Resea ch P ojec Co e Shee
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Za a , M. I. (2021). Imp o ing Flood Es ima ion in Ungauged Ca chmen s. Unde g adua e
Resea ch Repo No. 2021RP080. Depa men o Ci il Enginee ing, Uni e si y o B is ol,
B is ol, U.K.
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Da e: 28 h May 2021
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1
IMPROVING FLOOD ESTIMATION IN UNGAUGED
CATCHMENTS
Au ho : M. I. Za a , Uni e si y o B is ol, B is ol, U.K.
Resea ch Supe iso : M. Rico-Rami ez, Uni e si y o B is ol, B is ol, U.K.
ABSTRACT: The lood es ima es a e c i ical o s udies in ol ing lood mapping, hyd aulic s uc u e planning
and design, lood isk assessmen s, and ese oi ope a ions. Es ima es ha e adi ionally been ob ained by
eg ession equa ions. QMED is a medium sized lood ob ained om he median o annual-maximum (AMAX)
se ies – he highes low obse ed in each wa e yea . Fo gauged ca chmen s, echniques in ol ing he annual-
maximum-se ies (AMS) and peak-o e - h eshold (POT) a e adi ionally used. Howe e , o he ungauged si es,
in o de o link he index lood o ca chmen desc ip o s, s a is ical models such as mul iple eg ession a e mos
widely used. In his pape , he Flood Es ima ion Handbook (FEH) s a is ical me hodologies a e analysed and
hence ecalib a ed using all da a a ailable as well as c oss alida ion p ocess, he a ailabili y o mo e low
eco ds p oduced be e esul s. Simila ly, using co ela ion analysis, app op ia e ca chmen desc ip o s a e
selec ed, and a new simple non-linea eg ession model is p oposed. A i icial Neu al Ne wo ks (ANNs) ha e
been used o gauged ca chmen s bu a ely o ungauged ca chmen s. The use o ANNs is in es iga ed o
es ima e he lood index om he ca chmen desc ip o s and a e compa ed o adi ional non-linea eg ession
models. The Na ional Ri e Flow A chi e (NRFA) da a has been u ilized o es ima e he index lood (QMED)
o 337 ungauged ca chmen s in he UK. The esul s showed ha i) he e a e se e al ca chmen desc ip o s (e.g.
ca chmen a ea, mean annual ain all) ha a e di ec ly co ela ed o QMED; ii) he ecalib a ed FEH models
p oduce be e esul s han he o iginal models and so i is impo an o ecalib a e his model as new da a
becomes a ailable; iii) he p oposed non-linea powe -law model p oduces sligh ly be e esul s han he FEH
model; i ) he QMED es ima es ob ained om ANNs ha e shown imp o ed pe o mance as compa ed o he
adi ional non-linea eg ession models. In addi ion o ha , gi en he ac ha he numbe o ca chmen s is no
la ge enough o sepa a e he da a se in calib a ion and alida ion, we used c oss alida ion (whe e each model is
ained o n-1 da a poin s, and hen es ed agains he emaining 1 unseen da a poin demons a ing he eal
pe o mance o model), o es he ue pe o mance o he models. The c oss- alida ion esul s showed ha he
pe o mance o he models dec eases, bu he ANNs s ill p oduces sligh ly be e esul s compa ed o he non-
linea eg ession models.
KEYWORDS: QMED, Ungauged, Flood Es ima ion Handbook (FEH), A i icial Neu al Ne wo ks (ANN),
index lood, eg ession.
STATEMENT OF ORIGINALITY: In his pape , he QMED es ima ion model gi en in Flood Es ima ion
Handbook (FEH) published by Ins i u e o Hyd ology (IH 1999) and imp o ed FEH (Kjeldsen es al. 2008)
model a e ecalib a ed wi h he newe and be e pa ame e s making use o all low eco ds a ailable up un il he
end o Sep embe 2019. A new non-linea eg ession model o he es ima ion o QMED om lood da a is
cons uc ed using he mul iplica i e-s uc u e me hod. A i icial neu al ne wo ks (ANNs) a e used o p edic
QMED a ungauged loca ions, and he esul s ob ained om ANNs ou pe o med all p e ious app oaches.
1. INTRODUCTION
Floods a e one o he mos damaging na u al disas e s and conside ed a majo na u al haza d wi hin he UK, a
epo om En i onmen Agency (EA, 2012), shows ha he e a e o e and abo e 5 million people jus in
England and Wales ha a e li ing in lood p one a eas. In he las couple o decades, looding has no only
esul ed in huge economic damage bu also caused loss o li e in e e y co ne o globe (Gaume e al., 2009).
