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N~tiofl~l Technic31 Information Sen~
.... 'FIVE-TO
' '-FOR THE
60-MINUTE I~HECI1)ITATION FHEQUENCY
EASTEHN AND CENTHAL .UNITED STATES
Halph H. Frederick, et al
NOAA, National Weather Service
Silver Spring, Maryland
June 19~7
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NOAA Technical Uemorandum NWS HYDRO-35
! JUN I i
PB 272 112,
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FIVE- TO 60-MINUTE PRECIPITATION FREQUENCY
FOR THE EASTERN AND CENTRAL UNITED STATES
Silver Spring, ~d.
June ~977
ATMOSPHERIC ADMINISTRATION SerWCe
REPROOUCEO
NATIONAL TECHNICAL
INFORMATION SERVICE
National ~eethsr Service, Office of Hydrolo$¥ Series
The Office of Hydrology/ (~YDRO) of the National Weather Service (,~S) develops procedures for
~ Tactical M~or~da in the NW$ ~YD~O series facilitate prompt di~tribution of ~cientif~c and
~ be prel~ina~ in nature ~d ~ Be ~bl~sh~ ~o~all~ els~here at a later date. publication 1
ie~, ~A Tec~ical ~or~da, ~ather Bure~ Tactical ~oran~a (W~. ~e~i~in~ ~ith 1~,
~blicaticns llst~ below are a~ailable fr~ the National Tec~cal Inffo~on Se~ice, U.S. ~epart-
·ent o~ C~erce, Sills Bldg., S285 Port Re,al Ro~, Springfield, Va. 221S1. Price: $3.00 p~er
$1.45 ~lcrofiche. Order b~ accession n~ber sha~ ~n parentheses at ~d o~ each ency.
TN 4~ ~ 1 Infrar~ ~adiation ffro~ A~r tc ~nderl~in~ Surisce. V~ce A. ~ers, ~aF ~96~.
~SSA Technical Memoranda
HYDRO
HYDRO
~ORO
W~TM HYDRO 11
h~5 HYDRO 12
Annotated Sibliosraphy of ESSA Publications o~ Hydrological Inter, st. J. L. H. Paulhus,
February 1967. (Superseded by WST~ HYDRO 8]
- L
?. AUTHOR(S)
Ralph H. Frederick; Vance A. ~ars~ and Eugene P. Auciello
S. PERFORMING ORGANIZATION NAME AND AOORESS
NOAA, National ~/eather Service, O£f~ce o£ HTdrolo~
Silver S.pring, l~,
t~. SPONSORING ORGANIZATION NAME AND ADDRESS
U.S. Department of Ag~tcultu~e,
Soil Consarvatton Se=vice
June 1977
NOAA-TN-NWS HYDRO-35
10. PROJECT/TASK NO.
I(. CONTRACT/GRANT NO.
Tech. Me~o.
14.
NOAA Techn£csl Hemorandum NWS HYDRO-3/, June 1977. 40 p, 11 fig, 3 tab, 26 re£.
6 infolds
Precipitat£on-£requenc¥ values for durations o£ 5, 15, and 60 m/nutes at return
periods of 2 and 100 years are presented ~n map form for 37 states ~rom North
Dakota to Texas and eastward.. Equations are given to derive 1~- and 30-minvalues
fro~ the maps~ Equations are also given to compute values £or selected return
periods between 2 and 100 years. The basic /nput data to the study are the =axi~um
annual lrrecipitation values for 5, 10, 15, 30, and 60 minutes at about 200 stations
and the ma:c/mum annual 1-h~ events at about 1900 stations with recording rain gages.
Computer space-averaging techniques were used £or interstation inter~olatinn~
(Author)
17. KEY WORDS AND DOCUMENT ANALYSIS
*Precipitation, *Meteorological data, *Data processing
Eastern USA, Central USA
4B
~: AVAILABILITY STATEMENT
Released for distribution~ '.~
-!
NOTICE
THIS DOCUM. ENT HAS BEEN REPRODUCED
FROM THE BEST COPY FUI~NISHED US BY
THE SPONSOI~ING AGEN.CY. ALTHOUGH IT
IS I~ECOGNIZED THAT CEI~TAIN POI~TIONS
ARE ILLEGIBLE, IT IS BEING RELEASED
IN THE INTEREST OF MAKING AVAILABLE
'AS MUCH INFOI~MATION.AS POSSIBLE..
NOAA Technical Memorandum NWS HYDRO-S5
FIVE- TO SO-MINUTE PRECIPITATION FREQUENCY
FOR THE EASTERN AND CENTRAL UNITED STATES
Ralph H. Frederick
Vance A. Myers
Eugene P. Auciello
Office of Hydrology
Silver Spring, Md.
June 1977
Prepared for Engineering Division.
Soil Conservation Service,
U.S. Department of Agriculture
UNITED STATED
DEPARTMENT OF COMMERCE
Illtltl M. N~Is, Secretary
/NA[IONAL OC[ANIC ANO / NahonalWeather
ATMOSPH(RIC AOMINISTRAIION / Se,v,ce
./Robert M wmle Adm,nl$lrato, / George P Cressman
CONTENTS
Abstract ......................
Introduction ....................
N-mis data ....... . ........
Hourly data ...... , ..........
Canadian data ........ ... . . .
Data processing and testing ..............
Computer processing of data tapes .......
Frequency analysis ........
Conversion factors between annual ;nd ''''' '' 'Partial-durati°n'series
Frequency distribution ............
Data testing .................
Test for climatological trend .....
Justment of clock-hour to ; ues ...... .
Isopluvial maps ............
Methodology ...........
Space-averaging precipitation-frequent; ;alu;~
Map construction ........
2-yr 60-min (fig. 4) .....
100-yr 60-min (fig. 5) .....
5-mis maps (figs. 6 and 7)...
15-mis maps (figs. 8 and 9) . .
Maintenance of internal consistency
Intermediate durations and return periods
10- and 30-min relations ......
Intermediate return periods ....
Interpretation of results .............
Physiographic and meteorological effects .......
Comparison with previous studies .........
Illustration of the use of precipita[ion-frsquency maps, diagrams
and equations ................
Acknowledgements .......
References -
PAGE
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TABLES
1.--Factors for convertinE annual series to equivalent partial-
duration series ............
2.--Frequency of number of station values used to estimate srid
point values for 60 min .............
3.--Preclpitation frequency-values for 93°00' W, 37°00' N. . .
FIGURES
1.--Station index map ......
2.--Comparison of 2-yr 60-min precipitation values for 1923-47
and 1948-72 ..........
3.--Example of space-averaging of 2-yr 60-min precipitation
Values . .... · . · · .... · . ·
4.--2-yr 60-min precipitation..
5.--100-yr 60-min precipitation.
6.--2-yr 5-min precipitation . .
7.--lO0-yr 5-min precipitation .
8.--2-yr 15-min precipitation. .
