Introduction
The exchange of energy at the Greenland Ice Sheet (GIS) surface
must be thoroughly characterized to fully understand the processes that
govern surface temperature variability, which is important in monitoring and
modeling ice sheet mass balance . Observations suggest
near-surface temperatures are increasing; the GIS is showing a trend toward
greater spatial melt extent with increased melt runoff
due to atmospheric warming . The
amalgamated freshwater runoff, in combination with ice discharge, determines
how this major reservoir of northern hemispheric ice affects freshwater input
into the North Atlantic and Arctic oceans and, subsequently, global ocean
circulation and sea level rise. Surface melt processes currently account for
approximately half of the total mass loss of the entire GIS
, and during prolonged periods of elevated surface
temperatures this proportion is even greater . The melt
process occurs in two steps. First, energy flux to the surface is used to
increase the surface temperature. Then, after the melting point is reached,
excess net surface energy flux is used to convert ice into liquid water. As
an increasing area of the interior GIS approaches the melting point of snow
in summer, spatial and temporal variations of the net surface energy flux are
paramount in determining when the melting point is reached, over what spatial
area this occurs, and the amount and rate of melt after this threshold is
reached.
The surface energy budget (SEB) is a balance of radiative, turbulent, and
ground heat fluxes, which are coupled through a variety of processes. Once
the surface temperature reaches the melting point of snow, additional energy
goes toward melt, limiting the surface temperature to 0 ∘C. In the
absence of phase change, however, a change in one of the SEB terms must be
balanced by a change in another term or combination of terms. Importantly,
the surface temperature is related to multiple SEB terms including upwelling
longwave radiation, turbulent sensible heat, and ground heat fluxes. Over
timescales long enough for the surface temperature to adjust, closure of the
SEB is achieved and all of the energy exchange at the surface is accounted
for. Because of the high emissivity (and hence high longwave absorptivity) of
the snowpack, the surface is able to adjust relatively quickly to longwave
influences (e.g., whether that is a warm cloud or a cold, clear sky). In
contrast to its efficient ability to absorb longwave radiation, the GIS has a
high shortwave albedo and reflects much of the incoming solar radiation.
Liquid-bearing clouds are frequent above the GIS during summer
and have strong implications for increasing melt extent
and meltwater runoff . In
fact, clouds act to radiatively warm the central GIS throughout the year
, more than would occur via solar
radiation acting alone, as a result of the year-round high surface albedo.
Thus, the primary radiative influences on raising surface temperatures in
this region are the solar zenith angle and occurrence of clouds.
A change in the downwelling radiative flux caused by clouds and/or solar
radiation will induce a response of the atmospheric boundary layer and
surface. Boundary-layer depth and stability are influential for exchange
processes, such as sublimation fluxes, which modulate accumulation
. show a degradation of the
surface-based temperature inversion in the presence of liquid-bearing clouds,
which impacts the near-surface stability and thus
turbulent mixing. A regional modeling case study by
indicates also that the response of turbulent and conductive heat fluxes to
cloud radiative forcing (CRF) is important when considering surface–atmosphere
interactions. Investigating these responses and interactions throughout the
year is paramount for discerning the net effect of liquid-bearing clouds on
surface temperatures and, consequently, on subsurface temperatures and melt
processes.
The central GIS is a massive reservoir of snow and ice, responding to energy
changes at the surface by conducting heat into or out of the subsurface.
Thus, the ice sheet damps the effects of either strong radiative warming or
cooling at the atmosphere–snow interface. Warmer subsurface temperatures,
resulting from warming of surface temperatures, can change the snow
morphology and precondition the surface to have less capacity for removing
subsequent heat excesses generated by atmospheric processes
. Proper atmosphere–ice sheet coupling is important to
allow for physically realistic radiational cooling at the surface, in order
to minimize surface temperature biases in forecast models
.
Regional and global climate models are a critical tool for understanding the
fate of the GIS and attempt to capture the nontrivial interactions between
the atmosphere and the GIS. Early studies parameterized the SEB of the GIS
using meteorological measurements from summer camps in western Greenland and
observations of albedo from satellites
. More recently,
computationally advanced, fully coupled climate models project enhanced
surface melt as GIS surface temperatures increase under future CO2
forcing scenarios . However, these state-of-the-art climate
models have surface temperature biases over the GIS, likely due to the under
representation of liquid-bearing clouds . To better
understand and represent the important processes that currently hinder
models, detailed surface-based observations are valuable.
Estimated uncertainty in each surface energy budget
term.
LW↓ or LW↑
SW↓ or SW↑ *
SH
LH
C
S
5.0 Wm-2
1.8 % > 5.0 Wm-2
8.7 Wm-2
60 % > 8.0 Wm-2
26 % > 3.0 Wm-2
80 % > 10.0 Wm-2
* SW↑ in 2014 = 2.8 %
(> 5.0 Wm-2).
In western Greenland, detailed measurements of the surface mass balance
, surface radiation balance
, and surface energy balance
have been reported, all of which focus on the
ablation zone. In central Greenland, the most sophisticated and comprehensive
long-term observations of surface energy budget are made at Summit Station.
While a majority of the published literature has focused on the summer season
, some studies have targeted SEB
annual cycles in 2000–2001 , 2001–2002 ,
and 2000–2002 . In addition, various studies have
focused on specific components of the SEB, such as surface latent
or sensible heat
fluxes. Annual surface radiation
fluxes have been reported at Summit by ,
, and , as well as longwave flux
divergence in the boundary layer by and
. Yet, prior to May 2010 there have been limited
ground-based measurements of the atmospheric state and cloud properties to
complement these temporally sporadic SEB investigations and to support
process-based understanding of SEB variability on timescales from minutes to
seasons.
This study uses comprehensive ground-based measurements to investigate
interactions between the atmosphere and the central GIS throughout the year
in order to understand how energy exchange drives temporal variability in
surface temperature. Summit Station is currently within the accumulation
zone, recording only two melt events since 1889 . The lack
of melt events provides the opportunity to examine relationships between the
various surface energy fluxes in all seasons without the energetic influence
of phase change at the surface. We characterize the annual and diurnal cycles
of the radiative, turbulent, and conductive heat fluxes for 1 year and
evaluate SEB closure. Next, using a unique complement of data/measurements at
30 min temporal resolution, we present a pair of case studies to illustrate
cloud effects on the balance of energy at the surface and, consequently, the
subsurface snow in central Greenland. Finally, we investigate the seasonal
responses of the turbulent heat fluxes, subsurface heat flux, and upwelling
longwave flux to changes in downwelling longwave and net shortwave fluxes,
establishing process-based energy flux relationships.
Measurements and methods
Near-surface instrumentation at Summit Station (72∘ N
38∘ W, 3211 m) is used to characterize the surface energy
budget. Net radiative (Q), turbulent sensible (SH), turbulent latent (LH),
and total subsurface (G) heat fluxes determine the net surface flux
(Fs) according to the following equation:
Fs=Q+SH+LH+G.
The total subsurface heat flux (G) considered here is a combination of the
conductive heat flux (C) and heat storage in a near-surface layer (S),
detailed in Sect. . Each of these four terms is defined such
that a positive value sends energy towards the surface and vice versa. For
all measurements described here, a 30 min time window is used; this time
window was chosen to fit the constraints set by eddy covariance calculations
for sensible turbulent flux (Sect. ) but is
sufficiently brief to capture both the diurnal cycle and the SEB response to
atmospheric variability of interest here.
All SEB terms are estimated for 75.3 % of an annual cycle, spanning July
2013–June 2014, although Q, SH, and LH are also measured prior to July
2013. The techniques used to calculate each SEB term, the data availability
periods, and associated uncertainties are outlined in the following
subsections. The estimated uncertainty in each SEB term is summarized in
Table . While each component of the SEB has its own uncertainty,
at times the various estimates use the same input and are thus not
independent. For example the longwave measurements are used to derive the
skin temperature, which is input into both the bulk sensible heat flux and
conductive heat flux estimates.
List of measurements at Summit Station used in this study. Nominal
heights are given for measurements made at two levels.
