This supplemental information was submitted to the Journal of Geophysical Research:
Oceans in April 2017.
Text S1. Momentum Balance
Diagnosing the along- and cross-fjord momentum budget in the narrow and wide fjord (W = 2 and 10 km) lends insight into the dynamics of the exchange flow (Figure S2). Here we focus on the sill-glacier geometry employed in Figures 7-9 (Hgl / H = 1 and Hs / H = 0.5). For a fjord width of 2 km (dashed line) and 5 km (not shown), the along-fjord momentum balance in the plume and return flow is primarily between the pressure gradient and viscosity (Figure S2a,b). Smaller contributions from along-fjord nonlinear advection and Coriolis acceleration are present in the plume and increase toward the north wall; these terms are negligible in the return flow. The cross-fjord plume and return flow momentum balance in the narrowest case is approximately geostrophic with maxima in the Coriolis and pressure gradient terms near the fjord centerline (i.e., y / W ~ 0.5) (Figure S2c,d). As the fjord width increases to 10 km (solid line), the along-fjord momentum balance exhibits more complex spatial structure and balance (Figure S2a,b).
In the plume, the dominant along-fjord geostrophic terms are largest below the fjord centerline, with the ageostrophic balance between smaller advective and viscous terms.
Above y / W ~ 0.6, the ageostrophic balance dominates, peaking near the north wall. The cross-fjord balance in the plume is primarily geostrophic and oppositely directed above and below the fjord centerline, with a small contribution from nonlinear advection in the plume core at y / W ~ 0.8 (Figure S2c). Both along- and cross-fjord momentum budgets
are approximately geostrophic in the return flow, with peak magnitudes occurring between y / W = 0.3-0.4 (Figure S2b,d). For the equivalent fjord width, the along- and cross-fjord plume and return flow momentum budget for the shallow grounding line case (i.e., surface-confined plume) is also dominated by the pressure gradient and Coriolis terms, albeit with larger contributions from the viscous and nonlinear terms (not shown).
Text S2. Effect of Forcing on Hydrography
We summarize the effect of vertical plume, tide, and wind forcing on fjord hydrography for both shallow and deeply-grounded glaciers (Figure S4). Subglacial discharge emerging from a shallow grounding line results in a cold, fresh surface-confined plume (red line), pulling near-surface potential temperature/salinity (θ-S) downward towards the runoff line (Figure S4a). A deep grounding line produces a warm, salty subsurface plume that pulls θ-S in the upper 110 m upward toward the runoff line (Figure S4b). Simulations with vertical plume and tidal forcing (blue lines) show that tide-sill interactions result in significant mixing at depth, eroding ambient stratification in the upper 200 m. In contrast, wind forcing events (green and purple lines) have a limited effect on deep fjord hydrography, with mixing primarily confined to the upper 75 m of the water column. In the shallow grounding line case, wind-driven mixing of near-surface waters alters the ambient waters entrained in the vertical plume, resulting in cooler, fresher plume waters (Figure S4a). For the deep glacier, wind forcing pulls θ-S in the near-glacier plume upward and along-isopycnal toward the runoff line between 75 and 200 m depth, with a slight increase in salinity and cooling in near-surface waters (Figure S4b).
Figure S1. Transient evolution of volume transport at the fjord mouth for varying sill, fjord, and glacier geometry. Volume transports are time averaged into 3-day bins. Colors represent grounding line depth. Dashed-dot line represents Hs / H = 0.25, dashed line represents Hs / H = 0.5, and solid line represents Hs / H = 1, respectively.
Figure S2. Along- and cross-fjord momentum budget for the plume (a,c) and depth-averaged return flow (b,d) as a function of normalized cross-fjord position. Sill-glacier geometry corresponds to Hs / H = 0.5, Hgl / H = 1; subglacial discharge flux is 250 m3 s-1. Dashed line represents fjord width of 2 km, solid line is 10 km. Terms shown are:
nonlinear advection (red), Coriolis (blue), pressure gradient (green), viscosity (purple), and budget (black). Budget represents the sum of terms in the momentum equation.
Momentum terms are averaged over day 90 to 120 and evaluated 15 km downstream of the glacier (x = -15 km). Momentum terms in the plume and return flow are computed at z = -45 m and depth-averaged between the sill and basin depth, respectively. Note the different scales used on the x-axis.
-0.150 -0.075 0 0.075 0.15
Figure S3. Temporal evolution of DST fraction in the fjord basin for varying fjord-glacier geometry and forcing. Sill geometry corresponds to Hs / H = 0.25; subglacial discharge flux is 250 m3 s-1. Solid colored lines show simulations with plume forcing only, colors represent grounding line depth. Thick solid black line shows simulations with only tidal forcing, and dashed lines show simulations with both vertical plume and tidal forcing. Simulations that include tidal forcing are filtered with a Godin filter. Note the different scales used on the y-axis.
Figure S4. Mean potential temperature-salinity profiles at the sill crest and 5 km down-glacier for shallow (a) and deep (b) grounding lines with varied forcing. Fjord width is 10 km; all profiles are averaged in the cross-fjord direction. Simulations with tidal forcing are filtered with a Godin filter, vertical plume and vertical plume and tidal forcing simulations are averaged over day 84 to 114 (to account for Godin filter window).
Vertical plume and three day along-fjord (τX) and along-shelf wind stress (τY) simulations are averaged over day 150 to 160. Black dashed line represents the mixing line between initial fjord hydrography at the grounding line depth and subglacial discharge (i.e., runoff line). Gray contours represent isopycnals spaced at 0.5 kg m-3 intervals; open red
triangles and circles show -75 m and the sill depth (z = -200 m) for the vertical plume case, respectively.
Figure S5. Upper layer volume transport (a) and cross-section of along-fjord velocity (b) for a three day along-fjord wind stress (τX) simulation. Fjord width is 2 km; sill-glacier geometry corresponds to Hs / H = 0.25, Hgl / H = 0.25. subglacial discharge flux is 0 m3 s
-1 (i.e., wind forcing only). Upper layer volume transport is computed across the fjord as the integrated transport from the free surface to the depth of the first zero crossing in along-fjord velocity. Shaded colors in (b) represent along fjord velocity; black contours represent zero.
Movie S1. 3-D visualization of sill-tide interactions for a fjord width of 2 and 10 km.
Sill-glacier geometry corresponds to Hs / H = 0.25, Hgl / H = 0.25; subglacial discharge flux is 250 m3 s-1. Colored slices represent alongfjord velocity (color scale ranges from -0.1 to -0.1 m s-1). Blue and magenta colors represent plume and DST tracer concentrations of 0.1, respectively.
Movie S2. Plan view of simulation shown in Movie S1.
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