9.--lO0-yr 15-min precipitation.
10.--Duration-interpolation diagram for 10- and i30~min estimates
Il.--Illustrative example using figure 10 ......
iii
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DISCLAIMER
Mention of a commercial company or product does not constitute an endorse-
ment by NOAA or the National Weather Service. Use for publicity or ad-
vertisement purposes of information from this publica~ion concerning
proprietary products or the tests of such products is not,authorized.
FIVE-TO 60-MINUTE PRECIPITATION FREQUENCY
FOR THE EASTERN AND CENTRAL UNITED STATES
RALPH H. FREDERICK. VANCE A. MYERS
AND
EUGENE P. AUC[ELLO
NOAA, NATIONAL WEATHER SERVICE. SILVER SPRING.
MD.
ABSTRACT. Precipitation-frequency values for dura-
tions of 5, 15, and 60 minutes at return periods of 2
and 100 7ears are presented im map form for 3l states
from North Dakota to Texas and eastward. Equations
are Eiven to derive 10- and 30-min values from the
maps. Equations are also given to com~ute values for
selected return periods between 2 and 100 years.
The basic input data to the study are the maximum
annual precipitation values for 5, 10, 15, 30, and
60 minutes at about 200 stations and the maximum
annual 1-hr events at about 1900 stations with re-
cording rain gages. Computer space-averaging techni-
ques were used for interstation interpolation.
INTRODUCTION
The growing environmental awareness of the past few years has increased the
demand for hydrologic planning and design for sm.ll area drainages hay/rig
very short times of concentration. Examples of such drainage areas are
cattle feedlots and urban shopping and parking areas. Hydrologic design
practice and legal standards are generally expressed in terms of control of
storm flow of specified frequency of recurrence. Precipitation frequencies
for short durations are an essential input to evaluating the runoff frequen-
cies from small drainage areas.
Since 1961, U. S. Weather Bureau Technical Paper No. 40 (Nershfield 1961),
abbreviated TP-40, has been the standard for precipitation-frequency values
for durations from 5 minutes to 24 hours over the Eastern United States. For
durations of less than 1 hour, the TP-40 values are derived by using nation_-
V~, return-PeTiod.independent ~Atios of' shorte~urati0n values to~l-hr
values. While these average ratios are valid in many specific sections of
the country, they have an observed, ~es~i~'~'~eo~raphic pattern.. It has
also been found that the ratios vary with return period.
The present publication analyzes the above variations and d~rives new S- to
60-min precipitation frequencies for the 37 states, North Dakota to Texas and
eastward. These are presented in the form of maps for the 5-, 15- and 60-min
durations at the 2- and 100-yr return periods, together with equations and
nomograms for intraduration and intrareturn period interpolations.
2
This report is the latest in the precipitation-frequency'literature for the
United States that began in the 1930% when David L. Yarnell (1935) first
published generalized precipitation-frequency maps for durations of $ minutes
to 24 hours at return periods of 2 to 100 years. Since 1955, the National
Weather Service (Nws, ithen the Weather Bureau) and the Soil Conservation
Service, U. g. Department of Agriculture, have been engaged in a cooperative
effort to daf/ne the depth-area-~uration precipitation-frequency regime of
the entire United States. This effort is reviewed in the introduction to
the several volumes of NOAA Atlas 2, "Precipitation-Frequency Atlas of the
Western United States" (Hiller et al. t973).
' ' ' ' " .' ..;:;: "·'·BASIC DATA
· · : . N-MINUT£ DATA
The data for durations from 5 to 60 minutes are from recording rain gages
at naarly 200 first-order NW$ stations (fig. 1). The period of record
averages nearly 60 years. The measurements are mostly from tipping bucket
gages of 12-in. (305-m) diameter which mark each 0.01 i~. (0.15 ~) of
rainfall as a step on a recording s=r~p chart (Weather Bureau 1963). ~in-
falls for 5, 10, 15, 30 and 60 minutes that exceed certa~ intensity thresh-
olds have been tabulated for these stations since 1936 (1943 for 15-min
durations). These data are published in U. S. Meteorological Yearbook
(Weather Bureau 1936-49) and Cli~tolo~ical Data~ National Su~mry~ ~nual
(Envtro~ental Data Semite 1950-72). For the present study, annual ~xi~
for each dura=ion at each station were abstracted from these sources. For
the period prior to 1936 (1943 for 15-min values), m~i~ a~ual values for
the selected durations were transcribed ~n~lly several years ago from
station records at each field station (or reposito~ for stations closed),
tn response to a request from the office of the authors.
HOURLY DATA
A network of recording ra/n gages has been maintained by the NWS, with
cooperation from many agencies, since the early 1940s. Data from about
1,900 of these stations in the study area were analysed for this project,
(fig. 1). The basic rain gage was originally an 8-in. (203-mm) diameter
weighing rain gage in which the weight of precipitation collected in a
'bucket guides a pen arm recording on a clock-driven strip chart. During
recant years, some of these gages have been replaced by the newer Fischer &
Porter gage which records the accumulated precipitation by 0.10 in. (2.5 ~)
increments at 15-min intervals on punched paper tape.
Hourly precip~tation for clock hours (1:00 a.m. to 2:00 a.m., 2:00 a.m.
to 3:00 a.m., etc.) is abstracted from the charts of these gages and pub-
lished in the Hydrolo~ic Bulletin (Weather Bureau 1940-48), Climatological
Data (Weather Bureau 194g-51), and Hourl~ Precipitation Data (Environmental
Data Service 1951-72). The National Climatic Center, Environmental Data
Service, NOAA, which is responsible for abstracting and publishing the data,
began current punching of the data on cards in 1948 and later transferred
the information to magentic tape. This clock-hour data for 1948-72 .is avail-
able on magnetic tape. Maximum ann~l'-~lo~Z~ou~ ~recipitation magnitudes
/
NOT REPRODUCIBLE
extracted from this data set differ from, and may be smaller than, maximum
60-min magnitudes from the preceding data set. Statistical conversion of
clock-hour precipitation frequencies to 60-min frequencies is discussed
later. Stations with 15 or more years of data during the 1948-72 25-year
period were processed. Many stations had a complete 25-yr record, most had
more than 20 years and only a few as little as 15 years.
CANADIAN DATA
The Canadian Atmospheric Environment'Service (AES) recently prepared fre-
quency distributions of short-duration precipitation (Atmospheric Environ-
ment Service, Canada, 1974). AES methods are similar to those used in this
study. There are about 20 Canadian stations within about 100 miles of the
United States border with frequency distributior~ of 5- to 60-min rainfalls
based on records of 15 years or longer~ and many additional stations with
frequencies based on shorter records. The Canadian frequency values were
used in the analysis without additional testing or investigation, giving the
most weight to the longer record stations.