The e o e, he design o ex eme hyd ological e en s such as loods is an essen ial elemen o unde s anding
and mi iga ing lood isks. I is also equi ed o he planning o a ie y o wa e esou ces sys ems o educe he
ulne abili y o people and public and pe sonal p ope y. On he o he hand, accu a e es ima ion o lood e en s
a ungauged ca chmen s is e y complex p ocess and an uneasy one o unde s and. This pape he e o e makes
an a emp on in es iga ing he eliabili y o he exis ing QMED es ima ion models (IH 1999 and Kjeldsen es
al.2008) and explo es a po en ial o imp o e he es ima ion o QMED using ca chmen desc ip o s.
The e a e di e en lood es ima ion me hods a ailable in he li e a u e. These es ima es a e commonly
calcula ed by i ing annual maximum (AMAX) se ies o peak low o a ca chmen o egional combina ion o
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ca chmen s o he s a is ical models (S edinge e al., 1993). The e is a ange o egionaliza ion echniques o
choose om (Cunnane, 1988, 1989). Once he geog aphical egion is selec ed using egionaliza ion echniques
implemen ed by Cunnane (1988) o he de i a ion o egional lood equency cu es. Floods o a gi en e u n
pe iod can be measu ed om he index lood alues using he de eloped egional lood equency cu es and
he s eepness o a egional lood equency cu e can be measu ed ai ly well using only wo pa ame e s: annual
a e age ain all and he egion's median ca chmen a ea (Meigh e al., 1997). Dal ymple's (1960) index- lood
me hod (IFM) is a con en ional and s aigh o wa d echnique, o he ca chmen s whe e e y less low da a is
a ailable o ha a e ungauged. Howe e , in lood isk s udies his me hodology is s ill applicable because i
shows conside ably be e esul s han some ecen egionaliza ion me hods (Malekinezhad e al. 2011). And i is
a s anda d p ocedu e in Flood Es ima ion Handbook (FEH), he FEH is he es ablished c i e ia used in he
es ima ion o lood isks in a gi en egion and o es ima e local lood isks and, as a esul , designing a lood-
esis an in as uc u e, in i s applica ion o he UK, i uses median o he annual maximum lood as he index-
lood, QMED, his di e s om he mo e con en ional me hod o using he mean o he annual maxima.
Because he median is a mo e s able indica o ha is less in luenced by he magni ude o a pa icula ly la ge
lood e en , while he mean will luc ua e signi ican ly. In a s udy conduc ed by Sun e al. (2000), i was
disco e ed ha using ada da a in conjunc ion wi h ain all da a om nea by gauges, a me hod known as
cok iging, imp o ed he e iciency o lood es ima es. The unce ain y in he inpu da a used o modelling was
also quan i ied in he same analysis.
Fo any ungauged ca chmen , he index lood is es ima ed using a combina ion o a mul iple eg ession
non-linea model, which links he index lood o a se o ca chmen desc ip o s. The s a is ical model gi en in
he imp o ed FEH is ou inely used o ob ain he lood es ima es, i is assumed ha he index lood o QMED,
i.e., he median o he se o annual maxima (AMAX) lood da a, can be explained by ca chmen desc ip o s,
howe e , he unce ain y o he esul s is e y high (Kjeldsen, T. R., 2015). This pape a emp s o answe he
esea ch ques ion: Can we imp o e lood es ima es using models based on ca chmen desc ip o s? To achie e
his, he objec i es o his pape a e: (i) o implemen he cu en FEH me hod o es ima e QMED based on
ca chmen desc ip o s, (ii) o ecalib a e he models a ailable in he li e a u e wi h he a ailabili y o mo e low
eco ds, (iii) o ca y ou analysis o he a ailable ca chmen desc ip o s o choose o modelling, he ones seen
o be highly co ela ed, (i ) o de elop a new non-linea eg ession model, and ( ) o in es iga e he use o
a i icial neu al ne wo ks and hei e iciency compa ed wi h he adi ional non-linea me hodologies.
2. LITERATURE REVIEW
The Flood S udies Repo (FSR) was he p ima y comp ehensi e me hodology o lood equency es ima ion in
he UK, published by he Na u al En i onmen Resea ch Council (NERC, 1975). This epo was de i ed om
he Index Flood Me hod (IFM) de eloped by Uni ed S a es Geological Su ey (Dal ymple, 1960). The IFM is
based on he assump ion ha he lood lows in a hyd ologically simila egion, hese egions a e s anda dized
by index lood and a e iden ically dis ibu ed. Fo he es ima ion o he pa ame e s o a lood equency cu e
he da a is ga he ed om he s a ions wi hin a de ined egion and hen his dimensionless cu e is scaled by he
index lood o he ca chmen o in e es (G o e e al., 2002). Con en ionally, hese egions a e de ined by
poli ical o geog aphic bounda ies. Thomas and Benson (1970) p edic ed lood quan iles o ou di e en
egions in he Uni ed S a es using mul iple eg ession. Simila ly, Taske e al. (1996) obse ed mo e accu a e
esul s ound ha subdi ision in o smalle geog aphically based sub egions. In he same s udy, hey obse ed
ha using he “ egion o in luence” me hod o gene a e a unique a ea o each ungauged ca chmen ga e he
smalles Roo Mean Squa e e o in he 50-yea lood es ima e o he uncalib a ed ca chmen s in A kansas.