Parameters measured (≈ heights)
Instrument
Project – location
Atmospheric temperature profile
Vaisala RS92 radiosondes
ICECAPS – MSF
Snow temperature profile
Campbell Scientific 107 temperature probes
CIBS – 50 m tower
Surface height
Campbell Scientific SR-50A sonic ranger
CIBS – 50 m tower
Temperature (2 m, 10 m)
Logan RTD – PT139 special order
NOAA/GMD – met tower
Vaisala HMP 155 temperature probes
CIBS – 50 m tower
Metek USA1 sonic anemometers
CIBS – 50 m tower
Wind speed (2 m, 10 m)
Metek USA1 sonic anemometers
CIBS – 50 m tower
Met One 010-CA cup anemometers
CIBS – 50 m tower
Relative humidity (2 m, 10 m)
Vaisala HMP 155 RH probes
CIBS – 50 m tower
Water vapor mixing ratio (2 m, 10 m)
Picarro L2120 spectrometer
CIBS – 50 m tower
Barometric pressure
Setra 270
NOAA/GMD – met tower
LW↓, LW↑
Kipp and Zonen CG4 pyrgeometers
ETH – radiation station
Eppley PIR pyrgeometers
NOAA/GMD – radiation station
SW↓, SW↑
Kipp and Zonen CM22 pyranometers
ETH – radiation station
Kipp and Zonen CM22 pyranometers
NOAA/GMD – radiation station
Liquid water path
RPG microwave radiometers – HATPRO and HF
ICECAPS – MSF
Precipitable water vapor
RPG microwave radiometers – HATPRO and HF
ICECAPS – MSF
Cloud occurrence
Millimeter cloud radar – 35 GHz
ICECAPS – MSF
Meteorological and snow measurements
Redundancy of many direct measurements used to derive the SEB components is
imperative in the harsh Arctic environment where frost, rime, and extreme cold
create operational challenges. Certain measurement techniques are only valid
during specific atmospheric conditions and operational temperature ranges of
the instrumentation. As a result, redundant data streams and multiple
independent methodologies are considered whenever possible to investigate
suspected biases and fill in data gaps during instrument downtime.
Table summarizes the measurements made by the various
instruments described below.
Twice daily Vaisala RS92 radiosondes (0 and 12 UTC) from the Integrated
Characterization of Energy, Clouds, Atmospheric State, and Precipitation at
Summit ICECAPS, project are used to directly measure
the atmospheric temperature with an uncertainty of 0.5∘. A
near-surface meteorological tower, maintained by the National Oceanic and
Atmospheric Administration's Global Monitoring Division (NOAA/GMD), is the
primary source of the near-surface (≈ 2 and ≈ 10 m)
temperature measurements (Logan RTD – PT139 special order) with a specified
resolution of 0.1 ∘C. An experiment on Closing the Isotope Balance
at Summit (CIBS), approximately 1 km northeast of the NOAA tower, included a
broad suite of advanced meteorological measurements for evaluating surface
exchange processes, including aspirated temperature measurements at 2 and
10 m. The CIBS instruments were mounted on a 50 m tower operated by
the Swiss Federal Institute of Technology (ETH) Zürich. On average the CIBS
2 m temperatures are 0.72 ∘C greater than the NOAA/GMD 2 m
temperatures with a root mean square (RMS) difference of 1.64 ∘C. A
portion of the RMS difference is due to spatial distance between measurement
locations and possibly also due to local variability in snow accumulation
which would lead to differences in the measurement heights of the sensors. In
addition, CIBS included Metek USA1 three-dimensional ultra sonic anemometers
to directly measure orthogonal components of high-frequency fluctuations in
temperature and wind speed. The sonic anemometers (20 Hz sampling rate),
equipped with heated transducers to prevent riming or frost buildup, were
mounted at 2 and 10 m on the 50 m tower. Before 19 January 2013 the
heaters operated only when there were significant data dropouts due to
rime/frost; after this date the heaters were on constantly. Comparison of the
data before and after the heater configuration change indicate that sensible
fluxes generated by the heating elements are sufficiently small that they are
well within the measurement uncertainty. The high-frequency sonic anemometer
wind speed measurements are averaged to estimate the mean 30 min wind speed.
Redundant wind speed measurements are also made by CIBS cup anemometers,
which have moving parts that have a frictional threshold that requires a wind
speed of at least 0.5 ms-1 for reliable measurements.
Comparisons between the two measurements for conditions above
0.5 ms-1 show a RMS difference of 1.75 ms-1 and a
bias of -0.55 ms-1 in the cup anemometer data.
Subsurface temperatures are measured by Campbell Scientific 107 temperature probes
buried in the snow (every 20 cm in depth) near the 50 m tower. The
height of the surface relative to the thermistor string is estimated from a
downward facing sonic ranger mounted on the tower above the thermistor
string. During the single year when the thermistor data were available (July
2013–June 2014) the surface height increased by 0.68 m. Due to
scatter in the reported surface heights, the snow depths are smoothed using a
5-day running window to remove erroneous spikes in the snow depth. Realistic
longer-term discontinuities due to actual snow events were maintained by
limiting the period over which data smoothing occurred. Inexplicably, on
27 May 2014 the sonic ranger reported an abrupt 17.8 cm decrease in the
surface height. The near-surface thermistor variability indicates that this
was unrealistic; hence an offset of -17.8 cm was applied to the
thermistor depths thereafter through the end of the study period. The
standard deviation over 30 min of the 1 min subsurface temperature data
indicates that the variability decays as a function of depth because of a
decline in the thermal effects of wind ventilation and direct solar heating
due to solar penetration. To minimize the impact of these complicating issues
a standard deviation threshold of 0.1 is used to determine that the
acceptable minimum depth to use for the shallowest subsurface thermistor is
about -20 cm.
The specific humidity at 2 and 10 m, which is needed for deriving LH,
is calculated from the CIBS relative humidity, CIBS temperature, and NOAA/GMD
pressure measurements. The saturation vapor pressure, at a given temperature,
is calculated using the Goff–Gratch formulation and then multiplied by the
relative humidity to get the vapor pressure. Specific humidity is
proportional to the ratio of the vapor pressure to the difference in vapor
pressure and air pressure. To provide continuity in the LH estimates the
meteorologically derived specific humidity values are used as input to the LH
flux calculations, while direct measurements of water vapor are used to
estimate the uncertainty in this technique during overlapping time periods.
From July 2012 to December 2013 direct measurements of water vapor mixing
ratio are obtained via a Picarro model L2120 spectrometer, which was
calibrated using a LiCor LI160 dew point generator . The
instrument directly samples air moisture content once an hour at multiple
levels on the 50 m tower using a constrained inlet system to limit large
(> 50 µm) hydrometeors from being incorporated into the vapor
measurements. Comparing meteorologically derived specific humidity values at
approximately 1–2 and 9–10 m above the surface to the highly
accurate Picarro measurements reveals a small bias of
+0.065 gkg-1. The percent error, relative to the Picarro
measurements, at the 2 and 10 m levels are 53 and 30 %,
respectively.
Radiative flux
Four broadband radiation components comprise the net radiation at the surface
(Q):
Q=LW↓-LW↑+SW↓-SW↑.
At Summit Station ETH maintains broadband radiative flux measurements, at
approximately 2 m above the surface. The radiation station is located
between the 50 m tower and the NOAA/GMD met tower. Kipp and Zonen CG4
pyrgeometers measure the upwelling and downwelling thermal emission
(LW↑ and LW↓) in the spectral range of
4.5–40 µm and Kipp and Zonen CM22 pyranometers measure the
upwelling and downwelling solar irradiance (SW↑ and SW↓)
in the spectral range of 200–3600 nm. In this study the radiative
flux measurements extend from January 2011 to June 2014.
Data processing for radiation measurements used here is similar to
, including corrections to the LW↓ components
based on the net longwave radiation and comparison to
co-located broadband radiation measurements operated by NOAA-GMD. The
radiation components have an estimated Gaussian longwave radiation
measurement uncertainty of 4–5 Wm-2 .
Assuming an emissivity uncertainty of 0.005 a LW-derived surface temperature
has an approximate uncertainty of 0.6 ∘C, which is derived from the
radiation measurements thusly:
Tsurf=LW↑-1-ϵLW↓/ϵσ0.25,
where surface emissivity (ϵ)=0.985 and σ is the
Stefan–Boltzmann constant. Comparing LW↑ to similar, proximate
NOAA/GMD radiation measurements indicates that there is general agreement
within the estimated 4–5 Wm-2 uncertainty of the longwave
radiative components. Yet, for very cold surface temperatures (i.e.,
< -46 ∘C) differences between the NOAA/GMD and ETH LW↑
are more pronounced. Hence, a third degree polynomial was used to fit the
difference between the ETH and NOAA/GMD LW↑ as a function of the ETH
LW↑. A correction factor (y) was applied based on the measured ETH
LW↑ (x) value according to y=-14.99+0.1715x-0.000668x2+8.579×10-7x3, which assumes the more recently calibrated NOAA/GMD
pyrgeometers are accurate. After applying the adjustments to LW↑ and
LW↓ the 1 min LW data are consistent with a
total uncertainty of 4–5 Wm-2.