DATA PROCESSING AND TESTING
COMPUTER PROCESSING OF DATA,TAPES
The data tapes containing hourly precipitation values for the period 1948
through 1972 were computer analyzed to select the maximum hourly value for
each month for each station/year. From these monthly values, the computer
selected the largest as the maximom hourly value for each year. During
processing, the computer also tabulated the number of hours each month listed
as missing and the number which contained accumulated amounts. All data
~aximum monthly and annual values and number of missing or accumulated
values) were listed on the computer output and checked by technicians.
Errors sought included: (1) mispunched da~a still on the tapes and (2) a
maximum value chosen from an incomplete station year. The inspected data
sets used in the analysis are believed to be as reasonable and correct as
can be expected when dealing with data sets of this magnitude.
FREQUENCY ANALYSIS
There are two methods of selecting data for analysis of extreme values.
The first method selects the largest single event that occurred within each
year of record. For this annual series, the year may be calendar year, water
year, or any other consecutive 12-mo period. The second method recognizes
that large amounts are not calendar bound and that more than one large event
may occur within the time unit used as a year. In the latter, the partial-
duration series, all values above a base (frequently the smallest maximum
annual event) are used regardless of how many occur in the same year; the
only restriction is that independence of individual events be maintained.
The partial-duration series is not a complete series (Chow 1950) and thus
is difficult to handle mathematically.
1
5
One requirement in the preparation of this publication is that the results
be expressed in terms of partial-duration frequencies. To avoid the com-
plexities of handling the partial-duration series, the annual series data
for calendar years were collected and analyzed; and the resulting statistics
were transformed to partial-duration statistics.
CONVERSION FACTORS BETWEEN ANNUAL AND PARTIAL-DURATION SERIES
Table 1 gives the emp'irical factors used to multiply annual' series values
to obtain the equivalent partialrduration series values. It is based on a
sample of about 200 geographically well-distributed first-order NWS stations
(Hershfield 1961). The factors shown ia table 1 are reciprocals of the
factors in table 2 of TP-40.
Table 1.--Pactors for converting o~nuaZ series to
equivalent partiaZ-duratlon seriea
Return period Factor
(yr)
2 1.13
5 1.04
10 1.01
25 1.00
50 1.00
100 1.00
The rainfall frequency maps in this publication are for partial duration
occurrences, and are based on analysis of station annual series, adjusted by
factors from table 1.
FREQUENCY DISTRIBUTION
The Fisher-Tippett Type I frequency distribution is used in this study.
The fitting procedure is that developed by Gumbel (1958). This distribution
and fitting procedure were used by the NWS in previous studies of short-dura-
tion precipitation values (U. S. Weather Bureau 1953, 195~a, 1954b, 1955a,
1955b, 1956, 1957-60, Hershfield 1961, and Miller et al. 1973). Studies by
Hershfield and Kohler (1960) and Hershfield (1962) have demonstrated the
applicability of this distribution to precipitation extremes. Recently, in
conjunction with another study (Miller et al. 1973), a comparison of the
values obtained.by the Gumbel_technique, the Lieblein fitting.of the Fisher-
TiPpett Type I, the P~e~_r.p~n..!ype.~!!., and the LQg__P_~L~p~__T~p.e_!II distribu-
tions was performed. The data were for durations of 1, 6, and 24 hours.
Several thousand station years of data were examined by determining the per-
cent of observations that equaled or exceede~ the calculated values for cer-
tain return periods. Results of the four computation procedures did not dif-
fer significantly. Therefore, there is no reason tO use another
and by continuing the Gumbel fitting procedure, the study is comparable with
previous studies.
6
The Gumbel procedure uses the method of moments. The 2-yr value measures
the first moment, or central tendencY. 'The relation of the 2-yr to ~he .100-
yr value is a measure of the. second moment, or disp~rsion. Values for other
re~urn periods can be derived math~matically from the 2- and 100-yr rain-
falls.
DATA TESTING
Test for Cltm-toloiical Trend
The aim of this study is to depict the frequency of N-mia precipitation
values in a population~xtendin8 over a long period of time. A large share
of the data is from a'2$-yr record, but longer records are also used. To
test the hypothesis that there was no recent climatological trend that would
make different record, lengths incompatible, 68 8eographically well-distribu-
ted first-order NI4S stations within the study area were selected. These
stations had complete and concurrent records of maximum annual 5- and 60-mia
rainfalls for the $0-yr period 1923-72.
For the 68 stations, the data sample was divided into ~wo 25-yr sesments,
1923-47 and 1948-72, and means and standard deviation for the 2- and lO0-yr
5- and 60-mia values were computed. For each duration a t-test of the two
3.0
2.0
1.o
· 2"**** °
1.0 2.0 3.0
1923-47
Figure 2.--Comparison of 2-yr 60-min precipitation values for 1925-4? and
1948-?£, at 68 stations.
1
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1
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sample means (one mean for each data period) indicated a probability greater
than 0.90 that samples from the two periods were from the same populations
at the 5- and 60-men durations. Figure 2 is a plot of the 2-yr 60-men
values from the ~o different record periods.
Adjustment of Clock-Hour Data to 60-Min Values
A factor to adjust statistical 1-hr values to 60-men values was determined
empirically by NWS several years ago (Weather Bureau 1953, 1954a). It was
found that, on the average, the N-yr 60-men value derived from the series of
annual maximum 60-men events is 1.13 as great as the N-yr clock-hour value
estimated from the series of annual maximum clock-hour values. This does
not say that an annual maximum clock-hour event multiplied by 1.13 will give
the maximum annual 60-men event in a particular case. This adjustment
applies only to the results of a statistical analysis of a series of events.
Using probability theory, Weiss (1964) confirmed this adjustment. None-
theless, an investigation'was undertaken to insure that the adjustment of
clock-hour to 60-men data, as previously used, was applicable to the present
data set. Thirty first-order NWS stations, geographically well distributed
over the study area and possessing complete and concurrent records of both
maximum clock-hour and maximum 60-minprecipitation for the period 1948-72,
were chosen as a data sample. The series of annual maxima of the two types
for each station was analyzed using the Gumbel fitting of the Fisher-Tippett
Type I distribution. The ratios of the 60-minTl-hr values at the 2- and
100-yr return periods both confirmed the 1.13 factor. /
The geographical variability of the adjustment factor, if any, was also
investigated. A plot of' the individual station ratios of the 2- and 100-yr
return period clock-hour to 60-min values showed no discernible pattern.
The 1.13 factor to adjust'clock-hour values to comparable 60-min values was
therefore adopted and used throughout this s%udy.
ISOPLUVIAL MAPS
M~THOOOLOGY
The project objective is to define 2- to 100-yr precipitation at durations
from 5 to 60 minutes. The usual approach to such a task is to draw maps for
'the enveloping durati6ns and return periods and mathematically compute
values for intermediate durations and return periods (e.g., Miller et al.
