Ice Bridge Level-1 Science Requirements and Scientific Basis The IceBridge Science Team
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Ice Sheet Projected Requirements(1) Accumulation rate estimates are essential to flux gate estimates of mass balance, but the extent to which these measurement can be applied and the need for additional in situ data is required are poorly characterized. Accumulation rates contribute to the uncertainty in flux gate, gravity, and altimetry measurements, making the ability measure them highly desirable. While the ability to determine such rates is currently experimental, the collection of the radar data by OIB will provide an extremely important data set for developing and validating the methods for accumulation retrieval. Equation 1 under (IS1) illustrates that there are 7 distinct error terms contributing to the error in ice sheet thickening rate. Taking 15 cm/yr as the basin-averaged thickening rate accuracy, then each of the error terms on the right side of equation should be on the order of (15/(7)1/2) cm/yr of ice equivalent or about 6 cm/yr ice equivalent. This immediately gives an approximate bound on the required accuracy for the surface and basal mass balance (6 cm/yr ice equivalent). At sub-basin scales, the accuracy requirement is 4 cm/yr ice equivalent. 2) Subglacial water production and water migration are important controls on glacier flow. Techniques for measuring water distribution, distribution change and volume are successful for characterizing larger bodies of water (such as altimeter estimates of changing subglacial lake volumes). However techniques to sample the distribution of thin water layers and to directly estimate water production are still immature (Oswald and Gogineni, 2008). Models can be used to try and infer water production rates. Basal hydrostatic pressure gradients can be used to estimate locations where water will pond. Additional research is needed to effectively use current and future models to guide development of robust direct measurement methods. (3) Annual sampling is adequate but seasonal sampling would improve understanding of the stochastic processes that are superimposed the long term thickness change signal. Spatial and temporal sampling in the interior of Antarctica is more difficult because although accumulation and accumulation driven changes in density are less, dynamic thinning is also much less. Roughness is similar. A solution is to average over much larger areas than near the coast (100x100 km or more is the Cryosat estimate) and over longer periods of time than just one year (3 years or more). Note that while thinning at a point in the interior is less than at a point on the coast, the area of the interior is huge so a little thinning can result in a big overall mass change. 4) Geothermal heat flux is critical, unmeasured parameter in the basal heat balance beneath glaciers (Fahnestock and others, 2001. Other parameters such as basal drag can be inferred from modeling but no similarly robust technique is available for heat flux estimates. Magnetics suffices in some instances as a proxy indicator of changing heat flux magnitudes, but accurate estimates of the flux magnitude are difficult to obtain with any existing method other than direct sampling at boreholes. 5) Subglacial lakes are distributed across much of Antarctica. Lake discharge is believed to be directly responsible for changes in glacier motion (for example recent speed ups of Byrd Glaciers). Ice sounding radars and laser altimeters have been successfully used to map lake locations and to measure lake volume changes with time. The primary challenge for further lake studies is to have detailed (km scale surveys) and repeat measurements (months) to study lake processes. These requirements pose difficult logistical challenges that may only b e addressable with UAV type platforms. 6) Enhanced free air gravity is required to better map sea floor bathymetry down stream of marine terminating glaciers. Current systems mounted on the NASA P-3 and DC-8 aircraft are limited to features with wavelengths on the order of 10 km. A challenge for the future it so develop approaches that reduce the measurable wavelengths to several km. 7) As mentioned above the primary challenge demonstrating the utility of stereo photography to IceBridge ice sheet science is developing processing schemes for reducing a voluminous photographic data set into digital elevation models with absolute elevation and slope accuracies sufficient to measurably improve cross track slope correction on altimeter data. A second challenge is demonstrating whether stereo photography can be used for glaciologically meaningful elevation change measurements. 