The surface albedo is determined by dividing the measured SW↑ by the
measured SW↓ and for clear-sky days should have a minimum at solar
noon. During 2014 an asymmetry in the diurnal cycle is observed in the
measured albedo, where the albedo in the morning is up to 10 % lower than
in the evening. The NOAA/GMD measurements, which are mounted on the same
fixed arm, indicate the same issue (possibly a gradual slope to the surface
due to snow drifts). There is good agreement between the ETH SW↓
measurements and the total direct plus diffuse SW↓ values,
suggesting that asymmetry in the diurnal cycle of albedo is likely a problem
in the SW↑ component. Hence, the SW↑ value is estimated in
2014 using the SW↓ value according to SW↑=αSW↓, where α is the albedo. A linear
relationship between albedo and solar zenith angle (Z) for 2011–2013 is
used to estimate an albedo in 2014 according to α=0.798+0.00107Z.
Comparing the measured SW↑ to the parameterized SW↑ yields
an RMS difference of 5.7 Wm-2 for
SW↓ < 278 Wm-2 and 12.6 Wm-2 for
SW↓ > 278 Wm-2. Thus, the uncertainty in the
parameterized SW↑ component is ≈ 5.7 Wm-2 for
small sun angles and ≈ 2.8 % for larger SW↓ values.
These uncertainty estimates are larger than the reported uncertainty in the
measured SW components of 1.8 % because, in
addition to Z, albedo is dependent on other factors such as the optical
thickness of overlying clouds and surface snow properties.
During periods of 2013 and 2014 the SW↓ component has a bias that
is evident when the sun is below the horizon, hypothesized to be due to a
grounding issue. A bias correction of 2.45 Wm-2 was applied to
20 November 2013 to 30 January 2014, determined by the average value when the
solar zenith angle was greater than 95∘. From 31 January 2014 to
14 April 2014 a bias correction of 4.61 Wm-2 is applied to the
SW↓ to remove the negative bias.
Turbulent sensible heat flux
The net surface flux is influenced by the temperature of the overlying air;
i.e., warmer near-surface air will increase the sensible heat transferred to
the surface. Direct heat transfer, via conduction, from the atmosphere to the
snowpack is only prominent very close to the surface; thus heat is primarily
transferred via turbulent eddies. These eddies act to mix the air within the
surface layer, reducing the vertical temperature gradient. Estimates of the
sensible heat flux are calculated using two independent methods: eddy
correlation (EC) method and the bulk aerodynamic method.
The EC method e.g., calculates the
covariance between the anomalies in the vertical wind (w′) and temperature
(θ′) to determine the turbulent sensible heat flux according to the
following
equation:
SH=ρcpw′θ′‾,
where the constants are the density (ρ) and heat capacity
(cp) of air. By using direct measurements of wind speed and
temperature from a three-dimensional sonic anemometer, an accurate
calculation of the heat exchange at ≈ 2 m is obtained.
A 30 min averaging period is a short enough time window to exclude issues of
nonstationarity while still long enough to include low frequency
contributions to the turbulent heat flux. Various quality-control (QC)
measures are implemented to ensure the data is representative of the entire
sensible heat flux during the 30 min window. QC measures exclude large
changes in wind speed or wind direction, upwind contamination by the
experimental apparatus, and ±30 % deviations from characteristic
-5/3 slope in the inertial subrange. Applying the QC criteria flags
75 % of the available data, spanning September 2011–June 2014. Thus, for
the 85 % of this period that either has instrument downtime or where the
data are QC flagged, an alternative approach is used.
Due to the limited data set available from the EC method, a bulk aerodynamic
method is also used in order to fill in data gaps for the time period June
2011–June 2014. The bulk transfer method uses Monin–Obukhov similarity
theory to estimate turbulent sensible heat flux at the surface:
SH=ρcpChUTsurf-T2m,
where U is the mean horizontal wind speed at 2 m, Tsurf
is the skin temperature, T2m is the temperature at
2 m, and Ch is the sensible heat transfer coefficient for
the 2 m reference height . NOAA/GMD
meteorological data are the primary source of the 2 m temperature
measurements and data gaps are filled with CIBS temperature data. Cup
anemometer measurements fill in data gaps of the sonic anemometer-derived
2 m wind speed measurements. Ch is based on the roughness of the
surface and assumes scalar velocity and temperature roughness lengths with
corrections to account for boundary-layer stability. An optimal (as compared
to the EC measurements) velocity roughness length of 3.8×10-4 m and a roughness length for
temperature of 1×10-4 m are assumed
constant in time. Separate stability correction functions for stable or
unstable boundary-layer conditions are used to iteratively converge on the
best-estimate sensible heat flux .
Comparing the bulk sensible heat flux to the quality-controlled EC data gives
an indication of the uncertainty in the bulk method. Bulk data are deemed
valid when the surface friction velocity (u∗=[-u′w′‾]0.5) value exceeds 0.03 ms-1. A
correlation coefficient of 0.89 exists between the two techniques for the
subset of data deemed valid for both techniques. The RMS difference between
the two methods (8.7 Wm-2) is the net estimated uncertainty in
the sensible heat flux. Compared to the EC data the bulk method has a bias of
+7.0 Wm-2. For instances where the bulk sensible heat flux
magnitude is less than 10 Wm-2 the bias and RMS difference
decrease to +3.5 and 2.60 Wm-2, respectively. This improvement
suggests some of the differences could be due to inaccurate stability
correction functions, uncertainty in the surface temperature derived from LW
measurements and snow emissivity assumptions, or roughness length values.
Sensible heat flux discrepancies could also be due to measurement height
differences between the EC and bulk methods. While the bulk method uses the
measured surface skin temperature the EC values are measured at 2 m,
which could differ from the sensible heat flux directly at the surface under
very stable conditions. This suggests that the true SH uncertainty is smaller
than estimated here. The covariance u∗ and bulk u∗ are well
correlated (0.84) with a RMS difference of 0.55 ms-1 and the
bulk values are biased low (-0.026 ms-1). Changing the
velocity roughness length to 4.5×10-4 m, which was
determined for snow-covered multi-year sea ice
i.e.,, increases the RMS differences for the
sensible heat flux by 1.4 Wm-2, suggesting that variability in
the roughness of the surface could contribute to error in the bulk
parameterization. A majority of the 8.7 Wm-2 uncertainty in the
bulk estimates is likely due to uncertainties in the skin temperature as
estimated from a constant surface emissivity. From June 2011 to June 2014 the
bulk estimates are available for 78 % of the time period. Thus, filling
in EC data gaps with the bulk values vastly improves the temporal coverage of
the sensible heat estimates.
Turbulent latent heat flux and stability
Turbulent eddies also affect the surface energy budget by transferring latent
heat toward or away from the surface. Frequently the specific humidity
increases with height above the surface, resulting in a transfer of latent
energy toward the surface possibly resulting in deposition. The bulk method
used by assumes saturation conditions at the surface,
which is not always a valid assumption for dry snow
. In central Greenland the two-level profile
method has been shown to be superior to the bulk method
as it can account for sublimation and deposition to
the surface.
The profile method used here is similar to such
that the latent heat flux is calculated from near-surface horizontal wind
(U) and mixing ratio (q) gradients (Δ = value at
10 m - value at 2 m) according to the following equation:
LH=ρLvk2zr2(ΔUΔzΔqΔz)ϕmϕe-1,
where ρ is the density of air, Lv is the latent heat of
vaporization, k is the von Kármán constant (0.4), and zr is
the log mean height (Δzlnz2z1-1).
The stability functions for the transfer of momentum (ϕm) and
water vapor (ϕe) are corrections based upon the stability of
the boundary layer and will either increase (unstable conditions) or decrease
(stable conditions) the surface flux.