1973). For the present study, this would have meant drawing 5v and 60-min
maps for the 2- and 100-yr return periods and developing equations tO esti-
mate 10-, 15- and 30-min values. To investigate the feasibility of this,
data for the stations having N-min data were grouped geographically. Dura-
tion formulas for each such group for return periods of 2 and 100 years
were computed in the following form:
Rn=cn + (1-cn) (l>
where Rn is the required frequency value for N minutes, Rmi and Rm2 are
mapped values for a lesser and longer duration, and Cn is the interpolation
8
constant. C was found to vary both geographically and by return period
when the 10-~ 15- and 30-min values were related to the 5- and 60-min
values. For instance, interpolating the 15-m/n values between 5 and 60
minutes showed C ranging from 0.35 to 0.43 in different regions and for
different returnnperiods. 15-min values computed using an average C and
analyzed 5- and 60-min values differed by over 10 percent from value]
obtained by statistical analysis of the station data. However, by Interpo-
lating i0~m/n between 5- and 15-min ~nd 30-min between 15- and 60-min
values, ~stabilized with negligibl~ geographic and return period differ-
ences. '£~us, the decision was made to-prepare the six maps named in the
introduction.
In this study, the ratio of number of stations providing hourly values to
N-minute stations is about 10 to i and precipitation-frequency patterns can
be most accurately defined at the 60-min duration. Similarly, the period of
record is several multiples of t~o years, but only a fraction of 100 years.
Frequency pattern depiction is most accurate at the 2-yr return period. The
2-yr 60-min isopluvial pattern therefore was constructed first and used as a
guide in constructing maps for longer return periods and for shorter dura-
tions.
SPACE-AVERAGING OF PRECIPITATION-FREQUENCY VALUES
Individual station frequency values are necessarily derived from a small
sample of the entire precipitation population. In areas without strong
oro§raphic influences on precipitation, as in most of the study area, the
o~currence of heavy rainfall has a random component and the computed fre-
quencies at individual stations are variable due to sampling error. The
random component is especially pronounced at the short durations with which
this study is concerned. Some stations are expected to experience more ex-
treme events during the data period tha~ others in the same climatic regime.
For these reasons, all precipitation-frequency maps are constructed through
use of space-averaging techniques. The techniques may be either computa-
tionally explicit or implicit in the drawing of the isopluvials by an
analyst.
In this project, computerized space-averaging (or smoothing) technique[
were adapted from those used by the National Meteorological Cente~NMc)
of NWS for the objective analysis of a variety of weather maps, and from
Some experimental work in analyzing storm isohyets. 'The NMC methods de-
scribed by Cressman (1959) are designed toZ~liminate erroneous values and to
compute a smoothed data field closely fittimg widely space~ observed data.
Isohyetal analysis, ~Sing techniques similar t~ those described by Barnes
(1963) and Greene (1971), is designe~o produce a smoothed data field still
retaining detailed features of individual storm cells. ;The problem of pre-
cipitation-frequency analysis in an area free of marked 'or~graphic influences
is somewhat different from both'these problems.. The climatological pre-
cipitation-frequency field sought is smoother than individual storm isohyets
and,- compared w/th the NMC problem, is based on a greater density of data
points. Both differences suggest stronger areal averaging.- .....
The smoothing program employed the following steps to estimate precipita-
tion-frequency values at grid points spaced at eac_.._.h ~f de._e~e of latitude
and longitude:
1. Precipitation-frequency values from all stations within a given
latitude-longitude rectangle surrounding each grid point Were averaged,
weighted by a function of distance from the grid point, giving the £trst
esttm~te of the grid point value,
GPN=1 ='j~.k1 PF W
where k ia the number of stations within the chosen latitude-longitude
rectangle, PF~ a station precipitation frequency value, and Wj a weight for
that station derived from a distance weighting function.
2. The first estimates at the four grid points surrounding each sta-
tion are in turn used in double linear interpolation to estimate a new value
at each station, PFADJ:
(2)
GPNw, GPwE, GPsw, and GPsE are the closest grid points northwest, northeast,
southwest, and southeast of a station and DI and DJ delineate station loca-
tion in fractional latitude and longitude grid intervals.
The difference is computed between the original station value and this
interpolated value:
APF - PF - PFADJ
(4)
3. Each grid point first estimate from Step 1 is adjusted by the aver-
age of the differences from step 2, weighted by the distance function, for
all stations within a given distance (called the scan radius) of the grid
point:
OPN = OPN_1 + APFj W Wj (5)
GPN is the Nth grid point iteration and APF~ and W~ are precipitation fre-
quency difference from (4) and distance weighting Factors for k number of
stations within a given scan radius.
Steps 2 and 3 are repeated to progressively adjust the grid point esti-
mates.
10
The'degree of smoothing of a data field by this technique is a ~ecision o~
the._h~__an~lymt exercised through the choice of cop.~f, ants and w~ighting funk-
tio___~ns and based on a combination of professional-Judgment and any independent
statistical evidence, and is not inherent in the objective smoothing techni-
que. The r01e of the objective technique is to carry out the subjectively
determined degree of smoothing in a uniform, systematic and economical man-
ner. The scan radius, number of itera~ions, and form of weighting function
determine the'degree of smoothing.
Using a test area in the midwest, the"smoothing program was run on 60-mia
2-yr data with various scan radii, number of repeats of steps 2 and 3, and
linear and exponential weighting functions. In all cases the first grid
point estimate (step 1) was the weighted average of the station values in a
2" latitude X 2° longitude box centered on the grid point. A 2° latitude
and longitude scan radius (defining an ellipse with longest axis north-south)
3 iterations, and a linear weighting function ranging from a weight of 1.0 at
zero distance to zero at the scan radius, produced the degree of smoothing
illustrated in figure 3. This is Judged appropriate to the 60-mia data and
the factors indicated were adopted. Additional iterations after the third in
~he test runs produced little additional change in the variance of differ-
ences between original station values and interpolated values.
Table 2 illustrates the frequency distribution of the number of stations
which were used for estimation of the individual grid point values in step 3.
The grid points with the fewest influencing stations are, naturally, located
along the border of the s~udy area and in such protrusions as the Florida
peninsula, Maine and West Texas. Grid point values in such areas tend to be
overly influenced by values inward of the grid field with no opportunity for
influence from a gradient outside the grid field. In drawing lines in such
areas, the analyst kept this in mind and made adjustments to compensate for
it.
Table £.--?requency of number of station values used ~o es~ate grid point
values for ~0 m~nutes.
No. No. grid No. No. grid
stations point stations point
0-9 38 100-109 189
10-19 132 110-119 136
20-29 218 120-129 93
30-39 283 130-139 43
40-49 334 140-149 57
50-59 220 150-159 43
60-69 131 160-169 30
70-79 161 170-179 23
80-89 187 180-189 5
90-99 196
11
1.49 1.41 ,~ ~. 1.46 1:40
1.43 al.69 -
1.46 % ~, 1.57
1.51 1.28 1.51 !.56 "' ~ 1.38 1.60
~ 1.57 t.# 1.68 1.
