AFIM Sensitivity Study

This document describes the simulation setup and core methodologies implemented for an Antarctic Fast Ice Modelling (AFIM) sensitivity study and published here: [link to be provided once published]

0. Model Configuration & Setup

  • Simulation period : [1993-01-01 Fri] to [1999-12-31 Tue]

  • Grid : \(1/4^{\circ}\) global, tripole Arakawa-B (B-grid)

  • Modified Landmask : a grid cell is determined to contain a (or a number of) sub-grid scale grounded icebergs and a land cell is created where normally an ocean cell would exist see sea_ice_toolbox.sea_ice_icebergs.modify_landmask_with_grounded_icebergs()

  • dt : 1800 seconds

  • ndte : 240

  • kdyn : 1 \(\textrightarrow\) EVP solver

  • Initial conditions : None

0.1 forcing:

ocean

atmosphere

  • ERA5

  • regridded to the grid file above for 30-year period [1993-01-01 Fri] to [2023-12-31 Sun]

Fast-ice classification (sea_ice_classification.py)

This module classifies fast ice (FI), pack ice (PI), and total sea ice (SI) from CICE output using:

  1. a concentration threshold (aice), and

  2. a speed threshold applied to a T-grid speed magnitude ispd_T.

Because concentration is defined on the T-grid (cell centres) but model velocities may be staggered (legacy B-grid corners, or C-grid edges), the module first constructs ispd_T using one of several reconstruction strategies. It then forms a daily candidate mask and optionally applies (i) a centred rolling-mean diagnostic and (ii) a binary-day persistence filter.

1. Notation

Let:

  • a(t,i,j) be sea-ice concentration (aice) at day t on a T-cell (i,j);

  • |\vec{u}|_T(t,i,j) be the speed magnitude on the analysis grid (T-grid);

  • a_th = icon_thresh (typically 0.15);

  • u_th = ispd_thresh (e.g. 1e-3, 5e-4, 2.5e-4 m/s).

The speed is always computed as: $\( |\vec{u}| = \sqrt{u^2+v^2} \)$

2. Constructing T-grid speed (ispd_T)

The selection is controlled by BorC2T_type. Supported tokens:

2.1 B-grid derived options (can be combined and averaged)

These options start from corner-staggered B-grid components u_B, v_B.

(Ta) 2×2 corner mean (NaNs propagate)
$\( u_{Ta}(t,i,j)=\frac14\sum_{\delta i,\delta j\in\{0,1\}}u_B(t,i+\delta i,j+\delta j), \quad v_{Ta}(t,i,j)=\frac14\sum_{\delta i,\delta j\in\{0,1\}}v_B(t,i+\delta i,j+\delta j), \)\( \)\( |\vec{u}|_{Ta}=\sqrt{(u_{Ta})^2+(v_{Ta})^2}. \)$

(Tb) 2×2 corner mean with no-slip fill (NaNs → 0)
Same as Ta, but replace NaNs with 0 before averaging: $\( \tilde{u}_B=\mathrm{nan2zero}(u_B),\quad \tilde{v}_B=\mathrm{nan2zero}(v_B). \)$

(Tx) Regridding (weights, e.g. xESMF) Corner-staggered u_B, v_B are mapped to T-grid using a precomputed regridder, after NaNs are replaced by 0: $\( u_{Tx}=\mathcal{R}(\tilde{u}_B),\quad v_T^{Tx}=\mathcal{R}(\tilde{v}_B),\quad |\vec{u}|_{Tx}=\sqrt{(u_{Tx})^2+(v_{Tx})^2}. \)$

Composite (if multiple B-grid modes are selected)
If more than one of {Ta, Tb, Tx} is requested, the module forms a composite speed: $\( |\vec{u}|_T = \mathrm{mean}\left(\,|\vec{u}|_{Ta},|\vec{u}|_{Tb},|\vec{u}|_{Tx}\,\right) \)$ with missing values skipped.