4.1.Justifications of the Science Requirements for Sea IceSI 1. Make surface elevation measurements of the water, ice, or snow with a shot-to-shot independent error of less than 10 cm and correlated errors which contribute less than 1 cm to the mean height error in either sea surface or sea ice elevation. The spot size should be 1 m or less and they should be spaced 3 m or less. The primary purpose of the surface elevation measurements over sea ice is to obtain regional estimates of the sea ice thickness distribution. The thickness distribution is required, as opposed to a simple mean ice thickness, because of the nonlinear thermodynamic and dynamic processes important for the evolution of the ice pack. The community standard length scale for determining the thickness distribution, for example from submarines, is 50 km, as this length scale provides adequate opportunity to detect different ice types within a region and is small enough to resolve regional differences (Wadhams, 2002; Percival et al. 2008). The thickness distribution should be resolved to 10 cm bins in order to delineate level ice from ridged ice and in order to track changes in the mode of the distribution, since the mode often represents the thermodynamically dominated thickness. With 10 cm resolution, bins with as little as 5% of the area might have significant impact on the interpretation of the thermodynamic or dynamic properties of the ice pack. To adequately characterize these bins, the areal coverage for each bin should be resolved to less than 1%. Hence we end up with a basic requirement that the thickness distribution be determined with a resolution of 10 cm and an uncertainty of 1% or less for the fraction in each bin. However there are many sources of error in determining the ice thickness from surface elevation measurements including the discrimination of leads, determining the presence of thin ice in leads, interpolating water levels to ice-covered regions, geoid levels, and snow depth (Kwok and Cuningham, 2008; Kurtz et al., 2009). Most of these sources of error are beyond the control of the measurement system, so here we only consider the errors that are due entirely to the measurement system. We determine the measurement requirement for optimal conditions…a canonical ice cover…and realize that in practice the ice thickness estimate errors may be larger due, for example, to wide spacing between leads, small isolated leads, or uncertainties in the snow depth. The ice thickness hi is related to the freeboard hf of the ice as 
where ρw and ρi are the densities of water and ice. The ice thickness and uncertainties in the ice thickness are roughly 10 times those of the ice freeboard because the freeboard only represents about 1/10th of the ice thickness. The average freeboard for a set of laser shots over the ice is 
where  
For the thickness error to remain below 10 cm, If we assume the contribution of the independent errors is negligible and that  and  are equal and independent, both must be less than 0.71 cm to keep the error in the freeboard less than 1 cm. If they are correlated at very low frequencies or if the lead density is high so that the water level is determined from the average of several leads, the impact of the correlated errors will be smaller. In addition the elevation errors should ideally be independent of the reflectivity of the surface so that both leads and ice surfaces are equally well measured. Figure SI-1 shows a swath of ATM elevation data with the corresponding a visible images from the DMS camera illustrating the near-perfect alignment as well as the loss of ATM returns over open water leads and a drop in measurement density over some of the dark grey nilas.
Figure SI-1. DMS visible images and ATM elevation measurements for a lead observed in the 23 March 2010 flight north of Elsmere Island on a flight path called “ZZ west” (figure by R. Lindsay). Near repeat paths on a smooth ice sheet can be used to estimate some of the ATM errors. Figure SI-2 shows the difference in elevation measurements for a 10-km track in the so-called Camp Century Corridor. This corridor is often flown both on the outbound and the inbound legs of flights from Thule to the Greenland ice sheet on almost exactly the same path each way. Since the ice sheet is uniform and changes very little in the few hours between the overpasses, differences in the elevation measurements can be taken as an indication of the measurement error. A clear pattern in the differences is seen between the two passes that shows a small 0.014° bias in the roll corrections. This bias is consistent with the error analysis of Krabill et al. (2002). They analyzed the various sources of errors for the ATM instrument based on a 1999 campaign in Greenland and found the RMS variation of the pitch biases was 0.026° and the RMS variation of the roll biases was 0.017°. They state that the effect of a 0.017° roll error on an ATM measurement at 15° off-nadir angle with the aircraft at 500 m above the surface varies from about –4 cm on one side of the swath to +4 cm on the other side of the swath, similar to what we found for the 23 April 2009 flight. In the bottom panel the best-fit plane has been removed to show there are still quasi-periodic biases perhaps related to errors in the pitch corrections with spatial scales on the order of 1 to 2 km. Krabell (2002) state that the pitch bias is largely compensated for by the fore and aft looking beams of the instrument that give errors opposite in sign. The RMS error in the measurements is 1/  times the RMS difference, or 3.2 and 1.6 cm for the top and bottom panels respectively.