1.37 ,~'TET_ T.~ ~1.68 /~'"'~.3Q
,20 ~ ~"-"'h.,~' /1.48 '~ I 1.48 1.~12
1.48 ,~.. ~-
1.44. 1 3' / 1.69J1.54
I 49 1.3 1,6'. · 1.62 1.49
1.33 0 1 1.5B 1.90
lO · 1
---.... ~ ... i1'~7\l.Ml.~b~..,,' \
' 1 71' ~&,l.Sg "*--~ ~"-%.1.97 1.45
1.59 1.72 \ ~1~,~ ' 1.941.66 1.47
/~ 1.E2 1.72 *,l,0j/ ,~' 1.,.I 1.42
1.50 1.70 1.74\ [ 1.64
,o \ 1.,4 1.70 , 1.74~ \1.47
~ ,, 1.531 1.53 1.66 1.68 1.83 1.59
1.89
~o ~ 1.95 1.88 1.SO
x
\ """ I 1.~11.79 1.79
,,,,, ,.,4
I / 2.0o 1.8e 1,01
38oT l· ! /' t.e5
~'48~ 1..4
.,., LEGEND 1.48
~ 1.$g ~ .--... ANAL YSIS OF RAW 1.~2
1.52 STATION VALUES
1.,
FINAL FREOUENC¥ 1.89 {1.57\ 1.$3
ISOPLUVIAL
37o 1.$ 1.~9\ 1.71 1.90 ~\1.61.~
g8° 97° 96o gso g4o g3°W
Figure $.--Ex~ple of space-averaging of 2-yr 60-rain precipitation values.
12
Because data for the 5- and 15-min durations are one tenth as dense as
data for 60 minutes, the first estimate for these durations was made using
all stations within 2" of latitude or longitude of the grid point and the
adjustments using 4" scan radius. The first estimates plus three iterations
was continued. In practice, this means that despite using a scan area four
times as large as that used with 60-min data the number of stations bearing
on a given data point is only about 40 percent of the number shown in table
2. This is not, however, a serious problem since areal variability de-
creases as duration decreases: i.e., the data field for the $-min duration
shows less variation than does the 60-mln data field. To illustrate this
point, four data sets consisting of all 2- and 100-yr 5-min values and 2-
and lO0-yr 60-min values in the area bounded by the Gulf Coast on the south,
~5°N on the north, and 85°W and 95°w on the east and west sides were ana-
lyzed. At the 5-min duration.the coefficient of variation of the 2-yr data
set was 0.126 and at the 100-yr return period it was 0.121. The correspond-
ing coefficients of variation for 60 minutes were 0.245 and 0.207.
MAP CONSTRUCTION
2-Yr 60-Min (Fig. 4)
The individual station frequency values, calculated as previously describ-
ed, were plotted on a map. Most of these are derived from maximum annual
clock-hour values adjusted to 60 minutes by the 1.13 fac_~lor. Also plotted
on the half-degree latitude-longitude grid syste~were the values obtained
from the computer smoothing program. The final precipitation-frequency iso-
pluvials were derived by small additional manual smoothing of the grid point
values in areas with little or no orographtc influence, with constant con-
current reference to the unsmoothed station data. In the vicinity of the
Appalachian Mountains, there are believed to be substantial orographic in-
fluences on precipitation frequency at a scale finer than the station den-
airy available for this study. In NOAA Atlas 2 (Miller et al. 1973), this
characteristic was reco~nized in the 11 Western States by developing stati-
stical relations between precipitation-frequency and topographic parameters.
The latter can be defined by elevations read from toposraphic maps in what-
ever detail ia relevant. However, NOAA Atlas 2 was developed for longer
durations (6 and.24 hours) than thO"present study and for 24 hours was able
to use the more numerous data available from the NWS network of nonrecord-
ing rain gages to estimate isopluvtal variations. The development of simi-
lar statistical relations for the Appalachians was beyond the scope of the
present study. The precipitation-frequency isopluvials in the mountainous
regions in the Eastern United States were shaped subjectively to the topo-
graphy depicted on 1:1,000,000 scale World Aeronautical Charts With Some
guidance from valley vs. higher elevation data at a few pla~es.
Isbpluvtal variations due. to topographic influences are probably present
in the Black Hills region'and in the vicinity of the Ozark Mountains. The
station precipitation-frequency data were closely scrutinized for such in-
fluences in these areas but no consistent, explainable variations could be
detected and no nearby valley vs. mountain contrasts were found in the a-
vailable station data. Thus, the final isopluvials in the Black Hills and
Ozark Mountains are based on station data without regard to topography.
13
In addition, the isopluvials were tied into values calculated from or
implied by the precipitation-frequency maps for Montana, Wyoming. Colorado,
and New Mexico in NOAA Atlas 2 and the frequency values at nearby Canadian
stations.
100-Yr 60-Min (Fig. 5)-~ ¢'~'~ ~'~ ~^~ ~'~"~'~'(
No matter what distribution or fitting method is used in extreme value
analysis, the s~mpling, error at the 100-vr r~,,rn perio~ j~_gr~~_~
t~e 2-yr return period. The general form of the equation for any return
period is Yt ~ X + KS, where Yt is the value for the return period, ~ is the
annual series sample mean, and S its standard deviation. K is a factor that
differs with distribution assumed and the fitting method used, but K values
have a common trait no matter what the distribution or fitting method--they
increase with increasing return period.
For example, us~in~.mbel's method on a data sample of 25 items, at the
2-yr return period, K ;~' ~O.-'lb06~,'-"while at the 100-yr level, K 3.7283--in
absolute value the 100-yr K is about 25 times the 2-yr K. The noise compon-
ent brought about by the difference between S and the! population standard
deviation, o, is much greater at the lO0-yr return period than at the short-
est return periods·
Over t~he years, it has been found that the ratio of 100-yr to 2-yr preci-
pitation-frequency values is conservative over large contiguous areas and
varies less than the 100-yr values themselves. For example, the ratio ~f~. '-'~ '
the 100- to 2-yr 60-min values gradually _increases northward. . - -
The construction of the 100-yr 60-min map used the following aids: 1) sta-
tion data and smoothed grid point data developed from the station data by
computer .smoothing as previously described; 2) station 100-yr/2-yr ratios and
smoothed grid point values of that ratio; and 3) the isopluvial pattern of
the 2-yr 60-min ~ap.
5.-Min Maps (Figs. 6 and 7)
It was hypothesized that the maximum annual 5-min values at adjacent sta-
tions are mostly from different storms and may be treated as statistically
independent. This hypothesis was examined by comparing data from all sta-
tions in a 240-mi (385-km) square centered on Iowa. The period of record
was 1907-72, but not all stations had data for all years. There was a total
of 264 station years at seven stations. About 11 percent of the 5-min annual
maxima occurred on the same date as an annual maximum at another of the seven
stations. However, only about a quarter of these equaled or exceeded the 2-
yr return period value. Essential independence of the more significant maxi-
mum annual 5-min rainfalls was considered established.
