Sea ice leads are an important feature in pack ice in the Arctic. Even covered by thin ice, leads can still serve as prime windows for heat exchange between the atmosphere and the ocean, especially in the winter. Lead geometry and distribution in the Arctic have been studied using optical and microwave remote sensing data, but turbulent heat flux over leads has only been measured on-site during a few special expeditions. In this study, we derive turbulent heat flux through leads at different scales using a combination of surface temperature and lead distribution from remote sensing images and meteorological parameters from a reanalysis dataset. First, ice surface temperature (IST) was calculated from Landsat-8 Thermal Infrared Sensor (TIRS) and Moderate Resolution Imaging Spectroradiometer (MODIS) thermal images using a split-window algorithm; then, lead pixels were segmented from colder ice. Heat flux over leads was estimated using two empirical models: bulk aerodynamic formulae and a fetch-limited model with lead width from Landsat-8. Results show that even though the lead area from MODIS is a little larger, the length of leads is underestimated by 72.9 % in MODIS data compared to TIRS data due to the inability to resolve small leads. Heat flux estimated from Landsat-8 TIRS data using bulk formulae is 56.70 % larger than that from MODIS data. When the fetch-limited model was applied, turbulent heat flux calculated from TIRS data is 32.34 % higher than that from bulk formulae. In both cases, small leads accounted for more than a quarter of total heat flux over leads, mainly due to the large area, though the heat flux estimated using the fetch-limited model is 41.39 % larger. A greater contribution from small leads can be expected with larger air–ocean temperature differences and stronger winds.
Leads are linear structures of the ocean surface within pack ice that are
exposed to the atmosphere during an opening event caused by various forces,
such as wind and water stresses. In winter, thin ice forms quickly in newly
opened leads due to the large temperature difference between the ocean and
the atmosphere (Kwok, 2001). The opening of leads breaks the continuity of
insulating ice and creates windows for a stronger air–ocean interaction.
Newly opened leads are the main source of ice production, brine rejection,
and heat transfer from the ocean to the atmosphere (Alam and Curry, 1998).
Turbulent heat flux over open water could be 2 orders of magnitude larger
than that through mature ice (Maykut, 1978). Although decreasing rapidly
with growing ice thickness, ice growth rates can still be an order of
magnitude larger for 50 cm thick young ice than for 3 m thick ice (Maykut,
1986). In the central Arctic, open water usually comprises no more than
1 % of the ice pack area during the winter. However, open water, together
with thin ice (
Leads also allow more surface absorption of radiation due to their lower albedo compared to thick ice. This will accelerate sea ice thinning in summer and delay refreezing in early winter and therefore decrease the mechanical strength of the ice cover and allow even more fracturing, larger drifting speed and deformation, and faster export of sea ice to lower latitudes (Rampal et al., 2009). As the ice pack gets thinner (Kwok and Rothrock, 2009) and more mobile (Spreen et al., 2011), favorable for deformation and opening, networks of more intensive lead with stronger local influence are expected.
Since the late 1970s, remote sensing images obtained by satellite sensors,
including optical, thermal, and microwave, have been used to detect sea ice
leads in the Arctic (Fetterer and Holyer, 1989; Fily and Rothrock, 1990; Fett
et al., 1997). Lindsay and Rothrock (1995) promoted the concept of potential
open water for lead detection, which requires both temperature and albedo
differences between ice surface pixels and open water tie points. Based on
different emissivities of thin ice at two microwave frequencies available
for the Advanced Microwave Scanning Radiometer for the Earth Observing
System (AMSR-E), Röhrs and Kaleschke (2012) developed a retrieval
algorithm to estimate Arctic lead concentration, similar to sea ice
concentration. The algorithm could provide subpixel information on lead
distribution, but the resolution is still too coarse to detect small leads
prevailing in pack ice. Willmes and Heinemann (2015) mapped pan-Arctic lead
distribution at 1 km resolution using the local temperature anomaly
Regardless of spectral characteristics used for lead detection, the scale dependence of lead statistics was explored in a few studies (Key et al., 1994; Weiss and Marsan, 2004; Marsan et al., 2004). Key et al. (1994) studied the effects of the sensor's field of view (FOV) using degraded optical images from the Landsat Multi-Spectral Scanner (MSS). They suggested that the mean lead width expands, and the lead fraction drops as the pixel size builds up in gradually degraded images. Assuming higher heat flux over narrow leads than wider leads, estimated turbulent heat flux was reduced by 45 % as the FOV was degraded from 80 to 640 m, mainly due to reduced lead fraction.
