P o c e d i a E n g i n e e i n g 7 0 ( 2 0 1 4 ) 1 0 9 4 – 1 1 0 1
1877-7058 © 2013 The Au ho s. Published by Else ie L d. Open access unde CC BY-NC-ND license.
Selec ion and pee - e iew unde esponsibili y o he CCWI2013 Commi ee
doi: 10.1016/j.p oeng.2014.02.121
ScienceDi ec
12 h In e na ional Con e ence on Compu ing and Con ol o he Wa e Indus y, CCWI2013
Wa e managemen solu ion o ese oi s o age unc ion unde
condi ion o measu emen unce ain ies in hyd ological inpu da a
D. Ma ona, M. S a ýa, P. Menšíka*
aB no Uni e si y o Technology, Facul y o Ci il Enginee ing, Ins . o Landscape and Wa e Managemen , B no 612 00, Czech Republic
Abs ac
The pape desc ibes a possible p ocedu e o he a e unce ain y implemen a ion o he con inuous wa e s age measu emen and
unce ain ies o s a e - discha ge a ing cu e poin posi ions, which he s age -discha ge a ing cu es we e i ed in o he
unce ain ies o he eal discha ge se ies membe s. Then he membe s o discha ge se ies unde unce ain y impac we e es ed
on he calcula ed alues o he ese oi s o age olume. The nex s ep was he implemen a ion o he unce ain ies o he eal
discha ge se ies membe s on he gene a ion o he a i icial discha ge se ies o mean mon hly discha ge using he AR and
ARMA gene a o s and he de e mina ion o hei impac on he calcula ed alues o he ese oi s o age olume.
© 2013 The Au ho s. Published by Else ie L d.
Selec ion and pee - e iew unde esponsibili y o he CCWI2013 Commi ee.
Keywo ds: Measu emen Unce ain y; Sampling Wa e S age; S age - Discha ge Ra ing Cu e; Real Discha ge Se ies; A i icial Discha ge
Se ies; Mon e Ca lo Me hod; Rese oi S o age Capaci y; AR and ARMA Models.
1. In oduc ion
Access o wa e has de e mined he de elopmen o human socie y om ancien imes. The p oblem o wa e
supply solu ion has had a long adi ion no only in he Czech Republic bu also in he wo ld. Wa e esou ces can
be gene ally di ided in o wo ca ego ies, i.e. su ace wa e esou ces and g oundwa e esou ces. A p esen he
wa e ese oi s a e he mos impo an as a s o age o su ace wa e . Wa e ese oi s se e o many pu poses. I
is especially a s o age and lood p o ec i e pu pose as well as a hyd opowe and ec ea ion pu pose and o he s.
* Co esponding au ho . Tel.: +420- 541-147-773; ax: +420-541-147-771.
E-mail add ess: [email p o ec ed]
© 2013 The Au ho s. Published by Else ie L d. Open access unde CC BY-NC-ND license.
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A ailable online a www.sciencedi ec .com
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D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
I can be expec ed ha he signi icance o wa e supply wi h su ace wa e sou ces will u he s eng hen in he
u u e. The eason is he g adual dec ease o ese es o g oundwa e esou ces which b ings he g adual expansion
o he a eas a ec ed by d ough . In he Czech Republic his e ec can be signi ican ly obse ed mainly in he
Sou he n Mo a ia egion. The e is cu en ly mo e and mo e discussed he p oblem o ein o cemen o he
impo ance o su ace wa e esou ces because g oundwa e esou ces a e mo e and mo e uns able. The main
eason is especially he g adual change in he clima e sys em and he ela ed dis ibu ion o ain all du ing he
hyd ological yea . Howe e , he su ace wa e esou ces a e no comple ely sa e. Changes in p ecipi a ion, ai
empe a u e and ai humidi y du ing he hyd ological yea will esul in a g adual change in he hyd ological
egime in he wa e shed. Acco ding o he s udy Kašpá ek e al. (2005), i is possible ha he e ec s o clima e
change and he associa ed g adual changes in he hyd ological egime in he wa e sheds, dec ease long- ange
a e age discha ge Qa in he i e ne wo k o 20 o 40 pe cen . Empowe ing s a egic signi icance o wa e
ese oi s on one hand and hyd ologic s ess on he o he hand, lead o a e i al o esea ch asks conce ned wi h
he supply and quali y o wa e in he wa e shed. Tasks ela ed o wa e managemen solu ion o s o age ese oi
unc ion, o a ese oi sys em, as well as he issues o unce ain ies o hyd ological inpu s a e cu en and jus i ied.