In view of the above, new data series were constructed, consisting of all
maximum annual 5-min events at all the stations within overlapping 4° lati-
tude-longitude boxes. This new series was analyzed by the Gumbel fitting of
the Fisher-Tippett Type I distribution, as previously discussed. The
resulting 0.5 and 0.01 probability events (~quivalent to 2-yr and 100-yr
27
return period) for each box were plotted at positions within the box de-
termined by weighting tile latitude and longitude of each contributing sta-
tion by its length of record. In some regions of sparse data, only one sta-
tion was available within a 4° box, but more generally the station years per
box exceeded 100. The computer smoothing program was also run on the sta-
tion 5-min valuer within the scan radius increased to 4°. Station ratios of
5- to 60-min values were similarly smoothed.
In sunmaary, data used in construction of the 5-min maps included: 1) fre-
quency values computed from all station data within each 4° latitude-longi-
tude box and centered according to station location and length of record,
2) the computed frequency values and 5-min to 60-min ratio for the indivi-
dual stations, 3) computer smoothed grid values for both frequency values
and ratios, and 4) the isopluvial pattern developed for the 2-yr 60-min map.
The character of tile 2-yr 5-rain data (fig. 6) (and the climate) required
all nnqrtbodox analysis ill the central part of tile country, the shaded area
labeled 0.45 region. All puints within tile area are to be considered to
have a 2-yr 5-min frequency value of 0.45 in. (11.4 n~), with values grad-
ually Increasing southward and decreasing northward beyond this region.
Considerable time and effort were spent attempting to define a precise lo-
cation for the 0.45-in. isopluvial. The station data and the several forms
of grid point data indicated that within this area values were equal to or
within a few hundredths of an inch of 0.45, with no definable gradient.
Since the placement of the line is a subjective judgment, the decision was
made to treat the area as one broad line with all values equal to the value
of the isoline.
15-Min Maps (Figs. 8 and 9)
As previously mentioned in the section "Methodology, Isopluvial Maps,"
the relationship between the 5-, 15- and 60-min precipitation frequencies
was fonnd to vary both geographically and by return period. Therefore, as
an aid in the drawing of 15-min maps, the compnter smoothing program was
run on station values of the coefficient C15:
J
Ri5 = C15 R60 + (1 - C15) R5 (6)
separately for the 2- and lO0-yr return periods to obtain grid point values.
Stlt~c~ssive iterations of computer smoothing followed by manual adjustment
were made to obtain consistent smooth fields of both C15 and R15, holding
R60 and R5 fixed.
MAINTENANCE Of INTERNAL CONSISTENCY
Once preliminary 5-, 15- and 60-min isopluvial frequency maps for the 2-
and 100-yr durations were completed, values were read from the analyzed maps
at 0.5° latitude-longitude grid points. These values were used to produce
maps showing ratios at the grid points between the various durations and re-
turn periods. The ratio fields were then scanned for consistency and cor-
respondence to ratios from the station data. The preliminary isopluvial
map~ wt.i-c :ldjusted t~ removt, any Inconsistencies in the ratio fields. Next,
Preceding page blank
2.5
2.(
1.0
5 MIN 10 MIN 15 MIN 1,5 MIN
Figure 11.--IZlustra~ive example using figure 10.
3O MIN
60 MIN
values (in.) for 93°00'W, 37o00'N
2-yr
$-yr
10-yr
25-yr
50-yr
100-yr
5-min 10-min 15-min 30-min 60-min
0.45 0.94 1.59
0.85 (~ 1.79 3.43
Note: Circled valu~:s are computed from the other valoes.
ACKNOWLEDGEMENTS
Sponsorship and finaocial sopport for this project were provided by Soil
Conservation Service, U.S'. Dept. of Agriculture. Coordination with
the Soil Conservation Service was maintained through Robert E. Rallison,
Chief, Hydrology Branch, Engineering Division.
34
REFERENCES
Atmospheric Environment Service (Environment Canada), 1974: "Short Duration
Rainfall Intensity-Duration-Frequency Data," (unpublished graphs and com-
puter output). .
Barnes, S. L., 1963: "A Technique for Maximizing Details in Numerical
Weather Map Analysis" Technical Report ARL-1326-8, Atmospheric Research
Laboratory, University of Oklahoma Research Institute, Norman, Okla.
Chow, V. T., 1950: "Discussion of Ann~ai Floods and the Partial-Duration
Flood Series, by W. B. Langbein," Transactions of American Geophysical Union~
31, pp. 939-941.
Cressman, G. P., 1959: "An Operational Objective Analysis System," Monthly
Weather Review, 8~ pp. 36?-374.
Environmental Data Service, 1950-72: Climatolostcal Data~ National Summary,
Annual, NOAA, U.S. Dept. of Comerce, Asheville, N.C.
Environmental Data Servic~ 1951-72: Hourly Precipitation Data, NOAA, U.S.
Dept. of Commerce, Asheville, N.C.
FuJita, T., 1976: "Graphic Examples of Tornadoes," Bulletin of the American
Meteorolosical Society, 57, pp. 401-412.
Greene, D., (Texas A & M University, College Station) 1971: "Numerical
Techniques for the Analyses of Digital Radar Data with Applications to
Meteorology and Hydr61ogy," Ph.D. Thesis.
Gumbel, E. J., 1958: Statistics of Extremes, Columbia University Press, New
York, 375 pp.
Hershfield, D. M., 1961: "Rainfall Frequency Atlas of the United States for
Durations from 30 Minutes to 24 Hours and Return Periods From 1 to 100
Years," Technical Paper No. 40, Weather Bureau, U.S. Dept. of Commerce,
Washington, D.C., 115 pp.
Hershfield, D. M., 1962: "An Empirical Comparison of the Predictive Value
of Three Extreme-Value Procedures," Journal of Geophysical Research, 67, pp.
1535-1542.
Hershfield, D. M., and M. A. Kohler, 1960: "An Emprical Appraisal of the
Gumbel Extreme-Value Procedure," Journal of Geophysical Research, 65, pp.
1737-1746.
Miller, J. F., R. H. Frederick and R. J. Tracey, 1973: "Precipitation-Fre-
quency Atlas of the Western United States, Vol. I: Montana; Vol. II: Wyo-
ming; Vol. III: Colorado; Vol. IV: New Mexico; Vol. V: Idaho; Vol. VI:
Utah; Vol. VII: Nevada; Vol. VIII: Arizona; Vol. IX: Washington: Vol. X:
Oregon; Vol. XI: California," NOAA Atlas 2, National Weather Service, NOAA,
U.S. Dept. of Commerce, Silver Spring, Md.