Bulk aerodynamic formulae are frequently used in climate models to generalize the turbulent heat flux from open water in Arctic pack ice (Lindsay and Rothrock, 1994; Walter et al., 1995). The bulk formulae attribute heat flux over leads to wind speed, temperature differences between the surface and the atmosphere, and a turbulent transfer coefficient for heat, which is a function of the stability of the near-surface atmosphere and the roughness of the surface. In this approach, Lindsay and Rothrock (1994) estimated sensible heat flux using surface temperature retrieved from the Advanced Very High Resolution Radiometer (AVHRR), while observations suggest that for small leads, down to dozens of meters in width, the discontinuity between leads and pack ice causes the creation of a thermal internal boundary layer (TIBL) in the bottom atmosphere, reducing turbulent heat exchange on the downwind side (Venkatram, 1977; Andreas et al., 1979). Convective plumes formed above leads may further complicate the process within the TIBL (Tetzlaff et al., 2015).
Models were developed for estimation of TIBL thickness and turbulent heat
flux over coastal polynyas, leads, and ice edges (Alam and Curry, 1997;
Andreas and Cash, 1999; Renfrew and King, 2000; Chechin and Lüpkes,
2017). Chechin and Lüpkes (2017) modeled boundary layer development
downwind of the ice edge, potential temperature, and mix-layer height, and
wind speed variation was analyzed as well. Renfrew and King (2000) modeled
turbulent heat flux over large fetch (5–50 km wide, typical for coastal
polynya) during cold-air outbreaks. The dependence of turbulent heat flux on
lead width was estimated in several studies (Andreas and Murphy, 1986; Alam
and Curry, 1997; Andreas and Cash, 1999). On the basis of the Monin–Obukhov
similarity theory and the surface renewal theory, Alam and Curry (1997)
estimated turbulent heat flux over leads using an intricate surface
roughness model (Bourassa et al., 2001). Sensible heat flux across a single
lead is integrated from fetch 0 to fetch
A power law distribution of lead widths was also reported in various studies (Wadhams, 1981; Wadhams et al., 1985; Lindsay and Rothrock, 1995), indicating that small leads prevail in the Arctic. Impacts of lead width on heat flux were reported by Maslanik and Key (1995) and Marcq and Weiss (2012) using different width distribution models. However, fetch-limited models have not been applied to surface temperature fields retrieved from remote sensing imagery to estimate turbulent heat flux at regional scale, due to the coarse resolution of operational thermal sensors. Fortunately, the launch of Landsat-8 in February 2013 has provided a unique opportunity for the estimation of turbulent heat flux with finer-resolution temperature fields.
In this paper, we derive lead distribution using thermal images from two sensors, Moderate Resolution Imaging Spectroradiometer (MODIS) and Thermal Infrared Sensor (TIRS) aboard Terra and Landsat-8, respectively, at different resolution scales. Then we estimate heat flux over leads with remote sensing temperature fields using both the bulk formulae and a fetch-limited model proposed by Andreas and Cash (1999). With the result, we analyze how the scale property of leads may affect the calculation of heat exchange through leads.
Three successive scenes of Level 1 terrain-corrected (L1T) Landsat-8 TIRS
images and one corresponding MODIS image acquired on 26 April 2015 were
used in this study (Table 1). As shown in Fig. 1, the mosaic image of the
three TIRS scenes covers an area of about 98 000 km
Satellite images and other data used in this study.
