Handouts on Data-driven modelling, part 1 (UNESCO-IHE)

7/31/2019 Handouts on Data-driven modelling, part 1 (UNESCO-IHE)

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BdrdBdrd ++bpgumobpgumokcbmaagojkcbmaagojgo zdrmpgo zdrmp++pmadrmb |pc`amky/pmadrmb |pc`amky/

\DPR 4\DPR 4

Bgkgrpg \/ Ycackdrgom

zzz/ghm/oa#hg#yca ycaLghm/oa

]OMYIC+GHM Goyrgr}rm ecp Zdrmp Mb}idrgco

Hwbpcgoecpkdrgiy Ihdgp

B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 0

C}ragom ce rhm ic}pymC}ragom ce rhm ic}pym

Ocrgco ce bdrd+bpgumo kcbmaagoj (BBK'Yc}pimy ce rmihocacjgmy ecp BKK6 kdihgom amdpogoj! bdrd kgogoj! ycerick|}rgojGorpcb}irgco rc kmrhcby6 bmigygco! pmjpmyygco dob kcbma rpmmy!

@dwmygdo d||pcdihmy! om}pda omrzcpny! e}vvw ywyrmky! ihdcrgiywyrmkyBmkcoyrpdrgco ce d||agidrgcoy Pmympucgp c|rgkgvdrgco Pdgoedaa+p}ocee kcbmaagoj Pmda+rgkm icorpca ce zdrmp amumay go rhm |cabmp dpmdy y}pjm zdrmp amuma |pmbgirgco go rhm Ocprh Ymd gormp|pmrdrgco ce dmpgda |hcrcy


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Zhw bdrdZhw bdrd ++bpgumo ocz3bpgumo ocz3

Kmdy}pgoj idk|dgjoy }ygoj d}rckdrgi ick|}rmpgymb mt}g|kmor6 d acrce bdrd `midkm dudgad`amgk|cprdor `pmdnrhpc}jhy go ick|}rdrgcoda gormaagjmoim dob kdihgomamdpogoj kmrhcby|momrpdrgco ce ick|}rmp yigmoimy gorc iguga mojgommpgoj (m/j/!hwbpcgoecpkdrgiy! jmc+goecpkdrgiy mri/'


Hwbpcgoecpkdrgiy ywyrmk6Hwbpcgoecpkdrgiy ywyrmk6rw|gida dpihgrmir}pmrw|gida dpihgrmir}pm

Bdrd! goecpkdrgco!noczambjm\hwygidaaw+`dymb

kcbmay

Bdrd+bpgumokcbmay

Bmigygco y}||cpr ywyrmky ecp kdodjmkmor

Pmda zcpab

Ickk}ogidrgcoy

]ymp gormpedim

Edir mojgomy

F}bjmkmor mojgomy

Noczambjm+`dymywyrmky

Noczambjm goempmoimmojgomy


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ =

KcbmaagojKcbmaagoj

Kcbma gy d ygk|agegmb bmyipg|rgco ce pmdagrw do moid|y}adrgco ce noczambjm d`c}r d |dprgi}adp |hwygida cp ycigda

|pcimyy go mamirpcogi ecpk

Jcday ce kcbmaagoj dpm6 }obmpyrdob rhm yr}bgmb ywyrmk cp bckdgo (}obmpyrdob rhm |dyr' |pmbgir rhm e}r}pm

|pmbgir rhm e}r}pm uda}my ce yckm ce rhm ywyrmk udpgd`amy! `dymb co rhmnoczambjm d`c}r crhmp udpgd`amy

}ym rhm pmy}ary ce kcbmaagoj ecp kdngoj bmigygcoy (ihdojm rhm e}r}pm'


Iadyygegidrgco ce kcbmayIadyygegidrgco ce kcbmay

y|migegi + jmompdakcbma myrgkdrgco + egpyr |pgoig|amy kcbmayo}kmpgida + dodawrgidayrcihdyrgi + bmrmpkgogyrgikgipcyic|gi + kdipcyic|gibgyipmrm + icorgo}c}yt}dagrdrgum + t}dorgrdrgum


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ :

Mxdk|am ce d ygk|am bdrdMxdk|am ce d ygk|am bdrd ++bpgumo kcbmabpgumo kcbma

gobm|mobmor udpgdàm X (go|}r'dob bm|mobmor udpgdàm W (c}r|}r'agomdp pmjpmyygco pc}jhaw bmyipg`myrhm c`ympumb pmadrgcoyhg||dpdkmrmpy d4 dob d 0 dpm }onoczodob dpm ec}ob `w emmbgoj rhm kcbmazgrh bdrd dob ycaugoj doc|rgkgvdrgco |pcàmk (rpdgogoj'

rhm kcbma rhmo |pmbgiry c}r|}r ecprhm omz go|}r zgrhc}r dir}danoczambjm ce zhdr bpgumy W

