The quality of this digital copy is an accurate reproduction of the original print copy Schoo ! of Cì¥i ì Engiiìtarln g
'S .Î - if î' » o Í s s r
í: -lì - o V w -»' S i s < ^ ^x -i -iXU ' »íii. ' Ji ^ V» i v« " .í - Ä- - ^ C , _ •ÍSJ* - Á :
íw- i m fi-. -í ?! 'ká'^tAüww mj^m^um
^ m s BM.. ©rid , i«E « Aytt . University of New Sduth Wales
School of Civil Engineering
Master of Engineering Science Project:
.-•A .u-MA
V: • -
FLOOD FREQUENCY ANALYST S OF
SOME N.S.W. COASTAL RIVERS.
IC. M , Conway, B . Sc . , B.E. , Grad, I.E. Aust
Dec. 1970 CONTENTS
Section 1 Introduction Page 1
Section 2 Basic Statistical Parameters Page 3 used in the Analysis
Section 3 Fundamental Concepts in the Page 6 Time Series Analysis
Section 4 Types of Probability Distributions Page 9
Section 5 Procedure of Analysis Page 12
Section 6 Discussion of Results Page 16
Section 7 Selection of Method Page 19
Section 8 Conclusions Page 21
Section 9 Further Investigations Page 24
Section 10 Acknowledgements Page 25
References Page 26 1. INTRODUCTION
All engineering structures are de55igned for future use, and as a x'esult, some degree of uncertainty will always t>e associated with the life of the structure. The structural engineer needs to make decisions as to what earthquake and wind loadings his building will be subjected, and he then designs the building applying a generous factor of safety. He still cannot be absolutely certain, however, that his building will nox: be subjected to greater loads than allowed for.
The designer of water resources systems is even less certain of the "loads" (i.e., supply and demand) which will be applied to his system. These uncertainties are not solely confined to hydrologie phenomena, but involve the prediction of future economic and sociological patterns as well. However, the economic basis of t±Le project depends very largely on the degree of certainty made in predicting the fu'k.ure hydrology for the system
Probabilistic m.etliods have become increasingly important in recent years in the prediction of :clood flows and water availability and the need for a uniform approach has been recognised in America. Only in this way will the relative -2- economies of two alternate water resource systems put forward for example by different government bodies be satisfactorily compared.
Three basic methods of flood determination are currently used in hydrology; these are:-
(i) rational method
(ii) unit hydrograph metht>d
(iii) frequency analysis
Each of the first two has been more commonly used but neither gives any direct indication of the return period of the particular flood chosen. This is the distinct advantage of the frequency analysis approach.
This project will restrict itself entirely to a fairly exhaustive investigation of flood frequency applied to some N.S.Wo coastal rivers. The work is modelled on the approach undertaken by the United States Water Resources Council
Work Group on Flood Frequency Methods reported by Benson
(reference 1). In addition, some further attempt will be made to régionalisé the results into catchments, and to make recom- mendations on the appropriate frequency distribution to be used. 2. BASIC STATISTICAL PARAMETERS USED IN THE ANALYSIS
2,1 Definitions
Three baaic statistical parameters were used in the treatment of the raw data. These are:-
(i) the arithmetic mean, referred to simply as the
mean is defined by
X = ^ ^ where N X is the varia te and N is the total nurriber of
observations in the sample. The sample mean (given
above) gives an unbiased estimate of the population
mean.
(ii) the most commonly used and most easily adaptable
measure of variability of a set of data is the standard
deviation, or the root mean square deviation. The
population standard deviation is represented by
N where Jli^ is thIe population mean. An unbiased estimate
of this parameter from the sample is given by Yix-l? JL N-» where ^ H^ -4-
(iii) The skewness of a set of data measures the lack of
symmetry of the data. The population skewness is
defined by
An unbiased estimate from the sample is defined by
(.M-OW-a)
The coefficient of skewness is then defined by
Cs.^ . ii.
For a symmetrical distribution, C^ = O; for a
distribution skewed to the right, C is greater than s
O, and for a distribution skewed to the left, C s is less than 0.
2.2 Statistical Moments
It can be shown that the above three defined parameters correspond to the so called statistical moments; in particular, the mean is the first moment about the origin of the distribution, the standard deviation squared (which is equal to the variance) is the second moment about the mean, and the skewness is the third moment about the mean divided by the cube of the standard deviation. -5-
It is coramoniy agreed that the use of moments of order higher than three cannot be justified in the statistical analysis of hydrologie data since the data do not have sufficiently long record to give accurate estimates of the lower moments. Indeed, it was found in the current investigation that the coefficient of skew was extremely susceptible to small changes in the standard deviation. This is almost certainly due to the short length of record available. 3. FUNDAMENTAL CONCEPTS IN THE TIME SERIES ANALYSIS
3.1 Time Series
Records of streamflow kept by the responsible authorities are available in chronological order. Those at the Water
Conservation and Irrigation Coiranission are available as monthly maximum floods, as well as individual daily flows. Two series are generally formed from this data^ viz
(a) Annual maxima
(b) Annual exceedances.
It has to be agreed that the great majority of individual streamflow records have no significance in the analysis of flood frequency, since the design is usually governed by critical conditions. The annual maxima series, as its name implies, takes the maximum flood occurring in each year Oiormally, the water yeai3 of record, and ranks these values in descending order of magnitude. On the other hand, the annual exceedances series takes those floods which exceed a certain base flood and again arranges these values in order of magnitude. The base flood is taken so that the number of exceedances is equal to the number of years of record.
There is a great deal of uncertainty in tne selection of time .series, and generally the choice is resolved by the object of the investigation. Where the design is controlled by tne most -7- critical condi-i-.ions, as for example in the design of large spillways, the annual maxima are normally used. On the other hand/ where the critical condition is likely to be caused by repetition of floods rather than by a single peak as for example in culverts then the annual exceedances are used.
Chow (reference 2) has shown that for large return periods, there is little difference in the predicted floods using both methods. However for small return periods, the annual exceedance series seem.s to give results which more closely follow observed floods.
In this investigation, the annual maxima series was used, the selection being quite arbitrary from a theoretical point of view. Of course, the annual maxima floods can be determined much more rapidly than can the annual exceedances from a set of chronologic data.
3.2 Recurrence Interval
The recurrence interval or return period T is defined as the average interval of time within which an event of a certain magnitude will be equalled or exceeded.
It can be shown that I 1 T = -8-
whereX is a prescribed event and P(x^x) is the
probability that this event will be exceeded once in
T years.
3.3 Frequency Factors
Chow (reference 9) proposed the following general
formula for Hydrologie frequency analysis
X = X -f •O' K where K is a frequency factor.
The frequency factor so defined depends on the type of distribution,
the recurrence interval and where applicable, the coefficient of
skew.
