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Package ``BBL'' is a simple bottom boundary layer scheme. The bottommost wet |
Package ``BBL'' is a simple bottom boundary layer scheme. The initial |
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grid cell of thickness |
motivation is to allow dense water that forms on the continental shelf around |
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Antarctica (High Salinity Shelf Water) in the CS510 configuration to sink to |
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the bottom of the model domain and to become a source of Antarctic Bottom |
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Water. The bbl package aims to address the following two limitations of |
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package down_slope: |
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Thk = hFacC(kBot) * drF(kBot) |
(i) In pkg/down_slope, dense water cannot flow down-slope unless there is a |
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step, i.e., a change of vertical level in the bathymetry. In pkg/bbl, dense |
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water can flow down-slope even on a slightly inclined or flat bottom. |
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at each horizontal location is divided in two levels: |
(ii) In pkg/down_slope, dense water is diluted as it flows into grid cells |
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whose thickness depends on the model's vertical grid and that are typically |
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much thicker than the bottom boundary layer. In pkg/bbl, the dense water is |
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contained in a thinner layer and hence better able to preserve its tracer |
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properties. |
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1. A bottom boundary layer with temperature bbl_theta, salinity bbl_salt, |
Specifically, the bottommost wet grid cell of thickness |
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density bbl_rho, thickness bbl_eta, and volume bbl_Volume. |
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2. A residual thickness resThk and T/S properties resTracer such that volume |
Thk = hFacC(kBot) * drF(kBot), |
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integral is consistent with Tracer properties of bottommost wet grid cell. |
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of tracer properties Tracer, and of density rho is divided in two sub-levels: |
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1. A bottom boundary layer with T/S tracer properties bbl_Tracer, density |
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bbl_rho, thickness bbl_eta, and volume bbl_Volume. |
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2. A residual thickness |
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resThk = Thk - bbl_eta |
resThk = Thk - bbl_eta |
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with tracer properties |
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resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk |
resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk |
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such that the volume integral of bbl_Tracer and resTracer is consistent with |
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the Tracer properties of bottommost wet grid cell. |
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At every model time step, the bottom boundary layer properties bbl_theta and |
At every time step, the bottom boundary layer properties bbl_Tracer evolve as |
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bbl_salt evolve as follows: |
follows: |
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I. There is a vertical exchange between the BBL and the residual volume of |
I. There is a vertical exchange between the BBL and the residual volume of |
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bottommost wet grid cell: |
bottommost wet grid cell: |
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(i) If the density of the enclosing cell is greater than bbl_rho then set |
(i) If rho >= bbl_rho then set bbl_Tracer = Tracer |
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bbl_rho to density of enclosing cell. |
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(ii) If bbl_rho is denser than the density of the enclosing cell, the T/S |
(ii) If bbl_rho > rho , the T/S properties of the BBL diffuse into the |
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properties of the BBL diffuse into the residual volume with a relaxation time |
residual volume with a relaxation time scale of bbl_RelaxR seconds. |
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scale of bbl_RelaxR seconds. |
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bbl_Tracer(T+deltaT) = bbl_Tracer(T) + |
bbl_Tracer(T+deltaT) = bbl_Tracer(T) + |
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deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR |
deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR |
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wet grid box. They only redistribute properties between bbl_eta and resThk. |
wet grid box. They only redistribute properties between bbl_eta and resThk. |
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II. There is horizontal exchange between adjacent bottom boundary layer cells |
II. There is horizontal exchange between adjacent bottom boundary layer cells |
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when heavy BBL water is above or at the same level as lighter BBL level. The |
when heavy BBL water is above or at the same level as lighter BBL water. The |
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strength of the horizontal exchange is controlled by time scale bbl_RelaxH: |
strength of the horizontal exchange is controlled by time scale bbl_RelaxH: |
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(i) First this horizontal exchange is accumulated in BBL tracer tendency terms |
(i) First this horizontal exchange is accumulated in BBL tracer tendency terms |
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zonally: |
zonally and meridionally: |
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bbl_TendTracer(i) = bbl_TendTracer(i) + |
bbl_TendTracer(i) = bbl_TendTracer(i) + |
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( bbl_Tracer(i+1) - bbl_Tracer(i) ) / |
( bbl_Tracer(i+1) - bbl_Tracer(i) ) / |
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( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) / |
( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) / |
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( bbl_Volume(i+1) * bbl_RelaxH ) |
( bbl_Volume(i+1) * bbl_RelaxH ) |
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and meridionally. |
(ii) Then these tendency terms are applied to the BBL tracer properties: |
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(ii) Then these tendency terms are applied to BBL trace properties: |
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bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer |
bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer |
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bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk |
bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk |
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This scaled Tracer tendency will by applied to the model's tracer quantities |
and applied to the model's tracer quantities by bbl_tendency_apply. Apart |
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by the bbl_tendency_apply subroutine. |
from this lateral exchange of tracer properties between the bottommost model |
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grid cells, all other normal advection diffusion terms are also applied. |