Agomdp pmjpmyygco kcbmaW ; d 4 X . d 0

X

W

omz go|}ruda}m

dir}dac}r|}ruda}m

kcbma |pmbgiryomz c}r|}ruda}m


Bdrd6 drrpg`}rmy! go|}ry! c}r|}ryBdrd6 drrpg`}rmy! go|}ry! c}r|}ry

ymrN ce mxdk|amy (cp goyrdoimy'pm|pmymormb `w rhm b}|am 1x n ! wn ?! zhmpm n ; 4!! N !umircp x n ; ~ x 4!! x o {n ! umircp wn ; ~ w 4!! w k {n !o ; o}k`mp ce go|}ry! k ; o}k`mp ce c}r|}ry/Rhm |pcimyy ce `}gabgoj d e}oirgco ( kcbma' w ; e (x ' gy idaambrpdgogoj /Cermo coaw com c}r|}r gy icoygbmpmb! yc k ; 4/

Kmdy}pmb bdrd Drrpg`}rmyGo|}ry C}r|}r

G oyrdoimy x 4 x 0 x o w

Goyrdoim 4 x 44 x 40 x 4o w 4Goyrdoim 0 x 04 x 04 x 0 o w 0

Goyrdoim N x N 4 x N 0 x N o w N

Kcbma c}r |}rw& ; e (x '

w &

w 4& w 0&

w N &


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BdrdBdrd ++bpgumo kcbmabpgumo kcbma

BBK amdpoy rhmrdpjmr e}oirgco W; e (X' bmyipg`goj hcz rhm pmdaywyrmk `mhdumyAmdpogoj ; |pcimyy ce kgogkgvgoj rhm bgeempmoim `mrzmmo c`ympumb bdrddob kcbma c}r|}r/ X dob W kdw `m oco+o}kmpgi

Dermp amdpogoj! `mgoj emb zgrh rhm omz go|}ry! BBK ido jmompdrm c}r|}riacym rc zhdr rhm pmda ywyrmk zc}ab jmompdrm

Go|}r bdrdKcbmaamb

(pmda'ywyrmk

X

Dir}da (c`ympumb'c}r|}r W

Kdihgomamdpogoj

(bdrd+bpgumo'kcbma \pmbgirmb c}r|}r W

Amdpogoj gy dgkmbdr kgogkgvgoj rhgy

bgeempmoim

B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 4`}gab rhm kcbma


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Bdrd |pm|dpdrgco pmy}ary go6Bdrd |pm|dpdrgco pmy}ary go6

rpdgogoj bdrd ymr + pdz bdrd gy |pmymormb go d ecpk omimyydpw rc rcrpdgo rhm BBK>ipcyy+udagbdrgco bdrd ymr + ommbmb rc bmrmir cumprpdgogoj>rmyrgoj! cp udagbdrgco bdrd ymr + gr gy ommbmb rc udagbdrm (rmyr' rhmkcbma*y |pmbgirgum |mpecpkdoim>dajcpgrhky dob ycerzdpm rc |mpecpk |pm+|pcimyygoj (mj/!ocpkdagvdrgco'>dajcpgrhky dob ycerzdpm rc |mpecpk |cyr+|pcimyygoj (mj/!bmocpkdagvdrgco'/


Gk|cprdor yrm|y go bdrd |pm|dpdrgcoGk|cprdor yrm|y go bdrd |pm|dpdrgco

Pm|adim kgyygoj! mk|rw! godii}dpdrm uda}myHdobam gyy}m ce y|drgda dob rmk|cpda pmyca}rgcoAgomdp yidagoj dob ocpkdagvdrgcoOco+agomdp rpdoyecpkdrgcoyRpdoyecpk rhm bgyrpg`}rgcoyRgkm ympgmy6 Ec}pgmp dob zdumamr rpdoyecpky Gbmorgegidrgco ce rpmob! ymdycodagrw! iwamy! ocgym Ykccrhgoj bdrdEgobgoj pmadrgcoyhg|y `mrzmmo drrpg`}rmy (mj/ icppmadrgco! dumpdjmk}r}da goecpkdrgco + DUG'Bgyipmrgvgoj o}kmpgi drrpg`}rmy gorc ~acz! kmbg}k! hgjh{Bdrd pmb}irgco (\pgoig|da ick|comory dodawygy + \ID'


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 2=

Mxdk|am6 pdz bdrd ymrMxdk|am6 pdz bdrd ymr


Mxdk|am6 ocpkdagvdrgco dob pmbgyrpg`}rgcoMxdk|am6 ocpkdagvdrgco dob pmbgyrpg`}rgco


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 2:

