APPENDIX A: SPWW DIMENSIONS
Table A1 contains measured well dimensions from the SPWW log book and mea-
sured water consumption from weekly South Pole situation reports (sitreps). Bot-
tom depth (D) is the distance from the wellhouse floor to the bottom of the well;
water level (L) is the distance from the wellhouse floor to the top of the water pool;
pool depth (H) is the difference between bottom depth and water level (H = D L);
dQ/dt is the water volume consumed from the well during the one-week reporting
interval; and Q is the cumulative volume of water consumed during the life of the
well. Figure A1 plots these data as functions of time. Interestingly, the dimensions
vary nearly linearly with time shortly after initial startup and after the restart ne-
cessitated by the 1994 fire. Note that freezing of the pool caused a 4-m-thick ice
cover to form between 82.686.6 m depth.
Several "draw-down" tests were conducted during the history of the well to
determine its radius (R): a known volume of water was withdrawn from the well
and the drop in water level was measured. However, after consumption began,
withdrawals of about 5 m3 would only yield water-level drops of about 1 0.5 cm,
producing large uncertainty in the estimated pool radii. Indeed, the 14 draw-down
tests conducted in March/April 1995 yielded an average radius of 13.1 m with a
standard deviation of 2.4 m. However, because dQ/dt was recorded from the onset
of consumption, we may use these data in a water-balance formula to compute
pool radius.
Figure A2 shows a schematic of the well pool and the resulting changes in di-
mensions as the pool deepens. The pool volume, initially Vp, increases to Vp + dVp.
This melts additional ice volume,
dVi = dVp + πR2dL ,
(A1)
so the incremental water created is
(
)
dVw = γ pdVi = γ p dVp + πR2dL ,
(A2)
where γp is the average ice specific gravity along the pool walls. The increase in
pool volume then equals this increase in water created less any water volume con-
sumed. That is,
(
)
dVp = γ p dVp + πR2dL dQ .
(A3)
Rearranging eq A3 yields an expression for water consumption in terms of changes
in pool volume:
(
)
dQ = γ pπR2dL 1 γ p dVp .
(A4)
To use eq A4, we must assume an average shape for the pool. Lunardini and Rand
(1995) assumed that the well would develop a paraboloid-shaped pool. However,
shape data for previous Rodriguez wells (Rodriguez 1963, Russell 1965, Williams
1974, Lunardini and Rand 1995) and observed geometry from our 1995 deploy-
ments in the SPWW suggest that an ellipsoidal pool shape would also be a good
approximation. For either case,
π
α=
Vp = αR2 H where
for a paraboloid
2
2π
α=
for an ellipsoid
(A5)
3
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