Introduction
Surface turbulent heat fluxes play a significant role in the energy balance of mountain glaciers
, a crucial calculation for assessing melt and mass
balance using meteorological variables. Uncertainty assessment is necessary for sensibility studies
in distributed energy balance models dedicated to glacier melt estimation from meteorological
variables . Generally, energy balance studies precisely assess the radiation
components of the balance, as well as the related errors, but turbulent fluxes and associated errors
remain poorly understood. Commonly, turbulent fluxes are estimated with the bulk-aerodynamic (BA)
method, and only a few studies have relied on direct measurements with the
eddy-covariance (EC) method e.g.. Over
mountain glaciers, several characteristics of turbulent flows challenge the measurement of turbulent
fluxes, such as flux divergence between the surface and the instruments under frequent katabatic
winds , non-equilibrium surface layers related to large-scale orographic
disturbances , temperature overestimates due to strong shortwave radiation and
large surface albedo , or intermittency in weak wind and strong stable
stratification . These characteristics can cause significant errors in estimates of
turbulent fluxes and thus in the energy balance.
On the Alpine Pasterze Glacier, found evidence for the influence of outer-layer
turbulent structures on the surface layer that impacted turbulent fluxes, and
showed that under katabatic winds the BA method underestimated surface fluxes, albeit less so than
when applying the profile method between two measurement levels in the air.
studied the influence of uncertainties in roughness lengths, surface temperature and the choice of
stability corrections on the calculation of surface energy balance on a glacier in the Southern Alps
of New Zealand. studied impacts of uncertainties in roughness lengths and the
ill-defined zero-reference level on turbulent fluxes on the tropical Zongo Glacier in Bolivia. On
the same glacier, compared results of the BA method to those of the EC method and
attributed large underestimates of turbulent sensible heat flux (H) by the BA method to the
influence of katabatic flow oscillations or to the influence of outer-layer, large-scale
structures. However, a comprehensive study of errors is necessary to interpret such a potential
underestimate correctly.
Based on similarity theory, the BA method assumes that the vertical turbulent fluxes of momentum and
sensible and latent heat scale with mean vertical gradients of wind speed, temperature, and specific
humidity inside the surface layer . Divergence from similarity assumptions
or uncertainties in stability functions can lead to large
systematic errors. Random errors mainly result from random uncertainties in measurements or from
poor estimates of roughness lengths . With the EC method, turbulent fluxes are
derived from measurements of air temperature, specific humidity and three-dimensional fluctuations
in the wind speed. Systematic errors can arise from uncertainties in post-field data-treatment
methods, spectral losses at high frequency , underestimating the vertical
velocity component in non-orthogonal sonic anemometers and
nonstationarity of the flow . Random errors result from poor statistical sampling
of the largest eddies of the flow rather
than from the quite small random instrumental noise around measurements
. Finally both methods can be systematically affected by flux divergence,
advection and storage between the surface and the height of the sensors .
On high-altitude Andean tropical glaciers during the dry season, turbulent
latent heat fluxes (LE) are generally an important sink of energy
since they mainly consist of sublimation, which is favoured by the low
atmospheric pressure. The magnitude of H can change significantly between
night and day due to changes in thermal stratification
e.g.. Synoptic forcing generally remains
weak, and thermally driven winds dominate wind circulation .
At night and during the morning, a marked temperature inversion at low height
above the surface (2–3 m) favours the development of katabatic flows
. For weak synoptic forcing, a wind-speed maximum is
frequently observed at low height. Strong synoptic forcing causes strong
winds at the glacier surface, while complex outer-layer interactions with the
surface layer occur . During afternoons of the dry season,
anabatic valley winds are frequently observed , while
the temperature inversion is less marked. Net turbulent surface heat flux
(H+LE) and associated errors may strongly depend on these
wind-regime characteristics. A comprehensive review and quantification of
sources of uncertainties, and comparison of these errors with net turbulent
fluxes under different wind regimes, is required to improve uncertainty
assessment in energy balance studies.
This study is one of few concerning error assessment of turbulent fluxes
measurements on glaciers e.g.. It
focuses on some of the most important errors expected in flux estimates by
the BA and EC methods over the tropical Zongo Glacier. We describe
measurements from a micro-meteorological field campaign performed in the
ablation area during the 2007 dry season from July to September and
associated data analysis. Hourly mean incident and reflected shortwave and
longwave radiation and 2 m temperature, wind speed and humidity were
measured, as were 2 m EC data and temperature and wind-speed vertical
profiles with a 6 m mast. For each of the three wind regimes observed – i.e.
pure-katabatic flows, strong downslope flows and anabatic flows – we derived
H and LE using both the BA and EC methods and calculated their
main systematic and random measurement errors. We then identified the error
sources that most impacted estimates of net turbulent flux and those of
secondary importance. Finally, for each wind regime, we discuss changes in
its net turbulent fluxes and the influence of errors.
Characteristics of the sensors from the automatic weather station,
eddy-covariance systems and profile mast. Shown are random errors in
measurements provided by the manufacturer and those used in this
study.
Quantity
Instrument
Accuracy according to the manufacturer
Accuracy used in this study
Mean sensor height (m)
Profile mast
Aspirated air temperature, ∘C
Type-T thermocouple
0.1 ∘C
0.1 ∘C
0.1, 0.4, 0.6, 0.9, 1.2, 1.5, 1.7, 2.0, 2.7, 3.6, 4.8, 6.0
Wind speed, m s-1
Vector A100L2
1% of reading
0.1 ms-1
0.38, 0.68, 1.05, 1.58, 2.08, 2.78, 3.68, 4.88
Eddy-covariance systems
High-frequency wind speed components, ms-1
Campbell C-SAT3
w: ±0.040ms-1 u, v: ±0.015ms-1
<±0.04ms-1 ±0.015ms-1
1.9 and 2.1
High-frequency sonic temperature, ∘C
Campbell C-SAT3
0.025 ∘C
0.025 ∘C
1.9 and 2.1
High-frequency specific humidity, %
LICOR7500
2% of reading
2% of reading
1.9 and 2.1
Automatic weather station
Aspirated air temperature, ∘C
Vaisala HPM45C
±0.2∘C
±0.2∘C
1.0
and relative humidity, %
3%
3%
Wind speed, ms-1
Young 05103
0.3 ms-1
0.3 ms-1
2.5
Wind direction, ∘
Young 05103
±3∘
±3∘
2.5
Incident and reflectedshortwave radiation, Wm-2
Kipp and Zonen CM3
10% on daily sums
0.4%
0.8
Incoming and outgoinglongwave radiation, Wm-2
Kipp and Zonen CG3
10% on daily sums
0.4%
0.8
Surface elevation changes, m
Campbell SR50
±0.01m
±0.1m
1.5
Location and data
Site and measurements
The site and field campaign are extensively described in
and . A short description is given here for consistency. The
Zongo Glacier is a small (approximately 1.8 km2), high-altitude
(4800–6000 ma.s.l.) Andean Glacier located in the outer tropics of
Bolivia (16∘ S, 68∘ W) in the Cordillera Real.