35
Pitchford, K. L., and J. London, 1962: "The Low Level Jet as Related to
Nocturnal Thunderstorms over Midwest United States," Journal of Applied
Meteorolo~, 1, pp. 43-47.
Weather Bureau, 1940-48: Hydrologic Bulletin, U.S. Dept. of Commerce
Washington, D.C.
Weather Bureau, 1936-49: U.S. Meteorological Yearbook, U.S. Dept. of
Commerce, Washington, D.C..
Weather Bureau, 1948-51: Climatological Data, U.S. Dept. of Commerce,
Washington, D.C.
Weather Bureau, 1953, 1954a: "Rainfall Intensities for Local Drainage
Design in the United States for Durations of 5 to 240 Minutes and 2-, 5-,
and 10-Year Return Periods," Technical Paper No. 24, "Part I: West of the
ll5th Meridian," Washington, D.C., Revised February 1955, 19 pp., "Part II:
Between 105°W. and ll5°W.,'' U.S. Dept. of Commerce, Washington, D.C.,
9 pp.
Weather Bureau, 1954b: "Rainfall Intensities for Local Drainage Design in
Coastal Regions of North Africa, Longitude ll°W. to 14°E. for Durations of ~
5 to 240 Minutes and 2-, 5-, and 10-Year Return Periods," U.S. Dept. of
Commerce, Washington, D.C., 13 pp.
Weather Bureau, 1955a: "Rainfall Intensities for Local Drainage Design in
Arctic and Subarctic Regions of Alaska, Canada, Greenland, and Iceland for
Durations of 5 to 240 Minutes and 2-, 5-, 10-, 20-, and 50-Year Return
Periods," U. S. Dept. of Commerce, Washington, D. C., 13 pp.
Weather Bureau, 1955b: "Rainfall Intensity-Duration-Frequency curves for
Selected Stations in the United States, Alaska, Hawaiian Islands, and Puerto
Rico," Technical Paper No. 25, U.S Dept. of Commerce, Washington, D.C.,
53 pp.
Weather Bureau, 1956: "Rainfall Intensities for Local Drainage Design in
Western United States for Durations of 20 Minutes to 24 Ho]rs and 1- to 100-
Year Return Periods," Technical Paper No. 28, U.S. Department of Commerce,
Washington, D.C., 46 pp.
Weather Bureau, 1957, 1958, 1958, 1959, 1960: "Rainfall Intensity-Frequency
Regime," Technical Paper No. 29, "Part 1: The Ohio Valley;" "Part 2:
Southqastern United States;" "Part 3: The Middle Atlantic Region;" "Part 4:
Northeastern United States;" "Part 5: Great Lakes Region," U.S. Dept. of
Conm~erce, Washington, D.C.
Weather Bureau, 1963: "History of Weather Bureau Precipitation Measure-
ment,'' Key to Meteorolosical Records Documentation No. 3.082, U.S. De~t. of~
Commerce, Washington, D,C., 19 pp.
~6
Weiss, L. L., 1964: "Ratio of True to Fixed Interval Maximum Rainfall,"
Journal of the Hydraulics Division; Proceedtnss, ASCE, 90, RY-1, Proceedings
Paper 3758, pp. 77-82.
Yarnell, D. L., 1935: "Rainfall Intensity-Frequency Data," Miscellaneous
Publication No. 204,.U.$. Dept. of Agriculture, Washinston, D.C., &R ~.
-". NM~ HYDRO
*h~-~ HYDRO 18
NWS HYDRO 19
.N~S HYDRO 20
~S '~RO 22
"NW$~'~6~O*' 23
HYDRO 24
'NWS HYDRO 25
sins*; Ralph M. Frederick, June 1973. (COM-73-11169)
16J" A Dynamic Model of.Sta~e-Dlscharge Relations Affected by Changing Discharge, D, L,
17 .-Natlonal ..Weather Servi~e River Forecast Systma--Snow Accu~ulation a~d Ablation Hodel,
Eric A. Anderson, November 1973. (CC~1=74=10728)
Numerical Properties of Implicit Four-Point Finite Difference Equations of Unsteady
Flow. D. L. Freed, Hatch 1974.
Stor~ Tide Frequency Rnalysis for the Coast of Georgia. · Francis P. Ho, September 1974.
(COM-74-11746/AS)
Storm Tide Frequency forthe Gulf Coast of Florida From Cape San ~las to St. Petersburg
Seach,.~. Francis P. Ho and Robert J. Trace¥, April 1975. (COM-TS-109OI/AS)
Francis P. Ho and Robert J. Tracey, Nay 1979. (COM-7$-II000/AS)
Armotated Bibliography of NOAA Publications of Hydrometeorological Interest. John F.
Hillez, May 1975.
Storm Tide Frequency Analysis for the Coast of Puerto Rico. Francis P. Ho, May 1975.
(COM-I1001/A$)
The Flood Of April 1974 in Southern Mississippi and Southeastern Louisiana. Edwin H.
Chin, AUSUSt 1975.
The Use of a Hultizone Hydrolosic Model Hith Di}tributed Rainfall and Distributed Par-
1975.
N~S HYDRO 26
NWS HYDRO 27
NWS HYDRO 28
NWS HYDRO 29
~4NS HYDRO 30
NWS HYDRO 33
NWS HYDRO ~4
Moisture Source for Three Extreme Local Rainfalls in the Southern Intermountain Region.
B. Marshall Hansen, October 1979.
Stor~ Tide Frequency Analysis for the Coast of North Carolina, North of Cape Lookout.
Francis P. Ho and Robert J. Tracay. November 1979.
Flood Damage Redu~tion Potential of River Forecast Services in the Connecticut River
Basin. Harold J. Day and Kwang ~. Lee, February 1976. (PB-256798)
Water Availible £or Runo~£ for ~- to IS-Days Duration in the Snake River Basin in Idaho.
Ralph H. Frederick ~nd Robert -1~ Tracey, June 1976. (pB-298-427)
Meteor Burst C$~ainication Syste~~-Alaska Hinter Field Test Program. Henry 9. Santa-
ford, March 1976. (PB-260-419)
Catchment Modeling and Initial Pera~eter Estimation for the National Weather Service
River Forecast System. Eugene L. Peck, June 1976. (PB-2641S4)
atom?ida Frequency Analysis for the Open Coast of'Virginia, Maryland, and Delaware.
Francis P. Ho, Robert J. Tracey, Vance A. Hyers, and Not. alee S. Foal, August 1976.
(PB-261-969)
9hipe and John T, Rledel, Dec~ber 1976.
Annotated Bibliography oF NOAA Publications of Hydrometeorological Interest. John F.
5 MIN
10 MIN
15MIN 15MI~
30
Figure lO.--Duration-interpolation diagr~ for lO- and 30-rain estimates.