Frequency factors are readily available for the distributions studied, and so this approach greatly facilitates the calculations.
3.4 Plotting Positions
A great number of plotting position formulae have been derived by various people (see p. 8-29, reference 3). The one used in this investigation was derived by Weibull and is simply
T = N + 1 m where N = total number of items and m = order number (or rank) of items in descending order; that is, m=]. corresponds to the largest item. The choice of this method is based on the premise that it requires no prior knowledge of a frequence distribution and therefore shows no bias to any of the six distributions studied. -9-
4. TYPES OF PROBABILITY DISTRIBUTIONS
In this study, six probability distributions were applied to the data, viz:-
(i) Normal
(ii) Pearson type III
(iii) Gumbel (Type 1 Extremal)
(iv) Log-* normal
(v) Log-Pearson type III
(vi) Log Gumbel
These distributions are now described in some detail.
4.1 Normal Distribution
The normal distribution is essentially a two parameter, unskewed or symmetrical distribution based on the Gaussian law of errors, and has as its probability density the function '2 7 -Cx-/^) f' 2Tr where x is the variate
^ is the mean
is the standard deviation.
The frequency factor, K for this distribution is given by -10-
Values of K for corresponding values of P(X^-x) (which are related to the return period, T by T = —r were found from 1-P(x£x) reference 11. In addition. Chow (reference 7) has presented a graphical approach for the determination of the factor, K, more particularly for the log normal distribution.
4.2 Pearson Type III Distribution
This is one of several distributions proposed by Karl
Pearson to fit almost any set of data. These distributions have only meagre theoretical bases as far as their application in hydrology is concerned but have been widely used in statistics.
The type III distribution is a skew distribution with a lov/er bound: it may be either bell shaped or J shaped.
The probability density with origin at the mode is X c —cx/a defined by p(x) = po(l + —a.) e wnere c = —4 - 1 1
c ^ U2
N c+1 po = ~ _c ^ e^/-(c+l) 2
3 ^2 and \i2, 'J3 are the second and third moments about the mean and fi 1 /~(c+l) = c; is a gamma function. -11-
The frequency factors for this distribution were taken from the prepared tables in reference 1.
4.3 Gumbel Distribution
The Gumbel,, or type 1 extremal distribution has a constant coefficient of skewness equal to 1.139, and has a probability density given by p(x) = — e where x is the variate
a = io -
y = 0.57721 - a Euler's constant
u is the mean
(¡^ is the standard deviation.
The frequency factors for this distribution were calculated from the expression (see references 5 and 10)
K . ¥ where T is the recurrence interval in years.
4.4 Logarithmically Transformed Distributions
Each of the above three distributions was transformed by replacing the variate by its logarithmic value. That is, the variate x was replaces by, say, log y. -12-
5. PROCEDURE OF ANALYSIS
5.1 Collection of Data
Initially, some 46 stations on New South Wales coasta;l rivers were selected, (see table 1) purely on the basis of length of record of daily flows. The streamflow records of these stations were transcribed from the W.C.I.Co records, and a comparison was made between the maximum flood discharge inter- polated from a stage discharge curve and the maximum gauged discharge. An "extrapolation ratio" was formed, viz. the ratio of maximum .flood to maximum gauged flood. The final selection of gauging stations for further study was on the basis of the station's ratio being less than an arbitrary limit of 10.
This criterion was relaxed somewhat to include one or two stations with long length of record but poor gaugings.
The final list of gauging stations (see table 2) was then arranged into catchment areas. Those catchments south ox the Hunter were not considered further to avoid a protracted study; the Hunter, Clarence and Maclean basins were concentrated on. However, it is intended to make a more complete study of all New South Wales catchments. -13-
5.2 Outline of Procedure
For each gauging station selected for analysis, the
annual maximum floods were ranked in descending order of magnitude,
and were plotted on log-nomal probability paper, using the plotting position'formula described in section 3.4. Data values were then interpolated from this graph for the following
recurrence intervals; 2 yrs., 5 yrs,, 10 yrs., 25 yrs , and 50 yrs.
Figure 1 shows an example of the interpolation described.
Theoretical values for each of the six distributions
studied were obtained for the same recurrence intervals by using
Chow's general hydrologie frequency formula. That is, the
statistical parameters - mean, standard deviation and coefficient
of skew were computed for each gauging station (see table 3) and
the frequency factor K determined from the table appropriate to
the distribution considered.
All analyses were carried out on the raw data. That
is to say, no techniques were used to fill in gaps in the data, or to treat outliers and so on.
"Theoretical" and "Data" floods were compared by computing the percentage departure of the theoretical value from the data value at each recurrence interval, by the following -14- formula
Departure = ( ^^ ) x 100 Qa where Qd = data flow
Qth = theoretical flood.
The results obtained are shown in tables 4, 5, 6, 7 and 8.
5.3 Comments on Procedure
(i) The main concern in comparing a number of different statistical distributions applied to the prediction of floods is whether the distribution gives good agreement over the observed range of the data. To avoid any bias to floods of low or large return periods, the comparison between observed and predicted floods was made at both ends of the scale, vis at 2,
5, 10, 25 and 50 year return periods.
(ii) With regard to the use of the expected probability formula (i.e. plotting position formula), Benson (reference 1) states that very little difference was observed in the results when other plotting position formulae were used in lieu.
(iii) Furthermore, Benson and his group used extreme value probability paper in their study, but again he stated that the results are sensibly the same if log normal probability paper is substituted as it was in this study. (iv) The procedure is amenable to either hand or computer solution. The former method was chosen in this study«
four figure logaritltms were used for the transformed distributions, -16-
6. DISCUSSION OF RESULTS
The results shown in tables 6, 1 and 8 indicate that no one frequency distribution is consistently close to the data values. This exemplifies the immensity of the problem in determining flood flows by frequency methods under Australian conditions. However, the following points are valid:-
(i) For the higher return periods (25 years and 50 years) the logarithmically - transformed distributions give floods which are greater than the actual data floods, whilst the non-transformed distributions give floods which are less. In general, the opposite situation exists for floods of lower return periods (2, 5 and
10 years).
(ii) No two basins favour the same distributions for any return period with the exception of the 5 0 year return period for the Clarence and Hunter basins. In this case, the log
Pearson type III distribution give the closest positive departure, whilst the Pearson type III give the closest negative.
(iii) The Gumbel and log Gumibel distributions in general give departures which are either greater than or less than results given by other distributions.
(iv) As expected, the normal distribution, being unskewed gave large departures for floods of long return periods ( 25 and -17-
50 years). However, for floods of low return periods, this distribution gave on the average, the closest positive departures.