A measure of boundary-layer stability is attained via calculation of the bulk
Richardson number (Ri). The sign of Ri indicates whether
mechanical mixing (positive) or buoyancy (negative) is more important in
producing turbulence. Ri is dependent on the gradient in virtual
potential temperature (Δθv), wind speed (Δu), and
respective measurement heights (Δz) according to the following equation:
Ri=gθv‾ΔθvΔz-1ΔuΔz-12,
where g is the acceleration due to gravity (9.81 ms-2) and
θv‾ is the average virtual temperature (K) between
the two levels. In accordance with , Ri
is used to calculate the stability corrections. Coefficients for relating
Ri to the stability factors are obtained from a study conducted in
2000, which used EC turbulence measurements to obtain the
relationships in Table . For stable
Ri values greater than zero the stability functions act to reduce
the magnitude of the latent heat flux. For Ri greater than the
critical Richardson number (Ri = 0.25) vertical turbulence
becomes small and, in theory, results in laminar flow.
indicate that intermittent and nonstationary turbulence can exist even in
this super-critical regime. Assuming LH = 0 for Ri > 0.25
could underestimate latent heat flux from intermittent nonstationary
turbulence but isotopic closure calculations indicate that for very stable
boundary layers tracers are conserved, suggesting little to no net
water vapor exchange at the surface . Thus, for
Ri measurements which fall into the super-critical regime, 44 %
out of the 33 090 total measurements from March 2012 to June 2014, the
latent heat fluxes are set to zero, providing a reminder of the significance
of high stability in limiting mass transfer.
Stability functions for unstable and stable regimes from
.
Stability function
Unstable
Stable
(Ri < 0)
(0 < Ri < 0.25)
ϕm
(1+27|Ri|)-0.2
(1+4Ri1-4Ri)
ϕe
(1+19|Ri|)-0.55
(1+3Ri1-4Ri)
LH is the data set most susceptible to data gaps because there must be input
values of specific humidity, wind speed, and temperature at both the 2 and
10 m levels. Yet by using the best available meteorological data from
NOAA/GMD and/or the CIBS project we estimate LH for 81 % of the time
period from March 2012 to June 2014. The main driver of uncertainty is the
estimation of the mixing ratios with uncertainties of 53 and 30 % at 2
and 10 m, respectively, as compared to the Picarro measurements. The
resultant error contribution (60 %) to the LH estimate dominates the
contribution from uncertainty in the wind speeds.
Subsurface heat flux
The energy flux from the overlying atmosphere to the subsurface includes
direct radiative heating of the snowpack due to solar penetration
, the thermal effects of wind ventilation
, and conduction. To minimize the complications
in calculating subsurface heat flux caused by the other factors, an
estimation of the conductive heat flux (C) at a depth below the solar
penetration depth (at least 20 cm) combined with a heat storage (S)
in the snow above this level is used to provide an estimation of the total
subsurface heat flux (G), such that
G=C+S.
In this study we calculate the storage heat flux across the uppermost layer
and assume the heat flux to the subsurface below is equivalent to C.
The conductive heat flux (C) represents the diffusion of heat between the
subsurface and the overlying surface. The effectiveness of the heat transfer
is a function of the thermal conductivity of the snow (K) and the vertical
temperature gradient (ΔT/Δz):
C=-KΔTΔz.
The temperature gradient for the uppermost subsurface layer (ΔT01)
is estimated as the difference between the surface temperature
(Tsurf, Eq. ) and the temperature measured by the
shallowest, subsurface sensor. To estimate C, at ≈ 20 cm depth,
the conductive heat flux at the two levels bracketing this depth is
calculated and averaged, according to the following equation:
C=-12K01ΔT01Δz01+K12ΔT12Δz12.
The thermal conductivity of the upper most layers of snow is estimated from
average density profile measurements taken from five snow pits around Summit
Station in July 2014. The average standard deviation of density among pits at
all depths is 50 kgm-3. There is a known annual cycle in snow
density in this region based on seasonally varying thermal and snow
properties . The first two density minima with
increasing depth are assumed to be different solely due to compaction of the
snow over the course of a year, resulting in a linear compaction factor of
-22 kgm-3year-1. This factor is used to estimate the
annual evolution of near-surface snow density as a function of time from the
profile measurements collected July 2014. The adjusted density profile is
used to determine an average snow layer density for the representative
near-surface conditions from July 2013 to June 2014. The result is a range of
density values varying annually between 348 and 413 kgm-3. Snow
density is converted to thermal conductivity according to ,
resulting in a seasonally varying thermal conductivity with an average value
of 0.47 Wm-1K-1. The average value is higher than summer
sea-ice values of
0.3 Wm-1K-1, although the summer minimum conductivity
(0.39 Wm-1K-1) is more similar to the sea-ice values.
The uncertainty in the conductive flux is related to the uncertainties in the
calculated skin temperature, subsurface temperature, subsurface measurement
height, and snow conductivity estimate. The LW-derived skin temperature
uncertainty is approximately 0.6 K. The thermistor accuracy
specifications indicate an interchangeability tolerance of 0.38 K at
0 ∘C and 0.6 K at -40 ∘C. We estimate the
uncertainty in the measurement height of the shallowest thermistor as
2 cm. A 50 kgm-3 uncertainty in the snow density
translates to 0.1 Wm-1K-1 uncertainty in snow conductivity.
The average temperature difference between the surface and -40 cm
is about 7.2 ∘C. The resultant uncertainty in the conductive flux,
calculated by taking the quadrature sum of the fractional uncertainties, is
26 %.
The storage of heat in a layer is related to the time rate of temperature
change averaged over that layer. The storage heat flux (S) includes energy
associated with solar heating, longwave emission, and turbulent heat flux
within the snow. In the uppermost layer (≈ 20 cm), S is
calculated by the layer averaged temperature difference (δT)
between chronologically adjacent time steps (δt=30 min),
where T1 is the temperature of the shallowest thermistor at a depth
z1 (similar to ):
S=-ciceρ[δTsurf+δT12δt]-z1,
where cice is the specific heat of ice and ρ is the average
density of the layer. The large uncertainty in the skin temperature
measurements (0.6 ∘C) are close to the average temperature change
from one time step to the next (0.76 ∘C), resulting in an estimated
uncertainty in S of 80 %. The estimate of S is the most uncertain
term in the SEB.
Cloud properties and precipitable water vapor
Investigating the surface flux estimates in combination with active and
passive cloud property measurements yields a comprehensive understanding of
how clouds affect the GIS energy budget. In addition to the aforementioned
radiosondes, ICECAPS also measures the cloud properties via a comprehensive
suite of instruments, in operation since May 2010. ICECAPS is described in
detail by . Liquid water path (LWP) and precipitable water
vapor (PWV) are estimated using a physical retrieval via a pair of microwave
radiometers (MWR), similar to . In a dry environment,
such as Summit, it is advantageous to use a total of three channels (23.84,
31.40, 90.0 GHz) to increase sensitivity and effectively reduce
uncertainty in LWP (≈ 5 gm-2) and PWV
(≈ 0.35 mm) . The primary changes to
the LWP values estimated in are an improved liquid water
model TKC; and the use of three channels in the
retrieval instead of four. By excluding the 150.0 GHz channel, biases in LWP
retrievals due to precipitating ice hydrometers will not impact the overall
statistical results . The liquid present cloud
fraction for a given month is the number of LWP samples greater than
5 gm-2 divided by the total number of samples. During May and
June 2014 the microwave radiometer measuring 23.84 and 31.40 GHz was
off site for repairs and thus LWP and PWV are unavailable for these months. A
35 GHz millimeter cloud radar (MMCR) determines vertically resolved cloud
presence. Monthly cloud fractions are calculated using a MMCR detection
threshold of -60 dBz, retaining sensitivity to most hydrometeors.
Results
Observationally based results capture atmospheric–ice sheet interactions.
This section will first examine temperature profiles at Summit, providing a
foundational understanding for how the atmosphere and snowpack are related.
Secondly, investigation of the partitioning of surface energy flux over the
annual and diurnal cycles illuminates when various SEB terms are most
influential. Finally, quantifying the response of the SEB to changes in the
downwelling radiation, predominately affected by cloud presence and
insolation, shows how the non-radiative SEB terms effect the surface
temperature variability.
Temperature evolution from 1 July 2013 to 30 June 2014.
(a) Values between the solid horizontal lines indicate surface
temperatures (Tsurf). The dashed (dashed-dotted) line at 2 m
(10 m) level is NOAA/GMD measurements, and that from 20 m to
5 km a.g.l. is derived from twice-daily radiosoundings. The height
scale above ground level is logarithmic to emphasize the near-surface values
where the atmospheric and GIS are physically coupled. Subsurface temperatures
are on a linear scale. White areas indicate periods of data gaps and black
symbols indicate the height of the maximum temperature in each profile.
(b) Monthly mean temperatures at 500 m, Tsurf, and
-1 m.