Location of study area. Background image is brightness
temperature from Moderate Resolution Imaging Spectroradiometer (MODIS) band
31 (
Willmes and Heinamann (2015) used the MOD29 ice surface temperature (IST) product (Hall and Riggs, 2015) from the National Snow and Ice Data Center (NSIDC) to retrieve leads. The MOD29 product is filtered for cloud contamination using a cloud mask from MOD35. However, inspection of the corresponding MOD29 map of the study area revealed that the pixels within leads marked as clouds are likely open water with ocean fog or plume over the surface (Fett et al., 1997). Apart from that, the study area within the Landsat-8 frame is mostly unobstructed by clouds. To preserve potential lead areas, we applied the NSIDC algorithm (Hall et al., 2001) to thermal images from MODIS L1B to calculate IST instead of using the MOD29. Therefore, no cloud mask procedure was performed in our study.
The Landsat-8 satellite is in the same near-polar, sun-synchronous, 705 km
circular orbit and position as the Landsat-5 satellite decommissioned in
2013. Landsat-8 data are acquired in 185 km swaths and segmented into 185 km
Note that in the L1T product, the TIRS bands at 100 m resolution were resampled to 30 m by cubic convolution and co-registered with the Operational Land Imager (OLI) spectral bands. Apart from the TIRS thermal bands, the top of atmosphere reflectance from the Landsat-8 near-infrared band was used for classification between ice and open water in surface temperature retrieval. A panchromatic band with a resolution of 15 m was used as validation data for lead detection in this study.
Key et al. (1997) developed an SWA for IST retrieval from AVHRR, and the
algorithm was then adapted for MODIS thermal images with a different set of
coefficients (Hall et al., 2001). The equation is as follows:
Since there is no special SWA available for sea ice surface temperature
retrieval from Landsat-8, a land surface temperature formulation (Du et al.,
2015) developed for a wide range of surface types, including ice and snow,
was used:
As reported in previous studies (Montanaro et al., 2014a, b, c; Barsi et al.,
2014), thermal infrared radiance measured by Landsat-8 TIRS suffers from stray light, which is caused
by out-of-field radiance that scatters onto the detectors, adding a
nonuniform banding signal across the field of view. The magnitude of this
extra signal can be
In remote sensing images, leads (thin ice and open water) are represented by negative albedo anomalies in the optical range, negative brightness temperature anomalies in the near-infrared (NIR), and positive surface temperature anomalies compared to the surrounding thick ice (Fett et al., 1997). Variance caused by uneven illumination, view angle, and air temperature should also be taken into account.
Willmes and Heinemann (2015) reported the use of surface temperature
anomalies to detect leads. The temperature anomaly
Generally, surface temperature anomalies for thick ice follow normal
distribution with a mean of zero; thus any large deviation from the mean can
be assumed as a potential lead and extracted using a proper threshold.
Several image-based threshold selection techniques for binary lead
segmentation were compared in Willmes and Heinemann (2015), and an iterative
threshold selection method (Ridler and Calvard, 1978) was recommended for
extracting leads from a temperature anomaly map. Assuming an initial
threshold using the mean temperature anomaly (
Using width samples crossed by transects, Lindsay and Rothrock (1995) found
a mean lead width between 2 and 3 km in the Arctic winter; larger means are
found in peripheral seas. We modified the method by using an orthogonal
system (vertical, south–north; horizontal, west–east; Fig. 2) to determine
lead width for every lead pixel. A minimum lead extent in two orthogonal
directions was selected for the pixel; i.e.,
Detection of lead width using two orthogonal directions.
Turbulent heat flux between the Arctic Ocean and the atmosphere, including
sensible (
Assuming that temperatures in the atmospheric boundary layer are determined
by the heat balance over thicker ice and turbulent heat exchange does not
vary significantly across the narrow areas of leads, then turbulent heat
fluxes are mainly determined by temperature and humidity differences between
the surface and atmosphere at reference height
When cold air travels to a warmer surface, a convective atmospheric TIBL
forms and thickens with distance downwind of the surface discontinuity or
fetch
To estimate turbulent heat flux over small leads, fetch-limited models were developed based on a few observations (Andreas and Murphy, 1986; Alam and Curry, 1997; Andreas and Cash, 1999). However, the assumption of universal water surface in leads and the application of sea surface roughness model (Andreas and Murphy, 1986; Alam and Curry, 1997) are not applicable in our case, where open water and thin ice dominate. Since the signal of TIBL is absent in the coarse grid of 2 m air temperature from the ERA reanalysis dataset, the data might not be appropriate to demonstrate the Alam and Curry (1997) model, which relies on the accurate measurement of meteorological parameters, whereas the Andreas and Cash (1999) model is more sensitive to lead width than atmospheric conditions (Marcq and Weiss, 2012). Therefore, only the Andreas and Cash (1999) model was used in our experiment.