What might the impacts of these errors be on the determination of freeboard? Clearly if an open water area from one side of the swath were used to find the freeboard for ice on the other side, an 8 cm error might be incurred. However the net effect on the freeboard estimates of these errors using a true spatial distribution of leads is likely be quite different and much smaller. Determining the net impact on the freeboard estimates of the correlated errors of the ATM instrument requires further research. 
Figure SI-2. Elevation differences for near-exact repeat tracks in the Camp Century corridor from 23 April 2009. The orange and blue lines show the aircraft track on the outbound and inbound legs of the flight. They are within 50 m of each other. The colors in the top panel show the differences in the elevation averaged over 20 m (cross track) x 50 m (along track) boxes where the data swaths overlap. In the bottom panel the best-fit plane of the differences has been removed. Projected requirement SIP-1. Improve sea ice baseline requirement 1 to make surface elevation measurements with a shot-to-shot accuracy of 5 cm (versus 10 cm), assuming uncorrelated errors. This higher accuracy will allow for the use of smaller leads and a better definition of the sea surface elevation. SI 2. Make elevation measurements of both the air-snow and the snow-ice interfaces to an uncertainty of 3 cm, which enable the determination of snow depth to an uncertainty of 5 cm. Determining accurate snow depth is important both for determining the ice thickness and for mapping the distribution of snow over sea ice with a spatial coverage never before obtained. Snow is an important element in determining the thermal conductivity of the ice, the surface albedo and the evolution of melt ponds. Given the roughly ten-fold increase in the error of the ice thickness from the error in the snow depth (Kwok and Cunningham, 2008), an error of less than 1 cm would be desirable, but it is not possible for a single radar return. The snow depth (hs) is the difference in elevation between the air-snow (has) and snow-ice (hsi) interfaces:
For the Ultra Wideband snow radar, the range resolution is ~5 cm (free space propagation) (Panzer et al., 2010). Assuming we can locate the snow-ice interface and the air-snow interface to ~3 cm ( 
This assumes a nominal snow density of 0.3 g/cm3. For σc = 0.1 (the fractional uncertainty in the speed of light in snow) and a single return N=1, the expected uncertainty in snow depth is ~4.7 cm. However, if the air-snow interface were weakly scattering and more difficult to locate ( For a given radar return, the most important parameters are the range precision and the range resolution. We wish to have the platform be stable at the 500 m length scale (to centimeters) to ensure that the motion compensation processing provides sufficient precision such that it would not introduce significant variability in the pulse-to-pulse averages. This can be relaxed if the radar platform is stable over a longer flight segment. Figure SI-3 shows an example of the snow radar returns with the surface elevation estimated from the ATM data. While the top of the snow surface is well represented, the ice surface is harder to distinguish at all locations. For determining the snow depth for each freeboard estimate, further research is required to know how to assign the nadir snow depth measurements to the swath ATM measurements. This extrapolation will be the source of further error in the snow depth and ice thickness estimates. 
Figure SI-3. Snow radar returns with the top snow surface profile derived from the ATM added as a black line (figure by R. Kwok). SI 3. Provide annual acquisitions of sea ice surface elevation in the Arctic and Southern Oceans during the late winter in regions of the ice pack that are undergoing rapid change. Flight lines shall be designed to ensure measurements are acquired across a range of ice types including seasonal (first-year) and perennial (multiyear) sea ice to include, as a minimum: Arctic a) At least two transects to capture the thickness gradient across the perennial and seasonal ice covers between Greenland, the central Arctic, and the Alaskan Coast. Some of the most rapid changes in Arctic pack ice are seen in the Beaufort Sea and in the thick ice in the central Arctic Ocean (Lindsay and Zhang, 2005). To the extent possible given the limited coverage of the OIB program it is important to provide continuous monitoring of these rapidly changing regions. Much of the Beaufort Sea is transitioning from perennial ice to seasonal ice so previous observations of the ice characteristics in this region may need to be revised. Two long transects across the central Arctic Basin connecting the northern coasts of Greenland and Alaska will sample the ice thickness gradient across both the first-year and multi-year ice packs such that a representation of ice types in the Beaufort Sea is obtained. These transects are designed to provide data that will contribute to an assessment of the condition of the Arctic ice pack (e.g. the thickness distribution and relative amounts of multiyear and seasonal ice) on a yearly basis. b) The perennial sea ice pack from the coasts of Ellesmere Island and Greenland north to the pole and westward across the northern Beaufort Sea. The thick multiyear ice in this region is experiencing the most rapid thinning in the Arctic Ocean [Maslanik et al., 2007; Comiso et al., 2008; Farrell et al., 2009] and it is critical to continue observations in this region to record potential on-going thinning. In addition, the ice draft in this region has traditionally been under sampled by submarine transects since it lies outside of the data release area and is rarely visited by ice breakers because of the consolidated thick ice. No moorings are deployed here. For this reason any additional OIB ice thickness observations in this region are a particularly important contribution to our understanding of the changes going on in the Arctic pack ice. Continued monitoring of the multiyear ice pack in this region is needed to track the loss of older ice and its replacement by younger second-year or first-year ice. Flight lines will be designed to survey an area that includes the ice pack directly north of Greenland and Ellesmere Island, west toward Queen Elizabeth and Banks Islands, and north towards the North Pole.