A micro-meteorological field campaign was conducted in the ablation area at
5080 ma.s.l. from 22 July to 1 September of the 2007 dry season,
during the austral winter. Temperature and wind-speed vertical profiles were
measured using a 6 m high tower with 12 levels for temperature and 8 levels
for wind speed (Table and Fig. ). Data were
sampled every 10 s, and 15 min means were stored on a data logger.
Temperature sensors were shielded and continuously mechanically aspirated.
Two EC systems, measuring the three wind-speed components, temperature and
humidity at 20 Hz, were installed at roughly 2 m above the
ground, on two additional masts. The three masts were separated from each
other by approximately 20 m and aligned perpendicularly to the
glacier flow and to the main wind direction. An automatic weather station
(AWS) recorded half-hourly averages of all radiation components
SWinc, SWout, LWinc
and LWout (SW: shortwave; LW: longwave; subscripts inc and out for incident and
outgoing terms, respectively), wind speed and direction, mechanically aspirated relative
humidity (RH) and air temperature.
The surface below the masts remained homogeneous and relatively smooth
throughout the campaign. It was covered with snow at the beginning of the
campaign. Low melt rates were observed (mean daily melt <1cmSWE). The snow became slightly rougher over time and completely
disappeared from the ablation zone by the end of the campaign. Typical height
changes of the snow or ice surface were 10–20 cm over horizontal
distances of ∼10m . The local slope on the
glacial plateau around the measurement site is approximately ∼5∘.
Overview of Zongo Glacier and the instrumental set-up deployed
during the 2007 dry season campaign. (a) Picture of the glacier,
taken from the moraine at 5080 ma.s.l. The red circle indicates the
location of the measurement site. (b) Picture of the profile mast
and the eddy-covariance (EC) systems. The automatic weather station, located
behind the photographer, is not visible.
Data processing
All data were split into 1 h runs. High-frequency data from the EC systems
were checked for quality , and low-quality runs (∼16%) were discarded. A further ∼17% of the remaining runs
were removed because wind direction was ill-defined or wind blew through the
mast structures. The remaining good-quality runs (GQRs, ∼70% of all
runs recorded) were despiked . Planar-fit rotation
was applied in ∼10-day periods (between two
field visits) to derive longitudinal (u), lateral (v) and vertical (w)
wind-speed components. Use of constant rotation angles over a melting surface
may not be advisable. Since the daily melt rates were low (measured surface
height changes were 1.6 cmday-1) and no noticeable evolution
was reported in the rotation angles calculated on a daily basis, we assumed
the surface changes were sufficiently slow in order to apply the planar-fit
method between two field visits, in ∼10-day periods. Sonic air
temperature was corrected for the influence of water vapour content
. Comparison of aspirated air temperature measurements
from the profile mast with the temperature derived from the nearest
sonic anemometer
revealed residual influence from solar radiative heating, which was corrected
according to . Surface temperature was derived from
LWout assuming a surface emissivity of 0.99
. Since the emissivity of snow and ice can vary from
0.98 to 1.00 , we accounted for this uncertainty when
deriving random errors of surface temperature (see Appendix ).
Meteorological conditions and wind regimes
The austral winter dry season in the Cordillera Real in Bolivia, from May to
August, is characterized by clear skies, with a mean of 20 clear-sky days per
month . The air is dry at this high-altitude site since
more water is needed to reach the saturation pressure. Above the ablation
zone of Zongo Glacier, katabatic flows are regularly observed during the
night and late morning. They are associated with a strong thermal inversion
in the first few metres above the surface and a wind-speed maximum at low
heights, between 2 and 3 m. During the field campaign for these
conditions, we observed a mean wind speed of 1.8 ms-1 (maximum
3.9 ms-1), and the surface layer (the “constant-flux” layer)
was poorly defined .
Synoptic forcing is sometimes strong during the dry season and is associated
with a westerly wind in the Cordillera Real. This flow roughly aligns with
that of the Zongo Glacier, generating moderate to strong downslope winds,
mostly during the night. Under these conditions, we observed a mean wind
speed of 3.5 ms-1 during the campaign (maximum
9.5 ms-1). Temperature stratification in the first few metres
above the ground was also pronounced, but wind-speed maxima were not observed
below 5 m, and the surface layer was more developed .
Anabatic flows (referred to as “upslope” herein) generally occur around
midday and in the afternoon, when the surface is melting or near melting due
to large daytime radiative fluxes directed towards the surface. Due to the
high elevation, air above the glacier is rarely warmer than a few degrees
above 0 ∘C, which results in a nearly neutral thermal stratification
in the first few metres above the surface. During the experiment, wind speed
was moderate under these conditions: a mean of 2.1 ms-1, with
a maximum of 6.8 ms-1.
Cospectra of w with x=θ and of w with x=q measured in
the surface layer of Zongo Glacier during the 2007 field campaign with one of
the eddy-covariance systems adapted from. Cospectra were
calculated over 1 h runs and then averaged over each wind-regime subset. Mean
cospectra for the “upslope” and “downslope” subsets (dotted black line)
and the low-wind-speed “pure-katabatic” subset (solid black line) are presented
with the inertial subrange slope (solid green curve) and the reference Kaimal curve
(dashed red curve) for comparison. The peaks used to calculate
the integral length scale of the method are identified by the vertical
blue lines; LF and HF stand for high and low frequency, respectively. The
high-frequency losses assessed in Sect. are shaded in grey.
For these three wind regimes, low-frequency perturbations affect the
surface-layer flow . The mean cospectra of vertical wind
speed, w, with potential temperature, θ, and those of w with
specific humidity, q, are plotted in Fig. against
normalized frequency n=fz/u‾, where f is frequency, u is the
horizontal wind speed, z is the measurement height, and the overline
indicates a temporal average over a 1 h run. These cospectra reveal that the
low-frequency perturbations observed affect the turbulent fluxes since they
show stronger contributions at low frequency (below n=10-1) than the
reference curve of , which was measured under ideal
undisturbed conditions. At low wind speeds, in pure-katabatic flows, the
low-frequency perturbations likely result from oscillations in the katabatic
flow . When outer-layer forcing is strong, these
oscillations probably originate from interactions between outer-layer eddies
and the surface layer . Under these
conditions, the surface layer is probably out of equilibrium; i.e. local
production of turbulent kinetic energy (TKE) does not balance dissipation
since TKE transport might not be zero
e.g..
Methods
Run selection according to wind regimes
We classified the GQRs into three subsets corresponding to the main wind
regimes (Sect. ) to study characteristics of net turbulent flux
for each regime during the campaign. We tried to consider as many runs as
possible in each wind regime without selecting specific turbulent conditions.
Hence, selection was based only on wind direction and the detection of
a wind-speed maximum below the highest profile measurement.
Runs for which wind direction was downslope (between 260 and 360∘)
and for which a wind-speed maximum was observed below 5 m were
classified as “pure-katabatic” (42 % of the GQRs). The GQRs for which
wind blew downslope and no maximum was observed below 5 m were
classified as “downslope” (26 % of the GQRs). Runs with wind direction
of 45–180∘ were classified as upslope (32 % of the GQRs).
Throughout the text, temporal averages of a variable over the runs from one
subset are noted 〈〉.
