HW-8: Tracer modeling - due: Tu 5/6 (drop off at LDEO or
Barnard)
1) (20p) SF6 experiment in
the Hudson River
An SF6 tracer experiment was conducted on the Hudson
River in 2003. SF6 was injected on July 22, 2003 at kmp 132
(132 km north of the battery in Manhattan). Tracer distribution along
the length of the river for the next 4 days are given in the spreadsheet. The tab in the spreadsheet
identifies the date of sampling/measurement.
a) (5p) Plot SF6
concentration (fmol/L) for all 4 days as a function of kmp (distance
from the battery) in one graph. Also highlight the location of the
injection point (kmp=132). Ignoring any tidal effects, determine the
location of the SF6 peak for each day and use this infomation to
detemine the flow velocity of the Hudson during those days.
b) (10p) Assume that the tracer
data on any given day follow the normal distribution. For each day,
express the location of teh SF6 concentration data relative
to their center (so the peak should correspond to x=0). Then fit the
data with the function:
Sigma is the variance of the normal distribution, f the SF6
cocnentration. Play with the parameters a and sigma until you get a
good match between curve and data. Repeat this procedure for all 4
days.
Finally the, the longitudinal dispersion coefficient Kx
(surface water people use K, ground water people use D) can be
expressed as a function of the change of sigma as a function of time:
Determine the dispersion coefficients for the time interval between
day1 and 2, 2, and 3, and 3 and 4. Does it change with time/distance?
c) (5p) What characteristics of
the river could result in a change in K over time/distance?