Sea Ice Age�Climate Data Record

Anton Korosov, Leo Edel

Nansen Environmental and Remote Sensing Center

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With thanks to Heather Regan (NERSC) an Jakob Bӧrr (Bjerknessenter)

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IICWG-DA-11

2023.03.22

Motivation

• long TS (1980 - 2020)
• only oldest ice in each pixel
• gaps between pixels

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Tschudi et al., 2020

Sea ice age, 1 January 2016

NSIDC

SI-CCI

• smooth
• distribution of ice age fractions in each pixel
• short (2012 - 2017)
• too smooth

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Korosov et al., 2018

OSI-SAF climate data records

SIC: 1978 - 2020

SID: 1991 - 2020

https://osi-saf.eumetsat.int/products/osi-450-a

https://osi-saf.eumetsat.int/products/osi-455

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Lavergne et al., 2023:

https://essd.copernicus.org/preprints/essd-2023-40/

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Goals

1. To develop a new advection scheme with lower diffusion
2. To produce a longer SIA CDR
3. To analyse the new SIA CDR

New algorithm for advection

Lagrangian advection of a triangular mesh:

• To initialise from a triangular mesh (~25 km) ⇒
• To loop over ice drift files:
• To advect nodes of the mesh
• To remesh (optimise too large/small elements)
• To keep mapping from the initial mesh (t=n) to the advected one (t=n+1):

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Simple advection of element:

C_iⁿ⁺¹ = C_iⁿ

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Remeshing:

C_iⁿ⁺¹ = ∑w_jC_jⁿ

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j - overlapping elements, w - area of overlap

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Remeshing

1. For each node the sea ice velocity is interpolated from SID CDR.

Some nodes are not moving (land).

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1. Mesh is moved and some edges become too short and some too long.

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1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

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1. PyMesh splits long edges and collapses short ones.

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1. Optimesh optimizes mesh.

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1. Only some elements are remeshed (split/joined, optimized).

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1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

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1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. It also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

1. For each node velocity is interpolated from preprocessed CDR.

Some nodes are not moving (land).

​

1. Mesh is moved and some edges become too short and some too long.

​

1. PyMesh automatically identifies which edges need to be removed. I also find neighbors of affected elements.

​

1. PyMesh splits long edges and collapses short ones.

​

1. Optimesh optimizes mesh.

​

1. Only some elements are remeshed (split/joined, optimized).

​

1. For each remeshed element we find intersecting elements from the initial (donor) advected mesh.

​

1. Indices of the donor elements are saved. Weights of the donor elements are proportional to the area of intersection.

Remeshing

Main advantage

of the new advection scheme:

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No diffusion in the elements that are advected without remeshing.

Advection of sea ice concentration

The advected mesh product:

• X, Y - coordinates of nodes
• T - triangulation (indices of 3 nodes for each element)
• J - indices of the previous mesh elements
• W - weights

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Advection of sea ice concentration:

• Interpolate initial concentration from OSI-SAF CDR grid to initial mesh elements
• Loop over mesh files:
• Compute concentration on new mesh using the weights:

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C_iⁿ⁺¹ = C_iⁿ, i - new element and old element

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C_iⁿ⁺¹ = ∑w_jC_jⁿ, i-new element, j-neighbours, w-area overlap

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Accounting for sea ice deformation:

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C_iⁿ⁺¹ *= ∇ , ∇ - divergence

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Basic idea of the ice age algorithm

Multi-year ice

1991.09.15 – 1992.09.14

We start from minimum concentration on 15^th September 1991.

By definition, all of the ice that survived summer melt is multi-year ice.

Basic idea of the ice age algorithm

Advected multi-year ice

1991→1992.09.14

Basic idea of the ice age algorithm

Advected multi-year ice

1991→1992.09.14

Total concentration

1992.09.14

Basic idea of the ice age algorithm

Second-year ice (1+)

1991→1992.09.14

First-year ice (0+)

1992.09.14

Total concentration

1992.09.14

1YI = TC – 2YI

Basic idea of the ice age algorithm

Third-year ice (2+)

1991→1992.09.15

Second-year ice (1+)

1992.09.15

After 15th September, all ice fractions age by one year.