Eddy-covariance fluxes
We measured the turbulent fluxes with the two EC systems, following Eqs. () and (),
Hec=-ρ‾cpw′θ′‾,
LEec=-ρ‾Lew′q′‾+WPL,
where downward (upward) fluxes were set positive (negative). The ec
subscript indicates flux estimates derived from the EC method, ρ is the
air density (kgm-3) and cp is the specific heat of humid air
(Jkg-1K-1). The value of Le was set equal to the latent
heat of sublimation of the ice (283×104 Jkg-1) when the
surface was below freezing and to the latent heat of vaporization (250×104 Jkg-1) when the surface was melting. The primes denote
fluctuations of the variables around their 1 h means. The
Webb–Pearman–Leuning term (WPL) generally
remained below 2 Wm-2 throughout the campaign.
Potential random errors in eddy-covariance fluxes
For the EC method, the principal source of random error is poor statistical
sampling of the main transporting eddies . To characterize
this error, we applied the familiar and straightforward (ML)
and (HR) methods. Results are compared with those from
studies applying other methods i.e..The
ML method assumes that temperature and vertical velocity fluctuations are
joint-normally distributed. Under stable conditions, it expresses random
error σF in the flux F as
σFF=2τfP0.51+rwx2rwx20.5,
where τf is the integral timescale (s) of the flux, which
is related to the timescale of the largest transporting eddies of the flow;
P is the temporal averaging period; and rwx is the correlation
coefficient between w and the scalar variable x associated with the flux.
This method requires determining τf, and several methods
have been proposed to calculate it
. We calculated
τf using the cospectra of w and x; the integral
timescale is given by the inverse of the frequency of the maximum in the
cospectra . The mean cospectra, calculated over 1 h runs
and then averaged over each wind-regime subset (Fig. ),
exhibited two distinct peaks in the downslope and upslope subsets but
only one in the pure-katabatic subset . The
high-frequency peak is associated with small-scale fast turbulent eddies,
whereas the low-frequency peak is associated with large-scale slow eddies.
Within a 1 h run, fewer slow eddies are sampled than fast ones, which leads
to larger random errors. Thus we allowed τf to change
according to wind conditions: when a katabatic wind-speed maximum was found
and only a single peak was observed in heat fluxes' cospectra
(Fig. ), we used the frequency of this single peak. When no
maximum was detected below 5 m and two peaks were observed in the
cospectra, we used the frequency of the peak found at lowest frequency,
associated with the largest eddies, which control the random sampling error.
The method is based on the calculation of sub-record
fluxes, i.e. fluxes computed with timescales shorter than 1 h. It
evaluates the random error from the within-run variance of the sub-record
fluxes. The method is based on similar assumptions to
the ML method. A filter of changing time constant is applied to the 1 h flux.
Filtered fluxes with increasing time constant converge to the 1 h averaged
flux following a power law. show that the parameters of
this power law can be related to the random error in the flux. Both methods
have the advantage of not requiring an estimation of the integral timescale.
In contrast, the HR method assumes that two EC systems installed in separated
locations – but over similar terrain, wind conditions and fetch – measure the
same flux independently. This assumption holds if they are located far enough
from each other so that the largest eddies do not influence both sensors at
the same time. Let F1 be hourly fluxes measured with the first EC system,
F2 be those measured by the second one, and the true value of the flux be
F. If the conditions described above are fulfilled, the mean value of
F1-F2 during the campaign is 0. We have (i=1 or 2):
Fi=F+δFi,
where δFi is the random measurement error in each flux, which is
a random variable with mean 0 and standard deviation (SD) σ(δFi).
Since the mean F1-F2 is 0, the variance of F1-F2 is equal to the
variance of δF1-δF2:
σ2(F1-F2)=σ2(δF1)+σ2(δF2)+2cov(δF1,δF2).
And then, since the δFi are assumed to be independent, we have
σ(δF)=12σ(F1-F2),
where δF=δFi. The SD of δF provides an
estimate of the random error in the flux. This method requires collecting
enough pairs of flux samples representing each reported wind condition to calculate
a typical random error for each. We measured
12σ(F1-F2) over equally spaced bins of wind speed
over the 3 weeks of the campaign when both EC systems were available.
The effect of random instrumental noise on fluxes is expected to be small
because the C-SAT3 and the LICOR7500 are accurate sensors with small
measurement errors (Table ). The ML and HR methods implicitly
include this source of error , and we do
not calculate its individual contribution.
Potential systematic errors in eddy-covariance fluxes
Non-orthogonal sonic anemometers may underestimate vertical wind velocity
. Underestimates are larger when the
wind-attack angle, relative to the horizontal plane of the sonic anemometer,
increases, which can lead to underestimating fluxes by as much as 15 %.
Corrections have been proposed for several sonic anemometers
. To evaluate the
degree to which this error could affect our measurements, we selected runs
during specific events for which wind conditions were representative of the
three main wind regimes. For each event we compared the covariances of w
with θ and q, obtained without any correction related to the attack
angle, and covariances obtained after correcting the wind components for
transducer shadowing following the method proposed by . The
relative difference between these two covariances, plotted against ω,
the attack angle relative to the u-v plane of the instrument, helps us to
evaluate the degree of flux underestimation in each wind regime.
also showed that sensible heat fluxes at high wind speeds
might be underestimated in some EC systems (above 8 ms-1) due to firmware issues. This error may not be
of concern on Zongo Glacier, where wind speed remains moderate (Sect. ), but may be of importance over other glaciers where wind speed
is higher.
Flux losses at high frequency may occur due to inability of the EC system to
sample the fastest, small-scale eddies because of sensor path averaging or
because of sensor separation when the variable considered for the flux is
measured separately from wind-speed fluctuations . This
error is usually corrected using frequency-response corrections and transfer
functions e.g.. The method assumes a theoretical shape
for the cospectra. Since the cospectra measured on Zongo Glacier were
influenced by low-frequency perturbations and did not follow commonly
expected forms (Fig. ), we did not use this method. Instead,
we estimated these losses by adjusting, for the mean cospectra for each wind
regime, an inertial subrange curve that follows a n-5/7 slope
. The cospectra were adjusted over the frequency range in
which the expected inertial subrange slope was observed, i.e. from their
peak at n=5×10-1 up to the frequency at which the cospectra
deviated from the inertial subrange slope (Fig. ). Between
this frequency and the high-frequency end at n=101, deviations from the
n-5/7 slope were attributed to high-frequency losses
(Fig. ).
Insufficient averaging time can lead to incomplete sampling of the largest
eddies and to flux losses at low frequency and thus to systematic
underestimates of flux. Nevertheless, long averaging times would include
spurious fluxes due to changes in the state of the turbulent flow under the
effect of changes in external forcing, i.e. nonstationarity. A good choice
for the averaging timescale is a trade-off between these two constraints. To
check if the 1 h averaging timescale was appropriate, we calculated
multi-resolution decomposition MRD; cospectra of w
with θ and of w with q. This decomposition isolates the
contributions to H and LE coming from increasing timescales as if
the fluxes were estimated using increasing averaging periods. The sampling
must be long enough so that the MRD cospectra fall to zero at the longest
timescales considered. Another application of this method is identification
of a gap scale between the timescales of fast turbulent eddies and the
nonstationary fluctuations induced by the slowest motions.