60 MIN
30 Mil
5 MIN 10 MIN 15 MIN 15MIN
FigurelO.--Dura~zon_znterpoZation' ' d~agr~ for 10. and 30-mln estzmate~:
~0 MIN
5 MI~ 10 MIN 15 MIN 15 Mil 30 MIN
Figure lO.--Duration-interpolation diagr~ for 10- and $O-mln estimates.
60 MIN
5 MIN
10 MIN 15 MIN 15MIN 30
Pigure JO.--Duration_interpo[atlon dlagr~ for JO- and 30-m~n estimate,.
60 MIN
/ ! I
\
Preceding page blank
' blank
· *." Preceding page
2-Yrr. AR 5-MINUTE
\
Preceding. I]a~e J~lank
·
$00.YF~YR r~MINUTE PflECI,o/TATIO;~
IINCHESI
--' Preceding page blank
,, ,, , '.~-' ~-~:.~:.~' '-},~ "'*'" ~; Preceding page blank
H. HALFF
FINANCIAL STATISTICS
~ FY 1786 FY 19S§ FY 1984
($)
~ CASH 221~991 2.64 349~390 5.30 185,240 3.97
~TES REC'DLE 664,913 7.90 ' 0.00 0,00
! MD~K IN PROCESS 1~o~,4~ 1~.41 I~2{3~606 i8.41 654~098 14.03
· OTHER CURRENT 80&~2~ 9.58 219~144 3.33 i~,?12 2,79
i) TOTAL CURRENT
~FIXEO ASSETS
~"OTHER NON CURRENT
TOTAL ASSETS
ACCTS PAYABLE
MOTES PAYABLE
~CURRENT PORTI0N LTD
OTHER CURRENT
~ TD?ALCURAEHT
:DTHERLONS TERH
DEFERRED CRED)TS ·
~HET ~ORTH
TOTAL LIAR + NET NORTH
989~181 11.75 97%593 14.86 958~209 20.55
409~690 4.87 692~477 10.5i 445~65~ 9.5&
'8,420.372 lO0.O0 6~590~5~2 lO0.O0 4,662~794 100.00
18~082 0,21 724~103 10.9~ 619!874 13.29
19,317 0.23 0 0.00 0 0.00
215~880 2.56 217,016 3.29 156~537 3.36
1~270,852 15,1~ 0 0.00 0 0.0¢
1,532~131 IB,20 941,119 14.28 776~411 I8.65
223~711 2.66 481~78~ 7.31 271~706 5.03
2~2~5~389 2655 1~938~479 29.41 i~242~560 28.65
4,429~141 52.60 3~229,141 4%00 2,572,107 50,87
8,420~372 IO0,O0 61590~532 lO0.O0 4~682~784 100.00
SALES 13,990~15R, !00.00 10 602,297 iO0.O0 7~16,~,,0~.'~ '" iO0.O0
~8ROSS PROFIT 8,?02,i76 63.6~ 6~507~857 61.40 4~423~206 &1,76
"'*NET PROFIT AFTER T~X I~200~000 8.58 876~334 ~.27 513,174 7.17
~IVI DENDS/MI THDRA~AL9 0 0.00 19~300 O, iB 0 0,00
,m~OLVENCY~
QUICK RATIO (X)
~URRENT RATIO (X)
~:URR LIAR/NET WORTH (Z)
fOTAL LIAB/NET WORTH
FIXED ASSET/NET WORTH(%)
EFF1CIENCY:
...COLLECTION PERIOD (DAYS)
}9SETS TO REVENUE (2)
~ JEVENUE TO WET WORKING
CAPITAL ~X)
"'"aCTS PAY/REVENUE
PROFITABILITY
~ETURN ON REVENUE (Z)
RETURN ON ASSETS
._RETURN ON NET WORTH
~ETURN ON PRIOR YEAR
NET NORTH
KEY BUSINESS RATIOS
FY 198&
FY 1g85
FY 1984
2.55 2.67 2,89
0.13Z 6.83' 8.65Z
B.5EZ R.27Z 7,17Z
14.25Z 13.30Z ll.OiZ
27.09Z 27, I4Z 21.83Z
36.942
%.~7 107,97 116.69
60,192 62. I6Z 85.1CZ
2.56 3.70 ~,19
4.58 5.2~ 4.20
34,59Z 29.14Z 32.73Z
90.1IZ 104.10Z 96.57%
22.33Z 30.~4Z 40.39Z
a. Builu a camotuerized data base o+ clients, prospects, salesmen,
~ril l~86-did not make deadline: software under development but
orooress is slow. Have alternative of continulnq wit~ in house
Drooramer OM bu¥ind ready made software +ar ~OOO. with $~0£) per
input the material, Probably a 1/2 time person. - continue
D-i. excellent
c. Contac% ail exlstino clients
our oata mase is not
c-1 oooo idea i+ we co.id get it Done
U. Pus~ for comQletian of soeclaltv
Update the brochures every 12 to 1~ months.-- One brochure
complete-others in Process-did nat make oeadline
d-1 need to +inish them-R~ brochure ~ell received
e. Deveioo a simole sales traininq Orooram and teach the new
e-1 e~cellent iaea and should be continued
+. Fus~ for "December Idea Month" Draqram-dene but not analyzed
~-1 a qood idea Out incomolete due to lack o~
manoower-elther hire the people to get it ~one or Uroo it.
q. ~onsider aodinq the following ln+ormation to the marketlnq
oa'ca base: (1> ProOabilit¥ o+ getting a job: <Il> potential +es:
(iii) at what billing multiplier: and (iv) who will do the
~-1 item is essentially comolete and can be drooped
~. Each emolovee should oroYide ~esobeck tO marketind on the
oro+ltaOlllt¥. Right now we sell anythinQ we c~n get.
I. Hub£is~ 1~ oaoers per ¥ear-1/o Oone-not maKlno ou~ ooai
m-l. oood iosa and brlnqs in sales-keep tr¥ino
n. Advertise more in traoe ~ournals: seek publicity. Consider
~irino a ouolic relmtlons D~rson- OhS notice in D~ll~s Mornino
News- One write ua in Civil
Od the ~ob-coulO pro0uce results if Oone properly
p. ~n~er~aln our clients occaslonallv-worKzno
p-1. Pood broceeOure-keeo i% ub
~. ~end Chris~mas Cards-done
~-1 gets a dood reaction-keep it uo
r. invite a client to soeak at our thursday seminars once Der
month-had a% least three clients there
s. Find ~oint venture opportunities-tried several but none worked
s-I neeO to learn how
t. Identi~¥ and track competition-practically no work on this one
t-1 a Good idea to ~orm a competitor data base but never had
the manpower to do the
u. Each section to have an annual sales ouo~a an~ ~rv to meet
~ha% ~uota-done
u-1 good idea- keep it uo
v-1 a seeminolv pood i0ea that nas not materialized
w. Each ~erson wno lives in a smali town to subscribe %o the
x. ivv %0 hullo a da~a base
a.n.n. Ucc. 11, l~bb