Over glaciers in the outer tropics, during the dry winter season, turbulent fluxes are an
important sink of melt energy due to high sublimation rates, but measurements in stable surface
layers in remote and complex terrains remain challenging. Eddy-covariance (EC) and
bulk-aerodynamic (BA) methods were used to estimate surface turbulent heat fluxes of sensible
(

Surface turbulent heat fluxes play a significant role in the energy balance of mountain glaciers

On the Alpine Pasterze Glacier,

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

On high-altitude Andean tropical glaciers during the dry season, turbulent
latent heat fluxes (

This study is one of few concerning error assessment of turbulent fluxes
measurements on glaciers

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.

The site and field campaign are extensively described in

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

Overview of Zongo Glacier and the instrumental set-up deployed
during the 2007 dry season campaign.

All data were split into 1 h runs. High-frequency data from the EC systems
were checked for quality

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

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

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

Cospectra of

For these three wind regimes, low-frequency perturbations affect the
surface-layer flow

We classified the GQRs into three subsets corresponding to the main wind
regimes (Sect.

Runs for which wind direction was downslope (between 260 and 360

We measured the turbulent fluxes with the two EC systems, following Eqs. (

For the EC method, the principal source of random error is poor statistical
sampling of the main transporting eddies

The

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

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

Non-orthogonal sonic anemometers may underestimate vertical wind velocity

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

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

Sensible heat fluxes

The length scales

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

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

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.

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

The error related to the ill-defined zero reference level was studied by

Random error in fluxes derived from the eddy-covariance (EC) method
and covariance of fluxes between the two EC systems.

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

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 (

The random error in

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

On average, the relative random error was 34 % (Table

Relative difference between covariances corrected with the

Relative difference between uncorrected covariances
(

High-frequency losses calculated from the mean cospectra of

Evaluation of high-frequency losses in

Multi-resolution decomposition (MRD) cospectra (black lines)
of

Results of random-error calculations using the bulk-aerodynamic
method for the fifth level (

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

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 “

Turbulent fluxes derived from the bulk-aerodynamic method for the
fifth measurement level on the profile mast (

The MRD cospectra of

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

At a height of 2

At the fifth level (2 m height), total relative random error, calculated
as the interquartile range of all

In the pure-katabatic subset, the magnitude of BA-based

Vertical divergence was also observed in the downslope and upslope
subsets but was significant only at heights greater than 2.0

During the day and when the surface was not melting, surface temperature from
the

A warmer surface reduces the temperature gradient and thus the sensible heat
flux, and it also increases

At a 2

During the 2007 campaign on Zongo Glacier, sublimation was high (

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 (

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

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
(

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

We calculated turbulent sensible (

In general, fluxes

For moderate-to-high-wind-speed conditions (

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

For the BA method, the main source of random errors came from uncertainties
in roughness lengths; they were large at the hourly timescale
(

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

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

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

Surface temperature,

Humidity was determined from measurements of temperature at the level
considered (e.g. surface temperature when estimated at the surface), passing
through the formula for change in water vapour pressure with air temperature

We present in this appendix calculation of the terms of random error in the
bulk-aerodynamic estimation of turbulent fluxes. If we assume measurement
errors in each variable were independent, let us recall the formula for error
in bulk flux using a linear model, assuming the stability functions were
constant for small variations in

The relative error in wind speed propagates as follows:

Propagating the relative error in

Random error in the fluxes due to random error in measuring the height can be derived as follows:

Uncertainties in roughness lengths measurements propagate as follows:

Random errors in humidity measurements affect latent heat flux as follows:

The glaciological programme is supported by the Institut de Recherche pour le
Développement (IRD). The authors are grateful for the assistance provided
by IHH (Instituto de Hidraulica e Hídrologia), UMSA (Universidad Mayor de
San Andrés), in La Paz, Bolivia. This work was funded by the French
SO/SOERE GLACIOCLIM
(