Bulk-aerodynamic method
Sensible heat fluxes H and latent heat fluxes LE were estimated by
applying the BA profile method between the surface and
each of the eight measurement levels of wind speed and the corresponding
temperature levels from the profile mast (Table ). The
subscript ba on H and LE refers to fluxes estimated by
this method. Specific humidity was calculated from relative humidity measured
at the AWS and ventilated temperature profiles (see Appendix
). We have
Hba,j=ρ‾cpk2u‾j(θ‾j-θ‾s)lnzjz0-ψmzjL*lnzjzt-ψhzjL*,
LEba,j=ρ‾Lek2u‾(q‾j-q‾s)lnzjz0-ψmzjL*lnzjzq-ψqzjL*,
with the same sign convention as for the EC method. The subscripts j and
s refer to the jth wind-speed measurement level and the surface
level, respectively. The von Karman constant k was set to 0.4. The length
scale L* is the Obukhov length, defined as
L*=-θv‾u*3kgw′θv′‾,
with u* being the friction velocity and the subscript v referring to
virtual temperature. Stability corrections for momentum, sensible heat and
humidity transfers (respectively, ψm, ψh and ψq) were taken
from . The different forms of these corrections are
given by the following equations, where the variable x is defined as
x=(1-16z/L*)1/4. If z/L*<0, we have
ψm=2ln1+x2+ln1+x22-2arctan(x)+π2,
ψh=ψq=2ln1+x22;
if 0<z/L*<1, we have
ψm=ψh=ψq=-5zL*;
and if z/L*>1, we have
ψm=ψh=ψq=-5lnzL*+1.
The length scales z0, zt and zq are the momentum, thermal and
humidity roughness lengths (m), respectively. They were derived from
least-square iterative fitting of the mean temperature and wind-speed
vertical profiles and assuming zq=zt
. We use their median values, z0=2.07×10-3
m and zt=0.09×10-3 m, since they did not vary
significantly during the campaign.
The bulk formulation is designed for surfaces normal to the gravity vector
and might not be suitable for sloping surfaces under the influence of slope
flows e.g.. In that case, the formulation of
the Obukhov length in Eq. () may have to be modified to include
scalar fluxes tilted to the gravity vector .
We did not attempt to derive such a formulation in the present study. Rather,
we resorted to quantifying the bias of turbulent flux measurements over
glaciers resulting from the use of the bulk method in its conventional,
horizontal-surface form, which is typical of most glacier energy
balance studies.
Potential random errors in the bulk fluxes
We estimated errors of the fluxes derived from the BA method arising from
random noise around the measurements both analytically and with Monte Carlo
simulations. For error propagation in the functions H and LE=f(Δu,Δ(θ,q),z,z0,zt,q) (Eqs. and
), we used a local linearized model, assuming that the errors
were independent, normally distributed, and smaller than the partial
derivatives (δ are expected measurement errors, and Δ are
differences between the measurement height and the surface):
(δH)2=∂H∂u‾2(δu‾)2+∂H∂Δθ‾2(δΔθ‾)2+∂H∂z2(δz)2+∂H∂z02(δz0)2+∂H∂zt2(δzt)2,(δLE)2=∂LE∂u‾2(δu‾)2+∂LE∂Δq‾2(δΔq‾)2+∂LE∂z2(δz)2+∂LE∂z02(δz0)2+∂LE∂zq2(δzq)2.
Detailed calculation of each term on the right-hand side is found in Appendix .
We assumed the stability corrections were constant under
small variations δu‾, δΔθ‾,
δΔq‾ and δz, which greatly simplifies the
calculations. The effects of this simplification are discussed in Sect. . Values of δu‾, δΔθ‾, δΔq‾ and δz were
adjusted according to the expected errors for wind speed, air temperature,
relative humidity and height, respectively (Table ). The
manufacturer provides a value of δu‾ of 1 % of the
reading, but when wind speed is low the error may not tend to zero, so we
set it to 0.1 ms-1. The error in Δθ‾ was
set to 0.35 ∘C, larger than the expected thermocouple random noise
(σθ=0.1∘C, Table ), since
Δθ‾ was affected by surface temperature errors
(see Appendix ). The random error in Δq‾
depends weakly on the random error in air temperature and strongly on the
error in relative humidity (see Appendix ). We set the random
error in Δq‾ to 3 %, equal to the error in the relative
humidity. The sounding height ranger is quite accurate (±0.01 m),
but the surface was irregular at a local scale, so its error was set to
±10 cm. We used δz0 and δzt values derived from
the error analysis of : δlnz0=δlnzt=1.5.
The Monte Carlo-based error estimate was obtained, for each measurement, by
simulating 1000 dispersed measurements with a Gaussian random function whose
mean equaled the measurement and whose SD equaled the
expected random instrumental error previously mentioned. From these dispersed
data, we recalculated 1000 estimates of turbulent fluxes for each run and
profile level. Random errors in mean fluxes of a subset were calculated as
the interquartile range of the 1000 mean fluxes obtained from the simulated
measurements.
Potential systematic error in the bulk fluxes
Systematic errors in the BA method could originate from systematic biases in
the measurements. Air temperature can be overestimated due to heating of the
shelters by shortwave solar radiation . This bias was
considered negligible, however, since the air-temperature shelters were
continuously artificially aspirated, and residual deviations during clear-sky
days were corrected using air temperature derived from the EC systems
. Surface temperature measurements, derived from
measurements of the longwave emission of the snow or ice surface with
pyrgeometers, can be overestimated. This is due to the penetration of
shortwave radiation through instrument filters and heat transfers due to
heating by shortwave radiation of instrument domes .
This effect was evident during the day since estimates of surface
temperature reached 1.5 ∘K above the melting point. We tested
the impact of this bias on flux estimates by using two methods to correct it.
The first method set the surface temperature to 0 ∘C when the
raw estimate based on outgoing longwave radiation exceeded
0 ∘C ; we called this method
“Ts-blocking”. It gave an upper boundary for surface
temperature. The second method was inspired by ; we
corrected the outgoing longwave emission by a percentage of
SWinc. We chose to use a percentage of 0.6 %, half the
value of , since it yielded a surface temperature near
0 ∘C when field observations reported snow or ice melt. We
called this second method “Ts-corrected”.
The error related to the ill-defined zero reference level was studied by
. They showed that this effect had a weak influence on
final turbulent heat fluxes since the ablation zone of Zongo Glacier
remained quite smooth during the campaign.
Random error in fluxes derived from the eddy-covariance (EC) method
and covariance of fluxes between the two EC systems. (a) Change in the
random error (Wm-2) in sensible heat flux H over equally spaced
intervals of wind speed (width: 1 ms-1). Results are from the Hollinger
and Richardson (HR) method (blue line and circles) and the Mann and Lenschow (ML)
method (red line and circles). Small red circles indicate estimates of the ML method
for individual runs. (b) Results of the the HR and ML methods applied to
latent heat LE estimates. (c) Cospectra between the w′T′
time series of both EC systems. Results are for downslope (blue), “upslope” (red)
and “pure-katabatic” (black) subsets. Circles indicate medians of cospectral
values over equally spaced logarithmic intervals of normalized frequency. (d)
Cospectra between the w′q′ time series of both EC systems,
using the same notation as for w′T′.
