, respectively. Fc can be neglected on these
nights (Mahrt et al., 2001). The radiative flux divergence, estimated from the twostream model (Kiehl, 1996) indicates that radiative flux convergence (warming) in the
lower part of the layer nearly cancels radiative flux divergence (cooling) and in the
upper part of the layer. Observations can be used to evaluate the vertical flux divergence
of heat but not the horizontal flux divergences and horizontal advection terms. These
latter terms are relegated to a residual term in the layer averaged budget presented
below.
A layer-averaged temperature budget between the ground surface and the level of the
second sonic anemometer, 7.4 m, will be written as (Blumen et al., 1999):


 w'  '
 w

 R
t
z
z
where

(2)
designates a layer-average, defined as:
1

z i
z i
i
where the layer depth is z = 7.4 m and i denotes each measurement level. The
difference between
residual
R
w'  ' at the 7.4 m and 1.7 m levels is denoted by  w'  ' The
contains the layer-averaged horizontal flux divergences, horizontal
advection and errors associated with the measured quantities.
The time average of each of the terms retained in (2), is presented in tables I(a), I(b) and
II, for the nights 20-21 and 26-27, respectively.
The two turbulent events for night 20-21 (Table 1) corresponds to an overall warming
of approximately 3.3 and 3.2 degrees over approximately 50 minute periods, due
primarily to the vertical flux divergence term. The vertical advection is nearly balanced
by the residual term for the first event, from 2310 to 2400 (LST). For the second event,
the turbulence heat flux divergence actually exceeds the observed warming, in which
case the residual term must oppose the flux divergence.
For the turbulent event on night 26-27, the overall warming in the gully is 3.3 C over a
70-minute period. For this event, both vertical divergence of the heat flux and vertical
advection are important.
5. Turbulence classification
A variety of types of turbulence can occur in the SBL (Mahrt and Gamage, 1987). In
some situations, the turbulence is continuous over the whole depth of the SBL. In other
situations, the turbulence might be patchy, weak and intermittent and disconnected with
processes at the surface. In order to characterize the turbulence generated during the
periods when the drainage flow is eliminated by mixing, we have calculated the length
scale lB (Stull, 1988), the integral time scale R, the eddy diffussivities for momentum
and heat Km and Kh,, and the gradient Richardson number, Ri.
The length scale lB is defined as
l
B



N
BV
(3)
where w is the standard deviation of vertical wind velocity and NBV is the BruntVäisäla frequency defined as
N
BV

g 
 z
(4)
where  is the mean potential temperature over the depth of the gully flow and the
computation of the vertical gradient of potential temperature is detailed below. The
Brunt-Väisäla frequency is related to the period of oscillation of a parcel in a statically
stable environment. In very stable stratification NBV will be larger than in weak
stratification.
The length scale decreases with stability due to the suppression of vertical motions by
the static stability. It can range from a couple of hundred meters for weak stratification,
to less than a meter for strong stratification. Kaimal (1973) has analyzed the behaviour
of several schemes for estimating the characteristic length scales in stable conditions
and his analysis demonstrates that the lengths scales decrease with increasing
Richardson number.
The Eulerian integral time scale R, (Kaimal et al., 1994), is defined as
R 

1

2
R
w
( )d
(5)
w 0
where Rw() is the autocovariance function for vertical velocity and  is the time lag.
Here R, is estimated as the lag where the correlation coefficient crosses zero, using one
hour of data.
The eddy diffusivities are defined as:
Km 
u
u
2
Kh  
*
z
w'  '