Temperature profiles
The temperature variability at and below the ice sheet surface is important
for understanding the flow of heat through this interface and can influence
processes such as snow compaction and melt. Figure depicts the
variability in temperature above, below, and at the surface from 1 July 2013
to 30 June 2014. The maximum surface temperature (Tsurf) was
-3.1 ∘C on 10 July 2013 and the minimum was -68.8 ∘C on
23 March 2014 (Fig. a). A warm or cold pulse at the surface
propagates to deeper portions of the GIS over time and can take days to
influence the temperatures at 1–2 m depth. In general, the slope of a pulse
is about 10 cm of penetration per day.
In the spring, fall, and winter, surface-based temperature inversions are
prevalent and the warmest layers of the atmosphere occur
between 100 and 1000 m a.g.l. as can be seen in Fig. a.
In fact, the minimum temperature in the near-surface layer (-2 to
20 m) occurs at the surface 46 % of the year. At times the
subsurface is the warmest level in the full temperature profiles
(-2 m to 5 km) shown in Fig. a. The average
monthly surface temperature is colder than the average 500 and -1 m
temperatures from September to April (Fig. b), although January
2014 had anomalously warm (compared to Januaries 2011–2013) surface
temperatures. The maximum temperature in the near-surface layer occurs at the
surface only 3.4 % of the year, indicating that the default state of the
system is strong surface cooling to space.
Advection of air masses over the GIS is the foundational mechanism that
influences temperatures at the surface. Temperature changes at
1–5 km a.g.l. are indicative of synoptic influences that transport
warmer or colder air masses to Summit. During 10 January 2014
(Fig. a) warmer air advection corresponds to relatively warm
surface temperatures of -25 ∘C. Yet there are instances, such as
15 January–4 February 2014, with large variability in Tsurf that
are not associated with large-scale advection, as evidenced by fairly
constant temperatures from 50 m to 5 km in altitude. The
correlation between the temperatures at 5 km and the surface is 0.77
and from 1 to 2 km the correlation with surface temperature increases
to 0.87. Seasonal synoptic variations in the free troposphere above
≈ 1 km influences surface temperatures, especially when the
downwelling longwave emission originates from the warmest levels of the
atmosphere. Synoptically driven warm air advection enhances the formation of
optically thick liquid-bearing clouds, which decrease the difference in
emitted longwave radiation between the air aloft and the surface.
Surface energy budget
Annual cycle
Monthly averages of the four SEB terms from Eq. () illustrate
the seasonal balance of energy fluxes at the surface (Fig. ). The
bottom numbers in Fig. indicate the percentage of the month for
which all four SEB terms are available. In addition, Fig. includes
additional data for Q, SH, and LH indicating that July 2013–June 2014 is,
in general, consistent with previous years and indicates that January 2014
was somewhat anomalous. The extended data periods for Q, SH, and LH all end
June 2014 and include start dates of January 2011, June 2011, and March 2012,
respectively.
The sensible and radiative heat fluxes have nearly compensating influences on
the SEB during the non-summer months when temperature inversions are
prevalent. During the summer, on average, all SEB terms are relatively small
in magnitude. The monthly mean total radiative flux (Q) is positive in June
and July (Fig. ). Only these two months correspond to periods when
the amount of absorbed SW exceeds the net LW radiational cooling. June and
July are also when the sensible and latent heat fluxes are at their seasonal
minima. The subsurface heat flux monthly minimum values occur a month earlier
in the year, due to the cooler subsurface temperatures in the spring compared
to the fall (Fig. ). Colder subsurface temperatures enhance the
ability of the GIS to remove heat from the surface via conduction, resulting
in a mean cooling effect in the spring and warming effect in the fall.
Over the entire year the SEB residual, or the sum of all the SEB terms, when
available (75.3 % of the time), is 0.9 Wm-2. The monthly
residuals (top numbers in Fig. ) indicate that there are times of
the year when the residuals are larger but there is no apparent seasonality
in the combined SEB terms. Generally, the monthly mean residuals could be due
to energy imbalances, under sampling, measurement biases, and/or measurement
uncertainties. Each monthly residual is below the total SEB uncertainty
(excluding the S term) of 12.4 Wm-2.
Monthly mean values of the four SEB terms for the period July
2013–June 2014. The values at the top of the figure are the monthly residual
of the SEB (Wm-2). The values at the bottom of the figure are the
percentage of the month for which all four SEB terms are available.
Monthly–hourly mean values from July 2013 to June 2014 of
(a) total radiative flux, (b) sensible heat flux,
(c) conductive heat flux, and (d) latent heat flux. Black
contour lines indicate the solar elevation angle. Units on the color bars are
all in Wm-2.
Diurnal cycles
The magnitudes of the monthly mean SEB terms are small from May to August
(< 10 Wm-2), yet the diurnal variability peaks during this
period, driven largely by the solar cycle. The net radiative flux increases
during times of peak insolation (Fig. a), although the high
surface albedo limits the maximum Q to 40 Wm-2. The maximum
values of the net radiative flux occur in July, when the sun still rises more
than 30∘ above the horizon and liquid-bearing clouds are frequent
(Fig. a, b), which act to radiatively warm the surface at
Summit Station year round .
Counteracting the net radiative flux, the sensible heat flux is negative for
large sun angles and warms the surface by approximately 20 Wm-2
when the sun is below the horizon (Fig. b). The diurnal
variability for this term is largest in summer due to an enhanced diurnal
cycle of the near-surface temperature gradient . The
cooling effect of the conductive heat flux (Fig. c) is most
prominent when the sun is above the horizon and is maximized at solar noon.
In agreement with the results in Fig. , more conductive surface
cooling occurs in the spring compared to the fall due to the lag in
subsurface response, which results in relatively colder subsurface
temperatures in the spring. The diurnal variability of the latent heat flux
is largest in June ranging from hourly average values of -33 to
12 Wm-2 (Fig. d) due to an increase in available
moisture (Fig. c).
Sun angle, and the associated change to the net radiative flux, is a main
driver of energy fluxes at the surface (Fig. ). The monthly–hourly
energy fluxes in Fig. b–d are generally anticorrelated with the
net radiative flux in Fig. a (correlation coefficients are b= -0.81, c= -0.65, d= -0.69). The following case studies
investigate how liquid-bearing clouds effect the surface energy budget by
increasing the net surface radiation.
(a) MMCR derived cloud fraction (solid) and MWR derived
liquid present fraction (dotted, LWP > 5 gm-2),
(b) liquid water path, and (c) precipitable water vapor.
Statistics shown in black (red) are for available data spanning July
2013–June 2014 (January 2011–June 2014). Distributions are represented by
box-and-whisker plots (the box indicates the 25th and 75th percentiles, the
whiskers indicate 5th and 95th percentiles, the middle line is the median,
and the * is the mean).
A case study from 12 UTC on 10 November 2013 to 12 UTC on
11 November 2013. (a) Cloud occurrence as seen by the MMCR;
(b) liquid water path; (c) longwave upwelling and
downwelling radiation; (d) Richardson number; (e) surface
energy fluxes: total radiation, sensible heat, latent heat, conductive heat,
and heat storage/10.0; and (f) subsurface temperatures.
Cloud forcing case studies
Liquid-bearing cloud without insolation
A case study (12 UTC 10 November to 12 UTC 11 November 2013) is used to
illustrate how the different terms of the SEB interact to influence the
surface temperature and surface heat exchange. Variability in this case is
driven by low-level liquid-bearing clouds and the case was intentionally
chosen to minimize the effects of solar influences. Cloud occurrence as
measured by the MMCR up to a height of 5 km (Fig. a)
indicates a clear-sky scene at the beginning of the case study, a low-level
cloud from 17 to 2 UTC, then a brief period of clear-sky from 2 to 3 UTC,
and finally a deep cloud (> 3 km) during the end of the case
study. The radar reflectivity measurements indicate the presence of ice
crystals in most of these clouds. LWP values ranging from 20 to
60 gm-2 from 17 to 24 UTC on 10 November (Fig. b)
show that the low-level cloud at this time is mixed phase, in contrast to the
deep ice cloud at the end of the case study with little liquid present.
Coincident with the appearance of the liquid-bearing cloud, the
LW↓ increased by 88 Wm-2 from 15 UTC (clear) to
23 UTC (cloudy), similar to the LW CRF value in
for optically thick liquid-bearing clouds
(≈ 85 Wm-2). This cloud radiative effect resulted in an
increase in Tsurf and thus LW↑ of 43 Wm-2
(Fig. c). During the clear-sky period the boundary layer was
weakly stable (Ri = 0.15), but the occurrence of the
liquid-bearing cloud and its warming effect on the surface changed the
stability to neutral (Ri ≈ 0) (Fig. d). During
the transition back to clear-sky (2 UTC), LW↓ decreased by about
70 Wm-2 and the Richardson number became critically stable.
LW↓ was smaller in the presence of the deep ice cloud, compared to
the liquid-bearing cloud, resulting in a much smaller LW↑ at the
time. In the presence of the deep ice cloud the boundary layer became weakly
stable again (Ri = 0.2).