2.2 C-grid derived option (Tc; exclusive)

For C-grid output, velocities are provided as east/north components on edge staggers:

  • U-stagger: uvelE, uvelN

  • V-stagger: vvelE, vvelN

Edges are mapped to centres by adjacent averaging along the staggered direction, then combined (default: mean of U→T and V→T estimates): $\( E_T=\tfrac12(E_{U\to T}+E_{V\to T}),\qquad N_T=\tfrac12(N_{U\to T}+N_{V\to T}), \qquad |\vec{u}|_{Tc}=\sqrt{E_T^2+N_T^2}. \)$

Important: Tc is enforced as exclusive and is not mixed with Ta/Tb/Tx, because it is a different reconstruction pathway.

3. Daily candidate fast‑ice mask

For a chosen T‑grid speed product \(s_T\), AFIM defines a daily candidate mask

\[\begin{split} \mathcal{M}_{\mathrm{FI,day}}(t,i,j) = \begin{cases} 1, & a(t,i,j) > a_{\text{thresh}} \;\wedge\; 0 < s_T(t,i,j) \le s_{\text{thresh}},\\ 0, & \text{otherwise}. \end{cases} \end{split}\]

The thresholds are:

  • \(a_{\text{thresh}} = 0.15\) (15% concentration)

  • \(s_{\text{thresh}} = \varepsilon\) (default \(\varepsilon = 5\times 10^{-4}\,\mathrm{m\,s^{-1}}\), with sensitivity tests at other values)

Important: the strict inequality \(s_T>0\) is deliberate: it reduces false positives from land‑adjacent no‑slip zeros.

3.1 Pack ice (PI):

\[ \mathcal{M}_{PI,day}(t,i,j)=\mathbb{I}[a(t,i,j)>a_{th}]\ \mathbb{I}[|\vec{u}|_T(t,i,j)>u_{th}]. \]

3.2 Total sea ice (SI):

\[ \mathcal{M}_{SI,day}(t,i,j)=\mathbb{I}[a(t,i,j)>a_{th}]. \]

4. Rolling‑mean fast‑ice mask (thresholding the smoothed speed)

AFIM also implements a rolling‑mean approach that mirrors common practice in the literature. Let \(P\) be the rolling‑mean period (default \(P=15\) days). Define the centred rolling mean speed:

\[ \overline{s}_T(t,i,j)=\frac{1}{P}\sum_{\tau\in\mathcal{P}(t)} s_T(\tau,i,j), \]

and then apply the same daily threshold logic to \(\overline{s}_T\):

\[ \mathcal{M}_{\mathrm{FI,roll}}(t,i,j) = \mathbf{1}\left(a(t,i,j)>a_{\text{thresh}}\right)\, \mathbf{1}\left(0<\overline{s}_T(t,i,j)\le s_{\text{thresh}}\right). \]

AFIM returns (when requested) the triplet of masks: \({\mathcal{M}_{\mathrm{FI,day}}, \mathcal{M}_{\mathrm{FI,bin}}, \mathcal{M}_{\mathrm{FI,roll}}}\).

5. Binary‑days persistence fast‑ice mask (primary diagnostic)

The binary‑days method imposes persistence using a centred rolling count. Let \(W\) be the window length (days) and \(N\) the required number of “fast‑ice days” in the window. Define:

\[ \mathrm{C}(t,i,j) = \sum_{\tau \in \mathcal{W}(t)} \mathcal{M}_{\mathrm{FI,day}}(\tau,i,j), \]

where \(\mathcal{W}(t)\) is the centred \(W\)-day window around \(t\). The persistent fast‑ice mask is then:

\[\begin{split} \mathcal{M}_{\mathrm{FI,bin}}(t,i,j) = \begin{cases} 1, & \mathrm{C}(t,i,j) \ge N,\\ 0, & \text{otherwise}. \end{cases} \end{split}\]

Default AFIM values are \(W=11\) and \(N=9\), allowing up to \(W-N=2\) “mobile” days inside the window while still classifying the cell as persistently fast.