The Fram and Nares Straits are the two most important locations for ice export from the Arctic Ocean. In order to better constrain the rate of ice export, knowledge of the ice thickness across the Straits is required. While single transects cannot be used to determine the time-averaged flux, the thickness measurements can be used to asses the errors in model estimates of the ice thickness and, hence,the ice flux. An ongoing monitoring effort to measure ice flux will provide a budget for winter-time loss of sea ice volume from the Arctic Ocean to the North Atlantic Ocean. d) The sea ice cover of the Eastern Arctic north of the Fram Strait. This region is the location of the transpolar drift stream, the major conduit for ice exiting the Arctic Ocean via Fram Strait. Much of this ice originated on the Siberian shelves or in the Beaufort Gyre. Monitoring the thickness of this ice will help establish the rate of ice production far upstream. Figure SI-4 shows examples of the suggested flight tracks, in this case the actual flights flown in the spring of 2009 and 2010, along with an estimate of the mean ice thickness from the PIOMAS model (Polar Ice and Ocean Modeling and Assimilation System, Zhang and Rothrock, 2003). The flights sample the thick multiyear ice near the Greenland and Canadian coasts and the thinner ice in the Beaufort Sea.
Figure SI-4. Flight tracks from 2009 and 2010 along with estimates of the mean ice thickness from the PIOMAS model for the month of March. Antarctic a) The sea ice of the Weddell Sea between the tip of the Antarctic Peninsula and Cape Norvegia. IceBridge measurements over sea ice will extend the record of observations begun by ICESat such that continued monitoring of a key transect across the Weddell Sea will be conducted on a yearly basis. Ice export from the Weddell Sea is typically computed along a “flux-gate” which spans the Weddell Sea from the northeastern tip of the Antarctic Peninsula to Cape Norvegia. An IceBridge transect between these two points will provide gradients in ice thickness along the flux-gate. The total volume of sea ice exported into the Antarctic Circumpolar Current is a combination of sea ice growth within the Weddell Sea, the inflow of sea ice from the eastern Weddell, and the ice produced in polynyas located in the southern Weddell. b) The mixed ice cover in the western Weddell Sea between the tip of Antarctic Peninsula and Ronne Ice Shelf. A transect across the mixed ice cover in the western Weddell Sea between the northern tip of the Antarctic Peninsula and the Ronne Ice Shelf will provide an optimal sampling of ice types in the Weddell Sea including first year ice in the northern Weddell, and multiyear ice in the southern Weddell. This transect will allow us to constrain the overall thickness distribution of the Weddell Sea ice pack and monitor any change in the state of the multiyear ice pack. c) The ice pack of the Bellingshausen and Amundsen Seas. The aim is to provide a constraint on the thickness distribution of the ice pack buttressing the West Antarctic Ice Sheet (WAIS). This region exhibits high variability in sea ice extent, and potentially thickness, where such variability is linked to the modes of the Southern Oscillation. The flight line shall be repeated on a yearly basis to establish a multi-year record of sea ice thickness in this region. Figure SI-5 shows the three requirements as flown in the 2009 Antarctic campaign.
