The Echogram JPEG files include an altitude correction, but the netCDF files do not. In the case of the netCDF files, correction can be applied by shifting a record from bottom to top by the altitude correction value. To this end, altitude variations within a data file are removed by subtracting the minimum altitude from all values. The result is variation in meters from the minimum. These values are then converted to whole pixel values given the following radar parameters: sampling frequency, pulse duration, FFT length, and bandwidth. Sampling frequency before the 2009 Greenland campaign is 58.32 MHz, whereas after the Greenland campaign it was set to 62.5 MHz.

Flat Surface Range Resolution

For a flat surface the range resolution r is expressed by Equation 1:

Table 3. Flat Surface Range Resolution

Variable	Description
kt	kt = 1.5 due to the application of a Hanning time-domain window to reduce the range sidelobes of the chirped transmit waveform.
c	Speed of light in a vacuum
B	Bandwidth, nominally 3500 MHz (13 to 16.5 GHz range)
n	Index of refraction for the medium

Examples of range resolutions for several indices of refraction are shown in Table 4.

Table 4. Range Resolutions for Indices of Refraction

Index of Refraction	Range Resolution (cm)	Medium
1	6.4	Air
sqrt(1.53)	5.2	Snow
sqrt(3.15)	3.6	Solid Ice

Index of Refraction

The index of refraction n can be approximated by the calculation in Equation 2:

ρ_snow is the density of the snow in grams per cm³. In the data, a dielectric constant of 1.53 is used, which corresponds to a snow density of 0.3 g/cm³ (Warren 1999).

Bandwidth

The bandwidth B for a particular segment can be determined by reading the param_get_heights.radar.wfs structure in the netCDF files or by looking at the parameter spreadsheet values f0, f1, and fmult and doing the calculation in Equation 3:

Table 5. Segment Bandwidth Variable Definitions

Variable	Name in netCDF file	Description
param_radar.f1	param_get_heights(1).radar(1).wfs(1).f1	Stop frequency of chirp out of Direct Digital Synthesis (DDS) and into Phase-Locked Loop (PLL)
param_radar.f0	param_get_heights(1).radar(1).wfs(1).f0	Start frequency of chirp out of DDS and into PLL
param_radar.fmult	param_get_heights(1).radar(1).wfs(1).fmult	PLL frequency multiplication factor

Along-Track Resolution

Before any hardware or software coherent averages have been applied, the resolution of the raw data in the along-track direction is derived in the same manner as in the cross-track direction. However, a basic form of focusing is applied called Unfocused Synthetic Aperture Radar (SAR) Processing, also known as stacking or coherent averaging. If all effects are accounted for, the data may be coherently averaged to the SAR aperture length L, defined by Equation 4:

Table 6. SAR Aperture Length Variable Definitions

Variable	Description
H	Height above ground level
λc	Wavelength at the center frequency

For H = 500 m and a center frequency of 14.75 GHz, the data are averaged to an aperture length L of 2.25 m. The resolution turns out to be approximately equal to this with the exact definition given below. However, these data are only coherently averaged 16 times which includes both hardware and software averaging, and decimated by this same amount. At a platform speed of 140 m/s this is an aperture length, L, of 1.12 m. The sample spacing is likewise 1.12 m. The approximation for the actual resolution, which is substantially less fine, is given in Equation 5:

Table 7. Actual Resolution Variable Definitions

Variable	Description
H	Height above ground level
λc	Wavelength at the center frequency
L	Aperture length

For H = 500 m, the along-track resolution is 4.54 m. A 1 range-bin by 5 along-track-range-line boxcar filter is applied to the power detected data and then decimated in the along-track by 5 so the data product has an along-track sample spacing of 5.6 m.

Fresnel Zone and Cross-Track Resolution

For a smooth or quasi-specular target, for example internal layers, the primary response is from the first Fresnel zone. Therefore, the directivity of specular targets effectively creates the appearance of a cross-track resolution equal to this first Fresnel zone. The first Fresnel zone is a circle with diameter given by Equation 6.

Table 8. First Fresnel Zone Diameter

Variable	Description
H	Height above the air/ice interface
T	Depth in ice
λc	Wavelength at the center frequency

Table 9 gives the cross-track resolution for this case.

Table 9. Cross-track Resolution example

Center Frequency (MHz)	Cross-track Resolution H = 500 m T = 0 m
14750	4.5

For a rough surface with no discernible layover, the cross-track resolution will be constrained by the pulse-limited footprint, approximated in Equation 7.

Table 10. Pulse-Limited Footprint

Variable	Description
H	Height above the air/ice interface
T	Depth in ice
c	Speed of light in a vacuum
kt	kt = 1.5 due to the application of a hanning time-domain window to reduce the range sidelobes of the chirped transmit waveform
B	Bandwidth in radians

Table 11 gives the cross-track resolution with windowing.

Table 11. Cross-track Resolution with Windowing

Bandwidth (MHz)	Cross-track Resolution H = 500 m T = 0 m
3500	16.0

For a rough surface where layover occurs, the cross-track resolution is set by the beamwidth, β , of the antenna array. The antenna beamwidth-limited resolution is expressed by Equation 8.

Table 12. Antenna Beamwidth-limited Resolution

Variable	Description
H	Height above ground level
T	Depth in ice
βy	Beamwidth in radians

Footprint

The antenna installed in the bomb bay of the P-3 aircraft and in the wing roots of the DC-8 aircraft is an ETS Lindgren 3115. The E-plane of the antenna is aligned in the along-track direction for the P-3 aircraft and in the cross-track direction for the DC-8 aircraft. The approximate beamwidths are 45 degrees in the along-track direction and 45 degrees in the cross-track direction. The footprint is a function of range as shown in Equation 9.