Andreas and Cash (1999) gave direct formulations of heat fluxes as a
function of lead width
The coefficient
Turbulent heat flux rises with increasing temperature
difference
Turbulent heat flux for each width at wind speed of
5 m s
IST maps retrieved from MODIS and TIRS using Eqs. (
Ice surface temperature (IST) maps from MODIS and
Landsat-8 Thermal Infrared Sensor (TIRS) using split-window algorithms:
Although the median and artifact images show a little bias around large leads, the corrected TIRS IST map is very smooth and more suitable for lead detection and heat flux calculation. Scatter plots of IST from MODIS and TIRS before and after correction are shown in Fig. 7. The correlation of IST from two sensors estimated by interpolating MODIS IST to the TIRS scale (30 m) is quite good, with a Pearson coefficient of approximately 0.9 (0.902 and 0.896 before and after correction for stray light, respectively). The primary coefficient of linear regression improved from 1.025 to 1.004 before and after correction, indicating that the corrected TIRS IST is in better agreement with MODIS. However, the root mean square error (RMSE) from regressions increased from 1.216 to 1.233 K. It also reveals that for the 250–270 K temperature range, IST retrieved from TIRS is generally 0.61–0.70 K higher than that from MODIS.
Local median and noise image from TIRS IST:
Correlation between IST from MODIS and Landsat-8 TIRS
before and after correction for stray light. Black lines are reference for
Regional temperature anomaly maps calculated from IST maps are shown in Fig. 8. The mean surface temperature anomaly is 0.116 K with a standard deviation (SD) of 1.180 K for MODIS and 0.283 K with a SD of 1.619 K for TIRS.
Local temperature anomalies from
Binary lead maps were generated using iterative thresholds (Fig. 9). Large floes and small leads dominate the northern part of the images, where temperature is lower, while two very large leads can be observed in the southern portion. The maps illustrate that the lead binary retrieved from MODIS captures major lead structures, but small leads are missed in most cases compared to leads detected from TIRS.
Binary lead maps from
Lead area estimated from MODIS is 8074.0 km
Lead width was calculated for every lead pixel in the binary maps from MODIS
and TIRS and divided into three categories (Table 2): small leads (width
Retrieved leads from MODIS and TIRS and turbulent heat flux estimated using bulk formulae.
The width distribution of leads from MODIS and small leads from TIRS is plotted in Fig. 10 relating to the lengths of leads. Similar to the concept of number density, the length of each lead width can be fitted with a power law distribution, and the exponents from power law fitting are 2.241 and 2.346 for leads from MODIS and TIRS, respectively. The power law distribution indicates that narrow leads are prevalent, while a larger exponent implies that smaller leads are more dominant at TIRS scale.
Width distribution of leads from MODIS and TIRS in
a log–log plot. Data points from MODIS and TIRS are plotted as orange and blue
dots, respectively. Power law fitting is applied. Fitting equations and
The total length of leads with various widths is 10 150.3 km from TIRS,
including 8502.2 km (83.76 %) from small leads with width no more than 1 km,
compared to a total length of 2746.4 km from MODIS, where the narrow
leads (1 km wide) only account for 1050.0 km (38.23 %). Total length of
leads is underestimated by 72.9 % in MODIS data compared to TIRS data. As
for the area of leads, small leads (width
IST, described in Sect. 4.1, and lead width from TIRS (Sect. 4.2) were used in bulk formulae and the fetch-limited model along with ERA-Interim reanalysis data to estimate turbulent heat flux through leads. For consistency, the estimated heat flux is positive from the ocean to the atmosphere.