In he wa e managemen solu ion o he ese oi s o age unc ion he cou se o wa e in low in o he ese oi
Q( ) is he basic piece o in o ma ion (bounda y condi ion), which is ime dependen . I is possible o desc ibe his
ime sequence by ime se ies o he a e age daily, mon hly o annual low. The basis o each low se ies is he ime
cou se o discha ge Q, which is de i ed om measu emen s o he wa e s age in he Hyd ome ic gauging s a ion.
To ob ain he ac ual measu ed discha ge Q, he pieces o in o ma ion om measu emen s o wa e s age o he
sampling wa e s age hp a e necessa y as well as s age - discha ge a ing cu e, in e spe sed wi h long- e m
epea edly measu ed (Q,h) poin s. The discha ge Q is sub ac ed om he wa e s age and s age - discha ge a ing
cu e.
Sampling wa e s ages hp a e ob ained by means o epea ed eading om he measu ing de ice ins alled in he
hyd ome ic gauging s a ion (p essu e ansduce , bubble wa e le el senso ), he alues o coo dina es (Q,h) o
poin s o s age - discha ge a ing cu e o hyd ome ic gauging s a ion a e also deduced om he measu emen . I
hese alues a e ob ained by he measu emen , i is necessa y o ake in o accoun ha hey a e loaded by andom
e o s, which a ise du ing he measu emen s. Acco ding o alid cu en Eu opean o a he Czech Di ec i es and
S anda ds WECC 19/90 (1990), TPM 0051 – 93 (1993), ČSN EN ISO 748 (2001) he e has been he s anda d
de ining he e o s eme ged du ing he measu emen as he unce ain y o measu emen o many yea s.
Suppose ha du ing he whole p ocess o measu emen o he wa e le el a ises a numbe o e o s. These e o s
can be andom o sys ema ic. Random e o s a e e lec ed in o he s a is ical p ocessing o epea edly measu ed
alues and he unce ain ies measu emen ype A a e de e mined om hem. The unce ain y ype B is de e mined
indi ec ly. I means ha he measu emen s unce ain y is de e mined in ano he way han he epea ed measu ing.
Basically I is possible o ake in o accoun ha he unce ain y o ype B a e made wi h sys ema ic e o s. In his
case I Gene ally, measu emen unce ain ies de ine he a ea o possible occu ence o alues a ound he mean o
measu ed magni udes. Unce ain ies ype A a e he s anda d de ia ions o a selec i e mean; hey a e called he
s anda d unce ain ies uA. S anda d unce ain ies uA can be geome ically added oge he wi h he s anda d
unce ain ies uB in o he combined unce ain y uC. I we mul iply he combined unce ain y by coe icien k, we
ob ain he expanded unce ain ies U. All o i can be ca ied ou assuming ha he p obabili y dis ibu ion o
obse ed alues a ound he mean µ is a no mal dis ibu ion. Then he in e al 〈µ - U ; µ + U〉 de ines he a ea, in
which he obse ed alue wi h measu ed e o e ec can occu wi h he p obabili y o 95% o k = 2 and
p obabili y o 99,75% o k = 3 Palečář e al. (2001).
Taking in o accoun he unce ain y eme ging om he de e mina ion o alues o sampling wa e s ages hp and
(Q,h) poin s o s age - discha ge a ing cu e, i is i al o conside hese unce ain ies u he wi hin he de i a ion
o discha ge alues, o a he membe s o low se ies. I we de e mine hese unce ain ies, i will be possible o
make ano he s ep in he solu ion, which is hei inclusion in ela ed calcula ions o he ese oi s o age olume.
1096 D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
2. Me hods
Fo he de e mina ion o unce ain y o mean mon hly discha ges on de ices desc ibed sizes o s anda d
unce ain ies ype B uB we e used, which he p oduce indica es in he p oduc speci ica ion. The measu ed alues
o sampling wa e s ages hp wi h he ime s ep o one hou and coo dina es o (Q,h) poin s o s age - discha ge
a ing cu e we e conside ed as means μ(hp). The s anda d unce ain y uB,z was conside ed like s anda d de ia ion
σ(hp). Unce ain y measu emen was in oduced in o he solu ion using Mon e Ca lo Me hod. These assump ions
allow o look a measu ed alues like andomly de e mined alues om he in e al o possible ealiza ion, which
was always gi en as he no mal dis ibu ion N(μ(hp), σ(hp)). The esul o he epea ed gene a ion was andom
p ocessing o sampling wa e s ages Rhp a ound μ(hp) and andom (RQ,Rh) poin posi ions o s age - discha ge
a ing cu e a ound empi ical s age - discha ge cu e μ(Q,h). The p inciple o he gene a ion o andom poin
posi ions o s age - discha ge a ing cu e is indica ed in he Fig. 1.
