As part of surface energy balance models used to simulate
glacier melting, choosing parameterizations to adequately estimate turbulent
heat fluxes is extremely challenging. This study aims to evaluate a set of
four aerodynamic bulk methods (labeled as

Mountain glaciers of British Columbia are experiencing significant mass loss
in response to ongoing climate change and are projected to lose most of their
current volume by the end of the century

The turbulent sensible- and latent-heat fluxes are recognized as important
components of the SEB over midlatitude glaciers worldwide

Despite the common usage of bulk methods in glacier SEB studies, its
application is often problematic. Main limitations of the bulk method applied
to glacier SEB studies include the following:

In light of the above, further research is needed to evaluate and develop methods that are suitable for determining near-surface turbulent fluxes over sloping glacier surfaces subject to katabatic flows. In particular, our objective is to evaluate the existing framework of bulk approaches commonly used for parameterizing the turbulent momentum and heat fluxes at a glacier surface. We achieve this by comparing the modeled fluxes, i.e., output of the bulk approaches, to measured fluxes, i.e., the fluxes derived from an open-path eddy-covariance (OPEC) method. OPEC measurements are obtained from a mountain glacier in British Columbia (BC), over a short-term window (weeks) for two summer seasons. We first provide a brief overview of the field site, data collection, eddy-covariance data treatment, and overall methodology. This is followed by a detailed description of the bulk approaches and their evaluation results, and finalized with the discussion and conclusions.

Castle Creek Glacier lies in the Cariboo Mountains, BC
(Fig.

The AWS

We applied a series of data processing steps

The covariances of the 3-D wind velocities, temperature, and specific
humidity, derived by the OPEC system for each 30 min data segment, relate to
the friction velocity (

Turbulence flux data from OPEC systems often contain spurious measurements.
The roughness lengths derived from
Eqs. (

“Basic” filter for

“Stationarity” filter: only use steady-state runs following the method
of

“Neutrality” filter: select near-neutral conditions

“Wind direction” filter: restrict wind direction to a

“Wind speed” and “

“Temperature gradient” filter for

“Moisture gradient” filter for

“Small values” filter applied to

“Large values” filter: no study of turbulent fluxes over glaciers determined roughness lengths larger than 1 m. We thus consider any values of roughness length that exceed 1 m as spurious.

All bulk methods used in this study are rooted in the gradient transport
theory or

We provide an overview of the methodology used to compare and analyze the
performance of bulk methods in simulating the turbulent fluxes of momentum,
heat, and humidity. By definition, the bulk method parameterizes the turbulent
fluxes with the use of mean meteorological variables (e.g., wind speed,
near-surface temperature and relative humidity) and the bulk exchange
coefficient. In total we evaluate two groups of bulk methods (i.e., the
integrated form of
Eqs.

According to the mixing-length theory

This method assumes the same parameterization for

Starting from the parameterization for neutral conditions
(Eq.

In all the parameterizations for

Rather than integrating the flux–gradient relations with a chosen
parametrization for

Our data are not suitable to adequately test this bulk method since we do not
have the vertical profile observations of potential temperature needed to
estimate

Similarly to the

To adequately determine

For each 30 min roughness length estimate
(Eqs.

We quantify uncertainties in the modeled 30 min fluxes due to (1) the
uncertainty in the roughness lengths; (2) the assumption that the surface
temperature is at melting point; and (3) the systematic error in air
temperature due to radiative heating of the temperature sensor. To estimate
errors in (1), for each modeled 30 min flux, we use a Monte Carlo approach
so that the bulk method is run 1000 times with randomly perturbed roughness
length values. The roughness length values are randomly picked from a derived
normal distribution of their log values, using the OPEC-derived mean log
value and standard deviation (applying all the filters from
Sect.

