800 WEATHER FORECASTING 
incorporating the ideas of all the forecasters as to basic 
causes or simultaneous relationships [26]. A study such 
as this is a major project in itself and is practicable only 
for a forecasting staff whose members are highly co- 
operative and willing to put aside work on other study 
projects to collaborate on an intensive study of a single 
weather element. The resulting report, aside from the 
immediate value which it may have for conventional 
forecasting techniques, furnishes a sound background 
of ideas for testing and development. 
Another source of hypotheses which has not heen 
sufficiently exploited is the ‘‘case study” approach. The 
preparation of ‘‘case books” consisting of detailed an- 
alyses of a number of individual weather situations such 
as cases of heavy snow at a city or in an area, or cold- 
wave cases, has sometimes been suggested as a useful 
aid for forecasting. Case studies alone may suggest 
necessary criteria, but further testing is necessary in 
order to establish sufficient criteria. 
Testing Procedures. Although objective forecasting 
procedures are distinguished from conventional fore- 
casting techniques chiefly by the fact that they are 
based on objectively expressed and tested ideas rather 
than on subjective and untested judgment, very little 
has been written about the testing procedures which are 
applicable. The reason for this appears to be the lack 
of any standard set of procedures which are sufficiently 
generalized that they can be advocated for use on all 
forecasting problems. A number of papers on objective 
forecasting have been published, most of them in the 
Monthly Weather Review since 1948, representing nearly 
as many different methods of procedure as there are 
papers. Other projects now under way will undoubtedly 
present improvements from the standpoimt of more ac- 
curately representing the complex division of different 
weather types with which a forecaster must deal. 
Brier [5] first presented a method of combining any 
number of meteorological variables by means of scatter 
diagrams to produce a weather forecast. The forecast 
can be expressed either in terms of the probability of 
occurrence of an event, or as a forecast of the magni- 
tude of the weather element. The use of scatter diagrams 
in the search for forecasting relationships was not new, 
but Brier’s study appears to be the first to combine a 
large number of variables into a simple forecasting pro- 
cedure by this method. The use of scatter diagrams has 
since been widely adopted, and it has been a useful sub- 
stitute for more rigorous methods of testing. 
The statistical methods of correlation and regression 
are suitable for expressing forecasting relationships and 
testing the validity of those relationships if the assump- 
tions which underlie their use are valid. Thus the rela- 
tionship between temperature and predictors such as 
normal temperature, temperature of the approaching 
air mass, expected turbulence, and expected cloudiness 
may be expressed by a multiple regression equation. 
This is possible even if the relationships are nonlinear, 
provided the form of the relationship is known so that 
a transformation to a linear form can be made. If a 
long record of observations were available so that the 
present climatic era could be randomly sampled, valid 
tests of significance of the relationships could also be 
made. 
For practical purposes, although rigorous statistical 
methods are useful in guiding the selection and process- 
ing of data, it is not often possible to make valid tests 
of significance, and the forecaster must depend upon an 
independent data sample to indicate the reliability of 
the forecasting relationship being tested. In investiga- 
tions such as these, observational data may indicate 
how selected atmospheric events are interrelated, and 
thus stimulate the conception of new hypothetical re- 
lationships, or they may be used as evidence of the 
truth or falsity of a priori, objectively expressed hy- 
potheses. In selectmg data for testing purposes, the 
investigator must adopt the role of impartial umpire; 
otherwise he is likely to select or reject cases according 
to whether they do or do not support the relationship 
under test. 
RECOMMENDATIONS FOR FUTURE RESEARCH 
The development and use of objective forecasting 
methods encounters various unsolved problems such as 
inadequate data and insufficient time for the fore- 
caster to work through the procedure. However, the 
basic problems which are encountered in common with 
any other method of forecasting are a lack of under- 
standing of the physical processes in the atmosphere 
and an inability to apply to practical problems such 
knowledge as now exists. Most of the research in ob- 
jective forecasting has been done by meteorologists 
whose primary interest is in forecasting and who feel 
the need for more systematic tools. Further progress 
could be expedited if a closer working relationship could 
be established between theoreticians and forecasters 
having an interest in the development of objective 
methods. As pointed out above, qualitative descrip- 
tions of how a forecaster can use the results of basic 
research are useful as a source of ideas, but assumptions 
must be made before the new parameters can be meas- 
ured from observational data or from analyzed maps 
and expressed quantitatively, and the theoretician can 
best say which assumptions are most in accord with 
the theory. 
Many of the objective forecasting methods developed 
in recent years make use of variables derived directly 
from station observations. The result is that changes in 
station location or the discontinuance of a station may 
invalidate a method until it can be tested by using a 
substitute variable. Claims have sometimes been made 
that the methods are more accurate when station data 
rather than values interpolated from analyzed maps 
are used. This subject needs more investigation, for if 
the claims are valid, it follows that administrators 
should be more slow to move or to discontinue stations, 
and further that much of the emphasis on centralized, 
accurate analysis is misplaced. The success of some of 
the objective methods which use station data is so 
great that this point cannot be lightly dismissed. 
Graphical techniques such as the scatter-diagram 
technique used in searching for and testing relation- 
ships are unsatisfactory in spite of their success, because 