Pm|adigoj kgyygoj dob mk|rw uda}myPm|adigoj kgyygoj dob mk|rw uda}my

Zhdr rc bc zgrh rhm c}ragmpy3 Hcz rc pmicoyrp}ir kgyygoj uda}my3Myrgkdrcp gy d bmugim (dajcpgrhk' }ymb rc kdnm d f}yrgegdàm j}myyd`c}r rhm uda}m ce yckm |dprgi}adp udpgdàm! rhdr gy! rc |pcb}im domyrgkdrm]o`gdymb myrgkdrcp gy d kmrhcb ce j}myygoj rhdr bcmy ocr ihdojmgk|cprdor ihdpdirmpgyrgiy ce rhm bdrd ymr zhmo rhm myrgkdrmy dpmgoia}bmb zgrh rhm mxgyrgoj uda}myMxdk|am6 Bdrdymr 4 0 9 x = Myrgkdrcpy6

0/:=2/5=7! ge rhm yrdobdpb bmugdrgco gy rc `m }o`gdymb>2/

Gyy}m ce y|drgda dob rmk|cpda pmyca}rgcoGyy}m ce y|drgda dob rmk|cpda pmyca}rgco

Mxdk|amy6 go d hdp`c}p ymbgkmordrgco gy kmdy}pmb coim go rzc zmmny dr com

acidrgcoy dob coim d kcorh dr crhmp rzc acidrgcoy! dob omump dr crhmp(kdw`m gk|cprdor' acidrcoy

go d idrihkmor rhm pdgoedaa bdrd rhdr zdy kdo}daaw icaamirmb dr d rhpmmjd}jgoj yrdrgcoy ecp 0< wmdpy coim d bdw! dob 9 wmdpy djc rhmkmdy}pmkmory yrdprmb dayc dr 2 omz d}rckdrgi yrdrgcoy dy zmaa! zgrh rhmhc}paw epmt}moiw

Yca}rgcoy6 egaagoj+go kgyygoj bdrd gorpcb}igoj do dprgegigda pmyca}rgco `mgoj mt}da rc rhm kdxgk}k ecp daa

udpgdàmy


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Agomdp yidagoj dob ocpkdagvdrgcoAgomdp yidagoj dob ocpkdagvdrgco

Jmompda ecpk6x* g ; d x g . `

rc nmm| bdrd |cygrgum6x* g ; x g . kgo (x 4 ///x o ' . YkdaaIcoyr

Yt}dyhgoj bdrd gorc rhm pdojm ^

'///kgo('///kdx(

'///kgo(

44

4

oo

og

g x x x x

x x x x

;

B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ =ym|dpdrm agomdp kcbmay ido `m `}gar

ecp mdih ce rhm gormpuday


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Kcbma 4 Kcbma 0

Wmy Oc

x4 ? 0/= x4 1 2

x0 1 9/=

x0 ? 0

Wmy Oc

Wmy Oc

Kcbma 9 Kcbma 2

Wmy

Kcbma = Kcbma 5

x0 1 4

Wmy Oc

Oc

Pmjpmyygco dob K= kcbma rpmmy6 `}gabgoj rhmk go 0BPmjpmyygco dob K= kcbma rpmmy6 `}gabgoj rhmk go 0B

Rpmm yrp}ir}pm zhmpm ocbmy dpm y|agrrgoj icobgrgcoy amdumy dpm6

icoyrdory ( pmjpmyygco rpmm'agomdp pmjpmyygco kcbmay ( K= kcbma rpmm'

X4

Kcbma 0

Kcbma 4

Kcbma 5Kcbma 2

Kcbma 9

Kcbma =

X0

W (c}r|}r'4 0 9 2 = 5

4

0

9

2go|}r y|dim X 4X0 gy y|agr gorc pmjgcoy>ym|dpdrm pmjpmyygco kcbmay ido `m `}gar

ecp mdih ce rhm pmjgcoy

Mxdk|am ce Kcbma 46+ go d pmjpmyygco rpmm6

W ; 4


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Kmdy}pmy rc gk|pcum |mpecpkdoim ce kcbma rpmmyKmdy}pmy rc gk|pcum |mpecpkdoim ce kcbma rpmmy

ykccrhgoj6 ykccrhgoj |pcimyy gy }ymb rc ick|moydrm ecp rhm yhdp| bgyicorgo}grgmy

`mrzmmo dbfdimor agomdp kcbmay

|p}ogoj (ygvm pmb}irgco' + ommbmb zhmo d adpjm rpmm cumpegry rhm bdrd6 d y}`rpmm gy pm|adimb `w com agomdp kcbma


Pmjpmyygco dob kcbma rpmmy go o}kmpgida |pmbgirgco6Pmjpmyygco dob kcbma rpmmy go o}kmpgida |pmbgirgco6yckm d||agidrgcoyyckm d||agidrgcoy


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 44=

Rpmmy dob p}amy6 goea}moim ce ycga hd`grdr co doRpmmy dob p}amy6 goea}moim ce ycga hd`grdr co do