Fig. 1. Scheme o Gene a ion o Random Posi ion (RQj,Rhj) Poin s o he Empi ical S age - discha ge Ra ing Cu e a ound Measu ed Poin s
μi(Q,h) using Mon e Ca lo Me hod.
The assessmen o andom alues o immedia e hou ly discha ges was as ollows. E e y se o andomly
gene a ed (RQ,Rh) poin s o s age - discha ge cu e was i ed by he eg ession cu e by means o so wa e
HYDROM by S a ý (1995). To each eg ession cu e andom se ies o sampling hou ly wa e s ages was assigned,
om which andom se ies o hou ly lows was deduc ed. By he epea ed p ocedu e o he selec ed numbe o
epe i ions andom se s o immedia e hou ly discha ges we e compiled. Then he immedia e hou ly discha ge
alues we e ans e ed o he mean daily discha ge alues Qd and o he alues o mean mon hly discha ges Qm.
The esul was andom sequences o a e age mon hly discha ge se ies, which ha e been u he s a is ically
e alua ed in o he ch onological s a is ical cha ac e is ics. The mean in each mon h was conside ed as he esul o
a e age mon hly discha ge. The s anda d de ia ion in each mon h σ(Qm) was conside ed as he s anda d
unce ain y o a e age mon hly discha ge uQm.
Analogically i was possible o gene a e andom sequences o eal discha ge se ies epea edly i he a e age
mon hly discha ge alues Qm and s anda d unce ain y alues uQm we e known, using Mon e Ca lo me hod. F om
each gene a ed andom eal discha ge se ies he ese oi s o age capaci y was de e mined based on he basic
ese oi equa ion (1).
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D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
()
()
∑
=
⋅−+=
n
1i
iii,mi,m0n VOQVV
Δ
(1)
whe e:
V0 … is he ini ial illing o ese oi ( ull ese oi ),
Om,i … is a e age mon hly in low o ese oi ,
Qm,i(Vi) … is con olled a e age mon hly ou low om ese oi and is subs i u ing as imp o ed ou low Op, i
ese oi doesn´ ull, o he wise Om,i = Qm,i,
Vi … is inished illing o ese oi a he end o each ime s ep Δ i,
Vn … is inished illing o ese oi a he end o he sol ed pe iod,
n … is he o de o sol ed ime s ep.
By epea ed calcula ion a se o andom s o age olumes was c ea ed, which was s a is ically e alua ed. Then
each andomly gene a ed eal discha ge se ies was used as inpu da a o epea edly gene a ing o a i icial
discha ge se ies o a e age mon hly discha ges.
Fo gene a ing o a i icial discha ge se ies om sequences o eal discha ge se ies AR and ARMA models
we e chosen. AR and ARMA models we e desc ibed by Hi sch (1979), which subsequen ly p og ammed by Pilař
(1988). Repea edly gene a ed andom sequences o a i icial discha ge se ies we e used again o calcula e supply
unc ion o he isola ed ese oi . The esul was a se o calcula ions o s o age olumes ha was e alua ed by
using app op ia e s a is ical me hods.
3. Applica ion
The applica ion was ca ied ou on he p o ile Bo o nice on he S a ka Ri e , in which hyd ome ic gauging
s a ion is si ua ed. The loca ion is si ua ed in he Vysočina Region. Da a o hyd ome ic gauging s a ion we e
p o ided by he Czech Hyd ome eo ological Ins i u e, Subdi ision B no. In he p o ile he e is he annual mean
discha ge Qa = 1.53 m3 s-1.
Fig. 2. Hyd ome ic Gauging S a ion S a ka / Bo o nice.
The annual se ies o sampling wa e s ages wi h ime s ep o one hou om 2009 and coo dina es (Q,h) o
poin s o he s age - discha ge cu e we e a ailable o he es ima ion o mean mon hly discha ge unce ain ies.
These poin s we e made by he e alua ion o hyd ome ic measu emen s. S anda d unce ain ies Type B o inpu
alues we e de e mined by he ollowing alues. The unce ain y measu emen o wa e s ages has been speci ied
1098 D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
o he loa measu ing de ice LU 503 G o size uB, hp = ± 0.133% o eading alues. The size o unce ain y was
ob ained om he echnical documen a ion o his de ice. The unce ain y o eading on he e ical line a
hyd ome e ing has a alue o ub,h = ± 0.166 cm om he measu ed alues. The unce ain y o discha ge a e
ob ained by e alua ing o hyd ome ic measu emen s co esponded o he alue o ub,Q = ± 2.0% (UQ = ± 6.0%).
