We present a 1986 through 2017 estimate of Greenland Ice Sheet ice discharge.
Our data include all discharging ice that flows faster than 100 m yr

The mass of the Greenland Ice Sheet is decreasing (e.g.,

The total mass of an ice sheet, or a drainage basin, changes if the mass gain
(SMB inputs, primarily snowfall) is not balanced by the mass loss (

Discharge may be calculated through several methods, including mass flow rate
through gates (e.g.,

Conventional methods of gate selection involve hand-picking gate locations,
generally as linear features (e.g.,

Here, we present a discharge dataset based on gates selected in a
reproducible fashion by a new algorithm. Relative to previous studies, we
employ ice velocity observation over a longer period with higher temporal
frequency and denser spatial coverage. We use ice velocity from 1986 through
2017, including 6 d velocities for the last

Historically, discharge gates were selected along well-constrained flight
lines of airborne radar data

Ice velocity data are available with increasing spatial and temporal
resolution (e.g.,

The discharge gates in this study are generated using only surface speed and
an ice mask. We use the MEaSUREs Greenland Ice Sheet Velocity Map from InSAR
Data, Version 2

For ice thickness estimates, we use surface elevation from GIMP
(

This work uses 308 different velocity maps, biased toward the last 500 d of the time series when 6 d ice velocities become available from the Sentinel-1 satellites. The temporal distribution is 1 to a few velocity maps per year from 1986 to 2000, 9 to 13 velocity maps per year from 2000 through 2015, 24 in 2016, and 55 in 2017.

Summary of data sources used in this work.

We use the following terminology, most displayed in Fig.

“Pixels” are individual

“Gates” are contiguous (including diagonal) clusters of pixels.

“Sectors” are spatial areas that have 0, 1, or

“Regions” are groups of sectors, also from

The “baseline” period is the average 2015, 2016, and 2017 winter velocity from MEaSUREs 0478.

Overview showing fast-flowing ice (orange, greater than
100 m yr

“Coverage” is the percentage of total, region, sector, or gate
discharge observed at any given time. By definition coverage is 100 %
during the baseline period. From the baseline data, the contribution to total
discharge of each pixel is calculated, and coverage is reported for all other
maps that have missing observations (Fig.

“Fast-flowing ice” is defined as ice that flows at more than
100 m yr

Names are reported using the official Greenlandic names from

Although we refer to solid ice discharge, and it is in the solid phase when
it passes the gates and eventually reaches the termini, submarine melting
does occur at the termini and some of the discharge enters the fjord as
liquid water

Gates are algorithmically generated for fast-flowing ice (greater than
100 m yr

We select a 100 m yr

Heatmap and table showing ice-sheet discharge as a function of gate buffer distance and ice speed cutoff. The colors of the numbers change for readability.

We select gates at 5000 m upstream from the baseline termini, which means
that gates are likely

We derive thickness from surface and bed elevation. We use GIMP 0715 surface
elevations in all locations, and the BedMachine bed elevations in most
locations, except southeastern Greenland where we use the

2-D histogram of velocity and thickness at all gate pixels.

The baseline data provide velocity at all gate locations by definition, but
individual non-baseline velocity maps often have missing or invalid data.
Also, thickness provided by BedMachine is clearly incorrect in some places
(e.g., fast-flowing ice that is 1 m thick, Fig.

We flag invalid (outlier) velocities by treating each pixel as an individual
time series, applying a 30-point rolling window, flagging values more than 2
standard deviations outside the mean, and repeating this filter three times.
We also drop the 1972 to 1985 years from

This outlier detection method appears to correctly flag outliers (see
the
Appendix

We generate an ice speed time series by assigning the PROMICE, MEaSUREs 0478,
MEaSUREs 0646, and pre-2000 products to their respective reported time stamps
(even though these are time-span products) or to the middle of their time
span when they cover a long period such as the annual maps from

The thickness data appear to be incorrect in some locations. For example,
many locations have fast-flowing ice but report ice thicknesses of 10 m or
less (Fig.

We calculate discharge per pixel using density (917 kg m

We calculate discharge using the gate-orthogonal velocity at each pixel and at each time stamp – all velocity estimates are gate-orthogonal at all times, regardless of gate position, orientation, or changing glacier velocity direction over time.

Annual averages are calculated by linearly interpolating to daily, and then
calculating the annual average. The difference
between this method and averaging only the observed samples is

A longer discussion related to our and others' treatments of errors and
uncertainty is in the
Appendix

At each pixel we estimate the maximum discharge,

We use

Our gate placement algorithm generates 6002 pixels making up 276 gates,
assigned to 176 ice-sheet sectors from

The widest gate (

The average unadjusted thickness of gates is 405 m with a
standard deviation of 260. The average thickness after adjustment is 439 m
with a standard deviation of 225. A histogram of unadjusted and adjusted
thicknesses at all gate locations is shown in Fig.

Our ice discharge dataset (Fig.

At the regional scale, the SE glaciers (see Fig.

Focusing on the top eight contributors (mean of last year) at the individual
sector or glacier scale (Fig.

Different ice discharge estimates among studies likely stem from three
categories: (1) changes in true discharge, (2) different input data (ice
thickness and velocity), and (3) different assumptions and methods used to
analyze data. Improved estimates of true discharge are the goal of this and
many other studies, but changes in true discharge (category 1) can happen
only when a work extends a time series into the future because historical
discharge is fixed. Thus, any inter-study discrepancies in historical
discharge must be due to category 2 (different data) or category 3 (different
methods). Most studies use both updated data and new or different methods,
but do not always provide sufficient information to disentangle the two. This
is inefficient. To more quantitatively discuss inter-study discrepancies, it
is imperative to explicitly consider all three potential causes of
discrepancy. Only when results are fully reproducible – meaning all
necessary data and code are available (cf.