(v) Stations within the Hunter basin gave the most highly skewed data, which is due in the main to the greater variability of rainfall in this area. The only reflection of this character- istic in the results is the appearance of the Gumbel distribution
in table 9 for the 10 and 25 year return periods. The Gumbel distribution is an extremal distribution and ought to therefore fit better the more highly skewed data. On the other hand, the
Gumbel distribution has a constant coefficient of skew, which,
appears not to suit the data analysed for other return periods
and the other basins.
(vi) Only four stations (two in the Clarence and two in the
Hunter) had records in excess of 50 years, which is admittedly
a poor basis on which to carry out an investigation such as this
and to draw conclusions therefrom. The fact that the average
departures favoured the same distributions is however significant
and will form the basis of t?ie recommendations.
(vii) For both the Clarence and Hunter basins, the log Pearson type III distribution has the smallest average negative departure for the 2 year return period. -18-
(viii) Where one expects some uniformity between the methods, that is for floods of low return periods, little uniformity occurs
This is even more surprising in the light of the uniformity at the other end of the scale for 25 and 5 0 year return periods.
(ix) The stations within the Clarence basin all have records of reasonable length (see table 1), and accordingly, a greater degree of confidence may be attached to the results for this basin. -19-
7. SELECTION OF METHOD
The ideal frequency distribution would be one character-
ised by having small average departures randomly distributed
about zero throughout the entire range of return periods. No one
distribution studied fits these requirements; not that the
investigation was really expected to give any clear cut and
definite answers in this regard. The log Pearson type III
distribution will be recommended for use for the following reasons:
(1) The method includes the coefficient of skew as a
statistical parameter, and is therefore a more flexible method
than the others. It is also probable that data from stations
in inland and southern coastal basins in New South Wales will have more highly skewed data than that analysed. It is thus very
important to have a method which considers skewness as a variable.
(2) The distribution gave the smallest positive departures on the average for the 25 and 5 0 year return periods for both the Hunter and Clarence basins. It is considered important to have a method which slightly over estimates floods of high return period since these fl6ods are normally associated with the design of hydraulic structures, the failure of which might result in catastrophic damage and loss of life.
The method also gave the smallest overall average for all return periods for all stations analysed. -2 0-
(3) The departures are more or less distributed randomly about zero both within each particular return period and at each end of the scale of return periods. The method gives the closest negative departures for the 2 year return period for the Clarence and Hunter catchments.
(4) The log - normal distribution is a special case of the log Pearson typelll, and occurs when the skew of the logarithms is zero.
(5) The method was recommended for use in the United States as the result of an investigation carried out by the Work Group of the Water Resources Council's Hydrology Committee (see refer- ence 1).
(6) The method is favoured by the longer record stations of the Clarence Basin. -21-
8. CONCLUSIONS
It must be strongly emphasised that even if one frequency distribution is recommended for use in the analysis of streamflow records, entirely different results may Etill be obtained by independent investigators analysing the same data. This is because the selection of data is still very much an individualistic operation where judgement plays an important part. Different techniques are available for filling in missing records, treating data due to change of station location and so on.
It is not sufficient therefore tc specify a method of flood frequency analysis and leave it at that. Total uniformity can only be achieved when methods for the treatment of data are universally accepted, or more practically, when they are accepted within one particular country.
The selection of the log Pearson type IH method was based principally on the observation that over tlie range of return periods studied, the method gave the smcillest departures.
However, an analysis of additional stations in other basins within Australia may favour a distribution other than the log Pearson type III. -22-
Another important point to consider is the length of record. Unfortunately, very few stream flov/ records are longer than 30 years, the generally accepted minimum requirement.
Only 4 (out of 23) stations analysed had records longer than
5 0 years and 9 had records less than 3 0 years. The effect of this lack of record length is to give poor population estimates for the statistical parameters, mean, standard deviation and coefficient of skew. This problem will only be effectively solved by time, even though Monte Carlo methods have been developed to generate artificial records.based on an existing small sample.
The extrapolation ratio defined in section 5.1 shows that very poor gauging exists on some streams, whilst good gauging exists on others. This is just another variable, unable to be separated and treated, and therefore how it affects the results is just not known. Suffice to say that stations with low extrapolation ratios ought to give better agreement with the selected distribution. This is confirmed by the results (for example, most of the stations in the Clarence basin have good gaugings; the departures on the average favour the log Pearson type III). -23-
Regarding the régionalisation of flood frequency- distributions, no satisfactory conclusions could be drawn, due to the small number of basins analysed and the variation in the smallest departures for each basin as per table 9. Further work on this point is required.
The most salient feature of the whole investigation is that, due to insufficient length of record on the majority of rivers studied, no definite recommendation can be made at this stage. Regarding this thesis as an interim report on a current investigation, it may be possible to make definite recommendations when more records have been analysed. However, the results to date show a trend towards the log Pearson type
III method as being the most appropriate to New South Wales coastal conditions. -24-
9. FURTHER INVESTIGATIONS
It is proposed to continue and extend this study to other basins in New South Wales, both coastal and inland to ascertain whether the general conclusions of this project are upheld. With more basins studied, conclusions may be able to be drwn regarding the régionalisation of frequency distribution use
Another point which will be considered is whether the results would be substantially altered if only long period (viz greater than 30 years) records were used.
Some further investigation will also be undertaken with a view to modifying the constant coefficient of skew used in the
Gumbel distribution. In this way, a more appropriate distribution might be form.ulated for Australian conditions. -25-
10. ACKNOWLEDGEMENTS
The writer wishes to acknowledge the help and
supervision of Dr D. Pilgrim of thcSchool of Civil Engineering,
University of New South Wales in undertaking this project. The
cooperation extended by Mr G. Whitehouse of the Water Conservation
and Irrigation Commission is also gratefully acknowledged. -26-
RSFERENCES
Benson, M.A« "Uniform Flood - Frequency Estimating
Methods for Federal Agencies".
Jnl. Water Resources Research, Vol, 4, No. 5,
October, 1968.
2. Chow, V.T. "Frequency Analysis of Hydrologie Data
With Special Application to Rainfall Intensities".
University of Illinois Engineering Experiment Station,
Bulletin Series 414, Vol. 50, No. 81, July,1953.
3. Chow, V.T. (editor) "Handbook of Applied Hydrology".
McGraw-Hill, 1964.
4. Chow, V.T. "The Log Probability Law and its Engineering
Applications", Proc. A.S.C.E., Vol. 80, Paper No. 536,
pp. 1 - 25, November, 1954.
5. Gumbel, E.J., "Statistical Theory of Droughts"
Proc. A.S.C.E., Vol. 80, Sep. No. 439, pp. 1 - 19,
May 1954 -27-
Beard, L.R., "Estimation of Flood Probabilities",
Proc. A.S.C.E., Vol. 80, Sep. No. 438, pp. 1 - 21,
May, 1954.