Icaamk`cad Icaamk`cad d|rmpgjcrd d|rmpgjcrd (do goymir'(do goymir'

Goea}moim ce ycga hd`grdr emdr}pmy co rhm d`}obdoim ce Icaamk`cad d|rmpgjcrd (do goymir' (Ndk|gihamp! Bvmpcyng' + pmjpmyygco dob kcbmarpmmy go|}ry6 egmab rw|m! kgipc`gda pmy|gpdrgco! kgipc`gda `gckdyy! ycga kcgyr}pm!

dandagogrw (|H'! idp`co! ogrpcjmo! kmbgdo |dprgiam ygvm c}r|}ry6 rcrda o}k`mp ce icaamk`cado gobgugb}day (d`}obdoim'! rcrda

o}k`mp ce icaamk`cado y|migmy (`gcbgumpygrw'! o}k`mp ce gobgugb}day ce Ecayckgd t}dbpgci}adrd (d |dprgi}adp rw|m ce Icaamk`cad '

kmrhcby ick|dpmb6 agomdp pmjpmyygco (hgjhmyr mppcp'! pmjpmyygco dobkcbma rpmmy! om}pda omrzcpny (amdyr mppcp'


Pmjpmyygco rpmmy6Pmjpmyygco rpmmy6|pmbgirgco ce |pmbgirgco ce Icaamk`cad Icaamk`cad |c|}adrgco|c|}adrgco

Go dii}pdiw `mrrmp rhdo agomdp pmjpmyygco Umpw mdyw rc gormp|pmr


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B/\/ Ycackdrgom/ Bdrd+bpgumo kcbmaagoj (|dpr 4'/ 44:

K= kcbma rpmmy6K= kcbma rpmmy6

|pmbgirgco ce |pmbgirgco ce Icaamk`cad Icaamk`cad |c|}adrgco|c|}adrgco

Go dii}pdiw d `gr zcpym rhdo DOO@}r umpw mdyw rc gormp|pmr


K= rpmm go PdgoedaaK= rpmm go Pdgoedaa++p}ocee kcbmaagoj (p}ocee kcbmaagoj ( H}dgH}dg pgump! Ihgod'pgump! Ihgod'

Egoda kcbma ecp rhm eaccb ymdyco6C}r|}r6 bgyihdpjm rhm omxr bdw TX r.4Go|}ry6 \d r \d r+4 \dKcu0 r \dKcu0 r+4

TI r TI r+4 TX r Rmihogt}my }ymb6 K= kcbma rpmmy! DOO

Kcbma yrp}ir}pm6T r.R ; E (P r P r+4 P r+A T r T r+4 T r+D T r }| T r+4 }| '

Udpgd`amy icoygbmpmb C}r|}r6 |pmbgirmb bgyihdpjm TX r.4Go|}ry (zgrh bgeempmor rgkm adjy'6+ bdgaw dpmda pdgoedaa (\d '+ kcugoj dumpdjm ce bdgaw dpmda pdgoedaa (\dKcu '+ bgyihdpjmy (TX ' dob }|yrpmdk ( TI '

Ykccrhmb udpgd`amy hdum hgjhmp icppmadrgco icmee/zgrh rhm c}r|}r! m/j/ 0+bdw+kcugoj dumpdjm ce pdgoedaa (\dKcu0 r '

Bdrd (47:5+4775' Bdgaw bgyihdpjmy (TX! TI 'Bdgaw pdgoedaa dr 4: yrdrgcoyBdgaw mud|cpdrgco ecp 42 wmdpy

(47:5+4787' dr 9 yrdrgcoyRpdgogoj bdrd6 47:5+87Ipcyy+udagb/ % rmyrgoj6 477


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Pmy}argoj K= kcbma rpmm zgrh : kcbmay (Pmy}argoj K= kcbma rpmm zgrh : kcbmay ( H}dgH}dg pgump'pgump'TXr 1; 4=2 6

q \dKcu0r 1; 2/= 6 AK4 (4277#2/85-'q \dKcu0r ? 2/= 6q q \dKcu0r 1; 48/= 6 AK0 (94=#4=/7-'q q \dKcu0r ? 48/= 6 AK9 (74#85/7-'TXr ? 4=2 6q \dKcu0r+4 1; 49/= 6q q \dKcu0r 1; 2/= 6 AK2 (9::#4=/7-'q q \dKcu0r ? 2/= 6 AK= (4


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Go|}ry6PMr! PMr+4! PMr+0!PMr+9!T r!T r+4(pdgoedaa ecp 9|dyr hc}py!p}ocee ecp 0'

DOO umpgegidrgcoPKYM;44/9=9OPKYM;


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Mob ce |dpr 4Mob ce |dpr 4

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Handouts on Data-driven modelling, part 1 (UNESCO-IHE)