Turbulent heat flux over lead area is obtained by summing up sensible and
latent heat flux from Eqs. (
As we can see in Fig. 11 and Table 3, total heat flux over leads estimated
by the Andreas and Cash (1999) model is
Spatial distribution of heat flux derived from MODIS and
Landsat-8 using bulk formulae and a fetch-limited model.
Estimated turbulent heat flux (
Inspection of input data revealed that the 2 m air temperature from
ERA-Interim has almost the same mean value around 262 K as the surface
temperature from Landsat-8. The temperature difference between air and
surface,
The operational definition of a lead is a fracture or passageway through ice that is navigable by surface vessels (Canadian Ice Service, 2005; World Meteorological Organization, 2014). However, within any optical, thermal, or microwave image, the radiometric signature of a narrow lead with open water may be identical to that of a wider lead with thin ice. In most studies involving the utility of remote sensing data, any linear features of open water or thin ice within pack ice are regarded as leads for convenience (Fetterer and Holyer, 1989; Fily and Rothrock, 1990; Lindsay and Rothrock, 1995). Due to the confusion in the definition of leads in remote sensing images and the need to extract lead signatures from the background, threshold segmentation has been frequently used (Eppler and Full, 1992; Lindsay and Rothrock, 1995; Weiss and Marsan, 2004; Marcq and Weiss, 2012). Willmes and Heinemann (2015) presented several threshold selection techniques for binary lead segmentation. However, thresholds given by image-based methods can vary significantly depending on noise level (caused by air temperature variance) and lead distribution.
In our study, a set of thresholds was tested for extracting leads from
temperature anomaly maps, areal fractions of leads from fixed thresholds,
SD thresholds, and an iterative threshold are shown in Table 4. The
obtained lead fractions are a composite of thresholds and contrast in
surface temperature of leads compared to the surrounding ice, i.e.,
temperature anomaly
Validation with Landsat-8 panchromatic images shows that the iterative threshold detects most lead structures (89.5 %) and exhibited better resistance against air temperature noise. Thus, iterative thresholds were selected for lead extraction in this study.
Distribution of 2 m air temperature over leads and
surface temperature of all leads, small leads with width
Threshold candidates for lead detection and corresponding lead fractions.
Lead geometry and distribution in the Arctic have been studied using optical
and microwave remote sensing data (Fily and Rothrock, 1990; Lindsay and
Rothrock, 1995; Tschudi et al., 2002). A simple one-parameter exponential
model was used for the number density distribution of lead width (Key and
Peckham, 1991; Key et al., 1994; Maslanik and Key, 1995):
In our study, although lead width follows the power law distribution at both scales, the fitted exponents vary from 2.241 to 2.346 at resolution from 1 km to 30 m. Since the 30 m L1T images were resampled from the original 100 m TIRS data, the actual distribution of leads less than 100 m wide is debatable. In comparison with Landsat-8 TIRS and panchromatic images, we find that the lead map generated from the MODIS IST data neglects very small leads but overestimates the width of other leads approximately 1 km wide. Overall, the 1 km wide lead category at MODIS scale should provide a reasonable guess of potential small or subpixel leads. The small leads retrieved using TIRS provide a valuable reference for the capacity of MODIS to detect narrow leads.
In both the Andreas and Murphy (1986) and Andreas and Cash (1999) models,
for reference height
Our results suggest that the contribution of heat flux from small leads mainly results from their large length, or number density, and vast area instead of efficiency. Though small leads are more efficient for heat exchange between the ocean and the atmosphere, thin ice growing in newly opened leads can quickly cover the exposed ocean surface, thus reducing heat exchange. Moreover, due to the mixture of subpixel leads and thick ice, the surface temperature of some pixels in small leads is much lower than the freezing point.