7. Chow, V.T.', "Determination of Hydrologic Frequency
Factor" Jnl. of Hydraulics Division, Proc. A.S.C.E.,
HY7, July, 1959.
8. Chow, V.T., "On the Determination of Frequency Factor
in Log-Probability Plotting", Trans. A.G.U., Vol. 36,
No. 3, June, 1955.
9. Chow, V.T., "A General Formula for Hydrologic
Frequency Analysis", Trans. A.G.U., Vol 32, No. 2,
April, 1951.
10. Gumbel, E.J., "The Return Period of Flood Flows",
Annals of Mathematical Statistics, Vol. 12, 1941,
pp. 163 - 190.
11. Lindley, D.V., & Miller, J.C.P., "Cambridge Elementary
Statistical Tables'', Cambridge University Press, 1962. TABLE 1 - PRELIMINARY SELECTION OF GAUGING STATIONS
CLARENCE RIVER BASIN
Length of Highest Highest Extra- Period of Station River Record Flood Gauging polation Record (yrs) (cusecs) (cusecs) Ratio
1 Lilydale Clarence 1922-1968 46 646000 244329 2.65
2 Tabulam Clarence 1910-1968 50 240000 94127 2.55
3 Grafton Majors ck 1925-1930 6 85 0 . Road 1937-1953 17 3200
4 Jackadgery Mitchell 1920-1968 49 480000
5 Buccarumbi Nyinboida 1923-1967 45 284000 2 8200 10.1 1.62 6 Nyniboida Nymboida 1909-1967 58 197628 122000 (1 missing) 7 Dorrigo Rocky Ck 1924-1930 7 1420 35 40.5 1949-1960 12 4350 726 5.98
8 Maida Vale Jock's Water 1926-1931 6 2311 21 3200 1936-1966 20 9 Broadmeadows Little 652 00 1947-1966 10 Ebor Giiy Fawkes 7 4000 887 4.51 19^4-1931937-1960 22 8800 3210 2.74 HUNTER RIVER BASIN
Period of Length of Highest Highest Extra- Station River Record Record Flood Gauging polation (yrs) (cusecs) (cusecs) Ratio
3.3 1 Windermere Stewart's 1947-1968 22 4600 1390 Brook 5.58 2 Muswellbrook Hunter 1918-1927 10 140000 25080 Weir 1930-1962 33
Glenbairn Hunter 1941-1968 28 41000
Roma Omadale 3k 1941-1968 28 2000 209 9.57 20904 3.64 5 Halton Ally El 1941-1968 28 5750 140000 1324 105.5 6 Coggan Goulburn 1913-1968 56 2300 7 Moonan Bk Moonan Bk 1941-1968 28 1932-1969 36 26600 4603 5.77 8 Tillegra Williams (1 missing) 37 7476 Warkworth Wollombi 1909-1948 92330 12.3 1955-1967 12 161000 5708 28.2
1916-1968 53 442000 4.01 10 Singleton Hunter 1102 02 1912-1953 42 4631 4.75 11 Moonan Flat Hunter 22000 1941-1968 27 2 09 00 12 Moonan Dam Hunter Site (1 missing) 1941-1968 153000 1900 80.5 13 Kerrabee Goulbourn 28 RICHMOND RIVER BASIN
Length of Highest Highest Period of Station River Record Flood Gauging Record (yrs) (cusecs) (cusecs)
1920-1927 14260 532 Repentance Cooper's Ck 8 1952-1965 14 24000 4511
18650 825 Blakes Terania 1948-1965 18
1944-1969 150000 63806 Casino Riclunond 26
MACLEAY RIVER BASIN 1948-1965 19 1 Euringelly Chandler 21000 8600 1919-1966 48 31000 9880 2 Jeogla Styx 1928-1966 39 146 00 3313 o Tia Tiä 1937-1968 31 46 00 895 4 Yarrowitch Yarrowitch 1925-1955 31 29200 10670 5 Kemp^ey Road Oaky Ck 1949-1968 21500 11240 6 Coninside Wollomombi 20 1924-1931 13200 50 7 Gara 8 Gara 1949-1967 19 30000 3029 HASTINGS RIVER BASIN
Period of Length of Highest Highest Extra- No, Station River Record Record Flood Gauging polation (yrs) (cusecs) (cusecs) Ratio
1 Elaands Big Creek 1937-1961 25 4870 17 286
2 Glenwarren Ellensborough 1937-1961 25 12250 165 74.1
3 Ellensborough Hastings 1946-1961 17 69000
KARUAH RIVER BASIN
Monkerai Karuah 1946-1969 24 38250
TWEED RIVER BASIN
Eungella Tvv^eed" 1948-1968 21 86300 7976 10.8
HAWKESBURY RIVER BASIN
Upper Wollondilly 1926-1932 7 33800 2695 12,6 Burragorang 1943-1954 12 64760 3778 17.1
Kurrajong Burralow Ck 1927-1962 36 4489 SHOALHAVEN RIVER BASIN
Length of Extra- Station River Period of Highest Highest Record polation Record Flood Gauging (yrs) (cusecs) (cusecs) Ratio
1 Warren Shoalhaven 1915-1946 31 218000 46970 4.64
2 Welcome Reef Shoalhaven 1910-1953 41 312500 4000 78.1
BEGA RIVER BASIN
Tantawanglo Tantawanglo 1944-1965 22 16200 620 26.2 School
MANNING RIVER BASIN
Nowendoc Nowendoc 1947-1967 21 7000 ' 4660 1.50
Rock ' s Nowendoc 1946-1967 22 77960 2037 38.3 Crossing Bob's Cros£JÌng Barrington 1944-1968 19 1690 276 6.1 (incomplete) 4 ' Killawarra Manning 1946-1967 22 198000 TABLE 2 FINAL SELECTION OF GAUGING STATIONS
CLARENCE RIVER BASIN
Length of Catchment Max. Flood Extra- No. Station River Record Area Area of polation (yrs) (sq.mls) Catchment Ratio
1 Buccarumbi Nyirboida 45 2030 139.9 10.1