In he same way he Flood S udies Repo (FSR) di ided he UK in o 10 geog aphical egions. Fo each
egion, lood equency cu e speci ic o each ca chmen can be ob ained as he p oduc o a egional
dimensionless g ow h ac o and index lood, es ima e o index lood can be de i ed om a eg ession model
es ablished om he ca chmen desc ip o s such as ca chmen a ea, annual a e age ain all, soil ype, e c o
could be di ec ly ob ained om he obse a ion as he mean annual maximum lood. Whe eas lood equency
cu e is a p obabilis ic model linking a lood magni ude o lood a i y, he in e se o e u n pe iod. Residual
mapping done using geos a is ics is an al e na e app oach o he de elopmen o sepa a e models o each
egion. The esidual map a emp s o elimina e he bias caused by geog aphic di e ences ha a e no conside ed
in he model.
Following he b eak h oughs achie ed in he es ima ion o egional lood equency, and he “ egion o
in luence” (ROI) me hod (Bu n, 1990) and as he me hod o L momen s was in oduced (Hosking and Wallis,
1993), he Ins i u e o Hyd ology (IH) published he Flood Es ima ion Handbook (FEH) wi h imp o ed
p ocedu es o lood es ima ion. The key de elopmen s in lood equency es ima ion include: (i) use o
hyd ological simila i y o he o ma ion ca chmen speci ic g ow h cu e ins ead o egional alues gi en in
FSR, (ii) in he ungauged ca chmen s o he es ima ion o index lood s anda dised a me hodology o da a
ans e om nea by hyd ological analogous (dono ) si es (iii) he FEH adap ed he median annual maximum
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lood, QMED, as he measu e o index lood because o he sho e da a se ies median is ound less sensi i e o
he i egula i ies han mean, and (i ) he ca chmen desc ip o s a e de i ed au oma ically om g idded
elec onic da a and i is no longe limi ed by he need o be able o compu e desc ip o s manually om 1:50000
pape maps. The e iew o ele an li e a u e showed ha he Index Flood Model and p ocedu es simila o he
FEH ha e also been de eloped o o he pa s o he wo ld, i was ound ha he Meigh e al. (1997) me hod, he
Gö gens (2007) Join Peak-Volume (JPV) me hod and he Haile (2011) me hod a e a ailable o applica ion
such as o : A ica (Mkhandi e al., 2000), and Eu ope (Cas ella in e al., 2012).
The c ea ion o much imp o ed da abase o sys ema ically eco ded lood da a done by HiFlows-UK
ecommended he changes in he FEH me hodology. The imp o ed FEH p ocedu es we e de eloped by he
En i onmen Agency (2008), i has kep he use o hyd ological simila i y me hod and he Index Flood Me hod
(IFM). Howe e , he s a is ical models o he es ima ion o index lood and dimensionless g ow h cu e we e
imp o ed and hese a e implemen ed in he WINFAP-FEH 3 so wa e (WHS, 2009). Due o he lexible
s uc u e o s a is ical models, hey ha e be e desc ip i e abili y han he physically based models (B a h e al.,
2009). Fo he calcula ion o design loods, a ious p ocedu es a e p o ided in he imp o ed FEH, ne e heless,
dependen o he a ailabili y o da a. Al hough ha dly any guidance is p o ided on how o assess he unce ain y
o hese es ima es (Kjeldsen e al., 2008). Fo example, he 95% o 68% con idence in e als a e gene ally used
and ha a e mainly alid o he ans e o da a om nea by gauged ca chmen s in o de o ge accu a e
es ima es o QMED, index lood, a he ungauged ca chmen s. While he si es whe e no lood da a is a ailable,
eg ession models a e used o di ec ly es ima e index lood om he ca chmen desc ip o s. The s udies by
Pappenbe ge and Be en (2006); and Hall, (2011) showed ha in lood managemen he e is u gen need o gi e
c ucial impo ance o isk and unce ain y. Fo he assessmen o unce ain y in he s a is ical models o design
lood es ima es new me hods ha e been de eloped by Kjeldsen e al., (2008). I also assessed he accu acy o
index lood (QMED) es ima es a he ungauged si es, used in he imp o ed FEH.
2.1 The Flood Es ima ion Handbook me hod (1999)
The median annual maximum lood (QMED) model desc ibed in he Ins i u e o Hyd ology's (IH 1999) Flood
Es ima ion Handbook (FEH) is a well-known model o his kind in he UK. This model has been widely used in
he Uni ed Kingdom, o example, in lood de ence planning, lood isk analysis, new cons uc ion planning,
and de e mining he a i y o signi ican ain alls o loods.