Implementation details:

  • AFIM uses rolling(time=W, center=True, min_periods=N) so edge times can still be classified when at least \(N\) days are present.

  • Internally, the time range is extended by \(\max(\lfloor W/2\rfloor, \lfloor P/2\rfloor)\) days (where \(P\) is the rolling‑mean period) to minimise edge effects, then cropped back to the requested \([t_0,t_N]\).

Operational detail: the workflow evaluates daily masks over an extended time span (padding by approximately \(⌊W/2⌋\) days, and by \(⌊R/2⌋\) when rolling output is enabled), then crops back to the requested analysis interval. This reduces edge artefacts from centred windows while retaining daily timing information.

Unless otherwise stated, AFIM’s primary fast-ice diagnostic uses \(\mathcal{M}_{FI,bin}\) rather than the instantaneous candidate mask \(\mathcal{M}_{FI,day}\).

2. Fast‑ice metrics (SeaIceMetrics)

AFIM computes time‑series metrics (area/volume/thickness) and gridded diagnostics (persistence, stability index, persistence distance) using generic “hemispheric” operators applied to fast‑ice‑masked fields.

2.1 Notation and masking convention

Let:

  • (A_{ij}) be the grid‑cell area (tarea; m(^2)).

  • (a(t,i,j)) be sea‑ice concentration (aice; 0–1).

  • (h(t,i,j)) be sea‑ice thickness (hi; m).

  • (\mathcal{M}(t,i,j)\in{0,1}) be a chosen fast‑ice mask (typically (\mathcal{M}_{\mathrm{FI,bin}})).

Define masked fields:

[ a_{\mathrm{FI}}(t,i,j)=a(t,i,j),\mathcal{M}(t,i,j), \qquad h_{\mathrm{FI}}(t,i,j)=h(t,i,j),\mathcal{M}(t,i,j). ]

AFIM then computes metrics from (a_{\mathrm{FI}}) and (h_{\mathrm{FI}}), optionally applying a concentration threshold (default (a>0.15)) within the metric operators.

2.2 Fast‑ice area (FIA)

The concentration‑weighted fast‑ice area time series is:

\[ \mathrm{FIA}(t)=\sum_{i,j} A_{ij}\,a_{\mathrm{FI}}(t,i,j). \]

Many studies report a purely Boolean area, \(\sum \mathrm{A}_{ij}\mathcal{M}\); the concentration‑weighted form above is what AFIM’s area operator computes when given a concentration field already masked by \(\mathcal{M}\).

Grounded icebergs (optional): in experiments with grounded‑iceberg (GI) masking, AFIM reports:

\[ \mathrm{FIA}_{\mathrm{tot}}(t)=\mathrm{FIA}(t)+A_{\mathrm{GI}}, \]

where \(A_{\mathrm{GI}}\) is the (time‑invariant) grounded‑iceberg footprint area on the model grid.

2.3 Fast‑ice volume (FIV)

Fast‑ice volume is computed as the area integral of concentration‑weighted thickness:

\[ \mathrm{FIV}(t)=\sum_{i,j} A_{ij}\,a_{\mathrm{FI}}(t,i,j)\,h(t,i,j). \]

(Equivalently, \(\sum \mathrm{A}_{ij}\,h_{\mathrm{FI}}\,a\); both are identical given the masking convention.)

2.4 Mean fast‑ice thickness (FIT)

The mean thickness of fast ice is defined as the volume‑to‑area ratio:

\[ \mathrm{FIT}(t)=\frac{\mathrm{FIV}(t)}{\mathrm{FIA}(t)} =\frac{\sum_{i,j} A_{ij}\,a_{\mathrm{FI}}(t,i,j)\,h(t,i,j)} {\sum_{i,j} A_{ij}\,a_{\mathrm{FI}}(t,i,j)}. \]

This is an area‑weighted thickness over the fast‑ice footprint.