2 Nymboida Nymboida 58 640 308.8 1.62
3 Lilydale Clarence 46 6440 100.3 2.65
4 Tabulam Clarence 50 1710 140.4 2.55
5 Jackadgery Mitchell 49 3010 159.4
6 Ebor Guy Fawkes 29 12 733.3 3.17
AVERAGE 46.2 HUNTER RIVER BASIN
Length of Catchment Max. Flood Extra- No. Station River Record Area Area of polation (yrs) (sq.mls) Catchment Ratio
37 75 354.6 5.77 1 Tillegra Williams 42 1630 85.9 5.58 Muswe1It rook Hunter Weir
42 290 75.6 4.75 Moonan Flat Hunter 79 264.5 3.64 Halton Allyn 28 55 1290 108.5 105.5 Coggan Goulbourn 53 6350 69.6 4.01 Singleton Hunter 25 40 50.0 9.57 Roma Qmadale Brook 23 65 70.6 3.3 8 Windermere Stewart's Brook
38.1 AVERAGE MACLEAY RIVER BASIN ,
Length of Catchment Max. Flood Extra- No. Station River Record Area Area of polation (yrs) (sq.mls) Catchment Ratio
1 Jeogla Styx 48 63 492.0 3.14
2 Tia Tia 39 97 150.5 4.41
3 Yarrowitch Yarrowitch 31 27 170.4 5.14
4 Kempsey Road Oaky Creek 31 78 374.3 2.74
5 Coninside Wollomornbi 20 145 148.3 1.91
6 Euringelly Chandler 19 2.44
AVERAGE 31.3
RICHMOND RIVER BASIN
1 Casino Richmond 26 690 217.5 2.35
MANNING RIVER BASIN
1 Bobs crossing Barrington 19 8 211.3 6.1Ü
2 Nowendoc Nowendcc 21 84 83.3 1.50
AVERAGE (Rich.& Mann)22.0
OVERALL AVERAGE 36.3 TABLE 3 ~ STATT STT-"AT. PARAMETERS
Standard Catchment Station Mean Plow Deviation
Clarence Buccarumbi 79871 86060 Nymboida 41068 41650
• Lilydale 186071 198030 Tabulam 56807 64010 Jackadgery 121853 130320 Ebor 1982 2051
Hunter Tillegra 8889 7179 Mu swe1lbrook Weir 20252 24140 Moonan Flat 6023 5027 Halton 5980 4606 Coggan 11691 23260 Singleton 39121 66220 Roma 766 462 Windermere 2185 1533
Macleay Jeogla 5285 6492 Tia 4285 4368 Yarrowitch 1018 1129 Kempsey Road 4311 6233 Cononside 8249 6755 Euringelly 7070 5589
Richmond Casino 42339 33530
Manning Bob's Crossing 770 423 Nowendoc 2733 2757 Standard loefficient Mean of Coefficient Deviation of Skewness )f Skewness Logs of Logs of Logs
1.56 4.6621 0.4771 0.1193 2.906 4.4180 0.4334 -0.2020 1.113 4.9899 0.5432 ' -0.0833 1.806 4.4020 0.6609 -0.6948 1.373 4.8075 0.5374 -0.1296 2.009 3.0708 0.4585 0
0.878' ' 3.7847 0.4042 -0.1316
3.17 4.0403 0.5316 -0.3614 1.235 3.6444 0.4262 -1.1448 1.289 3.6411 0.3677 -0.1595 3.745 3.4505 0.8314 -0.9468 4.636 4.1839 0.7080 +0.5369 0.954 2.8087 0.2654 -0.0545 0.410' 0.2091 0.3695 -0.3382
2.049 3.4504 0.4916 0.2835 1.050 3.3691 0.5099 0.0375 1.729 2.7472 0.5212 -0.2926 2.668 3.2806 0.5960 -0.2364 0.641 3.7372 0.4381 -0.2545 0.905 3.6281 0.5659 -1.2453
1.122 4.4637 0.4269 • 0.6473
0.651 2.8208 0.2523 -0.1616 1.646 3.1856 0.5272 -0.2653 TABLE 4 ~ THEORETICAL & IDATA FLOODS
CLARENCE RIVER BASIN
Return Pearson type Station Data Flood Normal Flood Period III flood
Buccaruinbi 2 44300 79871 58528 5 120000 152299 138478 LO 240000 190165 194417 25 296000 230536 265416 50
Nyitiboida 2 30000 41068 24824 5 55000 76121 59311 10 100000 94447 90798 25 158000 113985 135905 50
Lilydale 2 117000 186071 150030 5 430000 352733 333207 10 522000 439866 451629 25 622000 532762 595795 50
Tabulam 2 30800 56807 38692 5 122000 110678 97901 10 160000 138842 141172 25 201000 168870 197245 50 235000 188264 239236
Jackadgery 2 71000 121853 93052 5 223000 231530 214250 10 367000 288871 296221 25 420000 350004 398522
Ebor 2 1280 1982 1350 5. 2960 3708 3227 10 5360 4611 4650 25 8200 5573 6535 50 Log Normal Log Pearson Log Gumbel juiribel Flood Flood Type III Flood Flood
64380 45930 44930 37690 139855 115800 114900 88770 189081 187800 190300 185100 251991 314400 328600 413300
33571 26180 27060 21880 70098 60630 61200 52490 93922 94060 91870 92900 124368 150200 139800 192700
150426 97700 99420 77820 324098 280000 281100 233600 437371 485400 479600 477700 582131 872800 842000 1193000
45285 25230 30060 19190 101422 90820 92980 72880 138036 177400 153000 174100 184827 362200 243600 529400 224193 574400 318500 1350000
98395 64190 65970 51390 212686 181900 183100 152100 287229 313400 307500 308700 382493 560200 529400 762600
1613 1177 1177 9/3 3412 2863 2863 2457 4585 4554 4554 4493 6084 7473 7473 9723 _MACLEÄY RIVER BASIN
Return Pearson type Station Data Flood Normal Flood Period III flood
Jeogla 2 2270 5285 3253 5 9400 10749 9187 10 16000 13605 13712 25 19900 16651 19723 50.