Figure SI-5. Flight tracks from the 2009 Antarctic campaign, Green is an example of requirement (a), blue of requirement (b) and red of requirement (c). Projected requirement SIP 2. Extend sea ice baseline requirement 3 to other regions of the Arctic and Southern Oceans: Arctic (to better constrain estimates of sea ice volume change)
Antarctic (to better understand the process of sea ice formation and snow accumulation)
SI 4. Include flight lines for sampling the ground tracks of satellite lidars (ICESat-1 and ICESat-2) and radars (CryoSat-2 and Envisat) and, in the case of CryoSat-2, both IceBridge and CryoSat-2 ground tracks should be temporally and spatially coincident whenever possible. At least one ground track of each satellite should be sampled per campaign. The lapse in basin-scale monitoring of Arctic and Southern Ocean sea ice as a result of the delay between the end of the ICESat mission in late 2009 and the launch of ICESat-2 planned for 2016 will result in a gap in the long-term laser altimetry record over sea ice. CryoSat- 2, launched in early 2010, will help bridge this data gap to some extent, although the SAR/Interferometric Radar Altimeter (SIRAL) onboard will result in surface elevation measurements that are inherently different to those of the ICESat laser system (GLAS). IceBridge should include flight tracks that are spatially and temporally coincident with CryoSat-2 so as to improve our understanding of the differences between the laser (ICESat/ICESat-2) and radar (CryoSat-2) altimetric signals over sea ice. Further, it will allow placement of IceBridge data in the wider context of the CryoSat-2 dataset. As a lower priority, a portion of IceBridge flights shall be designed to refly ground tracks of Envisat radar altimetry data and historical ICESat laser altimetry. This data is helpful in providing a continuation of the long-term sea ice altimetry record in regions where the ice thickness distribution has already been established over a 5-6 year time-period. This will also allow for better interpretation of changes in the sea surface elevations related to changes in circulation and fresh water content and to increase our confidence that the changes are not associated with the unmodeled geoid variability.
Sea ice flights will be conducted at sea ice maximum extent (March – early April in the Northern Hemisphere; late September – early October in the Southern Hemisphere) to obtain winter-time data that is consistent with the limited operation periods of the ICESat laser campaigns (typically late February-March, and October-mid November). Furthermore, the likelihood of data acquired by the two IceBridge airborne radars, Ku-band and snow, being predominantly from the snow-ice interface [Beavan et al. 1995] is increased and thickness estimation improved if sea ice flights occur when snow cover is cold and dry, i.e. before the onset of the melt season. The dielectric properties of snow can be controlled by its liquid water content at temperatures above –5 °C [Willatt et al., 2010]. In order to mitigate the impact of a large variability in snow grain size on radar altimetry measurements over sea ice, we recommend that measurements are made before the onset of spring melt over both Arctic and Southern Ocean ice packs; air surface temperatures typically increase around late April in the Arctic and mid-October over Southern Ocean sea ice. The likelihood of getting the bulk of the radar returns from snow-ice interface within Antarctic sea ice is reduced relative to the Arctic due to flooding events in the Antarctic. Therefore our timing requirements are relaxed somewhat for Antarctic, i.e., we are resigned to higher liquid water content.