The ecommended me hod in FEH o he es ima ion o QMED a he si es whe e no lood peak da a is
a ailable, o a e ungauged, is o ans e da a om nea by dono si es o om dis an analogue ones. A
p econdi ion o such ans e is ha he dono si es mus be hyd ologically simila in e ms o ca chmen a ea,
soil ype and ain all. Howe e , using basic s a is ical eg ession echniques, i is possible o es ima e index
loods based on ca chmen desc ip o s such as a ea, base low index, and we ness. Dis inc algo i hms a e
p o ided in FEH o he QMED es ima ion in u ban si es and u al si es and e en o he indi idual ca chmen s.
On he o he hand, lood es ima es ob ained solely on he basis o ca chmen desc ip o s, acco ding o Reed and
Robson (1999), a e poo e han he ones ob ained di ec ly om he lood peak alues. Ca ego iza ion o he si es
in o simila g oups can be di icul and hence es ablishing a su icien collec ion o dono si es is no always
easible. FEH wa ns ha basic disc epancies be ween si es could lead o no only he ansmission o w ong
in o ma ion, bu also he es ablishmen o inco ec lood p ojec ions. E en hough a i icial neu al ne wo ks
ha e been used o he classi ica ions o ca chmen s (Thanda eswa a and Sajikuma , 2000),
2.2 The imp o ed FEH equa ion (2008)
The p oposed imp o emen s a e p omp ed in pa by he HiFlows-UK (En i onmen al Agency 2012) ini ia i e,
which esul ed in he cons uc ion o a much be e da abase o ou inely collec ed lood da a (Kjeldsen e al.,
2008). No only a e he in o ma ion eco ds signi ican ly longe han be o e, bu he HiFlows-UK p ojec also
in es ed a lo o e o on s anda dizing and assessing he en i e da ase . This means ha he amoun o da a
a ailable o analysis has signi ican ly inc eased. Feedback om FEH use s, bo h in o mal and o icial, has also
had an impac on he e ised p ocedu es. Mos echnical ea u es o he app oach can be changed wi hou
signi ican ly al e ing he app oach's s uc u e. Mos echnical speci ics o he s a egy a e e ised o imp o e he
p ocedu e's pe o mance wi hou signi ican ly modi ying he me hodology's s uc u e. The heo e ical s a is ical
unde pinning ha unde pins he echnique has been signi ican ly imp o ed as a esul o he upg ades. In
addi ion, ce ain no el desc ip o s o ca chmen opog aphy and na i e clima e ha ha e been p oposed since
he FEH s udy ha e been conside ed. A eplacemen desc ip o o measu ing loodplain ex en , in pa icula ,
has been de eloped and is now inco po a ed in he upda ed p ocesses. Following Kjeldsen e al. (2008)'s s udy,
he ollowing impo an changes ha e been made: a model o es ima ing he median using a eplacemen
eg ession model.
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2.3 Flood es ima ion using A i icial Neu al Ne wo ks (ANNs)
ANNs ha e been used o pe o m lood es ima ion in he pas (Dawson, C., e al., 2006). Since he e ec i e
aining echniques o ANNs we e de eloped (Rumelha and McClelland, 1986), hese models ha e been used
o sol e a a ie y o hyd ological p oblems, including ain all- uno modeling and i e discha ge o ecas s
(Ab aha e al., 2004). Das o ani e al. (2010) also e alua ed he applicabili y o ANN in he o ecas ing o
p ecipi a ion amoun be o e i s occu ence and epo ed i o be a eliable model o es ima ion. A s udy
conduc ed by (Liong e al, 2000) on he i e s age p edic ion and p oduced esul s wi h a high deg ee o
accu acy and a sho compu a ional ime, making ANNs a desi able o ecas ing ool, a sensi i i y esea ch was
also unde aken, which ecommended educing he numbe o inpu neu ons (in ha case om eigh o i e),
despi e he es ima ed accu acy le el no being conside ably a ec ed. Dawson and Wilby (2001) done esea ch
on he applica ion o ANNs in hyd ological modeling, desc ibing i as an eme ging ield o esea ch wi h a wide
ange o me hodologies. Two se s o s udies conduc ed by Go inda aju (2000) in es iga e he unc ion o
a i icial neu al ne wo ks (ANNs) in hyd ology and p o ide some undamen al c i e ia o hei use, as well as
hei s eng hs and limi a ions, and compa e hem o o he hyd ology modeling app oaches. The ANN model is
be e a de ec ing non-linea ela ionships be ween obse ed and an icipa ed da a se s (Hsu, K., L., e al, 1995
and El-Sha ie, A., e al, 2011). Lapedes, A., e al. (1987) used ANN models o s udy non-linea da a se ies and
disco e ed ha ANN models ha e supe io gene aliza ion capabili ies han eg ession-based models. Howe e ,
he e a e ela i ely ew s udies in ol ing he applica ion o ANNs o lood es ima ion a ungauged si es. Fo
example, a egionally ained neu al ne wo k was equi alen o ea lie Q2 eg ession es ima es in he Gul o
Texas (Mu iah e al., 1997), ano he esea ch was conduc ed o he US i e basin o assess he peak s o m
discha ge du ing a wo-yea pe iod. Hall and Minns (1998) epo ed ha he classi ica ion o hyd ologically
simila zones is an impo an componen o egionaliza ion echniques and he use o hese echniques on lood
da a om he sou hwes o England and Wales has shown ha g oups can be o med by Rep esen a i e Regional
Ca chmen s (RRCs), which ha e hyd ologically mo e sensible quali ies han hose p o ided solely by
geog aphical closeness. Using da a om si es in Suma a and Ja a, Hall e al. (2000) used ou o wel e inpu
ca chmen desc ip o s o p edic he scale and loca ion pa ame e o Gumbel dis ibu ion o annual loods,
howe e Das o ani and W igh (2001) epo ed ha o he index lood es ima ion, QMED, se en ca chmen
desc ip o s we e su icien o si es in he Uni ed Kingdom. This pape discusses he applica ion o ANNs o
p edic he index lood o a much la ge sample o selec ed ca chmen s in he UK. Reason why his esea ch
was conside ed essen ial is because in he mos ecen s udy ca ied ou by Dawson, C., e al., (2006) only
ained he ANNs wi h he da a o he u ban egions, in addi ion o ha , he s udy was also es ic ed only o he
loca ions ha had a leas en yea s o lood da a, and he index lood p edic ions we e ine i ably o e o unde -
es ima ed. Since ANNs ely hea ily on da a, new low eco ds ha e he po en ial o imp o e lood es ima es.
