THE HYDROLOGIC CYCLE AND RIVER FORECASTING 
a liberal factor of safety. However, such a procedure 
would result in excessive project costs, and it is neces- 
sary to adhere to estimates made on the basis of sound 
meteorological theory supported by professional judg- 
ment. Obviously, the answer to ths question, What is 
the maximum amount of rain which can fall over a 
given drainage basin in a specified time? requires the 
entire resources of the science and a considerable body 
of fact and theory not yet available. Consequently, 
any fundamental advance into the problems of me- 
teorology will ultimately contribute to the solution of 
the problems of hydrometeorology. 
RIVER FORECASTING 
Of all the applications of hydrology, perhaps the one 
of most interest to the meteorologist is river forecasting. 
In flood forecasting particularly, meteorology is the 
outpost which provides a warning of the earliest evi- 
dence of possible floods. Many countries have recog- 
nized this fact by combining their hydrological and 
meteorological activities in a single hydrometeorologi- 
cal service. In the United States, where most hydrologic 
work is assigned to other agencies, the U. S. Weather 
Bureau bears the responsibility for all types of river 
forecasts. 
The Organization of a River-Forecasting Service. 
The first essential of a river-forecasting service is a 
reporting network bringing current river stage and 
weather data to the forecast office. In terms of instru- 
mentation and types of observations, this network may 
be much simpler than that used for weather forecasting. 
River stages, precipitation depths, and occasionally air 
temperature and the water equivalent of snow are 
the essential items of data. Because small-scale varia- 
tions in weather are important in river forecasting, 
the network of stations must be far denser than is 
normally required for weather forecasting. The con- 
trolling factors for the frequency of reports are the 
size and the hydrologic characteristics of the river 
basin. Forecasts at the point of outflow from basins 
of 20,000 square miles or more can usually be made on 
the basis of daily reports, while for basins under 100 
square miles hourly reports may be inadequate because 
of the rapid concentration of flow. 
In addition to the reporting network, the service 
must, of course, have forecast offices staffed with an 
adequate number of trained personnel and equipped 
with properly developed forecasting relationships. Be- 
cause of the high peak work load during floods, the 
staff must be well-organized to accomplish its job in a 
minimum of time. 
Flood Routing. The forecasting operation naturally 
divides into several categories. In making forecasts 
along a large river it is necessary to estimate the speed 
of movement and the changes in shape which the flood 
wave undergoes as it moves downstream. In terms of 
theoretical hydraulics, this is a problem in wave mo- 
tion. However, the equations of wave motion are far 
too complex for application to natural channels within 
the time available for forecasting. Hydrologists have 
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therefore turned to a more empirical solution known as 
flood routing. 
The simplest flood-routing relation is the crest-stage 
relation, which is a plotting of historical flood crests at 
one station against the resulting crests at another sta- 
tion downstream. Used in conjunction with a time-of- 
travel curve, which shows the rate of crest travel at 
various stages, the crest-stage relation is a simple and 
often effective means of forecasting peak stages. How- 
ever, considerable flow may be contributed to the flood 
wave by tributaries entermg between the two stations 
and, unless this flow is always proportional to the up- 
stream inflow (or negligible in comparison to this in- 
flow), large errors may result. Moreover, crest fore- 
casts alone are frequently insufficient. When operation 
of reservoirs is involved, it is necessary to know the 
time distribution of all runoff which is to enter the 
reservoir in order to plan its effective operation. In 
addition, riverbank interests are almost as concerned 
with the time at which the river will rise to the critical 
level at their particular location as they are in the ulti- 
mate crest, since this time fixes the interval available 
to them for evacuation. 
Forecasts of the shape of the entire hydrograph may 
be made by use of storage routing based on the storage 
equation, 
ii = OF = AS. (2) 
where J and O are the rates of inflow to and outflow 
from a section of the river, ¢ is time, and AS is the 
change in volume of water within the reach during time 
t. If it is assumed that the average of the flows at the be- 
ginning and end of the routing period equals the av- 
erage flow for the period, this equation can be written as 
I + Ip as Case 
5 5 t= 8 — Sj, (3) 
where the subscripts 1 and 2 refer to the beginning 
and end of the period, respectively. Equation (3) con- 
tains two unknowns, O» and So, but by expressing S as 
a function of O (and sometimes /) a second equation is 
available for the solution. One of the more straight- 
forward, analytical solutions of the routing equation 
is the Muskingum method. This method assumes that 
the relation between storage and flow in a stream can 
be written as 
S = Kial + (1 — 2)O}, (4) 
where K is a storage constant having the dimension 
of time and z is a dimensionless ratio expressing the 
relative importance of O and J in determining the 
storage within the reach. 
Introducing equation (4) into equation (3) and solv- 
ing for Oz, we find 
Oz = Coli + C101 + Colo, (5) 
where the several C’s are functions of K, x, and ¢. If 
values of S are plotted against values of the bracketed 
term in (4), the best value of x is that which reduces 
the plotted points most nearly to a straight line, and 