Table 13. Footprint

Variable	Description
H	Height above ground level.
β	Beamwidth in radians

For H = 500 m, the footprint is 167 m in both the along-track and the cross-track directions.

Trajectory and Attitude Data

The trajectory data used for this data release was from a basic GPS receiver. Lever arm and attitude compensation has not been applied to the data.

Processing Steps

The following processing steps are performed by the data provider.

1. Set digital errors to zero. Error sequences are four samples in length and occur once every few thousand range lines.
2. Synchronization of GPS data with the radar data using the UTC time stored in the radar data files.
3. Conversion from quantization to voltage at the ADC input.
4. Removal of DC-bias by subtracting the mean.
5. For 2013 Greenland P3 and later, a tracking and truncation function has been implemented in the hardware which reduces the recorded data volume. Each range line is tracked and truncated separately and a step is added here to undo the tracking and truncation step so that the data can be placed in a matrix with constant time bins. This requires zero padding and time shifting of the data to get each range line to line up.
6. The quick look output is generated using presumming or unfocused SAR processing for a total of 16 coherent averages which includes hardware and software averages. If the PRF is 2000 Hz, the new effective PRF is 125 Hz.
7. A fast-time FFT is applied with a Hanning window to convert the raw data into the range domain, analogous to pulse compression. The data are flipped around based on the Nyquist zone.
8. A high pass filter is applied in the along-track to remove coherent noise.
9. A 1 range-bin by 5 along-track-range-line boxcar filter is applied to the power detected data and then decimated by 5 in the along-track direction.
10. The quick-look output is used to find the ice surface location, fully automated.
11. The output is elevation compensated to the nearest radar range bin and then truncated in fast time to reduce the data volume.

The purpose of the elevation compensation, when applied, is to remove the large platform elevation changes to make truncation more effective. The process is not designed to perform precision elevation compensation and is probably not sufficient for scientific analysis. The following steps are performed:

1. Let:
   1. Elevation_Orig be the 1 by N elevation vector before elevation compensation
   2. Data_Orig be the M_orig by N data matrix before elevation compensation
   3. Time_Orig be the M_orig by 1 fast-time time axis before elevation compensation
   4. Elevation be the 1 by N vector from the data product file
   5. Dat be the matrix from the data product file
   6. Time be the M by 1 fast-time time axis from the data product file
   7. maxElev = max(Elevation_Original)
2. dRange = maxElev - Elevation_Original
3. dt = Time_Orig(2) - Time_Orig (1)
   1. Sample spacing in fast-time (i.e. one range bin)
4. dBins = round(dRange / (c/2) / dt)
   1. This is a 1 by N vector of the number of range bins for each range line used to shift Data_Orig. In other words, this is the elevation compensation for each range line written in terms of range bins.
5. M = M_orig + max(dBins)
6. The original data matrix is zero padded to M and then each range line is shifted by the corresponding entry in dBins.
   1. Because of the round function for creating dBins, the elevation compensation is only done with range bin accuracy.
   2. The new Data matrix is similar to what would have been collected if the aircraft had flown at a constant elevation of maxElev.
7. The elevation matrix is modified according to the elevation compensation so that: Elevation_Orig = Elevation - dBins*dt*c/2. Once again, because of the round function, the Elevation vector will be nearly constant, but not quite: the quantization noise caused by the round function remains.
8. The Time_Orig vector is extended in length by the maximum bin shift to create the new Time vector.

Version History

Version 1 of the IRSNO1B data. All Version 1 contains data from 2009 to 2012, which were provided in binary format. For details on the Version 1 data, see the Version 1 documentation.

Version 2 of the IRKUB1B data: Version 2 data start in 2012 and are provided in netCDF format.

Error Sources

GPS Time Error: 
The CReSIS accumulation, snow, MCoRDS, and kuband data acquisition systems have a known issue with radar data synchronization with GPS time. When the radar system is initially turned on, the radar system acquires Universal Time Coordinated (UTC) time from the GPS National Marine Electronics Association (NMEA) string. If this is done too soon after the GPS receiver has been turned on, the NMEA string sometimes returns GPS time rather than UTC time. GPS time is 15 seconds ahead of UTC time during this field season. The corrections for the whole day must include the offset -15 second correction. GPS corrections have been applied to all of the data using a comparison between the accumulation, snow, and kuband radars which have independent GPS receivers. A comparison to geographic features and between ocean surface radar return and GPS elevation is also made to ensure GPS synchronization. GPS time corrections are given in the vector worksheet of the parameter spreadsheet.

The error affects Version 2 of the Level 1B CReSIS data sets. Ku-band radar data are affected for the time period: October 2012 - 2013. In the near future, the NSIDC DAAC will publish updated data files with a correction to the 'Time' field.

For the data on 19 May 2016, the Ku-Band Altimeter frequency band was set to a value between 12 GHz to 18 GHz, instead of the usual 12 GHz to 15 GHz. As these data were processed with the same settings as the previous data, the two-way propagation times for the ice or snow surface and the internal layers were incorrectly calculated. This error affected the calculation of the elevations of the internal layers, as well as the layer thicknesses. The data for 19 May 2016 have been reprocessed and replaced with the corrected data.