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whele qi is Deasureil outflot
r 1s lreasured ralnfall
u is unlt hydrograph oralinate
the aalvantage of t}le quaabatic proqramnlng technique over the sinht.matrix
lnverslon technique j.s the incluslon of th; second ..;ta;l;;-'
al1or,'1n9 only l)osttive unir hydrograph oratinates. rhe urrit ifarograpr,s
derlveal should therefore be Eore reaLlstic.
Unj-t hydrographs were derived fol each event indlviduatly fron each
of the 14 test catch.[1ents. Unit hydroglaphs could not hor,,ever be
obtalned fr@ severaf events due to nnmerical scali_]lg problems in the
quadratj.c progralurlng routj.ne. In general, individual ulit hydlograpns
!/eae rnolsy', shoying large variations a.bout an expecteal s.nooth snape,
This was partly due to the tine interval of the data being loo long
(I dinute) ln relation to catchment tiDe to peak (of the ortter of
2 rBinutes). fhe 1on9 tlrne inre.val made estinEtion of hydrograpir snape
in the r€g1on of the peak especlalty difficult. An atternpt to proatuce
a sdooth shape by applying a novLng averaqe filter to t_he derived
oralinates i{as abandoned because of the targe attenuatlon of peak
discharge produced - another effect of the snall nrdber of ordinates
near the peak, A furthe! cause of 'nolsy'
unj.t hydrograph snape was
ttlat no separatlon of response into slov (bas3) and quick (surface)
response nas bade. As a result, resialual non-zelo flotd at the end of
the event was leflected ln l"arge values fo! the Last few ordinates of
the derlved unlt hyalrographs anal coriesponallngly lorer values for
earlier oralinates. lihile separalion of the response vrould giv€ large
lnconslstencies betteen the unit hydlograph anal t}l€ other surface
routlng dodels, tie other nodels speclfy conceptual responses erhich
cannot yleld high oldinates at th€ end of the recesslon. rurthermore,
the.e
lnput
is s@e justlficatlon for using a separate rnechanistn fo! the
forced r€sponse before t-he j.nflexlon of recesslon l1lrll3 and the
free response aftelwards. Because of ther.r noisy shape, about a third
of the aletlved unlt hydrographs were lejecteal fron further analysis.
the remalnlng unit hydrographs (about five for each catchnent) t ere
avelaged afte! first synchlonising peaks. The catchroent-averaged unlt
hy&ographs sholred quite Large variatlons in skeeness bet\reen calchrnents,
anil as a result no singLe alinensionless unlt hydrograph could faithfully
flt all catchments. Thus a trlangular unit hydrograph was fitted by
eye to each cacchnen! average unlt hydrograph and the peak anal tine to
peak .neasureal (tine base is determlned frotn peak by the necesstty of
uit volune of dischalqe). Table 2l belor gives tie values obtained.
A leglesslon analysls was pelfolBed on these data to aletelrdre suitable
forns of equatton for boEh Q_ and T In order to allow fair conoparison
pp
between t.}11s Eodel and t'he othe! surface louting nodels, only one
palaneter (Qp o! Tp) should be aleterulned flon catchnent characteris tics ,
tie other being aleterrnined froB an irltehal relatiolship. (h facr, as
wilL be seen, the effect of deternining boti paraneters from catchnent
chatacterlstics would be small) . One catclunent, 4176, showed a narkedly
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