Tia • 2 2440 4285 3534 5 8200 7961 7570 10 12200 9883 10138 25 • 13900 11932 13156 50
Yarrowitch 2 550 1018 711 5 1910 1968 1757 10 2800 2465 2511 25 4300 2995 3483 50
Kempsey 2 1570 4311 1986 Road 5 7300 9557 7334 10 11900 12299 11965 25 24600 15223 18460 50
Coninside 2 4700 8249 7533 ' '5 14000 13934 13619 10 19800 16906 17233 25 50
Euringelly 2 6700 7070 6237 5 11400 11773 11362 10 16700 14233 14554 25 50 3umbel flood Log Normal Log Pearson Log Gurnbel Flood Type III Flood Flood
4116 2821 2675 2301 9810 7316 7178 6209 13523 12040 12400 11870 18269 20470 22750 27140
3499 2340 2323 1893 7329 6287 6272 5303 9828 10540 10590 10380 13021 18580 18570 24480
815 559 593 450 1805 1535 1555 1290 2451 2602 2492 2563 3276 4568 4028 6160
3189 1908 2013 1490 8655 6059 6135 4966 12221 11090 10650 10880 16777 21100 18790 29690
7033 5461 5697 4553 12957 12760 12900 11040 16821 19900 19290 19630
6064 4247 5526 3359 10966 12730 12710 10530 14162 22570 17260 . 22190 HUNTER RIVER BASIN
Return Pearson type Station Data Flood Normal Flood Period III flood
Tillegra 2 6350 8889 7851 5 16100 14931 14424 10 20000 1809 0 18495 25 24500 21457 23340 50
Musv7e lib rook 2 14400 20252 10445 Weir 5 37600 40568 29570 10 452 00 51190 48110 25 64000 62514 75291 50
Moonan Flat 2 5300 6023 5018 5 9300 10254 9678 10 11500 12466 12749 25 21100 14824 16655 50
Halton 2 5100 5980 5022 5 9800 9856 9296 10 11600 11883 12147 25 18800 14044 15680 50
Coggan 2 2990 11691 1433 5 10300 31267 17994 10 45000 415 01 36533 25 60000 51412 64840 50 126000 59460 88123
Singleton 2 18800 39121 54082 5 53500 94851 45279 10. 92000 123989 1005 07 25 144000 155052 191030 50 420000 175117 267315 Guitíbel Flood Log Normal Log Pearson Log Gumbel Flood Type III Flood Flood 7597 6091 6218 5151 13893 13340 13400 11650 17999 20080 19790 198850 23247 3109 0 29780 39180
15907 10970 11810 8802 37078 30750 31210 25750 5 0886 52700 49820 51870 68532 93560 79710. 126900
5118 4410 5298 3696 9257 10080 10120 8740 12402 15520 12950 15320 16077 24590 15870 31390
5151 4376 4477 3758 9190 8928 8973 7 896 11825 12960 12750 12810 15192 19270 18300 23800
7504 2821 3796 1999 27903 14150 14440 10720 412 08 32840 24920 32030 58211 80600 40230 129800 72516 143800. 51990 421300 27201 15270 13210 11390 85276 60260 56720 47570 123154 123500 132400 . 120900 171561 265300 349900 39800Ò 212286 434600 6805 00 1085000 HUNTER RIVER BASIN (CONT'D)
Return Pearson type Station Data Flood Normal Flood Period III Flood
Roma 2 580 766 693 5 1240 1155 1119 10 1400 1358 1385 25 1930 1575 1705 50
Windermere 2 1750 2185 2081 5 402 0 3475 3434 10 4524 4149 4205 25 50
RICHMOND RIVER BASIN
Casino 2 38000 42239 36203 5 67500 70558 67218 10 76000 85311 87303 25 140000 101040 111780 50
MANNING RIVER BASIN
Bob's Crossing 2 760 770 725 5 1230 1126 1106 10 1450 1312 1333 25 50
Mawendoc 2 2300 2733 2016 5 4480 5053 4575 10 • 6450 6266 6392 25 50 'Gumbel Flood Log Normal Log Pearson Log Gl^mbel Flood Type III Flood Flood
683 644 680 577 1088 1076 1086 986 1352 1409 1348 1398 1690 1877 1659 2185
1909 1618 1697 1389 3254 3313 3347 2928 4130 4817 4648 4764
36304 29100 26190 24390 65709 66580 63570 57730 84889 102600 107600 101300 109399 162800 198300 207800
694 662 672 596 1065 1079 1083 992 1307 1394 1379 1384
2237 1533 1617 1232 4655 4261 4313 3574
6232* 1 7269 6992 7455 ^BLE 5 - PERCENTAGE DEPARTURES
[LARENCE RIVER BASIN
DISTRIBUTION NORMAL
r- Return Period 2 D 10 25
Stations •
Buccarurribi 80.29 26.92 -20.76 -22.12 Nymboida 36.89 38.40 - 5.55 -27.86 Lilydale 59.03 -17.97 -15.73 -14.35 Tabulam 84,44 - 9.28 -13.22 -15.99 Jackadgery 71.62 "3.83 -21.29 -16.67 Ebor 54.84 25.27 -13.97 -32.04
Average 64.52 11.20 -15.09 -21.51
DISTRIBUTION PEARSON TYPE III
Stations
Buccarumbi 32.12 15.40 -18.99 -10.33 Nymboida -17.25 7.84 - 9.20 -13.98 Lilydale 28.23 -22.51 -13.48 - 4.21 Tabulam 25.62 -19.75 -11.77 - 1.87 Jackadgery 31.06 - 3.92 -19.29 - 5.11 Ebor 5.47 9.02 -13.25 -20.30
Average 17.54 - 2.32 -14.33 - 9.30 LOG NORMAL
50 2 5 10 25 50
3.68 - 3.50 -21.75 6.22
-34.06 -12.73 10.24 - 5.94 - 4.94 5.83
-16.50 -34.88 - 7.01 40.32
-19.89 -18.08 -25.56 10.88 80.20 144.43
- 9.59 -18.43 -14.60 33.38
- 8.05 - 3.28 -15.04 - 8.87
-26.98 -10.21 -12.57 - 8.91 24.22 75.13
LOG PEARSON TYPE III
1.42 - 4.25 -20.71 11.01
-10.60 - 9.80 11.27 - 8.13 -11.51 - 5.10
-15.03 , -34.63 - 8.12 35.37
+ 1.80 - 2.40 -23.79 - 4.38 21.19 35.53
- 7.08 »17.89 16.21 26.05
- 8.05 - 3.28 -15.04 - 8.87
- 4.4 - 6.82 -12.10 -12.10 12.21 15.22 CLARENC E RIVE R RAST> T (ROKRP'R^ ^
DISTRIBUTIO N GUMBE L
Retur n Perio d 2 5 10 25
Station s
Buccarumb i 45.3 3 15.4 0 -21.2 2 -14 . 8 7 Nymboid a 11.9 0 27.4 5 27.4 5 - 6.0 8 Lilydal e 28.5 7 "24.6 3 -16.2 1 - 6.4 1 Tabula m 47.0 3 -16.8 7 -13.7 3 - 8.0 5 Jackadger y 38.5 8 - 4.6 3 -21.7 4 - 8.9 3 Ebo r 26.0 2 15.2 7 -14.4 6 -25.8 0
