• On Ice Sheet Mass Flow
• Introduction
• Abstract & Methods
• Results
• Implementation
  • Greenland
    • Reset
    • Discharge
    • Basal melt
    • GZ retreat
    • SMB
    • Discharge
  • Antarctica
    • Export tables to CSV
    • Reset
    • Masks: East, West, Peninsula, Islands, Grounded and Shelves
    • SMB (MAR)
    • Basal melt
    • Antarctic Ice shelves
    • Shelf freeze/melt
• Misc
  • Export tables to CSVs
  • Convert PDFs to PNG

Sankey diagrams for mass flow in Greenland and Antarctica.

See ./ms.tex

trash G_GL
[[ -e ./G_GL ]] || grass -e -c EPSG:3413 ./G_GL

cat ~/data/Mankoff_2021/708/MB_SMB_D_BMB_ann.csv \
    | cut -d, -f1,6 \
    | sed -e '1,/^1999/d' \
    | sed  '/^2019/q' \
    | datamash -t, mean 1,2

2009.5,476.44290795
org_babel_sh_eoe

Then, subtract 25 from 475 based on citet:kochtitzky_2023 who report, in Section 3.3, 17 +- 6.8 and 14.5 +- 5.8 but that “[b]ecause our fluxgates were typically located tens to hundreds of meters lower than those in the similar studies (King et al., 2018; Mankoff et al., 2020), the melt correction for these studies would be higher than values presented herein, although it is beyond the scope of the current study to determine what those values would be.”

• 21 Gt/yr from Karlsson (2021) https://doi.org/10.1038/s41467-021-23739-z
• Assume steady state

From Millan (2022) https://doi.org/10.5194/tc-16-3021-2022

• Gz retreat is ~0.13 km/yr (Fig. 3a)
• Ice velocity is ~1200 m/yr (Fig. 3b) (not needed)
• 20 km wide

Rates are higher per Ciraci (2023) https://doi.org/10.1073/pnas.2220924120, but

• Ice surface close to flotation near GZ, and shelf is ~500 m thick, so estimate 600 m ice.

Therefore, gz retreat in Gt/year is width * thick * retreat rate * density

frink "0.13 km/yr * 20 km * 600 m * 917 kg/m^3 -> Gt/yr"

1.43052

Assume similar from other ice shelves too, for a total of ~5 Gt/yr GZ retreat in Greenland.

g.mapset -c MAR

ncdump -v TIME dat/MARv3.12-GRD-15km-annual.nc4 # 20-39 = 2000-2019
ncra --overwrite -d TIME,20,39 dat/MARv3.12-GRD-15km-annual.nc4 tmp/MAR_GL.nc

ncdump -v X10_110 tmp/MAR_GL.nc # 101
ncdump -v Y20_200 tmp/MAR_GL.nc # 181
g.region w=$(( -645000 - 7500 )) e=$(( 855000 + 7500 )) s=$(( -3357928 - 7500 )) n=$((-657928 + 7500 )) res=15000 -p

var=SF # debug
for var in SF RF RU SU ME SMB EVA CON DEP SUB MSK AREA; do
  r.in.gdal -o input=NetCDF:tmp/MAR_GL.nc:${var} output=${var}
  r.region -c map=${var}
done

r.mapcalc "GL_ice_all = (MSK > 50) & ((x()-y()) > 520000)" # Limit to ice and remove Canada
r.clump input=GL_ice output=clumps --o
main_clump=$(r.stats -c -n clumps sort=desc | head -n2 | tail -n1 | cut -d" " -f1)
r.mapcalc "GL_ice = if(clumps == ${main_clump}, 1, null())"
r.mask raster=GL_ice --o