Nonetheless, our results show that the fetch-limited model could be used to
estimate turbulent heat flux on a regional scale with surface temperature
fields from remote sensing. However, the fetch-limited model proposed by
Andreas and Cash (1999) was based mainly on a few observations over open
leads and polynya, while most lead pixels detected using temperature
anomalies in our study are likely covered by thin ice (surface temperature
For comparison, a test using preset meteorological conditions was performed
using the TIRS lead binary. Assuming the surface temperature in leads is
right at the freezing point, with a wind speed of 7 m s
Contribution of heat flux from each lead width using
bulk formulae and a fetch-limited model. Turbulent heat flux retrieved using
a fetch-limited model and bulk formulae are plotted using solid and dashed
lines, respectively. Heat flux calculated using satellite surface
temperature, air temperature, and wind speed from reanalysis datasets is
drawn in orange; simulated heat flux at
Turbulent heat flux (
Clearly, turbulent heat flux estimated using the Andreas and Cash (1999)
model is always higher than that using the bulk formulae. For both models,
estimated turbulent heat flux with
The distribution of turbulent heat flux estimated using bulk formulae with
When the Andreas and Cash (1999) model was applied, small leads were found
to have a larger contribution at higher
Although the same local temperature anomaly and threshold methods were
applied, leads retrieved at MODIS and Landsat-8 TIRS resolution scales
presented very different geometries and distributions. Within the studied
area, the total length of leads is 10 150.3 km from TIRS, including 8502.2 km
(83.76 %) from small leads with width less than 1 km. This is in
contrast to the total length of 2746.4 km from MODIS, where the narrow leads
(1 km wide) only account for 1050.0 km (38.23 %). The total length of
leads is underestimated by 72.9 % in the MODIS data. For the area of
leads, small leads (width
When bulk aerodynamic formulae are applied to the reanalysis dataset, the
heat flux estimated using TIRS data is
The turbulent heat flux over leads estimated from the TIRS data by the
Andreas and Cash (1999) model is
Top of atmosphere reflectance from Landsat-8 panchromatic images was corrected for solar zenith angle and mosaicked for validation. Using Jenks' natural breaks classification method (Jenks, 1963), panchromatic pixels were classified into three surface categories: open water and thin ice, refrozen leads, and pack ice. In terms of turbulent heat flux, only pixels in the open water and thin ice category were regarded as leads. As can be seen in Table A1, the producer's accuracy of lead detection using the iterative threshold is 89.5 %, with an omission error of 10.5 % and a commission error of 16.1 %.
Leads and pack ice pixels detected by Landsat-8 TIRS and panchromatic images at 15 m resolution.
Equations used for turbulent heat flux estimation using bulk formulae (Large
and Pond, 1981, 1982; Oberhuber, 1988; Goosse et al., 2001; Marcq and Weiss,
2012) are as follows:
Constants used in IST calculation from Landsat-8 TIRS (Du et al., 2015) are
as follows.
ASTER emissivity library (Skoković et al., 2014):
NIR reflectance threshold for classification between water and ice/snow: 0.1. Water vapor content from MOD05: RMSE: 0.34 K. Air pressure: Air density: Kinematic viscosity of air: Molecular diffusivities of heat in the air: Molecular diffusivities of water vapor in the air: Specific heat at constant pressure: Latent heat of vaporization or sublimation: Reference height: Gravitational constant: Salinity of seawater in the Beaufort Sea: Freezing point of seawater:
Constants used in turbulent heat flux estimation are as follows.
Landsat-8 L1T images are available at the
U.S. Geological
Survey (USGS) Earth Resources Observation and Science (EROS) Center
(
XP and XZ designed the experiments, and MQ carried them out. JZ provided valuable instructions on data acquisition and editing of the paper. QJ and PF helped to develop the model code. MQ prepared the paper with contributions from all co-authors.
The authors declare that they have no conflict of interest.
The authors acknowledge the NASA Goddard Space Flight Center, the U.S. Geological Survey (USGS), and the European Center for Medium-Range Weather Forecasts (ECMWF) for providing the images and datasets used in this study. We thank the anonymous reviewers and handling editor Christian Haas for their valuable comments, which helped improve our paper.
This research has been supported by the National Natural Science Foundation of China (grant nos. 41876223, 41576188, and 41606215) and the National Key Research and Development Program of China (grant nos. 2016YFC1402704 and 2018YFC1407100). Jinlun Zhang was supported by the NOAA Climate Program Office (grant no. NA15OAR4310170).
This paper was edited by Christian Haas and reviewed by two anonymous referees.