3. DATASETS
The da ase used in his pape is ob ained om he Na ional Ri e Flow A chi e (NRFA). I consis s o da a o
935 gauging s a ions con aining annual maximum (AMAX) se ies, peak o e h eshold (POT) and ca chmen
desc ip o s (CD). The AMAX se ies con ains he la ges obse ed low (in cubic me es pe second, abb e ia ed
o m3s-1 and some imes also e e ed o as 'cumecs') in each wa e yea . The Peaks O e Th eshold (POT) se ies
con ains all peak lows ha a e g ea e han a gi en h eshold low, he h eshold is gene ally se o include an
a e age o 5 e en s pe yea . The Ca chmen Desc ip o (CD) da a is a se o p ope ies ha de e mine he
hyd ological cha ac e is ics o he ca chmen . A o al o 544 s a ions a e ecommended o use in pooling
g oups, 337 s a ions a e sui able o QMED, i QMED is likely o be wi hin 30% o i s ue alue, and 53
s a ions a e sui able o nei he . A g oup o 337 s a ions is chosen o he analysis. Figu e 1a shows he loca ion
o all hese ca chmen s and hei ca chmen a ea whe eas Figu e 1b shows hei s anda d a e age annual ain all.
3.1 Da a quali y
Ou o al eady e y small numbe o a ailable ca chmen s, da a has o be sc eened o disco dancy. Fo he
ecalib a ion o pa ame e s o he model a ca e ul selec ion o da a poin s is e y c ucial. To a oid he es ima es
o be biased he chosen da a poin s should be conside ably consis en and in spi e o ha he e should be enough
da a o app op ia ely de ine he model pa ame e s (G o e e al., 2002). The e o e, he da a o 337 s a ions is
subjec ed o sc eening o look o any i egula i ies and independence. I was obse ed ha h ee s a ions,
25808, 25809 and 25810, ha e no iceably small ca chmen a eas o 0.75 km2, 0.05 km2, 0.04 km2, espec i ely.
Consequen ly, hese s a ions a e disca ded om he ecalib a ion and es ima ion o new pa ame e s.
The chosen da ase , sui able o QMED es ima ion, om Na ional Ri e Flow A chi e (NRFA) has 22
ca chmen desc ip o s (CDs) a ailable o each ca chmen , he summa y o CDs is shown in he Table 1. Fi s o
all, a MATLAB sc ip was un o ex ac he ca chmen desc ip o s o each si e om he da ase and hen all o
hem we e compiled in a single ile alongside o ca chmen numbe s and hei coo dina ed o he ease o
analysis. Al hough, some o hese desc ip o s upon analysis p o ed o be mo e c ucial in e ms o he sensi i i y
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o he models han he o he s. The annual maximum se ies (AMS) da a om he NRFA olde o each
ca chmen was hen ex ac ed and compiled in o a single ile using ano he MATLAB sc ip . Finally, he median
o AMS o each ca chmen was calcula ed o p oduce he inal alue o QMED measu ed.