# scale
## units are mm.w.eq. per grid cell. Grid cell areas are in km^2
## + mm.w.eq. -> m w.eq.: /1E3
## + m w.eq -> kg: *1E3
## + area in km^2 -> m^2: *1E3*1E3
## + kg -> Gt: /1E12
# ds = ds/1E3 * 1E3 * ds['AREA']*1E3*1E3 / 1E12
for var in SF RF RU SU ME SMB EVA CON DEP SUB; do
  r.mapcalc "${var} = (${var}/1000) * 1000 * (AREA * 1000*1000) / exp(10,12)"
done
r.mask -r

r.mapcalc "RFZ = ME + RF - RU"

for var in SF RF RU ME SMB EVA CON DEP SUB RFZ; do
  echo ${var} $(r.univar -g ${var} | grep sum)
done

SF sum=686.768815213334
RF sum=45.5535346610575
RU sum=440.665680238757
ME sum=589.542715610605
SMB sum=235.536411205988
EVA sum=7.9188290228966
CON sum=2.15906279235185
DEP sum=12.2697684982692
SUB sum=61.8983408836194
RFZ sum=194.430570032905

import pandas as pd
df = pd.read_csv('/home/kdm/data/Mankoff_2020/ice/GIS_D.csv', index_col=0, parse_dates=True)

df = df['2000-01-01':'2019-12-31']
df.resample('YS').mean().mean().round().astype(int).values[0]

487

Exported aq_baseline to ./dat/aq_baseline.csv

Exported aq_east to ./dat/aq_east.csv

Exported aq_west to ./dat/aq_west.csv

Exported aq_peninsula to ./dat/aq_peninsula.csv

trash G_AQ
[[ -e ./G_AQ ]] || grass -e -c EPSG:3031 ./G_AQ

grass ./G_AQ/PERMANENT

v.in.ogr input=${DATADIR}/NSIDC/NSIDC-0709.002/1992.02.07/IceBoundaries_Antarctica_v02.shp output=basins

g.region vector=basins res=10000 -pas

v.db.select map=basins|head
v.db.select -c map=basins columns=Regions | sort | uniq # East West Peninsula Islands
v.db.select -c map=basins columns=TYPE | sort | uniq # FL GR IS (float, ground, island)

v.to.rast input=basins output=east use=val val=1 where='(Regions == "East")'
v.to.rast input=basins output=west use=val val=2 where='(Regions == "West")'
v.to.rast input=basins output=peninsula use=val val=3 where='(Regions == "Peninsula")'
r.patch input=east,west,peninsula output=basins
r.category basins separator=":" rules=- << EOF
1:East
2:West
3:Peninsula
EOF

r.colors map=basins color=viridis

g.mapset -c MAR

ncdump -v TIME dat/MARv3.12-ANT-35km-annual.nc4 # 20-39 = 2000-2019
ncra --overwrite -d TIME,20,39 dat/MARv3.12-ANT-35km-annual.nc4 tmp/MAR_AQ.nc

ncdump -v X tmp/MAR_AQ.nc # 176
ncdump -v Y tmp/MAR_AQ.nc # 148
g.region w=$(( -3010000 - 17500 )) e=$(( 3115000 + 17500 )) s=$(( -2555000 - 17500 )) n=$(( 2590000 + 17500 )) res=35000 -p

var=SF # debug
for var in SF RF RU ME SMB EVA CON DEP SUB MSK AREA; do
  r.in.gdal -o input=NetCDF:tmp/MAR_AQ.nc:${var} output=${var}
  r.region -c map=${var}
done

# scale
## units are mm.w.eq. per grid cell. Grid cell areas are in km^2
## + mm.w.eq. -> m w.eq.: /1E3
## + m w.eq -> kg: *1E3
## + area in km^2 -> m^2: *1E3*1E3
## + kg -> Gt: /1E12
# ds = ds/1E3 * 1E3 * ds['AREA']*1E3*1E3 / 1E12
for var in SF RF RU ME SMB EVA CON DEP SUB; do
  r.mapcalc "${var} = (${var}/1000) * 1000 * (AREA * 1000*1000) / exp(10,12)"
done

r.mapcalc "RFZ = ME + RF - RU"

r.mask --o raster=basins@PERMANENT --q maskcats="1 thru 3 10 thru 20" # drop 0 and Islands
for var in SF RF RU ME SMB EVA CON DEP SUB RFZ; do
  echo -n "${var}"
  r.univar -gt map=${var} zones=basins@PERMANENT | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
  r.univar -g ${var} | grep sum
  echo "#"; echo "#"
done
r.mask -r --q