Basic idea of the ice age algorithm

Third-year ice (2+)

1991→1993.09.14

Second-year ice (1+)

1992→1993.09.14

Both fractions are advected for one more year.

Basic idea of the ice age algorithm

Third-year ice (2+)

1991→1993.09.14

Second-year ice (1+)

1992→1993.09.14

First-year ice (0+)

1993.09.14

Total concentration

1993.09.14

1YI = TC – 3YI – 2YI

Basic idea of the ice age algorithm

Fourth-year ice (3+)

1991→1993.09.15

Third-year ice (2+)

1992→1993.09.15

Second-year ice (1+)

1993.09.15

Total concentration

1993.09.15

Basic idea of the ice age algorithm

Fourth-year ice (3+)

1991→1993.09.15

Third-year ice (2+)

1992→1993.09.15

Second-year ice (1+)

1993.09.15

Ice age

1993.09.15

Ice age can be computed as a weighted average of age of each fraction:

A = 1 * 2YI + 2 * 3YI + 3 * 4YI

For a smoother transition we can add time since 15^th September (T):

A = T * FYI + (1+T) 2YI + (2+T) 3YI + (3+T) 4YI

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Comparison with SIA-SICCI v1

1 January 2016

New SIA SICCI v1

MYI 2^nd YI

Mosaic of Sentinel-1 SAR images and MYI ice outline

Korosov et al., 2018

Comparison with SICCI v1 and NSIDC

New SIA SICCI v1 NSIDC

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1 January 2016

Preliminary analysis of SIA CDR

SIA time series

Ice age fractions

2019 1996

Data for EOF analysis

Analysed variables:

• Total sea ice area
• Multi-Year Ice area
• Area of sea ice older than 5 years
• Geopotential at 500 hPa from ERA5 (similar to Dörr et al., 2023)
• Reflects large scale atmospheric circulation
• Has a climate change signal

Preprocessing:

• Monthly averages for December 1996 - 20019
• Gaussian spatial filter (5x5), Temporal uniform filter (l=3)

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Dörr et al., Forced and internal components of observed Arctic sea-ice changes, The Cryosphere Discuss., 2023

Mean STD

Geopotential height

EOF analysis (primer)

A quantity that is varying in space and time is presented as EOF (Y) and PC (B) that are varying either in space, or in time:

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X_T,S ≈ B_T Y_S

X_t=0

X_t=1

Y₀

Y₁

X₀ = Y₀ B₀₀ + Y₁ B₁₀

X₁ = Y₀ B₀₁ + Y₁ B₁₁

EOF analysis (preliminary results)

Old ice MYI ice Total ice Geopotential

EOF3 EOF2 EOF1

EOF1, PC1: - average state. Doesn’t change much over time.

Conclusions

What’s next?

Thank you for attention!

• A new method for advection of multi-year ice in a triangular mesh was developed.
• A new sea ice age CDR was generated for period 1991 - 2020 (with 7 SIA fractions from 1996).
• Replenishment of ice older than 5 year has practically stopped in 2011.
• Bi-polar structure of the Polar vortex is probably the reason for fast reduction in old ice during ~ 2001 - 2010.

• “To propose a more efficient estimator for high-dimensional, dynamical and non-Gaussian variables such as the Arctic sea ice thickness, using Machine Learning as a tool to extend the capabilities of Data Assimilation.” SIA will be used as a predictor for correcting biases in SIT reanalysis (TARDIS project, Laurent Bertino)
• Evaluate impact of uncertainties of the Sea Ice Drift product (+ compute SIA uncertainties).
• Evaluate impact of initial conditions (ice age fractions at t=0)
• To validate on buoys (at least, the upper boundary error)