Establishing the height of the open ocean surface is essential for determining the freeboard and hence the ice thickness (see S1 justification). The open water level is found from leads within the ice pack and these can be unambiguously determined from visible imagery. The leads in visible imagery appear dark compared to the ice and are easily identified. Visible images are a minimum requirement and high resolution (1-m) thermal images are a desirable projected requirement (see SIP 3). Projected requirement SIP 3. Collect thermal images for a swath that, as a minimum, covers the LVIS data swath with a resolution of 0.5 m or better, and are calibrated to brightness temperature with an accuracy of 0.1K. There can be a skim of thin newly frozen ice within the leads that is sometimes not apparent in the visible imagery. However, this ice can be identified in infrared images when the temperature of the lead is below the freezing point of sea water. The temperature of the thin ice, when compared to that of the thick ice, can be used to estimate the thickness of the lead ice. Since we cannot estimate the thickness of the thin lead ice identified in visible images, thermal images would help to establish this. Visible images are a minimum requirement and high resolution (1-m) thermal images are a highly desirable projected requirement in this regard. Projected requirement SIP 4. Improve sea ice baseline requirement 6 to collect coincident digital stereo imagery of sea ice conditions at a spatial resolution of at least 10 cm (versus 20 cm) per pixel, at a vertical resolution of 20 cm. Stereo imagery will enable direct interpretation of the altimetric data and provide a complimentary surface elevation product. SI 7. Conduct sea ice flights primarily in cloud-free conditions. Data shall be retained under all atmospheric conditions with a flag included to indicate degradation or loss of data due to clouds. Ideally IceBridge sea ice flights will be conducted under cloud-free conditions to obtain accurate visible imagery of the surface and to limit the effects of forward scattering on laser altimetric measurements. However, data should be retained under all atmospheric conditions and a flag should be included to indicate degradation or loss of data due to clouds. This will enable investigators to understand the impact of cloudy returns on elevation accuracy from laser altimetric data, whereby atmospheric optical depth can be directly related to surface elevation accuracy. This will support data simulations in preparation for the ICESat-2 mission. SI 8. Make precise full gravity vector measurements on all low-elevation (< 1000 m) flights over sea ice to enable the determination of short-wavelength geoid fluctuations (in a waveband of order 10 to 200 km) along the flight track to a allow the calculation of the geoid to a precision of 2 cm. An accurate, detailed knowledge of the marine geoid is critical for confident separation and isolation of the sea surface and sea ice topography signals in the IceBridge altimeter observations. Short-wavelength errors in our current knowledge of the marine geoid exceed 25 cm in a waveband of order 10 to 200 km over many areas of the Arctic Ocean. However IceBridge’s full-vector gravimetric (AirGRAV) observations can be used to isolate and reduce these geoid errors along flight tracks and to improve models of the Arctic marine geoid. SI 9. Actively seek out and coordinate with field campaigns that are consistent with IceBridge project objectives. Ground truth data from field campaigns will help to determine uncertainties in the OIB estimates of the snow depth and ice thickness (see S1 and S2 justifications). Ground truth data is the only way to obtain independent verification of the measurements obtained from the airborne instruments. In addition, aircraft survey data provided by OIB enables field data to be placed in a wider context. Such activities will substantially augment OIB outreach efforts and supports international collaboration. In all cases data sharing agreements must be in place. SI 10. Make available to the community instrument data on sea ice surface elevation and snow depth within 3 months of acquisition and derived products within 6 months of data acquisition. The utility of the OIB data for assessing and understanding the rapid changes we are seeing in the sea ice of the Arctic will be greatly enhanced if the data are made available to the science community as soon as possible after acquisition. Estimates of the ice thickness can be compared to recent retrospective model estimates to ascertain if the models are in error and to determine if model projections might be biased. In addition, any information that can help document or explain current ice conditions will contribute to OIB outreach efforts. Projected requirement SIP 5. IceBridge shall support the validation of operational sea ice analysis and forecast products by providing estimates of sea ice freeboard within 1 week of data acquisition and estimates of sea ice thickness within 2 weeks of data acquisition. An accelerated release of sea ice thickness products in near real time will allow for their operational use by the National Ice Center and other entities that analyze and predict ice extent and thickness.
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and 
are the mean heights of the Ni ice shots (where N is the number of shots) and the nearby Nw open water shots. The errors associated with each of these mean heights arise from determining the mean from a finite number of observations, each of which has an independent and normally distributed error 
and an additional error due to the spatial correlation of the errors, 
must remain below 1 cm. The number density of shots for the ATM instrument when the aircraft is flying low over sea ice is approximately 30000/km. In the case of a 10-m lead across the width of the swath the number of water shots is Nw = 300. Assuming an adjacent ice class occupies 100 m of the swath, then Ni = 3000. This implies that the error in the freeboard due to the independent errors is just 0.03 cm. The uncorrelated errors add little to the mean freeboard error because of the potentially large number of observations for leads or ice classes. The smaller number of shots within very small leads will increase the freeboard errors from this source, and a 
, half the range resolution) and we have an uncertainty of 0.1 g/cm3 in snow density (this translates into ~10% uncertainty in the speed of light in snow), then the uncertainty in snow depth over N radar pulses, 
is larger), then the per-pulse performance would degrade. Whether we can average over N pulses to produce a better estimate depends on the correlation length scale of the snow cover at the 10-20 m pulse-limited spot size of the snow radar. 