SF
East       1555.92838304071
West       868.756236659932
Peninsula  327.008298435155
sum=2751.6929181358

RF
East       1.37427316764175
West       0.67184557194045
Peninsula  4.4182855932415
sum=6.46440433282369

RU
East       3.03921478456715
West       0.036433758652
Peninsula  6.24173336942285
sum=9.317381912642

ME
East       41.8875327525325
West       13.5639532884436
Peninsula  51.8076872767586
sum=107.259173317735

SMB
East       1421.34893771318
West       856.678097752916
Peninsula  314.290356315015
sum=2592.31739178111

EVA
East       1.3076393190111
West       0.4376933850929
Peninsula  1.3900330901803
sum=3.1353657942843

CON
East       0.00461569848685
West       0.00432677288165001
Peninsula  0.0478741559012
sum=0.0568166272697001

DEP
East       42.1006070552508
West       28.4439147061151
Peninsula  6.8402185663563
sum=77.384740327722

SUB
East       174.090628819002
West       40.7804740506949
Peninsula  16.1757877048917
sum=231.046890574587

RFZ
East       40.2225911356072
West       14.199365101732
Peninsula  49.9842395005773
sum=104.406195737917

[Raster MASK present]

Van Liefferinge (2013) https://doi.org/10.5194/cp-9-2335-2013

Convert MAT file to XYZ for importing into GRASS

import scipy as sp
import numpy as np
import pandas as pd

mat = sp.io.loadmat('/home/kdm/data/Van_Liefferinge_2023/Melt_Mean_Std_15exp.mat')
X = mat['X'].flatten() * 1E3 # convert from km to m
Y = mat['Y'].flatten() * 1E3
m = mat['MeanMelt'].flatten() / 10 # cm to mm
e = mat['StdMelt'].flatten() / 10 # cm to mm

melt = pd.DataFrame(np.array([X,Y,m,e]).T, columns=['x','y','melt','err']).dropna()
melt.to_csv('./tmp/melt.csv', header=False, index=False)
melt.head()

grass ./G_AQ/PERMANENT
g.mapset -c liefferinge_2023
r.in.xyz input=./tmp/melt.csv output=melt sep=, --o
r.in.xyz input=./tmp/melt.csv output=err z=4 sep=, --o

echo "All: " $(r.univar -g map=melt | grep sum)
echo "All: " $(r.univar -g map=err | grep sum)
echo ""
r.univar -gt map=melt zones=basins | cut -d"|" -f2,13 | column -s"|" -t
echo ""
r.univar -gt map=err zones=basins | cut -d"|" -f2,13 | column -s"|" -t

All:  sum=69.3982306335468

All:  sum=20.0261054475124


label      sum
East       46.7540492694752
West       18.8528624157926
Peninsula  3.18704264192471


label      sum
East       14.784924204035
West       4.90322548927998
Peninsula  0.221183549670513

20/69 % = 28.9855072464

• Davison (2023) https://doi.org/10.1126/sciadv.adi0186

import pandas as pd

fname = '~/data/Davison_2023/adi0186_table_s2.xlsx'

loc = pd.read_excel(fname, sheet_name='Total mass changes', index_col = 0, usecols = 'B,C,D', skiprows = 4)
loc = loc.drop('Antarctic Ice Shelves')


df = pd.read_excel(fname, sheet_name='Steady-state',
                   index_col = 0, skiprows = 4, usecols=((1,4)))

df.columns = ['Mass']

df = loc.join(df)

import geopandas as gpd
fname = '~/data/NSIDC/NSIDC-0709.002/1992.02.07/IceBoundaries_Antarctica_v02.shp'
ew = gpd.read_file(fname)

df = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df['longitude'],df['latitude']), crs="EPSG:4326")
df = df.to_crs('epsg:3031')
e = ew.to_crs('epsg:3031')

idx = ew.sindex.nearest(df['geometry'], return_all=False)
df['Region'] = ''
for dfidx,ewidx in idx.T:
    arr = df.iloc[dfidx].copy(deep=True)
    arr['Region'] = ew.iloc[ewidx]['Regions']
    df.iloc[dfidx] = arr
df = df.drop(columns=['latitude','longitude'])
    
df.loc['Total'] = [df['Mass'].sum(), None, 'All']

df[['Mass','Region']].groupby('Region').sum().drop('Islands').round()

/tmp/ipykernel_3346806/3471234904.py:32: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.
  df.loc['Total'] = [df['Mass'].sum(), None, 'All']

Same as above, different sheet. Reuses variables from above, run that first.

fname = '~/data/Davison_2023/adi0186_table_s2.xlsx'

df = pd.read_excel(fname, sheet_name='Steady-state',
                   index_col = 0, skiprows = 4, usecols=((1,6)))

df.columns = ['Mass']

df = loc.join(df)

df = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df['longitude'],df['latitude']), crs="EPSG:4326")
df = df.to_crs('epsg:3031')
e = ew.to_crs('epsg:3031')

idx = ew.sindex.nearest(df['geometry'], return_all=False)
df['Region'] = ''
for dfidx,ewidx in idx.T:
    arr = df.iloc[dfidx].copy(deep=True)
    arr['Region'] = ew.iloc[ewidx]['Regions']
    df.iloc[dfidx] = arr
df = df.drop(columns=['latitude','longitude'])
    
df.loc['Total'] = [df['Mass'].sum(), None, 'All']

df[['Mass','Region']].groupby('Region').sum().drop('Islands').round()

/tmp/ipykernel_3346806/353247760.py:22: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.
  df.loc['Total'] = [df['Mass'].sum(), None, 'All']

Same as above, different sheet. Reuses variables from above, run that first.

fname = '~/data/Davison_2023/adi0186_table_s2.xlsx'

df = pd.read_excel(fname, sheet_name='Steady-state',
                   index_col = 0, skiprows = 4, usecols=((1,2)))

df.columns = ['Mass']

df = loc.join(df)

df = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df['longitude'],df['latitude']), crs="EPSG:4326")
df = df.to_crs('epsg:3031')
e = ew.to_crs('epsg:3031')

idx = ew.sindex.nearest(df['geometry'], return_all=False)
df['Region'] = ''
for dfidx,ewidx in idx.T:
    arr = df.iloc[dfidx].copy(deep=True)
    arr['Region'] = ew.iloc[ewidx]['Regions']
    df.iloc[dfidx] = arr
df = df.drop(columns=['latitude','longitude'])
    
df.loc['Total'] = [df['Mass'].sum(), None, 'All']

df[['Mass','Region']].groupby('Region').sum().drop('Islands').round()

/tmp/ipykernel_3346806/927385710.py:22: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.
  df.loc['Total'] = [df['Mass'].sum(), None, 'All']

[greene_Supplementary_Table_1.xlsx](https://github.com/user-attachments/files/15598602/greene_Supplementary_Table_1.xlsx)

I think the data in the attached spreadsheet from [Greene et al., 2022 ](https://doi.org/10.1038/s41586-022-05037-w) is everything needed for ice-shelf mass-change resulting from frontal advance/retreat, so in Excel `=BI189-O189` gives Antarctica’s net retreat from 1997 to 2021. Change the column to adjust the time period.