We also studied systematic errors related to unmet theoretical requirements
that could affect the BA method. First, advection or divergence of fluxes
below the sensors could be high when the surface layer was not well
developed, especially when a katabatic wind-speed maximum occurred at a low
height under low-wind-speed conditions . This probably led to
underestimating surface fluxes when they were assessed too high above the
ground, which also affected the EC method. Estimating fluxes with the BA
method, applied with increasing measurement heights on the profile mast,
helped us to document this issue. Second, low-frequency perturbations
affected the surface-layer flow (Sect. ). The additional TKE
induced intermittently by low-frequency perturbations probably did not scale
with mean gradients in the surface layer, potentially causing underestimates
of flux . Comparisons with the EC-based fluxes were used to
document this bias. Finally, use of inadequate stability functions could also
induce biases. The most commonly used functions lead to underestimating
fluxes since they do not account for intermittency under strong stable
conditions e.g.. These cases are related to
small fluxes under weak turbulent mixing, of secondary interest for surface
energy balance studies. Furthermore, this bias is expected to be small on
Zongo Glacier since the mean value of the bulk Richardson number
(Rib) between the first and fourth profile
levels was 0.07 . For this low stability, the formulas do
not differ much from each other, and intermittency related to weak wind and
strongly stable stratification is not a concern.
Overview of turbulent fluxes and related random errors calculated with the
eddy-covariance (EC) method and bulk-aerodynamic (BA) method using the fifth level
of the profile (∼2m height). Time occupied by the subset in the
campaign (first column), net turbulent exchange (H+LE) for each wind regime and its
ratio (%) to total net turbulent exchange of good-quality runs (GQRs) (second column), share
of H and LE in the net exchange and mean flux exchange over the GQRs (third and fourth columns).
Relative random errors calculated with the (for EC fluxes) and Monte Carlo
(for BA fluxes) methods in individual H and LE fluxes and net turbulent fluxes
(fifth to seventh columns). The two last lines show results obtained for all GQRs.
Time coverage
Net turbulent exchange and ratio to total net exchangea
Share of turbulent exchangeb due to H
Share of turbulent exchangeb due to LE
Relative random error on H+LE
Relative random error on H
Relative random error on LE
Pure-katabatic
42 %
(kJm-2)
EC
3574, 15 % ± 5 %
54 % (19 Wm-2)
46 % (-16Wm-2)
34 %
4 %
6 %
BA (fifth level)
-648, 5 % ± 2 %
46 % (6 Wm-2)
54 % (-7Wm-2)
35 %
6 %
4 %
Downslope
26 %
(kJm-2)
EC
-3547, 15 % ± 9 %
48 % (49 Wm-2)
52 % (-54Wm-2)
60 %
4 %
5 %
BA (fifth level)
-1256, 9 % ± 4 %
48 % (-31Wm-2)
52 % (-33Wm-2)
39 %
5 %
4 %
Upslope
32 %
(kJm-2)
EC
-23 554, 100 % ± 15 %
19 % (10 Wm-2)
81 % (-42Wm-2)
8 %
8 %
6 %
BA (fifth level)
-11 720, 86 % ± 6 %
21 % (6 Wm-2)
79 % (22 Wm-2)
4 %
6 %
4 %
Mean flux over the campaign
100 %
(Wm-2)
EC
-10
43 % (24 Wm-2)
58 % (-34Wm-2)
12 %
2 %
3 %
BA (fifth level)
-6
41 % (13 Wm-2)
59 % (-19Wm-2)
6 %
3 %
3 %
a Ratios to total net exchange were calculated as |〈H+LE〉|sub|〈H+LE〉|all, where the subscripts “sub” and “all” refer to averages over the subset considered and to averages over all availableruns during the campaign, respectively. The percentages after the ± sign indicate the SD of, or uncertainty in, this ratio.b The share of turbulent energy due to individual H and LE fluxes was calculated as |〈H〉|sub|〈H〉|sub+|〈LE〉|sub and |〈LE〉|sub|〈H〉|sub+|〈LE〉|sub.
Results and discussion
Eddy-covariance method
Random error calculations
The random error in Hec and LEec increased
with wind speed for the Mann and Lenschow (ML) method and did not change
significantly with wind speed for the Hollinger and Richardson (HR) method
(Fig. a and b). Both methods provided similar estimates for low
wind speeds below 2–3 ms-1, which represented the majority of
runs (u‾<2 ms-1 58% of time; u‾<3
ms-1 88% of time). For higher wind speeds, the random
error predicted with the ML method increased and was larger than that of the
HR method, which remained constant. Large random errors were probably due to
poor sampling of large-scale outer-layer structures, which were frequently
observed in the downslope and upslope subsets when wind speed was
high (Sect. ). We chose to use the highest error derived from the
ML method in the rest of this study. In relative terms, for hourly fluxes,
the random errors in Hec (LEec) derived
from the ML method were between 22 and 60% (between
36 and 98%). The same orders of magnitudes but slightly lower
values were derived by with their method, during the night
over a maize field (19% for H and 23% for LE). With their
filtering method found much lower values (10%) for
the random error on H for data collected in California. Interpreting these
differences is not straightforward since the context of
and was very different from ours. This comparison suggests
that our method tends to maximize the errors.
The HR method was probably not adapted for estimating errors using the
EC-mast configuration available, considering the flow characteristics
observed. In upslope and downslope subsets, outer-layer eddies that
interacted with the surface layer moved through the sensors in
50–100 s at wind speeds of about 3 ms-1
, which indicated that they were larger than the distance
between the two EC systems (roughly 20 m, Fig. ).
Under these conditions, fluxes measured by the two EC systems may not be
independent since they originated from the same eddies. This is confirmed by
analysing the spectral dependence of the covariance of fluxes between the two
EC systems (Fig. c and d). For low wind speeds in the
pure-katabatic subset, the covariance of fluxes from both EC systems was
near zero at all frequencies. For high wind speeds in the upslope and
downslope subsets, significant covariance was found at low frequency
(n<10-2), whereas near-zero covariance was found at high frequency
(except for the small sensible heat fluxes in the upslope subset). Fluxes
derived from each EC system were independent at short timescales but were
not so at the timescale of large eddies. This may explain why HR error
followed ML error at low wind speeds but was smaller at high wind speeds.
The ML method estimated the errors induced by poor sampling of the large
outer-layer structures by using an adapted τf, whereas the
HR method could not estimate it correctly.
On average, the relative random error was 34 % (Table ) of
net EC fluxes in the pure-katabatic subset. Relative random error was the
largest (60 %) for the downslope subset because net fluxes were weak
for this regime, and high wind speed was associated with large random errors
(Fig. a and b) due to the presence of outer-layer structures.
Relative random error was the lowest (8 %) for the upslope subset
because net fluxes were the largest for this regime. Over the campaign,
relative random errors derived from the ML method cancelled out to a mean
value of 12 %.