2.5 Fast‑ice persistence (FIP)

Given a binary mask \(\mathcal{M}(t,i,j)\), the persistence over an interval \(\mathcal{T}\) of length \(T\) days is:

\[ \mathrm{FIP}(i,j)=\frac{1}{T}\sum_{t\in\mathcal{T}} \mathcal{M}(t,i,j). \]

\(\mathrm{FIP}\in[0,1]\) is a fraction of days classified as fast ice. It is often reported as:

  • Percent persistence: \(100\,\mathrm{FIP}\) (%)

  • Days of persistence: \(T\,\mathrm{FIP}\) (days)

For climatological persistence maps, \(\mathcal{T}\) is typically the full analysis period or a season (e.g., austral winter).

2.6 Persistence Stability Index (FIPSI / PSI)

AFIM implements a “persistence stability index” (PSI) over winter months (default May–October). Let \(\mathcal{T}_w\) be the set of winter days and define winter persistence:

\[ P_w(i,j)=\frac{1}{|\mathcal{T}_w|}\sum_{t\in\mathcal{T}_w}\mathcal{M}(t,i,j). \]

Define:

  • A persistent winter mask: \(\mathcal{P}(i,j)=\mathbf{1}\left(P_w(i,j)\ge p_{\text{th}}\right)\), with default \(p_{\text{th}}=0.8\).

  • An ever‑fast winter mask: \(\mathcal{E}(i,j)=\mathbf{1}\left(\max_{t\in\mathcal{T}_w}\mathcal{M}(t,i,j)>0\right)\).

Convert these to areas:

\[ A_{\text{pers}}=\sum_{i,j} \mathrm{A}_{ij}\,\mathcal{P}(i,j), \qquad A_{\text{ever}}=\sum_{i,j} \mathrm{A}_{ij}\,\mathcal{E}(i,j), \]

and define the PSI:

\[ \mathrm{PSI} = \frac{\mathrm{A}_{\text{pers}}}{\mathrm{A}_{\text{ever}}}\in[0,1]. \]

Interpretation: PSI quantifies how much of the ever‑fast winter footprint is highly persistent.

2.7 Persistence distance metrics (mean and max)

AFIM also computes distance‑based persistence statistics relative to the coastline:

  1. Identify persistent fast‑ice grid cells (e.g., \(P_w \ge p_{\text{th}}\)).

  2. Compute the minimum Euclidean distance from each persistent cell centre to the nearest coastline point (using Antarctic polar stereographic coordinates, EPSG:3031).

  3. Report:

    • Mean persistence distance (km): \(\overline{d}\)

    • Maximum persistence distance (km): \(d_{\max}\)

These diagnostics summarise how far the most persistent fast ice extends offshore.

4. Thresholds

4.1 sea ice speed threshold ( \(u_\text{thresh}\) )

Choosing the appropriate \(u_\text{thresh}\) has a significant effect on the classification of fast ice. These are values that have been used thus far, and their physical representation.

  • \(10^{-3}~\text{m/s}\), which translates to roughly 86 meters of distributed ice movement with*in** an Antarctic coastal grid cell (see Grid under model configuration above)

  • \(5 \times 10^{-4}~\text{m/s}\), which translates to roughly 43 meters of distributed ice movement with*in** an Antarctic coastal grid cell (see Grid under model configuration above)

  • \(2.5 \times 10^{-4}~\text{m/s}\), which translates to roughly 22 meters of distributed ice movement with*in** an Antarctic coastal grid cell (see Grid under model configuration above)

4.2 sea ice concentration threshold ( \(a_\text{thresh}\) )

The selection of \(a\) (sea ice concentration) has been kept at 15% of a grid cell.