Initial number of observations for estimating the roughness lengths (from 30 min averages of OPEC data) and remaining number of observations after each filter is applied (ordered from top down) for 2010 and 2012 observational periods. Solid line represents the filters used to determine the roughness lengths, and dotted line represents the filters used to determine the fluxes of momentum, temperature, and humidity.

We apply the filters discussed in Sect.

Among all the filters, the neutrality filter

We determine the time windows of prevailing katabatic flows (shaded areas in
Fig.

Thirty-minute averages of meteorological variables and SEB fluxes
measured at the AWS

Mean and

Each roughness length estimate has its respective error (error bars in
Fig.

Comparison of 30 min observed (OPEC-derived) vs. modeled friction
velocity (

We compare 30 min turbulent fluxes of momentum, sensible heat, and latent heat,
derived from the OPEC data (observed fluxes) with the modeled fluxes from
each bulk scheme. To ensure that the evaluation is performed on high-quality
data, only the 30 min fluxes that pass the filters in
Sect.

Comparison between modeled and OPEC-derived sensible (

Modeled fluxes for the 2012 season (

The performance of the

Intercomparison of the

In the gradient–flux relation, the eddy viscosity is parameterized as a
function of

Comparison of 30 min values of observed (OPEC-derived) and modeled
sensible-heat flux (

The following results are found for both the 2010 and 2012 seasons:

Overestimation of

Measured eddy Prandtl number vs. the inverse of the wind speed.

The optimization of the

Observed 30 min sensible-heat flux (

In the original model

The relation between the optimized 30 min

The modeled

As already shown (Fig.

We summarize uncertainties between modeled and observed fluxes for the six
bulk methods used in the study (four types of

We discuss our findings in the order that we introduced uncertainties in the
bulk methods, particularly in simulating

In the absence of reliable measurements of surface temperature,

To estimate roughness lengths (

When testing the stability corrections in the bulk methods, we assumed
that the main predictor of the time-varying bulk exchange coefficient is the
time-varying local stability, not the changes in the surface roughness. Using
the two common parameterizations to account for the stability corrections
(

Under stable stratification and in the presence of a low-level jet
(katabatic flow), intermittent turbulence and gravity waves are present, and
steady-state conditions do not exist

The main objective of the study was to evaluate commonly used bulk methods
(

Bulk exchange coefficients can be derived from the OPEC-derived roughness
lengths for neutral stratification, where the mean log values for

The Monin–Obukhov stability functions widely used in glacier studies perform
relatively poorly at our site. The

If OPEC data are not available,

Contrary to the

The

The bulk exchange coefficient in the

All data used in this study are available upon request from the corresponding author. The raw data are not currently in a standard format, and the metadata are not fully digitized.

VR participated in the 2012 field campaign, developed and performed the analysis, and wrote the initial version of the manuscript. BM provided financial and field support and helped prepare and revise the manuscript. JS led the 2010 field campaign and contributed to the manuscript refinement. NF processed the OPEC data and contributed to the manuscript refinement. MAT contributed to the method development. SJD provided logistical support and meteorological data, and contributed to the manuscript refinement.

The authors declare that they have no conflict of interest.

Funding supporting this study was provided through the Natural Sciences and Engineering Research Council (NSERC) of Canada (Discovery grants to Valentina Radić, Brian Menounos, Stephen J. Déry), the Canada Research Chairs Program, and Science Horizons. Our eddy-covariance system and meteorological equipment were supported by a NSERC Research Tools and Instruments grant and a Canada Foundation for Innovation grant (Stephen J. Déry). Theo Mlynowski is thanked for the field setup in 2010, and Andrew Duncan for the field support in 2012. Special thanks to Zoran Nesić for all the technical support and training. Branko Grisogono; Christian Schoof; Elisa Mantelli; and the two reviewers, Jonathan Conway and Ruzica Dadic, are thanked for discussions and constructive criticism on the initial version of the manuscript. Edited by: Thomas Mölg Reviewed by: Jonathan Conway and Ruzica Dadic