Estimates of systematic errors
Relative difference between covariances corrected with the
method and uncorrected covariances for one of the EC systems are shown in
Fig. , for selected cases whose characteristics were
representative of the three wind-regime subsets. The difference is shown for
different attack angles. For most attack angles, corrected fluxes are between
3 and 6 % larger than the uncorrected fluxes, in agreement with findings from
. Corrections larger than 6 % are found only for the
pure-katabatic case, for both H and LE between -10∘
and 0∘ attack angles, and for LE in downslope cases
above 25∘ attack angles. On average over all attack angles, the
correction remains small; it is 5.6, 3.7 and 3.6 % for H in the
pure-katabatic, upslope and downslope cases, respectively, and
5.7, 3.9 and 2.6 % for LE, respectively. Consequently, we
assume that roughly both sensible heat and latent heat fluxes were
underestimated by about 6 %, as an upper boundary.
Relative difference between uncorrected covariances
(w′x′‾, x=θ,q) and covariances corrected for transducer
shadowing (w′x′‾c) for different attack angles and selected events
inside each of the main wind-regime subsets. Results for (a) w′θ′‾
and (b) w′q′‾ during “pure-katabatic” (black), “downslope”
(blue) and “upslope” (red) events are shown.
High-frequency losses calculated from the mean cospectra of w with θ
and with q were slightly more pronounced for latent than for sensible heat
fluxes, probably because latent heat calculations were affected by sensor
separation between the C-SAT3 and the LICOR7500 (about 0.30 m). We
also checked the ratio between the flux at the shortest timescales of the
MRD cospectra (i.e. estimated from two instantaneous measurements at
20 Hz) and the flux at the observed gap scale. If this ratio is low,
high-frequency losses must also be low . MRD cospectral
ratios and losses calculated with Fourier cospectra remained small for the
three subsets (∼3–4%, Table ), showing that
high-frequency losses were probably not too large.
Evaluation of high-frequency losses in Hec and LEec
fluxes. Spectral adjustment: percentage of flux losses estimated by adjusting an
inertial subrange on the high-frequency end of the mean cospectra of w with θ
and of w with q, for the three wind-regime subsets. Multi-resolution decomposition (MRD) ratio:
median ratio calculated over each subset of fluxes calculated at the shortest timescale of the MRD
cospectra and the flux calculated at the gap scale of the MRD cospectra.
Method
Upslope
Katabatic
Downslope
H
Spectral adjustment
2 %
2 %
2 %
MRD ratio
4 %
7 %
6 %
LE
Spectral adjustment
2 %
4 %
3 %
MRD ratio
2 %
3 %
3 %
Multi-resolution decomposition (MRD) cospectra (black lines)
of w with θ (upper panels, a, c and e)
and of w with q (lower panels b, d and f) from
individual runs of “pure-katabatic” (left, a and b),
“downslope” (centre, c and d) and “upslope” (right, e
and f) wind-regime subsets. Quantiles 25, 50 and 75 of the cospectra
at each dyadic timescale calculated over a subset (red curves) and the zero line (blue line) are plotted.
Results of random-error calculations using the bulk-aerodynamic
method for the fifth level (∼2.08m) of the profile mast.
(a) Change in individual random-error terms during the campaign
estimated with the analytical method: z0 error (black), zt,q error
(orange), θ error (red), u and q error (blue), and z error (green).
(b) Change in the random error in net turbulent flux during the campaign,
calculated with the Monte Carlo (black) and analytical (red) methods.
Mean turbulent flux exchange in the “upslope” (red), “pure-katabatic”
(black) and “downslope” (blue) wind regimes estimated with the bulk-aerodynamic
method and different profile mast levels, plotted against the height of measurement.
Results show dispersion from Monte Carlo simulations. The middle line in box plots
indicates the median, the boundaries of the boxes the quantiles 25 and 75 and the
whiskers the quantiles 5 and 95. Box plots of eddy-covariance (EC) flux influenced
by the error estimated using the Mann and Lenschow method are highlighted in grey
circles. Results are for (a) latent heat, (b) sensible heat and
(c) net turbulent flux.
Mean daily cycle calculated for the entire campaign, from midnight to
midnight local time (LT), of raw estimates of surface temperature (black),
surface temperature derived from the “Ts-blocking” method
(red), surface temperature derived from the “Ts-corrected”
method (blue) and incoming shortwave radiation (green).
Turbulent fluxes derived from the bulk-aerodynamic method for the
fifth measurement level on the profile mast (∼2.08m) with different
surface-temperature derivation methods over the entire campaign. (a)
Time series of fluxes H and LE estimated from surface temperature
derived from LWout measurements corrected with the “Ts-blocking”
method. (b) Net turbulent flux estimated with surface temperature corrected
with “Ts-blocking” (red) and “Ts-corrected” (blue)
methods (Sect. ).
The MRD cospectra of w with θ and with q for the three subsets are
shown in Fig. . In the pure-katabatic subset, no clear
separation appeared between short-timescale and long-timescale
contributions to fluxes. Starting from between 100 and 101 s,
towards longer timescales, contributions to fluxes evolved erratically
around zero (Fig. a and b). At the longest timescales, their
median contribution fell to zero, and the interquartile range of the
dispersion was comparable to the magnitude of the peak at the short
timescale (around 100 s). The 1 h sampling time was probably too
short to capture significant flux at the longer timescales, but on average
over several runs this led to a random error rather than to a systematic
bias. In the downslope subset, cospectra fell asymptotically to zero
towards the longest timescales, as a median over all the runs, and so did
dispersion (Fig. c and d). The fluxes seemed correctly sampled
with a 1 h averaging time. In the upslope wind regime, w and q
cospectra were similar to those of the downslope subset; thus, latent heat
flux seemed correctly sampled, but sensible heat flux remained weak, and the
cospectra of w with θ were small and erratically dispersed around
zero (Fig. e and f).
These results suggest that systematic errors in EC fluxes led to
underestimating the fluxes. The main source of underestimation was probably
related to potential underestimates of w in non-orthogonal
sonic-anemometers (∼6%, Fig. ). Putting aside
flux divergence between the surface and the sensors and including the
high-frequency spectral losses (∼4%, Table ),
underestimates from the EC method could be as large as 10 %.
Bulk-aerodynamic method
Random error calculations
At a height of 2 m, the fifth level on the profile mast, the largest
contribution to random errors came from roughness length uncertainties
since they were poorly known (Fig. a). This was also
observed for the other measurement heights (not shown). The second-largest
random error arose from temperature uncertainties. The errors in Δu
and Δq were of secondary importance for the fluxes. The random error
resulting from height uncertainty was the lowest (green curve, barely visible
in Fig. a). Analytical and Monte Carlo-based
error-calculation methods produced similar results (Fig. b).
The Monte Carlo method predicted slightly larger uncertainties, probably
because it accounted for variations in stability functions due to measurement
errors, which were ignored in the analytical calculations. In relative terms
(not shown), the difference was <5%. We used Monte Carlo analysis in
the rest of this study since it provided an upper boundary to the error.
Random errors decreased with increasing measurement height
(Fig. ), probably because random measurement errors
(δu, δθ, δq, δz or δz0,t,q)
had similar magnitudes, whereas differences (Δ) between air variables
and surface variables increased.
At the fifth level (2 m height), total relative random error, calculated
as the interquartile range of all H+LE estimates obtained from
Monte Carlo runs divided by their median, was sometimes as large as
30–40 % (≃20Wm-2 in absolute value,
Fig. ) of net fluxes at hourly time steps. Random errors in
repeated measurements of the same variable tend to cancel out; thus,
cumulative random errors for the entire campaign were reduced to
∼6% (Table ). Since net turbulent fluxes were small for
the downslope subset and random errors were high, no clear cancellation
of the random errors was observed for this subset, and they remained
relatively high on average (39 %, Fig. and
Table ). Similarly, the median relative random error was 35 %
for the pure-katabatic subset. It was only 4 % for the upslope
subset since net turbulent fluxes were high for this subset.