Changes to the net radiative flux caused by the cloud (Fig. e)
elicited a response in the other SEB terms. On 10 November from 15 UTC to
23 UTC the sensible heat flux decreased by a factor of 2, from 36 to
18 Wm-2. The conductive heat flux changed from having a warming
effect on the surface by +8.1 Wm-2 to having a
-0.3 Wm-2 cooling effect by 23 UTC. The average latent heat
flux increased from 0.8 Wm-2 during the clear-sky period
(12–18 UTC) to an average value of 2.4 Wm-2 during the cloudy
period (18–24). The net result is that the liquid-bearing cloud increased
the surface temperature from -47.8 ∘C (15 UTC) to
-33.0 ∘C (23 UTC). This is half the temperature increase that
would have occurred (≈ 28.4 ∘C) if the entire
LW↓ increase (88 Wm-2) had gone toward heating the
surface. This example demonstrates how changes to the turbulent and
conductive heat fluxes are an important compensation mechanism that modulates
surface warming due to CRF. This damping effect on the
radiative forcing by the response terms was noted by previous Arctic
researchers e.g.,.
The subsurface cooled in response to the surface cooling during the clear-sky
period on 10 November (Fig. f), yet the minimum measured
temperature at -0.2 m (-41.8 ∘C) was not realized until
18 UTC. This shallowest subsurface temperature sensor (-0.2 m)
cooled by 0.8 ∘C from 12 to 18 UTC on 10 November. The cooling from
above at -0.2 m on 10 November was damped by the relatively warm
snowpack below. During the liquid-bearing cloud period the subsurface layer
at -0.2 m was warmed from above and below allowing for a
1.8 ∘C temperature increase from 18 UTC on 10 November to 2.5 UTC
on 11 November. This suggests that a time lag of the effect of the surface
temperature on the subsurface temperatures is important in determining the
ground heat flux. The heat storage in the upper layer of snow had an average
value of -12.9 Wm-2 for the 24 h
period shown in
Fig. e, indicating that a portion of the increase in
LW↓ went toward increasing the internal energy of the top layer of
snow. Large negative values of S occur during the transition from clear to
the onset of the liquid-bearing cloud presence (17–20 UTC), as this layer
warms rapidly, and vice-versa during the transition back to a clear-sky scene
(0–2 UTC).
Liquid-bearing cloud with insolation
A case study on 6 August 2013 also illustrates the longwave warming effect of
liquid-bearing clouds and investigates the additional influence of shortwave
radiation. Similar to the first case study, surface temperature variability
is driven by the downwelling radiative flux, which in this case is a
combination of longwave and shortwave influences.
MMCR measurements (Fig. a) indicate a clear-sky scene from 2 to
6 UTC, a low-level cloud from 6 to 13.5 UTC, clear-sky from 13.5 to
16 UTC, a deep cloud from 18 to 22 UTC, and finally a low-level cloud
during the last hour of the case study period. The low-level cloud is mixed
phase from 6 to 13.5 UTC and LWP values ranging from 0 to
15 gm-2 (Fig. b) indicate that it is optically thin.
LWP values ranging from 0 to 20 gm-2 also indicate that the deep
cloud later in the day is mixed phase from 18 to 21 UTC, although after
≈ 19 UTC LWP values are low due to competition from falling ice
into the mixed phase layer from above. The low-level cloud from 23 to 24 UTC
is optically thicker then the previous low-level cloud with LWP ranging from
5 to 30 gm-2.
A case study on 6 August. (a) Cloud occurrence as seen by
the MMCR; (b) liquid water path; (c) longwave upwelling,
longwave downwelling, and net shortwave radiation; (d) surface
energy fluxes: total radiation, sensible heat, conductive heat, and heat
storage/10.0; and (e) subsurface temperatures.
The presence of the optically thin liquid-bearing cloud (6–13.5 UTC)
produces an approximate increase of 70 Wm-2 of LW↓
compared to the preceding clear-sky scene. Over this period shortwave
radiation increases the net radiation at the surface by an additional
5–75 Wm-2. In response, LW↑ radiation increases by
50 Wm-2. The combination of thin liquid-bearing clouds and
insolation produces positive net radiation at the surface from 9.5 to 13 UTC
(Fig. c). During the daytime clear-sky period the net radiation is
near zero, indicating that shortwave warming is offset by the longwave
cooling at the surface. Net radiation again goes positive in the presence of
liquid-bearing clouds that occur after 18 UTC. After 18 UTC the net
radiation declines as the solar radiation diminishes.
The compensating response of the non-radiative terms to changes in the
downwelling radiation, shortwave and/or longwave, is similar to the November
case study. The sensible heat flux decreases from 29 Wm-2 at
5 UTC to -9 at 12.5 UTC (Fig. d). The fact that the SH is
negative during the presence of the liquid-bearing cloud indicates that the
surface temperature is warmer than the 2 m temperature; thus the
near-surface atmospheric layer is unstable. The conductive heat flux
decreases from 9 Wm-2 at 5 UTC to 0 Wm-2 at
12.5 UTC, indicating the subsurface temperature gradient as been reduced
(Fig. e). The 10 m temperatures from 9 to 16 UTC are
questionable and thus LH is not shown during this period. During the daytime
clear-sky period (13.5–16 UTC) the net radiation is near zero as is the
ground heat flux and sensible heat flux. In the presence of the deep
mixed-phase cloud after solar noon the net radiation again is positive, the
sensible and ground heat flux are near zero, and the latent heat flux is
approximately -10 Wm-2. Section expands
the analysis to include annual responses of the LW↑, latent,
sensible, and conductive heat flux terms to changes in
LW↓ + net SW.
Responses to surface radiative forcing
The surface energy budget at Summit Station is largely driven by changes in
the downwelling radiation. In general, the LW↑, turbulent, latent,
and subsurface heat fluxes (response terms) respond to changes in the
LW↓ and net SW flux (forcing terms). The response terms are not
always governed by the forcing terms, as, for instance, under high wind
conditions the turbulent heat fluxes can operate independently as the
Ri in these cases is dominated by the wind shear (see
Eq. ). Cloud presence influences the radiational balance at
the surface by modulating the downwelling radiation; increasing
LW↓ and decreasing SW↓. show that
clouds increase the net surface radiation compared to an equivalent clear-sky
scene, because the high year-round surface albedo limits the magnitude of the
cloud SW cooling effect to less than that of the LW warming effect.
Statistical relationships for the current study reinforce the fact that
liquid-bearing clouds increase the forcing terms during two distinct periods:
with and without solar insolation (Fig. a). Hence, the occurrence
of liquid-bearing clouds correspond to warmer surface temperatures in both
circumstances (Fig. b) and consequently greater LW↑
(Fig. c), which is proportional to the surface temperature to the
fourth power. In addition, variability in surface albedo acts as a forcing,
although at Summit the magnitude of downwelling radiation variations are much
greater than the effect of albedo variations on forcing terms.
LW↑ has less variability (all cases in Fig. c) than the
variability of the forcing terms (all cases in Fig. a). In
addition, the differences between the cloudy and non-cloudy states are more
pronounced in Fig. a, compared to Fig. c. Thus,
compensation by the non-radiative SEB terms must account for imbalances to
the radiative flux at the surface, as illustrated in the case studies
presented in Sect. and in Figs.
and . The annual cycle of the responses of LH, SH, G, and
LW↑ are explored in Sect. after investigating the
effect of liquid-bearing clouds and/or sun angle on boundary-layer stability
(Sect. ).
Statistics of (a) LW↓+ net SW,
(b) surface temperature, and (c) LW↑ for the
period spanning January 2011–June 2014. (d) Statistics of the bulk
Richardson number for the period spanning March 2012–June 2014. The black
distribution represents all quality-controlled cases. The red (blue)
distributions represent periods when the wind speed < 8 ms-1
and the solar zenith angle is < 70∘ (> 90∘).
Distributions are represented by box-and-whisker plots (the box indicates the
25th and 75th percentiles, the whiskers indicate 5th and 95th percentiles,
the middle line is the median, and the * is the mean).
Boundary-layer stability response
The degree to which the overlying atmosphere can dynamically interact with
the surface is important for determining the turbulent heat exchange.