(a) (b)
Figu e 1: Loca ions o he ca chmen s used in his s udy displaying (a) hei ca chmen a ea (AREA) and
(b) s anda d a e age annual ain all (SAAR)
Table 1: All he a ailable ca chmen desc ip o s (CDs)
Desc ip o s
Uni
Summa y
ALTBAR
m
Mean ca chmen al i ude abo e sea le el
AREA
km2
Ca chmen d ainage a ea
ASPBAR
Mean di ec ion o all he in e -nodal slopes in he ca chmen – ep esen s dominan
aspec o ca chmen slope
ASPVAR
In a iabili y o slope di ec ion
BFIHOST
Base Flow Index - soil d ainage ype
DPLBAR
km
Mean d ainage pa h leng h
DPSBAR
m/km
Mean ca chmen slopes
FARL
Flood a enua ion due o i e s and lakes
LDP
km
Longes d ainage pa h
PROPWET
mm
P opo ion o ime when soil mois u e de ici ≤ 6mm
RMED1D
mm
Median annual max 1Day ain all
RMED1H
mm
Median annual max 1Hou ain all
RMED2D
mm
Median annual max 2Day ain all
SAAR
mm
S anda d a e age annual ain all 1961-90
SAAR4170
mm
S anda d a e age annual ain all 1941-70
SPRHOST
S anda d Pe cen age Runo - soil d ainage ype
URBCONC1990
Concen a ion o sub/u ban land co e 1990
URBCONC2000
Concen a ion o sub/u ban land co e 2000
URBEXT1990
Ex en o u ban and subu ban co e 1990
URBEXT2000
Ex en o u ban and subu ban co e 2000
URBLOC1990
Loca ion o u ban and subu ban co e 1990
URBLOC2000
Loca ion o u ban and subu ban co e 2000
4. METHODS
Due o i s lexible s uc u e, he s a is ical models ha e a s onge desc ip i e capaci y han he igidly
cons uc ed physical models. I is also e iden om he li e a u e ha he s a is ical indi ec me hods, such as
QMED eg ession model, a e mo e p ecise han he concep ual indi ec models o he p edic ion o QMED a
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he ungauged si es (B a h e al., 2009). The igid s uc u e o he concep ual app oach dec eases i s dependence
on he speci ic knowledge o he indi idual s a ions and, consequen ly, s eng hens i s s abili y. Consequen ly,
s a is ical models may no be able o p o ide physical in e p e a ion o insigh in o o he in e - ela ed ac o s in
looding, leading o possible changes in looding.
4.1 The Flood Es ima ion Handbook me hod (1999)
Va ious p ocedu es o es ima e QMED we e p o ided in olume 3 o he FEH (Reed and Robson, 1999), some
o he common ones a e; om annual maxima (AM), peaks o e h eshold (POT) and ca chmen desc ip o s
(CD). Annual maxima me hod is only used i he lood da a is a ailable o mo e han 14 yea s. The
ecommended me hod in FEH o he es ima ion o QMED a he si es whe e no lood peak da a is a ailable, o
a e ungauged, is o ans e da a om nea by dono si es o om dis an analogue ones. A p econdi ion o such
ans e is ha he dono si es mus be hyd ologically simila in e ms o ca chmen a ea, soil ype and ain all.
The s a is ical QMED model gi en in he FEH (1999) - ca chmen desc ip o me hod, is ad ised o be
used wi h he ans e o da a me hod om he nea by si es. This way he ob ained alues o QMED will be
e ined and i also uses a longe lood eco d. The eg ession equa ion can also be used wi h he ca chmen
desc ip o s only i ans e o da a is no possible because o una ailabili y o sui able si es nea by, and he si e
eco d is less han wo yea s long. This eg ession model was applicable o all he ungauged ca chmen s in he
UK wi h he a ea g ea e han 0.5 km2. The equa ion 1 is based on he analysis o o e 1000 s a ions, hei
QMED alues and ca chmen desc ip o s ob ained om he FEH CD-ROM 1. These a e essen ially he
ca chmen s wi h 𝑈𝑅𝐵𝐸𝑋𝑇<0.025.
𝑄𝑀𝐸𝐷𝑟𝑢𝑟𝑎𝑙 =1.172 𝐴𝑅𝐸𝐴𝐴𝐸 (𝑆𝐴𝐴𝑅
1000)1.560𝐹𝐴𝑅𝐿2.642(𝑆𝑃𝑅𝐻𝑂𝑆𝑇
100 )1.2110.0198𝑅𝐸𝑆𝐻𝑂𝑆𝑇 1.
whe e 𝐴𝐸 = a ea exponen = 1−0.015𝑙𝑛(𝐴𝑅𝐸𝐴
0.5 ) 2.
wi h 2 (coe icien o de e mina ion) = 0.916 (on log scale), 0.905 (GLS-scale, Gene alised Leas Squa e) and
he se ( ac o ial s anda d e o ) = 1.549.
The u ban adjus men ac o , which is calcula ed using he ollowing o mula, desc ibes how an u ban
ca chmen di e s om i s u al coun e pa .
𝑈𝐴𝐹= (1+𝑈𝑅𝐵𝐸𝑋𝑇)0.83𝑃𝑅𝑈𝐴𝐹 3.
whe e 𝑃𝑅𝑈𝐴𝐹=1+0.615 𝑈𝑅𝐵𝐸𝑋𝑇 ( 70
𝑆𝑃𝑅𝐻𝑂𝑆𝑇 −1) 4.