BI189 = 24596304.0 BI189 = 2021.2 Q189 = 24597630.0 Q189 = 2000.2

(24596304.0 - 24597630.0) / (2021.2-2000.2) = -63.1428571429

But we need to recreate this in code so we can split by east/west/peninsula

import pandas as pd
import geopandas as gpd
fname = "~/data/Greene_2022/data/greene_Supplementary_Table_1.xlsx"

df = pd.read_excel(fname, sheet_name='greene_iceshelf_area_and_mass',
                    index_col = 1, skiprows = 4)
df = df.rename(columns={'Unnamed: 2':'lat',
                        'Unnamed: 3':'lon'})

# drop uncertainty columns
unc = []
for c in df.columns:
    if type(c) == str:
        if c[0:8] == 'Unnamed:':
            unc.append(c)
df = df.drop(columns = unc)
df = df[['lat','lon',2000.2,2021.2]]
df = df.iloc[1:]

# Remove last two rows
aq = df.loc['Antarctica']
other = df.loc['Other']
df = df.iloc[:-2]

print(df.sum())
print("")
print(aq)
print("")
print(other)

lat       -12882.373098
lon         6279.268331
2000.2    682491.281291
2021.2    681213.775349
dtype: object

lat            -90
lon          every
2000.2    24597630
2021.2    24596304
Name: Antarctica, dtype: object

lat            NaN
lon            NaN
2000.2    23915136
2021.2    23915090
Name: Other, dtype: object

shelf = df.sum()
print("All AQ loss: ", (aq[2021.2] - aq[2000.2]) / (2021-2000))
print("Named shelf loss: ", (shelf[2021.2] - shelf[2000.2]) / (2021-2000))
print("Other loss: ", (other[2021.2] - other[2000.2]) / (2021-2000))
print("Named + Other: ", (((other + shelf)[2021.2] - (other + shelf)[2000.2]) / (2021-2000)))
print("Named %: ", 2.19/63.02*100)

All AQ loss:  -63.142857142857146
Named shelf loss:  -60.83361628651619
Other loss:  -2.1904761904761907
Named + Other:  -63.02409247699238
Named %:  3.4750872738813077

import geopandas as gpd
fname = '~/data/NSIDC/NSIDC-0709.002/1992.02.07/IceBoundaries_Antarctica_v02.shp'
ew = gpd.read_file(fname)
ew.drop(columns=['geometry']).head()

gdf = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df['lon'],df['lat']), crs="EPSG:4326")

gdf = gdf.to_crs('epsg:3031')
ew = ew.to_crs('epsg:3031')

idx = ew.sindex.nearest(gdf['geometry'], return_all=False)
gdf['Region'] = ''
for gdfidx,ewidx in idx.T:
     arr = gdf.iloc[gdfidx].copy(deep=True)
     arr['Region'] = ew.iloc[ewidx]['Regions']
     gdf.iloc[gdfidx] = arr

gdf.head()

gdf.loc['Total'] = gdf.sum(axis='rows')
gdf.loc['Total', 'Region'] = 'All'

gdf['frontal change'] = (gdf[2021.2] - gdf[2000.2]) / (2021.2-2000.2)
pos = gdf[gdf['frontal change'] > 0]
neg = gdf[gdf['frontal change'] <= 0]
# gdf

print('neg', neg[['Region','frontal change']].groupby('Region').sum().round().abs())
print('')
print('pos', pos[['Region','frontal change']].groupby('Region').sum().round().abs())
print('')
print('all', gdf[['Region','frontal change']].groupby('Region').sum().round().abs())

neg            frontal change
Region                   
All                  61.0
East                 79.0
Peninsula           122.0
West                145.0

pos            frontal change
Region                   
East                181.0
Peninsula             1.0
West                103.0

all            frontal change
Region                   
All                  61.0
East                102.0
Peninsula           121.0
West                 42.0

Email from Davison

(220+230+200+420)/(2021-1997) = 44.5833333333

import xarray as xr
ds = xr.open_mfdataset("~/data/Paolo_2023/ANT_G1920V01_IceShelfMelt.nc")
ds = ds[['melt','melt_err']].sel({'time':slice('2000-01-01','2017-12-31')}).mean(dim='time')

delayed_obj = ds.to_netcdf('tmp/shelf_melt.nc', compute=False)
from dask.diagnostics import ProgressBar
with ProgressBar():
    results = delayed_obj.compute()

print(ds)