Atmosphere–ice sheet interaction is modulated by low-level stability, which
can be influenced by both thermodynamic and dynamic processes. Mechanical
mixing, via high wind speeds, is one way to decrease near-surface stability
and increase turbulence near the surface. The 10 m wind speed is
greater than 8 ms-1 for 16 % of 32 130 stability estimates.
The median Richardson number decreases from 0.19 for all cases to 0.06 for
the cases that report higher wind speeds (> 8 ms-1), showing
the expected decreases of stability. In addition, cloud-driven atmospheric
mixing can also affect the low-level atmospheric structure
and liquid-bearing cloud presence, especially in
combination with enhanced solar radiation, decrease the near-surface
temperature gradient .
This study explicitly shows that the radiative influences of liquid-bearing
clouds and/or insolation create neutral or unstable boundary-layer
conditions. When the sun is below the horizon, as for the first case study
(Sect. ), the presence of liquid-bearing clouds
decreases the stability such that a majority of the cases are weakly stable
(0< Ri < 0.25) (Fig. d). In the absence of
liquid-bearing clouds (LWP < 5 gm-2) the surface radiatively
cools, the stability increases, and consequently a majority of the cases are
strongly stable (Ri > 0.25). Solar radiation
(SZA < 70∘) warms the surface sufficiently to decrease the
near-surface stability (Fig. d). When the sun is present yet
there are no liquid-bearing clouds the median Ri is weakly stable.
However, when optically thick liquid-bearing clouds
(LWP > 30 gm-2) are present the boundary layer is
near neutral on average. Interestingly, optically thin liquid-bearing clouds
(5 gm-2 < LWP < 30 gm-2) lead to more
frequent occurrence of more unstable conditions in the presence of
insolation, because these clouds emit significant longwave radiation while
also allowing significant penetration of solar radiation, thus producing the
maximum surface heating. Our results that liquid-bearing clouds of
intermediate thickness lead to higher instability agree with studies that
show these clouds produce the maximum CRF for elevated
sun angles . Hence, liquid-bearing clouds
and/or solar insolation enhance turbulent mixing, facilitating sensible and
latent heat exchange, although instability (negative Ri) requires
SW↓.
Linear regression of data from July 2013 to June 2014.
(a) Total response (SH, LH, -LW↑, and G) as a function
of the forcing terms (LW↓+ net SW). (b) LW↑,
(c) conductive heat, (d) sensible heat, and
(e) latent heat flux as a function of the forcing terms. The slope
of the best fit linear regression is included in each panel.
SEB responses
Process-based relationships distill our understanding of the underlying
physical processes into a succinct form that is informative, yet practical.
While clouds, the solar cycle, and other processes can influence the
downwelling radiation, process relationships between response terms and
forcing terms reveal how variability in downwelling radiation affects the
other SEB terms. Performing a linear fit fitexy, on
the relationship between the forcing and response terms, which includes
uncertainties in both terms, yields a slope of -1.01 (Fig. a),
indicating that the SEB is largely radiatively driven, the response terms
account for all of the forcing energy flux, and there is approximate closure
for the SEB terms calculated here. The scatter in this relationship is due to
measurement uncertainties, mismatches of response times in different terms,
and the spatial distribution of the instrumentation. The annual evolution of
this slope (Fig. ) shows that the SEB response terms balance the
forcing terms to within ≈ 10 % in all months of the year. Thus,
any change in forcing terms elicits an approximately equal change in flux
through the combination of response terms.
The response to the radiative forcing can be evaluated for each term
independently (Fig. b–e), and as a function of month, showing
that each term responds differently throughout the annual cycle
(Fig. ). The slope of the linear fit provides an estimate of the
relative magnitude (percentage) of the response of each term. The RMS error
of the monthly response estimates in Fig. is calculated by
comparing the estimated values, using the linear fit, to the measured values
(Fig. ). The RMS error includes the uncertainty of the
measurements involved, any delay in response time greater than
30 min, and variability in the physical response not represented by
the linear fit. Generally, the RMS error of the linear fits of all response
terms to the driving terms are on the same order of magnitude as the combined
uncertainty of the SEB components.
Annual cycle of monthly linear regression of responses to the
forcing terms. The solid lines are for data spanning July 2013–June 2014
during which all SEB estimates are available. The dashed lines are
representative of all available data for the given subset. Note that the
y axis decreases upwards.
The annual response in the LW↑ term (77 %, Fig. b)
is the largest out of all the response terms, as its magnitude is directly
proportional to the surface temperature to the fourth power. The annual cycle
of this response shows a weaker response in summer (50–60 %) and a
stronger response in winter (65–85 %). The lower response of the
LW↑ term in June 2014, compared to winter months during December
2013–February 2014 (or compared to values from June 2011 to 2014), is
partially due to the increased response of the latent heat flux for this
specific month (Fig. ). Any increase (decrease) of response of an
individual term will effectively decrease (increase) the change in surface
temperature, and hence the response of LW↑, to radiative forcing.
The response of the sensible heat flux (11 %, Fig. d) is
fairly constant throughout the annual cycle (Fig. ) due to its
dependence on both the near-surface temperature gradient and stability (heat
transfer coefficient – see Eq. ). For weakly stable
conditions, the former term dominates decreasing (increasing) the heat flux
for surface warming (cooling), while for very stable conditions the latter
term dominates limiting turbulent exchange and increasing (decreasing) the
sensible heat flux for surface warming (cooling)
e.g.,. Since these Summit data generally show a
decrease in sensible heat flux for an increase in the forcing terms (surface
warming), this is consistent with weakly stable conditions on the unstable
side of the stability transition shown by . Therefore,
the response of the sensible heat flux to changes in the surface temperature
is similar throughout the year and does not show an annual cycle. However,
the RMS error of the linear fit (Fig. ) during winter
(9.7 Wm-2) is greater than during summer (6.0 Wm-2)
(i.e., there is more scatter in the sensible heat response in winter),
suggesting that conditions in winter are at times very stable and that the
sensible heat flux response to radiative forcing is then different. In
summer, conditions are rarely very stable so the response in sensible heat
flux is more strongly correlated with the change in the forcing terms.
Root mean square error (Wm-2) computed from the
differences between the measured response of a given term (or combination of
terms) and the estimated monthly responses in
Fig. .
The response of the latent heat flux (1.5 %, Fig. e)
increases in summer compared to other months of the year (Fig. ).
The amount of available moisture (Fig. c) peaks in summer and
average PWV values for non-summer (winter) months are below 2 mm
(1 mm). Thus, changes to near-surface stability due to changes in the
forcing terms produce a smaller response when moisture gradients are small in
magnitude.
The response of the conductive heat flux to radiative forcing (10 %,
Fig. c) is greatest in winter (December–February) at 23 %
compared to 9 % in summer (June–August). Seasonal changes in the
conductive heat response are due to changes in snow density, thermal
conductivity, and subsurface temperatures. Warmer subsurface temperatures
resulting from prior warm surface temperatures precondition the snowpack,
reducing its ability to remove heat from the surface. Decreased density in
the summer decreases the thermal conductivity of the near-surface snow pack,
also limiting the ability of the subsurface to remove energy from the
surface. The RMS error of the linear fit of the conductive heat flux to the
forcing terms is relatively low with an annual mean of 3.2 Wm-2.
The response of the heat storage in the upper subsurface layer is important
to consider when accounting for all the energy responses at the surface. Even
though the annual mean of S is less than 1 Wm-2 (i.e., there
is effectively no annual net change in temperature in the near-surface snow),
it is highly variable (annual standard
deviation = 62.5 Wm-2) as this layer can warm or cool
rapidly from one half hour period to the next. The heat storage response to
the forcing terms also accounts for subsurface heating due to solar
penetration. Over the annual cycle the response of S ranges from 4 % in
June to 8 % in March, with an average monthly response of 6 %
(Fig. ). The slightly larger response of S in March–April
indicates the relatively cold near-surface snow is able to store larger
amounts of energy originating from radiative sources.
Since scatter in S in response to forcing is so large, we first examine the
scatter of all the other terms jointly. The RMS error of the linear fit of
(LH + SH +C-LW↑) vs.
(LW↓ + net SW) is maximum in July (19.6 Wm-2)
and has an annual mean value of 15.0 Wm-2 (Fig. ).
The maximum RMS error occurs in summer due to an increase in the latent heat
RMS error of the linear fit from an annual average value of 9.1 to
15.7 Wm-2 in summer. The RMS error of the linear fit of S is
lowest in January (36 Wm-2) and highest in August
(89 Wm-2) and has monthly mean RMS error of
63 Wm-2. The high variability, uncertainty, and generally weaker
relationship of S with the forcing terms indicate that the estimation of
S is the largest unknown in closing the energy budget on short timescales.