The QMED ob ained om equa ion 1 is hen co ec ed o he unsuccess ully mi iga ed e ec o u banisa ion
using he ollowing o mula:
𝑄𝑀𝐸𝐷=𝑈𝐴𝐹 𝑄𝑀𝐸𝐷𝑟𝑢𝑟𝑎𝑙 5.
The o iginal FEH model (Equa ion 1), is also e alua ed o RMSE, KGE and BIAS in o de o ensu e he ai
compa ison o all he models in his pape . In he Figu e 5(a) he es ima ed QMED om his model is plo ed
agains he measu ed QMED om he AMS.
4.2 The imp o ed FEH equa ion (2008)
The Cen e o Ecology and Hyd ology modi ied he olde model eleased in Flood es ima ion manual (1999) in
2008. (CEH), The wo k o Kjeldsen e al. (2008) on he calcula ion o loods om mino ca chmen s is no
wi hou laws. Al hough he 602 lood da ase s used o gene a e he e ised QMED equa ion appea o ep esen
a sizable sample size, only 46 o he 602 lood da ase s d ain an a ea o less han 25 km2. In addi ion, emo ing
epea ed en ies o h ee o hose ca chmen s dec eases he numbe o mino ca chmen s in he sample o jus
41. Pe haps because he p ojec eam was able o quickly ge he yea ly maximum lood le el. Kjeldsen e al.
(2008) did no a emp o c ea e an equa ion specially a ge ed a small ca chmen s o eplace he QBAR
eg ession equa ion p esen ed in IH 124, possibly because he esea ch eam was able o ga he yea ly maximum
lood peak alues om jus a small sample. Kjeldsen (2010), on he o he hand, o e s new ecommenda ions o
al e ing QMED u al o accoun o u baniza ion.
𝑄𝑀𝐸𝐷𝑟𝑢𝑟𝑎𝑙 =8.306 𝐴𝑅𝐸𝐴0.8510.154(1000
𝑆𝐴𝐴𝑅)𝐹𝐴𝑅𝐿3.4450.046(𝐵𝐹𝐼𝐻𝑂𝑆𝑇)2 6.
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The esul s om he modi ied FEH (Kjeldsen e al. 2008) app oach showed conside ably smalle e o s han he
p e ious FEH app oach (IH 1999), as shown in Figu es 5a and 5b.
(a) (b)
Figu e 5: The plo s o es ima ed QMED agains QMED measu ed (a) displaying esul s o (FEH 1999)
model (b) displaying esul s o (FEH 2008) model
4.3 New non-linea model
A new mul iplica i e non-linea powe -law model (equa ion 7) is p oposed o es ima e QMED. The changes in
ca chmen desc ip o s (CDs) ha e a scaling e ec on he QMED and he deg ee o his e ec is in luenced by
he exponen e ms b, c, d, …. This o m o he equa ion yields a linea s uc u e ha can be used wi h no mal
mul i a ia e s a is ical p ocedu es.
𝑄𝑀𝐸𝐷=𝐴 𝑋1
𝑏 𝑋2
𝑐 𝑋3
𝑑… 7.
Whe e A, b, c … ep esen he model pa ame e s ha ha e o be es ima ed, Xi ep esen a gi en ca chmen
desc ip o s. W i ing he equa ion in his o m gi es a linea s uc u e ha allows s anda d mul i a ia e s a is ical
p ocedu es o be applied. The subs an ial esea ch on mul iple eg ession analysis conduc ed by Thomas and
Benson (1970) esul ed in he ma hema ical equa ion o he simila o m.
4.4 A i icial Neu al Ne wo ks (ANNs)
A neu al ne wo k's compu a ional capaci y is e iden ly de i ed om wo ac o s: i s , i s massi ely pa allel
dis ibu ed s uc u e, and second, i s capaci y o lea n and hence gene alize. And i is designed o use a
compu a ional app oach o simula e na u al neu al ne wo ks (Hayek, S., 2009). A neu al ne wo k consis s o a
numbe o in e connec ed nodes called neu ons ha a e linked oge he by weigh s be ween laye s. They a e
di ided in o h ee undamen al laye s: an inpu laye , does no pe o m any calcula ions and jus eeds he
ne wo k wi h in o ma ion, an in e media e hidden laye , and an ou pu laye ha p oduces esul s. The
a chi ec u e o a ypical ANN is shown in Figu e 2, hough i a ies. The mos ex ensi ely used among se e al
a ie ies o ANNs is he eed- o wa d neu al ne wo k, i ge s his name because da a goes h ough he ne wo k
om he inpu laye o he hidden laye , and hen o he ou pu laye .
Figu e 2: Typical wo laye ed eed- o wa d neu al ne wo k
4.5 Pe o mance Indica o s
Fo an objec i e e alua ion o model pe o mance, goodness-o - i measu es a e c i ical. I is essen ial o selec
objec i e pe o mance indica o s in o de o e alua e he pe o mance o p edic ion app oaches using a ious
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es ima ion me hods and model pa ame e s. To compa e he es ima ed QMEDs wi h he ac ual QMED alues,
he ollowing objec i e unc ions we e used.