[########################################] | 100% Completed | 7.79 s
<xarray.Dataset> Size: 68MB
Dimensions:   (y: 2916, x: 2916)
Coordinates:
  * x         (x) float64 23kB -2.798e+06 -2.796e+06 ... 2.796e+06 2.798e+06
  * y         (y) float64 23kB 2.798e+06 2.796e+06 ... -2.796e+06 -2.798e+06
Data variables:
    melt      (y, x) float32 34MB dask.array<chunksize=(486, 486), meta=np.ndarray>
    melt_err  (y, x) float32 34MB dask.array<chunksize=(486, 486), meta=np.ndarray>

g.mapset -c Paolo_2023

ncdump -v x tmp/shelf_melt.nc # 2916x2916
ncdump -v y tmp/shelf_melt.nc

x0=-2798407.5
x1=2798392.5
y0=-2798392.5
y1=2798407.5

g.region w=$(( -2798407 - 960 )) e=$(( 2798392 + 960 )) s=$(( -2798392 - 960 )) n=$(( 2798407 + 960 )) res=1920 -p
r.mapcalc "area = area()"

r.in.gdal -o input=NetCDF:tmp/shelf_melt.nc:melt output=melt
r.in.gdal -o input=NetCDF:tmp/shelf_melt.nc:melt_err output=err
r.region -c map=melt
r.region -c map=err

## + kg/m^2 -> Gt: / 1E12
r.mapcalc "melt = melt * 1000 * area / exp(10,12)" --o
r.mapcalc "err = err * 1000 * area / exp(10,12)" --o

r.mapcalc "melt_on = if(melt > 0, melt, null())"
r.mapcalc "err_on = if(melt > 0, err, null())"
r.mapcalc "melt_off = if(melt < 0, melt, null())"
r.mapcalc "err_off = if(melt < 0, err, null())"

r.colors -ae map=melt color=difference
r.colors -ge map=melt_on color=viridis
r.colors -ge map=melt_off color=viridis

# d.rast melt
# d.rast melt_on
# d.rast melt_off

r.mapcalc "basins = if((basins@PERMANENT == 1) | (basins@PERMANENT == 11), 1, 0)"
r.mapcalc "basins = if((basins@PERMANENT == 2) | (basins@PERMANENT == 12), 2, basins)"
r.mapcalc "basins = if((basins@PERMANENT == 3) | (basins@PERMANENT == 13), 3, basins)"
r.colors map=basins color=viridis
r.category basins separator=":" rules=- << EOF
1:East
2:West
3:Peninsula
EOF

echo "NET"
r.univar -gt map=melt zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
r.univar -gt map=err zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
# r.univar -g melt | grep sum

echo ""
echo "FREEZE_ON"
r.univar -gt map=melt_on zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
r.univar -gt map=err_on zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
# r.univar -g melt_on | grep sum

echo ""
echo "MELT_OFF"
r.univar -gt map=melt_off zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
r.univar -gt map=err_off zones=basins | cut -d"|" -f2,13 | column -s"|" -t | sed 's/label.*//'
# r.univar -g melt_off | grep sum

NET

East       -314.59815832386
West       -516.40649095369
Peninsula  -144.781596164836

East       1262.04130311163
West       1500.90827154852
Peninsula  230.826477084729


FREEZE_ON

East       199.82814766386
West       146.110647983701
Peninsula  10.5669662518996

East       462.492239471166
West       576.342637546049
Peninsula  35.4516506207232


MELT_OFF

East       -514.426305987718
West       -662.517138937384
Peninsula  -155.348562416735

East       799.549063640453
West       924.565634002478
Peninsula  195.374826464004

(save-excursion
  (goto-char (point-min))
  (re-search-forward (concat "^#\\+name: " tbl) nil t)
  (next-line)
  (org-table-export (concat "./dat/" tbl ".csv") "orgtbl-to-csv")
  ;;(shell-command-to-string (concat "head " tbl ".csv"))
  (message (concat "Exported " tbl " to " (concat "./dat/" tbl ".csv")))
  )