and standard deviation at the end of the month
gible but evaluate it for the pairs of months of
are given in Table 2. December 1977 and January
largest flow increase and decrease in the period
1980 were the months of maximum ice growth,
of record. Qsub in eq 8 can be evaluated consider-
and February 1976 was the month of maximum
ing each component of the water balance as a
melt in this period of record.
random variable. The measurement error for dis-
Figures 4 and 5 give results for January 1979,
charge at the gages in winter is typically about
the coldest month of the study. The mean, stan-
8%, as reported on the USGS discharge measure-
dard deviation, and corresponding beta distribu-
ment notes. We will use this value as the coeffi-
tion for Qice and Qsub of each main-stem White
cient of variation for the measured monthly aver-
age discharges at the gages. Qin and Qout correla-
River reach are presented in Figure 4. The storage
tions were computed for each pair of gages over
of water as ice is an important term in the water
the period of study and have coefficients that in-
balance of the White River below Oglala, but it is
crease with distance downstream.
of less significance farther upstream and on the
Little White River, where the stream widths are
small and the flows are relatively high. The
CrawfordOglala subbasin had a negative yield
RESULTS
to the river. The distributions for Qice and Qsub
Seven consecutive winters from November 1974
have similar shapes in the two reaches below
to February 1981 provide a representative range
of temperature and hydrologic conditions for
Kadoka subbasin had a negative yield and the
analysis. Mean monthly air temperatures are avail-
KadokaOacoma subbasin had a positive yield to
able at the 11 meteorological stations in Figure 1
the river. The mean and standard deviation data
for the seven-winter study period. To account for
are repeated in Figure 5 from upstream (left) to
the variability indicated by these temperatures, a
downstream (right), together with corresponding
basin mean temperature and standard deviation
flows at the gages. The river flows diminished
were obtained and are presented in Table 2. The
from Crawford to Kadoka and then recovered
coldest winter of the study period was 197879,
somewhat at Oacoma, due to a significant inflow
and January 1979 was the coldest month. Five of
from the Little White River. The mean water stor-
the six other winters had less than half of the
age as ice increased in successive reaches down-
freezing degree-days of this winter. With these
stream, as did its variance. The variance of sub-
temperatures as input, we obtained the ice growth
basin flow exchange with the river also increased
or melt for each month, and the mean thickness
in the downstream direction.
Table 2. Mean and standard deviation for monthly air temperature over the basin Ta
(C), and corresponding cumulative ice thickness hf (m).
Year
Variable
November
December
January
February
197475
Ta
2.8, 1.2
2.2, 1.1
4.4, 0.9
7.2, 0.9
hf
0, 0
0.19, 0.072
0.40, 0.056
0.61, 0.047
197576
Ta
1.1, 1.0
1.7, 1.3
5.0, 1.4
1.7, 1.2
hf
0, 0
0.15, 0.096
0.40, 0.074
0.12, 0.23
197677
Ta
0.6, 0.6
2.8, 0.8
10.6, 1.3
1.1, 1.2
hf
0.06, 0.06
0.26, 0.054
0.63, 0.046
0.45, 0.20
197778
Ta
0.6, 2.1
-6.1, 1.2
12.8, 1.4
10.0, 1.4
hf
0, 0
0.38, 0.052
0.75,0.046
0.93, 0.045
197879
Ta
3.9, 1.0
8.3, 1.4
13.9, 0.9
8.9, 1.8
hf
0.28, 0.051
0.58, 0.051
0.89, 0.041
1.0, 0.045
197980
Ta
0, 1.7
0.6, 1.3
6.1, 1.1
3.3, 1.1
hf
0, 0
0, 0
0.38, 0.048
0.49, 0.052
198081
Ta
3.9, 1.5
1.7, 1.0
0.6, 0.7
1.7, 0.9
hf
0, 0
0.16, 0.073
0.20, 0.080
0.28, 0.076
8