∆*x *(Bin + *B*out )

where *A *is cross-sectional area, *K *is hydraulic con-

(hf - *h*i )

=

(4)

ductivity of the alluvium, and *J *is the hydraulic

∆*t*

2

gradient. Rothrock (1942) obtained the data needed

to evaluate the downvalley groundwater flow near

where ∆*x *is the reach length (m) and *B *is channel

Kadoka as *Q*int = 0.017 m3/s. The net groundwa-

width at the upstream (*in*) and downstream (*out*)

ter exchange of a subbasin with its neighbors is

ends of the reach. Equation 4 assumes that the

the difference between *Q*int values at the bound-

average width of the river in a reach can be ob-

ing stream gages. The downvalley groundwater

tained by averaging the widths at each end.

flow along the main-stem White River is small

relative to the subbasin flows given in Table 1,

and the net exchange is probably even smaller.

Therefore, we will assume that *Q*gw is supplied

by the subbasin.

The flow storage in the channel *Q*st caused by

Over the period of record, the annual and win-

significant changes in the monthly average flow

ter water yields to the White River indicated a

can be computed for a river reach as

wide range of subbasin hydrologic conditions. In

particular, major differences in subbasin yields to

*B*in ∆*Y*in + *B*out ∆*Y*out

∆*x*

the river were evident in the winter. We now de-

(7)

∆*t*

2

velop a monthly winter water balance for a river

reach that includes variable water storage in the

where ∆*Y *(m) is the channel depth change at the

river channel with large changes in flow, the for-

mation or melt of river ice, and flow exchange

upstream (*in*) and downstream (*out*) ends of the

with the corresponding subbasin. The effects of

reach, assuming that depth change can be ad-

unsteadiness on the water balance are negligible

equately described by averaging the end values.

during low-flow periods and will be neglected.

The depth changes can be determined from the

The net inflow to the river from a subbasin *Q*sub

measured average discharge at each gage for the

has tributary and groundwater components:

present and previous months and corresponding

river stage data.

The winter water balance for a river reach de-

(5)

lineated by a pair of stream gages is depicted in

Figure 3 and written as

and *Q*t3 are tributary inflows. The net groundwa-

(8)

ter exchange between adjacent subbasins is needed

to determine if *Q*gw is supplied by the subbasin

where *Q*in and *Q*out are the flows measured at the

or if it contains a significant intersubbasin com-

upstream and downstream gages, respectively. In

ponent. The groundwater flow in the alluvium

low-flow months the subbasin flow exchange may

be almost exclusively with the groundwater. As

Law as

tributary inflows are always nonnegative, *Q*sub <

0 implies groundwater recharge from the river.

(6)

Storage in CV

Stream

Gages

Q ice , Qst

Q out

Q in

Control

Volume (CV)

Q sub

6