(6)
z
where fluxes of momentum and heat are calculated from the sonic anemometers.
The gradient Richardson number is defined as (Rees, 1991),
R
i
g 
 z
(7)
 u     
  u 
 z 
 z 
2
2
2
Where , u and  are respectively the mean potential temperature, wind speed and wind
direction. The vertical gradients are computed by fitting five minute averages to a
second order polynomial in log z using least squares (Högström, 1988). The gradient of
the mean wind direction has been evaluated from fitting a log linear profile to the
corresponding wind data.
When the gully flow is eliminated by mixing, the length scale lB at the two different
levels, 1.7 and 7.4 m, increases from order of 10
–2
- 10
–1
m in strong stratification
before the mixing event, to 1m - 3m after the mixing event. The behaviour of the time
scale is similar. During stable periods, the time scale is only 15 seconds for the night
20-21 and 10 seconds for the night 26-27. During turbulent periods when the drainage
flows break down, the time scale increases to about 70 seconds and 230 seconds for the
nights 20-21 and 26-27 respectively.
With the onset of mixing and elimination of the drainage flow, the eddy difussivities Km
and Kh increase from very small values, on the order of 0.0001 m2/s, to larger values on
the order of 0.2 m2/s for Kh and 0.8 m2/s for Km.
In the early evening from 1755 (LST) to 1840 (LST), Ri for the layer between the two
eddy correlation levels is positive but very small, on the order of 10-2, indicating that the
flow is turbulent or dynamically unstable. During the night when the drainage flow is
well established, Ri becomes greater than the critical value, indicating dynamical
stability of the layer. During the mixing events and breakdown of the drainage flow, the
Richardson number decreases back down to the order of 10-2, corresponding to
dynamically unstable flow. After these periods, the flow becomes more stable, and Ri
once again exceeds the critical value. The gradient Richardson number is a good
indicator of the turbulence generated during the mixing events. However, the gradient
Richardson number not can be used to predict the breakdown, because Ri does not
decrease right before the mixing starts. Ri begins to decrease only when the mixing
starts and the temperature begin to increase. This could means that the breakdown is
caused by turbulence spreading downward from above and is not determined by local
instability, as suggested by the downward transport of vertical velocity variance,
(Section 3.2).
6. Relationships between different variables.
The above discussion is based on only case study nights and we now examine the intervariable relationships for the entire observational period. Figure 10 shows that with
drainage flow down the gully (northerly winds), the turbulence is very weak with w
usually about 0.1 m/s . For these small values, noise and wave-like motions could
account for much of the w values (Figure 11). With elimination of the gully flow and
replacement by southerly winds in the gully, the turbulence and w increases
substantially.
For Ri higher than the critical value, w is usual only about 0.1 m/s and the length scale
Lb is smaller than 0.5 m (Figure 11 a-b). When Ri decreases to smaller values, on the
order of 10-2, Lb and w increases substantially.
For modelling applications, we fit the eddy diffusivites as a function of the gradient
Richardson number. For the functional forms tested, the best form is K= B* ln(Ri) +A.
For Kh, the values are A= -0.0105, B= -0.01028 and the regression coefficient is
R=0.71.
For Km the regression is less successful with R= 0.60, A= -0.0238 and B=-0.0309.
7. Conclusions
This observational study of a nocturnal drainage flow in a shallow gully of
approximately 8-m depth and width of several hundred metres verifies that drainage
flow down the gully is best defined with clear skies and weaker ambient flow. The
drainage flow is only at a few metres deep. If the wind immediately above the gully
flow increases to values greater than about 2 m/s, a critical value of the wind shear is
reached, the flow becomes dynamically unstable and the gully flow breaks down.
However, the origin of this flow acceleration appears to be instability over a much
deeper layer, corresponding to downward transport of vertical velocity variance. At this
time, turbulence mixes momentum and warm air downward and the air temperature in
the gully can increase by more than 6 C. The magnitude of this warming is sufficient to
increase the subsoil temperature and to decrease the upward soil heat flux. During these
mixing events, the gradient Richardson number decrease to the order of 10-2, while w,
the time scale R, the length scale lB and the eddy diffusivities Km and Kk all increase
considerably.
Acknowledgements
This research was funded by the CYCIT (projects CLI95-1794, CLI97-0343 and action
CLI99-326-E). The radiative cooling rate estimates were provided by professor KjungJa Ha of Pusan University.
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Tables
Table I (a)
Time average values of the terms in the temperature budget (2) for the period 2310 to
2400 (LST) during night 20 –21
Budget term
T
t
w
Value (x10-3 ks-1)
1.1
T
z
( w' T '
z
 R

0.10
1.26
-0.26
Table I (b)
Time average values of the terms in the temperature budget (2) for the period 0135 to
0225 (LST) during night 20 –21
Budget term
T
t
w
1.06
T
z
( w' T '
z
 R

Value (x10-3 ks-1)
0.3
2.08
-1.32
Table II
Time average values of the terms in the temperature budget (2) for the period 2210 to
2320 (LST) during night 26 –27
Budget term
T
t
w
7.85
T
z
( w' T '
z
 R

Value (x10-4 ks-1)
1.65
2.1
4.1
Figure Captions
Figure 1: A map of the gully substudy for CASES99. “H”, refers to the Handar sonic
anemometers and “TH” to the thermistors. The meandering broken dotted line is the
gully bottom.
Figure 2: Diurnal variation of 5-minute averaged wind speed and wind direction for the
two sonic anemometers, SA1 and SA2, located on the gully tower at 1.7 and 7.4 m
respectively. (a) night 20-21, (b) night 26-27, October.
Figure 3: The dependence of the north-south wind component in the gully on the
temperature difference between (9.7 m) and (0.2 m).
Figure 4: Five minute averaged temperature and Handar wind vectors.
Figure 5: Two hours evolution of wind components and temperature for the sonic
anemometer located on the gully tower at 1.7 m. Breakdown at the gully flow due to
mixing can be observed during: (a) night 20-21, (b) night 26-27, October.
Figure 6: Diurnal evolution of 5-minute averaged turbulent heat flux calculated from the
two sonic anemometers at 1.7 and 7.4 m respectively. (a) night 20-21, (b) night 26-27,
October.
Figure 7: Diurnal evolution of 5-minute, averaged turbulent momentum flux, calculated
from the two sonic anemometers at 1.7 and 7.4 m respectively. (a) night 20-21, (b) night
26-27, October.
Figure 8: Diurnal evolution of 5-minute averaged, (a) friction velocity (night 26-27
October) and (b) turbulent kinetic energy (night 20-21 October), calculated from the
sonic anemometers at 1.7 and 7.4 m.
Figure 9: Time evolution of subsoil temperature measured at 2 cm deepness.
Figure 10: The dependence of the north-south wind component in the gully on the
standard deviation of the vertical velocity.
Figure 11: The dependence of (a) standard deviation of the vertical velocity and (b) the
length scale Lb, on the gradient Richardson number.