Estimates of systematic errors
In the pure-katabatic subset, the magnitude of BA-based H, LE
and their sum decreased as measurement height increased
(Fig. ). At a 2.0 m height (fifth level), sensible
(latent) heat flux was 90 % (62 %) of that obtained at 0.70 m
(second level). Higher up, at 5 m (eighth level), this flux was only
17 % (16 %), probably due to the shallow depth of the surface layer
when a wind-speed maximum was observed at low height, around 2.0 m
.
Vertical divergence was also observed in the downslope and upslope
subsets but was significant only at heights greater than 2.0 m. We
found similar latent and sensible heat fluxes at 2.0 and 0.7 m, but
those at 5.0 m were only 70–80 % of those at 0.7 m. When
no wind-speed maximum was observed, the surface layer was probably slightly
thicker than that in the pure-katabatic regime, due to increased mixing
induced by higher wind speeds , but its extent
above the ground probably remained low. Nevertheless, our observations show
that measurements at a height of 2 m provide reliable estimates of surface
fluxes in downslope and upslope wind regimes. For all wind regimes,
the relative thinness of the surface layer probably also led the EC method to
underestimate surface fluxes.
During the day and when the surface was not melting, surface temperature from
the Ts-blocking method was often slightly warmer than that
from the Ts-corrected method (Fig. ). In
general, the Ts-blocking method predicted greater losses of
turbulent energy (Fig. b). Averaged over the campaign, the
magnitude of net turbulent fluxes estimated with the
Ts-corrected surface temperature was 56 % (≃4Wm-2) of that estimated with the
Ts-blocking surface temperature. This percentage was
64 % (≃10Wm-2) in the upslope subset. Because
net turbulent fluxes were low in the pure-katabatic and downslope
regimes, the relative difference was large, but less than 2 Wm-2
in absolute value.
A warmer surface reduces the temperature gradient and thus the sensible heat
flux, and it also increases qs and thus Δq, leading to
higher sublimation rates. When shortwave radiation influenced longwave
radiation measurements, but actual surface temperature was below
0 ∘C, the Ts-blocking method probably
overestimated surface temperature because it applied no corrections in such
a case (Fig. ). When uncorrected radiative temperature was
above 0 ∘C, but the surface was not melting, the
Ts-blocking method set the surface temperature to
0 ∘C (Fig. ), also leading to
overestimation of the temperature. In contrast, the
Ts-corrected method is physically based, and the correction
was tuned to obtain a surface temperature of 0 ∘C when we
observed melt during field trips. In this sense, the
Ts-corrected method seems more accurate than the
Ts-blocking method. Still, the former may still be
inaccurate and lead to uncertainties in surface temperature. This shows that
determining surface temperature is a critical point when estimating turbulent
fluxes with the BA method since it has a strong influence on flux estimates.
Since the Ts-blocking method provided an upper boundary to
surface temperature, it also provided an upper boundary to the magnitude of
the net turbulent fluxes derived from the BA method.
At a 2 m height, the BA predicted considerably smaller flux
magnitudes than the EC method for all subsets (Fig. , grey
circles), which suggests that a strong bias affected one or both methods.
Correcting for surface-temperature biases in the BA method, likely leading to
lower net fluxes in magnitude, and correcting the EC method for its
underestimates would lead to an even larger discrepancy between the fluxes
from both methods. Random errors in the BA-based and EC-based fluxes were too
small to explain this difference (Fig. ), except for
downslope net fluxes. Horizontal variability in fluxes between the masts
was probably negligible since the surface remained homogeneous and the
fluxes provided by both EC systems were similar (mean differences
<1Wm-2). The most reliable explanation is that the
interaction of outer-layer coherent eddies with the surface-layer flow or
oscillations in the katabatic flow induced turbulent mixing that did not
scale with local mean gradients, and thus that the BA method did not account
for a portion of the fluxes . Similar studies in
nonstationary turbulent flows showed that stability functions may be
overestimated, leading to systematic underestimates of fluxes
. Alternative formulations for Eqs. ()
and () that account for this influence cannot be derived easily
because the assumptions of similarity theory no longer apply to the flow in
these situations. Underestimates of net turbulent fluxes were significant
only for the upslope subset (〈H+LE〉ba,5 was only 16 Wm-2 when 〈H+LE〉ec was ∼32Wm-2,
Fig. ).
Net turbulent fluxes and wind regimes
During the 2007 campaign on Zongo Glacier, sublimation was high (-19 to
-34 Wm-2, Fig. a and Table )
because the air is very dry at high elevation due to its cold temperature and
low density. Sensible heat flux was generally opposite in sign to latent heat
flux but, on average, lower in magnitude (13–24 Wm-2
Table ). Net turbulent fluxes resulted in a loss of energy for
the glacier (Fig. b).
During the night, for downslope and pure-katabatic subsets,
temperature inversion in the first few metres above the surface favoured
downward sensible heat fluxes. When a katabatic wind-speed maximum was
observed at low height, sensible and latent heat fluxes were weak, the
closest to zero of all subsets (∼10Wm-2 at the fifth
level, Figs. and a), mainly because wind
speed was low. In downslope flows, due to strong winds, both sensible and
latent heat fluxes had large magnitudes (30–55 Wm-2 at a 2 m
height, Figs. and a). Net turbulent flux
was generally near zero in these two cases because the sensible heat flux was
opposed in sign and nearly equal to latent heat flux (Table ).
Systematic underestimation of fluxes by the BA method, due to the influence
of low-frequency perturbations, was similar in magnitude for H and
LE, and partly cancelled out in net turbulent flux. The BA method
predicted near-zero net fluxes, while the EC method predicted small losses in
the downslope subset and small gains in the pure-katabatic subset.
The effect of surface-temperature biases on BA fluxes probably remained
negligible because these regimes mainly occurred during the night, when solar
radiation was zero. Underestimates of flux by the EC method due to potential
underestimates of vertical wind speed probably cancelled out in net fluxes
since we considered that they were of the same magnitude for H and
LE.
These two types of downslope flows were dominant (68 % of the time) but
of secondary importance in net turbulent flux exchange during the campaign:
ratios of ∼15% between the mean net turbulent flux over these
subsets and the mean over the campaign are found with the EC method
(Table ). Since net turbulent fluxes were small, one may argue
that the significant divergence of fluxes (pure-katabatic subset) with
height and the large relative random errors (34 % in the
pure-katabatic and 60 % in the downslope subset) were probably
not a concern. However, the high uncertainty in flux leads to non-negligible
uncertainties in the contribution of these regimes to net turbulent exchange
over the campaign, which remains ill-defined, especially for the
downslope regime (Table ).