Averag e 32.9 1 2.0 0 -15.5 7 -14.2 2 i
HUNTE R RIVE R BASI N
DISTRIBUTIO N NORI^ L
Station s
Windermer e 24.8 6 -13.5 6 - 8.3 1 Muswellbroo k Wei r 40.6 4 7.8 9 13.2 5 - 2.3 2 Rom a 32.0 7 - 6.8 5 + 9.5 2 • -18.3 9 Halto n 17.2 5 0.5 7 2.4 4 -25.3 0 Cogga n 291.0 0 203.5 6 - 7.7 8 -52.8 1 Tillegr a 39.9 8 - 7.2 6 - 9.5 5 -12.4 2 Singleto n 108.0 9 77.2 9 34.7 7 7.6 8 Moona n Fla t 13.6 4 10.2 6 8.4 0 -29.7 4
Averag e 70.9 4 13.9 9 5.3 4 -12.7 6 LOG GIBIBEL
50 2 5 10 25 50
-14.92 -26.03 -22,88 39.63 -21.88 -27.07 - 4.56 - 7.10 21.96 85.31 -33.49 -45.67 - 8.49 91.80 - 4.60 -37.69 -40.26 8.81 163.38 474.47 -27.62 -31.79 -15.89 81.57 -23.98 -16.99 -16.18 ! 18.57
-13.24 -27.46 -27.55 -10.29 69.49 279.90
LOG NORMAL
- 7.54 -17.59 6.45 -23.82 -18.22 16.59 46.19 11.03 -13.23 0.64 - 2.75 -14.20 - 8.90 11.72 2.50 -52.81 - 5.65 37.38 -27.02 34.33 14.13 4.08 -17.14 0.40 26.90
-58.3 -18.78 12.64 34.24 84.24 3.48 -16.79 8.39 34.96 16.54
-55.56 - 8.96 - 2.08 9.75 29.71 8„81 • HUNTER RIVER RARTl^ (CONT'd)
DISTRIBUTIOlNl PEARSON TYPE III
Return Period 2 5 10 25
Stations
Windermere 18.91 -14.58 - 7.07 Muswellbrook Weir -27.47 -21.34 6.44 17.64 Roma 19.48 - 9.76 - 1.07 -11.66 Halton 1.53 - 5.14 4.72 -16.60 Coggan -52.07 74.70 -18.82 8.07 Tillegra 23.64 -10.41 - 7.53 - 4.73 Singleton -65.91 -15.37 9.25 32.66 Moonan Flat - 5.32 4. 06 10.86 21.07
Average -10.90 0.27 - 0.40 0.62
DISTRIBUTION GUMBEL
Stations
Windermere 9.09 -19.05 - 8.73 Muswellbrook Weir 10.47 -13.9 12.58 7.08 Roma 17.76 -12.26 - 3.43 -12.44 Halton 1.00 - 6.22 1.94 -19.19 Coggan 150.97 170.90 - 8.43 - 2.98 Tillegra 19.64 -13.71 -10.01 - 5.11 Singleton 44.69 59.39 39.86 19.14
Moonan Flat - 3.4 2.44 7.84 -23.81
Average 31.28 22.51 3.20 - 5.33 LOG PEARSON TYPE III
50 5 10 25 50
- 3.03 -27.16 2.72 -17.99 -16.99 10.22 24.55 17.24 -12.42 - 3.71 -14.04 -12.22 - 8.44 9.91 - 2.18 -30.06 26.96 39.81 -44.62 -32.95 -58.74
- 2.08 -16.77 - 1.05 21.55
-36.35 -29.73 6.02 43.91 142.99 62.02 - 0.04 8,82 12.61 -24.79
-33.21 - 2.61 - 3.39 3.75 16.45 1.64
LOG GUMBEL
-20.63 -27.16 5,28 -38.88 -31.52 14.76 98.28
- 0.52 -20.48 - 0.14 13.21
-26.31 -19.43 10.43 26.60
-42.45 -33.14 4.08 -28.82 116.33 234.37 -18.88 -27.64 - 0.75 59.92 176.39 158.33 -49.46 -39.41 -11.08 31.41 -30.26 - 6.02 33.26 48.77
8.18 77.07 196.35 -45.96 -26.00 -17.41 MACLEAY RIVER BASIN
DISTRIBUTION NORMAL
Return Period 2 5 10 25
Stations
Euringelly 5.52 3.27 -14.77 Jeogla 132.82 1 14.35 -10.97 -16.33 Tia 75.61 2.91 -18.99 -14.16 Yarrowitch 85.09 3.04 -11.96 -30.35 Kempsey Road 174.59 30.92 3.35 -38.11 Coninside 75.51 - 0.47 -14.62
Average 91.52 9.00 -11.99 -24.74
DISTRIBUTION PEARSON TYPE III
Stations
Euringelly - 6.91 - 0.33 "12.85 Jeogla 43.30 - 2.27 -14.30 - 0.89 Tia 44.84 - 7.68 -16.90 - 5.35 Yarrowitch 29.27 - 8.01 -10.32 -19.00 Kempsey Road 26.50 + 0.47 0.55 , -24.96 Coninside 60.28 - 2.72 -12.96
Average 32.88 - 3.42 -11.13 -12.55 LOG NORMAL
50 2 5 10 25 50
-36.61 11.67 35.15
24.27 -22.17 -24.75 2. 86
- 4.10 -23.33 -13.61 33.67
1.64 -19,63 - 7.07 6.23
21.53 -17.00 - 6.81 -14.23
16.19 - 8.86 0.51
3.82 -13.39 - 2.76 7.13
LOG PEARSON TYPE III
-17.52 11.49 3.35
17.84 -23.64 -22.50 14.32
- 4.80 -23.51 -13„20 33.60
7.82 -18.59 -11.00 - 6.33
28.22 -15.96 -10.54 -23.62
21.21 - 7.86 - 2.58
8/80 -13.01 - 9.41 4.49 MACLEÄY RIVER RA.qTN (PQNT'd)
DISTRIBUTION GUISIBEL
Return Period 2 5 10 25
Stations
Euringelly "9.43 - 3.81 -15.20 Jeogla 81.32 4.36 -15.4b - 8.20 Tia 43.40 -10.62 -19.44 - 6.32 Yarrowitch 48.18 - 5.50 -12.46 -23.81 Kempsey Road 103.12 18.56 2.70 -31.80 Coninside 49.64 - 7.45 -15.05
Average 52.70 - 0.74 -12.49 -17.53
RICHMOND RIVER BASIN
DISTRIBUTION NORMAL
Stations
Casino 11.42 4.53 12.25 -27.83
MANNING RIVER BASIN
Stations
Nowendoc 18.83 12.79 - 2.85 Bob's Crossing 1.32 - 8.46 - 9.52
Average 10.52 2.95 - 0.04 (Richmond & Manning) LO G GUi^dBE L 1 50 2 5 10 25 50
i- — --
-49.8 7 - 7.6 3 32 «8 7
1.3 7 -33.9 5 -25.8 1 36.3 8
-22.4 2 -35.3 3 -14.9 2 76.1 2
-18.1 8 -32.4 6 - 8.4 6 43.2 6
- 5.1 0 -31.9 7 - 8.5 7 20.6 9
- 3.1 3 -21.1 4 - 8.8 6
16.2 2 -27.0 8 - 4.2 9 , 44.1 1
LO G NORMA L
-23.4 2 - 2.3 6 35.0 0 16.2 9
-33.3 5 - 4.8 9 12.7 0
-12.8 9 -12.2 8 - 3.8 6 •
-23.2 2 - 3.0 9 14.6 1 16.2. 9 RJJ^HMOND RIVER BASIN (CONT'd)
DISTRIBUTION PEARSON TYPE III
Return Period 2 5 10 25
Stations
Casino - 4.73 - 0.42 14.87 -20.16
MAiTNING RIVER BASIN
Stations
Nowendoc -12.35 2.12 - 0.90 Bob's Crossing - 4.61 -10.08 - 8.07
Average - 7.23 - 2.79 1.97 -20.16 1 (Richmond & Manning)
DISTRIBUTION GL^MBEL
RICHMOND RIVER BASIN
Stations
Casino - 4.46 - 2.65 11.70 -21.86
MANNING RIVER BASIN
Stations.