4.5.1 Kling-Gup a E iciency (KGE)
The undamen al assump ions ha he da a a e linea and no mal in na u e, and ha ou lie s a e no p esen in
he da ase s a e inhe en in he calcula ion o KGE. The c i e ion o KGE is based on a weigh ed a e age o he
h ee componen me ics i.e., co ela ion, bias, and a iabili y.
To compu e γ and β, he bias be ween es ima ed and obse ed mean QMEDs and he bias be ween
es ima ed and obse ed s anda d de ia ion o QMED was used, espec i ely.
𝐾𝐺𝐸=1 − √(𝑟−1)2+(𝛾−1)2+(𝛽−1)2; 𝛾= 𝑐𝑑
𝑟𝑑; 𝛽=𝑐𝑚
𝑟𝑚 8.
whe e = is he linea Pea son co ela ion coe icien be ween es ima ed and obse ed alues, m is he a e age
o obse ed alues, cm is he a e age o es ima ed alues, d is he s anda d de ia ion o obse ed alues and cd
is he s anda d de ia ion o es ima ed alues (Gup a, e al. 2009).
4.5.2 Roo Mean Squa e (RMSE)
The s anda d de ia ion o es ima ion e o s is called Roo Mean Squa e E o (RMSE). RMSE is a measu e o
how a he da a poin s a e om he eg ession line. In o he wo ds, i indica es how igh ly he da a is clus e ed
a ound he line o bes i . calcula ing he a e age o squa ed e o s Taking he esul 's squa e oo .
In o de o calcula e he RMSE, i s o all he e o is calcula ed by sub ac ing he es ima ed alues
om obse ed alues. Then he es ima ion e o s a e squa ed, a e calcula ing he mean o squa ed e o s
inally he squa e oo is compu ed o he ob ained alue, ha is:
𝑅𝑀𝑆𝐸=√∑(𝑥𝑖−𝑥
𝑖)2
𝑛
𝑖=1 𝑁 9.
whe e 𝑁 is he o al numbe o da a poin s, 𝑥𝑖 ep esen s he es ima ed alues and 𝑥𝑖 he obse ed alues.
4.5.3 Bias
The Bias indica es whe he he model has a endency o o e -o unde -p edic es ima ed alues. I is simply
calcula ed by adding all he obse ed and es ima ed alues sepa a ely and hen by di iding es ima ed alues o
he obse ed ones.
𝐵𝐼𝐴𝑆= ∑𝑥
𝑖
𝑥𝑖
𝑛
𝑖=1 10.
whe e 𝑥𝑖 a e he es ima ed alues and 𝑥𝑖 a e he obse ed alues.
5. RESULTS AND DISCUSSION
Co ela ion analysis was ca ied ou assess he co ela ion be ween QMED and ca chmen desc ip o s. Figu es 3
and 4 show he op anked desc ip o s based on hei co ela ion wi h QMED a e an ex ensi e e iew. Ano he
possible bene i o doing his analysis is ha any ou lie s and non-linea in e ac ions can also be de ec ed by
plo ing desc ip o s agains each o he in he o m o a ma ix. The pa e n obse ed he e ends o di e sligh ly
om he one epo ed in Flood Es ima ion Handbook (IH 1999) which is due o he a ailabili y o new low
eco ds. Figu e 3 shows only he desc ip o s ha we e implemen ed in FEH model (IH 1999) i.e., AREA, SAAR,
FARL, SPRHOST and BFIHOST. Fo example, he desc ip o s ha shows high co ela ion o a leas 0.6 o high
wi h QMED a e AREA, LDP (Longes D ainage Pa h) and DPLBAR (mean d ainage pa h leng h). ALTBAR,
SPRHOST, DPSBAR, and SAAR, on he o he hand, exhibi a co ela ion o 0.3 wi h QMED.
Some c oss-co ela ion can also be seen in he Figu es 3 and 4, bu i is no desi able. Only a iables
wi h low c oss-co ela ion would be included in an ideal model. The e a e wo possible easons, i s , i leads o
a g ea numbe o al e na i e model choices which all ha e compa able i s and many o which ha e poo ly
s a ed pa ame e s. Secondly, i means ha a model has a ou ed a a iable a he han ano he a iable and so
con uses he in e p e a ion (Reed and Robson, 1999). And ha is why in he o iginal FEH model ce ain
s ongly c oss-co ela ed a iables we e ede ined. Fo example, SPRHOST and BFIHOST had ela i ely high
c oss-co ela ion o 0.93 and we e bo h e y signi ican o he model, hus a new a iable RESHOST was
es ablished in place o BFIHOST, and i was econs uc ed o ha e a low co ela ion wi h SPRHOST while
e aining he in o ma ion om BFIHOST.