For the daytime upslope subset, sensible heat flux was low (a few watts
per square metre) because stratification in the first few metres above the
surface was near-neutral, but latent heat losses remained high
(-25 Wm-2, Figs. and a;
Table ) since humidity gradients remained large; thus, net
turbulent flux was largely negative (Fig. b). Although this
regime was observed only 32 % of the time, it contributed significantly
to net turbulent exchange during the campaign: ratios of 86 and 100 %
between mean net turbulent flux over the subset and that over the campaign
are found for the BA and EC methods, respectively (Table ). Since
the net flux magnitude was high, relative random error derived from the ML
method remained moderate (8 %), and relative random error in net BA
fluxes was low (4 %). Errors in BA-method fluxes due to
surface-temperature uncertainties were probably high if the surface was not
melting during the daytime regime (Fig. b). Systematic errors
due to the influence of low-frequency perturbations did not have the same
magnitude in the small H as in the significantly negative LE,
which led to large systematic bias in net turbulent fluxes in the upslope
subset. Underestimates of fluxes H and LE due to underestimating
vertical wind speed probably did not compensate each other in net turbulent
fluxes, because H and LE were not of the same magnitude, and this
error should be considered with caution. The divergence with height was
moderate (8 % loss in net fluxes at 2 m, 20 % at
5 m), which suggests that this error is of secondary importance for
flux measurements at a 2 m height in upslope flows.
Overall, error analysis shows that the BA method severely underestimated the
magnitude of net turbulent fluxes. On average over the campaign, they were
only 60 % of net EC fluxes (Table ), an underestimation most
likely due to the inability of the BA method to account for the flux induced
by katabatic oscillations or outside-layer interactions with the surface
layer. These influences lead to nonstationarity of the flow and flux
divergence above the ground and thus to divergence from the required
conditions for similarity to hold, which may explain the observed flux
underestimations.
Conclusions
We calculated turbulent sensible (H) and latent (LE) surface heat
fluxes during a micrometeorological field campaign deployed at
5080 ma.s.l. in the ablation zone of the tropical Zongo Glacier
during 1 month of the austral winter of 2007. Both eddy-covariance (EC) and
bulk-aerodynamic (BA) methods were applied. We calculated the related random
errors in each flux and qualitatively estimated the main systematic errors.
We studied the importance for total turbulent energy transfer during the
campaign of the three dominant wind regimes: weak katabatic flows with
a wind-speed maximum at low height (∼2m), strong downslope
flows without a wind-speed maximum at low height, and moderate daytime
upslope flows. We finally studied the influence of errors in total net
turbulent fluxes.
In general, fluxes H and LE were a gain and a loss, respectively,
of energy for the glacier. Whereas turbulent fluxes had high magnitudes under
strong downslope flows, this regime was of lesser importance for net
turbulent flux because H and LE were of the same magnitude and
canceled out. The katabatic regime also had small fluxes that cancelled out.
The highest flux losses occurred during upslope flows because fluxes H
were low during the day due to a small temperature difference between the air
and the surface, whereas sublimation (LE<0) remained high due to
large humidity gradients .
For moderate-to-high-wind-speed conditions (>3ms-1) in
upslope and strong downslope flows, large outer-layer eddies interacted with
the surface flow, and large random errors in the EC method originated from
poor statistical sampling of these structures. The random error was moderate
when wind speed was low. We showed that the method, when
applied with the mast configuration of the 2007 campaign, was not adapted for
deriving sampling errors due to the presence of large-scale eddy structures
because the masts were too close to each other (∼20m). Instead,
we used the method.
When a wind-speed maximum was observed at low height, nonstationarity
affected individual fluxes erratically and led to additional random errors in
mean EC fluxes. Mean relative random error was 12 % over the campaign.
Biases could lead to underestimating flux magnitude by around 10 % using
the EC method. The largest bias was potential underestimation of vertical
wind speed by the non-orthogonal anemometers, which could lead to
underestimating fluxes' magnitudes by about 6 %. High-frequency losses
remained small, at most ∼4%.
For the BA method, the main source of random errors came from uncertainties
in roughness lengths; they were large at the hourly timescale
(∼40%) but decreased to 5 % for net turbulent fluxes estimated
for the entire campaign. Systematic errors were generally high.
Surface-temperature errors induced by solar radiation effects probably led to
overestimating energy losses in turbulent fluxes, especially in daytime
upslope flows. A larger bias arose, however, from nonstationarity induced by
interactions of low-frequency perturbations with the surface layer and
dominated overall systematic errors. This led to net underestimation of flux
magnitude: using the BA method, net turbulent flux over the entire campaign
was only 60 % of that measured with the EC method.
Apart from these effects, vertical divergence of fluxes probably occurred due
to the shallow depth of the surface layer, which affected both EC and BA
methods. Flux divergence had a limited effect below 2 m (<15%)
in strong downslope flows or upslope flows. It was large when a katabatic
maximum was observed (≃67% at 2 m). Nonetheless,
lowering the measurement height to reduce this effect would lead to larger
uncertainties in BA-based fluxes since it would result in an increase in
measurement random error. The results presented here suggest that a height of
1 m for estimating surface turbulence fluxes with the BA method could
be a convenient trade-off between these two constraints.
In the context of energy-balance studies on Zongo Glacier, random errors in
the BA and EC methods would be large when studying melt processes at short
timescales since they were occasionally large for short periods. But random
errors would probably be of secondary importance when calculating melt over
monthly timescales since random errors cancel out to moderate values.
Nonetheless, we showed that the contribution of strong downslope flows to net
turbulent exchange was not well defined because of large random errors
affecting small net fluxes. In night-time downslope flows, most systematic
errors were low or cancelled out, together with the fluxes. Only vertical flux
divergence, affecting both BA and EC methods, did not cancel out. In daytime
upslope flows, systematic biases in largely negative LE fluxes and
small H fluxes did not cancel out. Flux divergence remained moderate but
cannot be neglected because the net fluxes were large. Conversely, because of
the large net fluxes, relative random errors were lower in these cases. Since
this regime exhibited the largest net turbulent exchanges, these issues need
further investigation.
The measurements and calculation methods for estimating surface temperature
need improvement. Vertical divergence of flux must be studied in more detail;
contributions from modelling would be useful, but models are still
difficult to apply to katabatic flows disturbed by outer-layer interactions
e.g.. Similar studies are necessary for other glaciers,
influenced by different climates, where the contribution of turbulent
sensible and latent heat fluxes to surface energy balance differs from that
on tropical glaciers, e.g. at high latitudes and on low-altitude glaciers,
where sensible heat fluxes are large but sublimation is low and deposition
can be high. The role of the errors studied here might differ considerably at
sites with distinctly different meteorological characteristics, and the
influence of turbulent flux uncertainties on surface energy balance might
also differ. An estimation of the turbulent fluxes could be obtained from the
estimation of melt rates and of all other energy balance terms. Such an
independent estimation may help in understanding the origin of biases evidenced
herein. Since ice or snow temperature measurements are challenging due to
solar radiation contamination heating of the sensors below the surface
(Helgason and Pomeroy, 2012), the potentially large conduction flux below the
surface remained unknown during the 2007 campaign on Zongo Glacier. This
prevented us from conducting an energy balance closure check. Energy balance
closure studies should be conducted on temperate glaciers when the surface is
constantly melting, the temperature profile below the surface is isothermal
at 0 ∘C and conduction fluxes are zero. Such studies may improve the
estimation of measurement errors in turbulent heat fluxes.