The 1σ uncertainty of the response of
LH + SH +C+S-LW↑ to the forcing terms, shown
by the error bars in Fig. , is primarily due to the variability
and associated uncertainty in S. However, correctly accounting for the
ground heat flux in the upper most layer provides near closure of the surface
energy balance, a critical accomplishment of the synthesis of comprehensive
data sets given here.
At the ice sheet–atmosphere interface surface temperature is the linchpin
that connects the subsurface to the atmospheric boundary layer, responding to
changes in the net flux at the surface. The variability in the surface
temperature is controlled by changes in the forcing terms and modulated by
the response terms. An increase in radiative forcing warms the snowpack;
increasing the surface temperature and decreasing the near-surface
atmospheric stability. Not surprisingly, the response terms are all
associated with surface temperature – either directly proportional or a
function of the near-surface temperature gradient. Latent heat flux is also
dependent on the near-surface moisture gradient and the ground heat flux is
dependent on the thermal conductivity of the snow pack, leading to seasonal
differences in their responses. This study highlights the importance of the
seasonal changes in the non-radiative responses, which determine the annual
cycle of the LW↑ response.
Cloud effects on the SEB
The seasonal response of the SEB to cloud presence is estimated by combining
the radiative effects of clouds with the observationally based and
statistically derived relationships between the forcing and response terms.
CRF at the surface, as detailed in
, is the instantaneous net radiative effect of clouds.
Furthermore, changes in the forcing terms elicit a response of the surface
temperature and the non-radiative SEB terms. Thus, we combine the monthly CRF
values reported in and monthly responses, calculated
from the maximum available data (Fig. ), to estimate the
corresponding increase in LW↑ and decreases in SH, LH and G
attributed to cloud presence. Figure a shows LW↑ has the
smallest increase due to CRF in May (11.8 Wm-2), the largest
increase in October (33.2 Wm-2), and an annual mean response of
23.4 Wm-2. The non-radiative responses to the annual CRF value
of 32.9 Wm-2 are -3.0 (SH), -0.24 (LH), and -7.2
(G) Wm-2. Subtracting the monthly LW↑ response from
the monthly mean LW↑ yields an estimate for the amount of LW
radiation that would be emitted by the GIS surface in the absence of clouds.
Comparing the monthly mean surface temperatures, derived from the measured
LW↑ and the estimated clear-sky LW↑, produces the
approximate monthly differences shown in Fig. b, suggesting that
clouds increase the surface temperature by 7.8 ∘C annually during
the time period January 2011–October 2013.
(a) The annual cycle of cloud radiative forcing (black)
from January 2011 to October 2013 and estimated annual
cycle of responses, calculated from the values in Fig. , of
sensible heat flux, latent heat flux, ground heat flux, and LW↑.
(b) Monthly temperature effect due to clouds, estimated from the
difference between the measured LW↑ and the estimated clear-sky
LW↑ value, for the period January 2011–October 2013.
Summary
Characterization of surface energy
fluxes and their variability illuminates the important processes that control
surface temperatures in central Greenland. Here observations from Summit
Station are used to derive all terms of the surface energy budget and to
examine key relationships among these terms and with other key atmospheric
drivers. Despite the harsh Arctic environment SEB estimates could be made for
all the terms for 75 % of the year spanning July 2013–June 2014.
Over the annual cycle atmospheric temperatures in the free troposphere
(> 1 km) are well correlated with surface temperatures, although
energy exchange processes at the surface enhance surface temperature
variability. In general, time-series data, monthly mean values, and monthly
diurnal cycles all show that the non-radiative SEB terms oppose the increase
or decrease of the net radiation. Liquid-bearing clouds and solar insolation
strongly modulate the radiative flux that reaches the surface, which affects
subsurface temperatures, the stability of the boundary layer, and the
near-surface temperature gradients. A pair of case studies illustrate how all
the pieces fit together to depict how an increase in surface radiation
elicits a response in the surface temperature, while also indicating that the
increase in temperature is lessened by a decrease in sensible and conductive
heat fluxes. The resultant compensation of the non-radiative SEB terms
thereafter affects the net amount of surface warming that occurs due to cloud
radiative forcing and/or insolation. Similar compensation is apparent when
looking at longer-term averages.
To examine these relationships in more detail, radiative forcing terms
(LW↓ + net SW) were related to the response terms (SH, LH,
C, S and LW↑) throughout the annual cycle. Linear regression
analysis, for the year-round data set relating the response terms as a
function of the forcing terms, resulted in a -1.01 slope, indicating
general closure in the calculated SEB terms. On average LW↑, which
is directly linked to surface temperature, responds by about 70 % of a
perturbation in incident radiation, with a diminished response in summer.
Quantifying how each non-radiative response changes throughout the year
provides insight into how much SH, LH, and/or G limit the surface
temperature increase due to the occurrence of liquid-bearing clouds and/or
insolation:
Latent heat flux response is near-zero for much of the year, with an
increased response in summer.
Sensible heat flux response is fairly constant throughout the annual
cycle (≈ 9 %).
Ground heat flux, consisting of both heat storage in the upper most
≈ 20 cm of snow and the conductive flux below this layer, is
the largest non-radiative response for most of the year, with a decreased
response in summer.
The enhanced summer latent heat flux response is due to an increase in
available moisture and an increase in turbulence during relatively frequent
periods of neutral/unstable near-surface conditions. In winter the effect of
the stable boundary layer is to dampen the response of the turbulent sensible
heat flux, yet this dampening effect is offset by the enhanced near-surface
temperature gradient. The consequence of a limited sensible heat exchange
during periods of strong radiational cooling is that the sensible heat flux
response is relatively constant throughout the annual cycle. Finally, the
ground heat flux response decreases in the summer due to decreases in
near-surface snow density and warmer subsurface temperatures.
A previous study by , spanning the time period 17 June
2000–18 June 2002, also reports the annual cycle of the surface energy
budget components at Summit Station. Comparing the annual mean values of this
study to the earlier study reveals that Q is 6.8 Wm-2 smaller
and SH, LH, and G are 1.6, 0.9, and 4.8 Wm-2 larger,
respectively. The differences in the annual mean values could be due to
possible decreases in cloud cover , since the recent
annual forcing value is 7.3 Wm-2 smaller than the
190.1 Wm-2 reported by . July 2014 had the
largest occurrence of liquid-bearing clouds for the current study resulting
in an average Q of 6.1 Wm-2 compared to 15.6 Wm-2
reported by . The July 2014 forcing terms are
265.3 Wm-2 compared to 268.0 Wm-2 in 2000–2002,
suggesting that a 6.8 Wm-2 increase in LW↑ is likely
due to synoptically driven warmer air masses above Summit Station in 2014 and
not due to changes in CRF.
In central Greenland, cloud presence in winter (longwave forcing) is unable
to produce a neutral stratification. It is only with insolation that neutral
and unstable conditions exist. In contrast, over Arctic sea ice, wintertime
conditions are near neutral or even slightly unstable nearly 25 % of the
time . More instability over sea ice compared to the
GIS may be due to warming of the surface from below due to
oceanic influences. Springtime/summertime near-neutral and slightly unstable
conditions with shortwave forcing observed here is similar to that observed
over sea ice e.g.,.
Also in agreement with our findings are process diagrams obtained via a
modeling study over sea ice that found the non-radiative
SEB terms lessen the change in surface temperature due to changes in
downwelling radiation. Moreover, observational studies over sea ice
and in the Greenland ablation zone
suggest that if/when Summit Station more
frequently experiences melt the non-radiative compensation, detailed in this
study, may be significantly diminished as energy goes towards surface
melting.
These central Greenland results can be used to evaluate how well the annual
and diurnal cycles of the SEB terms are represented in climate models and
reanalyses, and specifically the relationship among key terms. It is known
that global climate models underestimate the occurrence of liquid-bearing
clouds above Greenland . We estimate that the
underrepresentation of clouds, especially liquid-bearing clouds, should
produce annual surface temperature biases ranging from 0 to
-7.8 ∘C. If the representation of liquid-bearing clouds were to
improve then the modeled downwelling radiation would likely also improve, but
it is unclear if the other SEB terms would realistically adjust. A regional
or global climate model's modus operandi is to achieve absolute closure of
the SEB; hence this study will be useful in future studies as a valuable tool
for pinpointing the processes responsible for possible model surface
temperature bias over Greenland and for evaluating model representation of
physical processes at the ice sheet–atmosphere interface.