FLOOD01900

• County: Statewide
• Community: Nationwide
• Title: Techniques of Weather-Resources Investigations of the USGS Book 4, Chapter A1
• Date: 1/1/1968
• Floodplain - Doc Type: Educational/Technical/Reference Information

28

TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

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1000
DRAINAGE AREA (A), IN SQUARE MILES

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MEAN FLOW (Q), IN CUBIC FEET PER SECOND
PER SQUARE MILE

General methods

Figure 20.-Gl'Ophical regression in which one variable is used twice.

All linear equations in two variables are of
the form

Y=a+bX,

and this general form is the equation of a
straight line on rectangular graph paper. The
linear form on log paper is

log Y=log a+b log X,

which, when expressed in the original variables,
is the power equation

Y=aX".

A straight line on semilog paper has the linear
form

log Y=log a+bX,

which reduces to the exponential equation,

Y=a(lO) 'x.
If b=c log k in the above equation, then
Y=ak"'.

Occasionally, points plotted on log paper

define a gentle curve rather than a straight line.
The locus of the points can sometimes be made
linear by adding or subtracting a constant from
one of the variables. The relation would be of
the form

.

log Y =log a+b log (X +c),

or

Y=a(X+c)'.

To determine the equation of any linear two-
variable relation, compute the slope of the line,
b, as vertical distance divided by horizontal
distance. These distances are always measured
in arithmetic units even though the plot is on
log paper (the b values are not transformed).
The scale interval should be the same on both
axes or an appropriate arithmetic adjustment
made. The intercept, a, is usually read off the
graph sheet on the ordinate scale at the appro-
priate value of X. For the relation

Y=a+bX,

Y=a when X=O,

and for the relation

log Y=log a+b log X,

Y=a when X=l.

.