= Solution
A <convective chimney> is a narrow, deeply mixed region within the surrounding stratified ocean, rather than a uniformly descending solid column. Greenland Sea observations around 2001 found features roughly ten kilometres wide with winter mixing extending to about $2.5$ km. Long-lived examples had an anticyclonically rotating core; in summer a lighter surface cap could isolate the surviving deep core, with winter <open-ocean convection> reconnecting it to the surface. https://pure.uhi.ac.uk/en/publications/convective-chimneys-in-the-greenland-sea-a-review-of-recent-obser/[Wadhams's 2005 observations] describe this structure. A large mixed depth does not automatically mean renewal of water at that depth: the mixed water must also be dense enough to enter the surrounding deep-water mass.
Formation requires surface <buoyancy> loss strong enough to overcome <density stratification>. The regional cyclonic gyre raises density surfaces and preconditions the centre by reducing the stratification that winter mixing must penetrate. Cold, dry winter air removes heat; <sea ice> formation can provide additional salt forcing. Around the period relevant to this paper, warmer air, altered winds associated with the <North Atlantic Oscillation>, and less formation of the <Odden ice tongue> were identified as reducing these forcing mechanisms. Fresh surface water also resists deep mixing. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2001gl014306[Wadhams and collaborators' 2002 study] discusses these possibilities, while emphasizing that its observed 2001 chimney formed through cooling without local ice formation.
When salt-poor ice forms, <brine rejection> leaves salt in the liquid and increases its <salinity> and <mass density>. Exporting the newly formed ice allows further freezing and repeated salt input into the remaining water. Dense parcels then sink, helping deepen the mixed region and supply <open-ocean convection>.
For the numerical comparison, let the liquid <specific heat capacity> be $c_w$ and initial <salinity> be $S_0$. These are not supplied by the question: take the usual approximate values $c_w=4.0\,\mathrm{kJ\,kg^{-1}\,K^{-1}}$ and $S_0=35$ psu for a numerical estimate. The ice heat capacity cannot replace $c_w$ during liquid cooling. Per unit area of a $100$ m column,
$$
Q=\rho_w(100\,\mathrm m)c_w(1.8\,\mathrm K),\qquad\boxed{Q\simeq7.38\times10^8\,\mathrm{J\,m^{-2}}.}
$$
The stated thermal density response gives
$$
\boxed{\Delta\rho_{\rm cool}=\frac{1.8}{10}\,\mathrm{kg\,m^{-3}}=0.18\,\mathrm{kg\,m^{-3}}.}
$$
Extracting the same $Q$ at the freezing point converts a liquid mass fraction $f_i=c_w(1.8)/L_f\simeq0.02143$ into salt-free ice. <Conservation of salt during freezing> gives
$$
S_1=\frac{S_0}{1-f_i},\qquad\Delta S=\frac{S_0f_i}{1-f_i}\simeq0.766\,\mathrm{psu}.
$$
Using the stated salinity-to-density conversion,
$$
\boxed{\Delta\rho_{\rm freeze}\simeq0.77\,\mathrm{kg\,m^{-3}},\qquad\frac{\Delta\rho_{\rm freeze}}{\Delta\rho_{\rm cool}}\simeq4.3.}
$$
The first-order approximation $\Delta S\simeq S_0f_i$ gives $0.75$ psu and a factor $4.2$. Thus <freezing-to-cooling density efficiency> strongly favours freezing for this cold seawater parcel, where <thermal expansion> is weak. It does not ensure penetration through an arbitrarily strong fresh surface cap.
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