Nowendoc - 2.74 3.SI 3.3S
Bob's Crossing - 8.68 -13.41 - 9.86 1
Average - 5.29 - 4.05 1.74 i (Richmond & Manning) 1 LOG PEARSON TYPE III
50 2 5 10 25 50
-31.08 - 5.82 41.58 41.64
-29.70 - 3.73 8.40
-11.58 -11,95 - 4.90
-24.12 - 7.17 15. 03 41.64
LOG GUMBEL
-35.82 -14.47 33.29 48.43
-46.43 -20.22 15.58
-21.58 -19.35 - 4.55
-34.61 -18.01 14.77 48.43 TABLE 6
SUMMARY OF DEPARTURES INTO CATCHMENTS
CLARENCE BASIN RETURN PERIOD
DISTRIBUTION 2 5 10 25 50
Normal 64.52 11.20 -15.09 -21.51 -26.98 Pearson type III *17.54 - 2.32 -14.33 - 9.30 - 4.40 Gurabel 32.91 2.00 -15.57 -14.22 -13.24 log normal -10.21 -12.57 - 8.91 24.22 75.13 log Pearson type III -6.82 -12.10 -12.10 -12.21 15.22 log Gurabel -27.46 -27.55 -10.29 69.49 279.90
HUNTER BASIN
Normal 70.94 13.99 5.34 -12.76 -55.56 Pearson type III -10.90 0.27 -0.40 0.62 -33.21 Gumbel 31.28 22.51 3.20 - 5.33 -45.96 log norm.al - 8.96 - 2.08 9.75 29.71 8.81 log Pearson type III -2.61 - 3.39 3.75 16.45 1.64 log Gumbel -26.00 -17.41 8.18 77.07 196.35
MACLEAY BASIN
Normal 91,52 9. 00 -11.99 -24.74 Pearson type III 32.88 - 3.42 -11.13 -12.55 Gumbel 52.70 - 0.74 -12.49 -17.53 log normal 3.82 -13.39 - 2.76 7.13 log Pearson type III 8. 80 "13.01 - 9.41 4.49 log Gumbel 16.22 -27.08 - 4.29 44.11
RICHMOND & MANNING BASINS
Normal 10.52 2.95 - 0.04 -27.83 Pearson type III - 7.23 - 2.79 1.97 -20.16 Gumbel - 5.29 - 4.05 1.74 -21.86 log normal -23.22 - 3.09 14.61 16.29 log Pearson type III -24.12 - 7.17 15.03 41.64 log Gumbel -34.61 -18.01 14.77 42.43 TABLE 7
VARIATION OF CATCHMENT AVERAGE DEPARTURES
WITH DISTRIBUTION TYPE
RIVER BASIN DISTRIBUTION RICHMOND & CLARENCE HLTSITER MACL;p;Ay MANNING
1 Normal 6.95 15.81 19.65 1.25
Pearson type III ~2»28 - 4.56 2.72 - 4.43
Guiribel 0.16 9.90 7.58 - 4.47
Log Normal 4.06 6,52 - 2.07 - 1.88
Log Pearson type III. -3,17 3, 04 - 2.90 - 0.71
Log Gumbel 22.50 19.71 3.89 - 7.11 TABI.E 8
AVERAGE DEPARTURES FOR EACH DISTRIBUTION
DISTRIBUTION DEPARTURE
Normal 12.60
Pearson type III - 2.05
Gurribel 4.88
Log Normal 2.54
Log Pearson type III - 0.62
Log Gumbel 12.81 TABLE 9 - SUMMARY OF SMALLEST POSITIVE & NEGATIVE DEPARTURES
RETURN PERIOD 2 5 1 ! CATCHMENT Smallest+I Smallest- Smallest+ Smallest-
Log Pearson Gumbel Pearson CLARENCE Pearson 17.54 2.00 - 2.32 - 6.82 i1
Leg Log Normal Pearson HUNTER Pearson Normal 13.64 ^ r 0.21 - .0± - 2.08
Log - Normal Gumbel MACLEAY Normal 3,82 9.00 - 0.74
RICHMOND & Normal Gumbel Normal Pearson MANNING 10.52 - 5.29 2.95 - 2.79
i1 IC 25 50
[[iallest + Smallest - Smallest + Smallest - Smallest-i - Smallest -
Lo g Lo g Lo g Pearso n Pearso n Norma l Pearso n Pearso n - 9.3 0 - 4.4 0 - 8.9 1 12.2 1 15.2 2
Lo g Gumbe l Pearso a Pearso n Gumbe l Pearso n Pearso n 3.2 0 ~ 0 . 4G " 0.6 2 - 5.3 3 1.6 4 -33.2 1
Lo g Lo g Lo g Norma l Pearso n Gumbe l - 2 4.4 9 - 4.2 9
Pearso n Norma l Norma ? Pearso n 1.9 7 - 0.0 4 16.2 9 -20.1 6 1000 0 r-. L J . 1 i n 25 yr . Dat e ri uu a p
1 i n 10yr . Dat e I F 00 d 500 0 \ \ NO l• E ^Linea r Interpolatio n 1 i n 5yr . Dat i F lo c d betwee n adjacen t diita ^n c IW S to e )iv e re1 q ui r ed df da i (0 :af l ioo c u a> (n o 3 oj 03 1 i n 2y r Dat a F 00 d O ^
< ^ o 100 0 X o
LEGEN D 50 0 ©DAT A FLOW S (Fro m // chronologica l record )
/f c/ Fl ( 3. 1
10 0 0.0 1 0.0 5 10 2 0 50 80 9 0 99 99. 9 99.9 9 PROBABILITY(x LOG-NORMA L PROBABILIT Y PLO T FO R GU Y FAWKE S STATIO N O N EBO R RIVE R (CLARENC E BASIN )