The algorithm-generated gates we present offer some advantages over
traditional hand-picked gates. Our gates are shared publicly, are generated
by code that can be audited by others, and are easily adjustable within the
algorithmic parameter space. This allows both sensitivity testing of gate
location (Fig.

Our gate selection algorithm also does not place gates in northeastern
Greenland at Storstrømmen, Bredebræ, or their confluence, because
during the baseline period that surge glacier was in a slow phase. We do not
manually add gates at these glaciers. The last surge ended in 1984

We instead attribute the majority of our discrepancy with

We are unable to attribute the remaining discrepancy between our discharge
estimates and those by

Our ice discharge estimates agree well with the most recently published
discharge estimate

It is unlikely that discharge estimates using gates that are only
approximately flow-orthogonal and time-invariant

This work in its entirety is available at

We have presented a novel dataset of flux gates and a 1986 through 2017 glacier-scale ice discharge estimate for the Greenland Ice Sheet. These data are underpinned by an algorithm that both selects gates for ice flux and then computes ice discharges.

Our results are similar to the most recent discharge estimate

The application of our flux-gate algorithm shows that ice-sheet-wide
discharge varies by

Transparency in data and methodology are critical to move beyond a focus of estimating discharge quantities towards more operational mass loss products with realistic errors and uncertainty estimates. The convention of devoting a paragraph, or even page, to methods is insufficient given the complexity, pace, and importance of Greenland Ice Sheet research. Therefore the flux gates, discharge data, and algorithm used to generate the gates, discharge, and all figures from this paper are freely available. We hope that the flux gates, data, and code we provide here are a step toward helping others to both improve their work and discover the errors in ours.

Here we describe our error and uncertainty treatments. We begin with a brief philosophical discussion of common uncertainty treatments, our general approach, and then the influence of various decisions made throughout our analysis, such as gate location and treatments of unknown thicknesses.

Traditional and mathematically valid uncertainty treatments divide errors into two classes: systematic (bias) and random. The primary distinction is that systematic errors do not decrease with more samples, and random errors decrease as the number of samples or measurements increases. The question is then which errors are systematic and which are random. A common treatment is to decide that errors within a region are systematic and that among regions they are random. This approach has no physical basis – two glaciers a few hundred meters apart but in different regions are assumed to have random errors, but two glaciers thousands of kilometers apart but within the same region are assumed to have systematic errors. It is more likely the case that all glaciers less wide than some width or more deep than some depth have systematic errors even if they are on opposite sides of the ice sheet, if ice thickness is estimated with the same method (i.e., the systematic error is likely caused by the sensor and airplane, not the location of the glacier).

The decision to have

This reduction is unlikely to be physically meaningful. Our 176 sectors, 276
gates, and 6002 pixels mean that even if errors were 100 % for each, we
could reduce them to 7.5, 6.0, or 1.3 %, respectively. We note that the
area error introduced by the common EPSG:3413 map projection is

We do not have a solution for the issues brought up here, except to discuss them explicitly and openly so that those, and our own, error treatments are clearly presented and understood to likely contain errors themselves.

We assume ice thicknesses

Statistics of pixels with and without valid thickness. Numbers
represent speed (m yr

When aggregating by gate, there are 276 gates. Of these, 187 (68 %) have
no bad pixels and 89 (32 %) have some bad pixels, 65 have

We adjust these thicknesses using a poor fit (correlation coefficient: 0.3)
of the

No adjustments made. Assume BedMachine thicknesses are all correct.

Same as NoAdj, but using the

If a gate has some valid pixel thicknesses, set the invalid thicknesses to the minimum of the valid thicknesses. If a gate has no valid thickness, set the thickness to 300 m.

Set all thickness

Use the thickness versus speed relationship described above.

Table

Effect of different thickness adjustments on baseline discharge.

Finally, Fig.

Gate locations and thickness quality.

Schematic demonstrating coverage. Velocities are filled with linear
interpolation in time, and coverage is weighted by discharge.

We estimate discharge at all pixel locations for any time when there exists
any velocity product. Not every velocity product provides velocity estimates
at all locations, and we fill in where there are gaps by linearly
interpolating velocity at each pixel in time. We calculate coverage, the
discharge-weighted percent of observed velocity at any given time
(Fig.

This treatment is applied at the pixel level and then weight-averaged to the gate, sector, region, and ice-sheet results.

Here we show the same time series as in Figs.

Same as Fig.

Same as Fig.

Same as Fig.

Differences between BedMachine

We use ESA Sentinel-1 synthetic aperture radar (SAR) data to derive ice
velocity maps covering the Greenland Ice Sheet margin using offset tracking

This work was performed using only open-source software, primarily

KDM conceived of the algorithm approach and wrote the code. KDM, WIC, and RSF iterated over the algorithm results and methods. ASO provided the velocity data. SAK supplied the surface elevation change data. All the authors contributed to the scientific discussion, writing, and editing of the manuscript.

The authors declare that they have no conflict of interest.

We thank the reviewers for their constructive input that helped improve the
paper. Data from the Programme for Monitoring of the Greenland Ice Sheet
(PROMICE) were provided by the Geological Survey of Denmark and Greenland
(GEUS) at

This paper was edited by Reinhard Drews and reviewed by Ellyn Enderlin and one anonymous referee.