The alue was ob ained by means o gene aliza ion o calcula ions using he HYDROS so wa e by S a ý (1991).
Fo Mon e Ca lo me hod he numbe o epe i ions NR = 300 was chosen.
Pa ial esul s o he unce ain y calcula ion a e age mon hly discha ges a e illus a ed in he se o h ee g aphs,
in which he e is a g aphical ep esen a ion o he s age - discha ge a ing cu e in hyd ome ic gauging s a ion
Bo o nice, whe e in he g aph a) is shown he p og ess o he measu ed alues o empi ical measu emen o poin s
o s age - discha ge cu e including hei i ing by he heo e ical cu e. The heo e ical cu e was cons uc ed by
combining wo eg ession unc ions, polynomial-powe unc ions. G aph b) shows posi ions o andomly
gene a ed (Q,h) poin s by Mon e Ca lo me hod o he epe i ion NR = 300. Posi ions o gene a ed poin s lie
a ound he a ea o measu ed alues, which a e lis ed in he g aph a). G aph c) shows he i ed s age - discha ge
a ing cu es co esponding o andom se s o (RQ,Rh) poin s o NR = 300.
Fig. 3. S age - discha ge Cu e C ea ed om Real Measu ed Values and G oup o S age - discha ge Cu es when Re lec ing Unce ain ies o
(Q,h) Poin s in P o ile S a ka/Bo o nice.
Table 1 shows he esul s o magni ude o he unce ain y a e age mon hly discha ges, which we e de i ed by
he desc ibed p ocedu e om andom sequences o hou ly wa e s ages and andomly assigned s age - discha ge
a ing cu es.
Table 1. S a is ical Cha ac e is ics o he A e age Mon hly Discha ges Qm Bu dened by Measu emen Unce ain y.
Janua y Feb ua y Ma ch Ap il May June July Augus Sep embe Oc obe No embe Decembe
μ(Qm)
[m3/s]
1.6 1.407 6.087 3.087 0.737 1.178 2.082 0.813 0.426 1.136 1.254 2.218
uQm
= σ(Qm)
[m3/s]
0.0107 0.0066 0.0563 0.0204 0.0048 0.004 0.011 0.0035 0.0018 0.0054 0.0058 0.0122
uQm [%] 0.669 0.469 0.925 0.661 0.651 0.340 0.528 0.431 0.423 0.475 0.463 0.550

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D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
Using he abo e men ioned esul s, he a e o s anda d unce ain ies o a e age mon hly discha ges uQ was
es ima ed. The de e mined unce ain ies om he Table 1. we e used o each mon h om 30-yea eal discha ge
se ies, which was he basis o he calcula ion o he s o age capaci y o he ic i e ese oi . The sol ed s o age
capaci y is de e mined depending on he imp o ed ou low Op and i s hyd ological eliabili y P, which is equal o
P = 100%. Gene a ing o eal and syn he ic discha ge se ies o a e age mon hly discha ges including he
calcula ion o ese oi s o age capaci y was made by UNCE-V so wa e by Ma on and S a ý (2012). Fo
gene a ing o a i icial discha ge se ies we e used gene a o s o ype LTAR (log - ans o med, Au o eg esi e
Model) and LTMA (log - ans o med, Mo ing A e age Model). The leng h o he gene a ed a i icial discha ge
se ies was de e mined o 10,000 yea s.
The ollowing ables show he size o he ese oi s o age capaci y Vz o he changing imp o ed ou low Op
alue and i s co esponding absolu e and ela i e size o he s anda d unce ain ies uVz and expanded unce ain ies
UVz. When expanded unce ain y is calcula ed o coe icien k = 3. The coe icien α is de ined as ollows
α=Op/Qa. Whe e Op is imp o ed ou low om ese oi and Qa is long- ange a e age discha ge.
The esul s o he calcula ion o unce ain ies o ese oi s o age capaci y pe o med by using andom
sequences o eal discha ge se ies we e p ocessed in Table 2.
Table 2. Unce ain ies o Rese oi S o age Capaci y, Calcula ion in he Random Sequences o Real Discha ge Se ies.
α 0.2 0.3 0.4 0.5 0.6 0.7
Op [m3 s-1] 0.306 0.459 0.612 0.765 0.918 1.071
μ(Vz) [m3] 1 068 219 2 806 661 5 165 432 7 579 770 9 994 109 15 803 573
uVz= σ(Vz) [m3] 4 207 7 050 10 123 10 122 10 122 44 120
UVz [m3] 12 621 21 150 30 368 30 366 30 366 132 360
uVz = σ(Vz) [%] 0.394 0.251 0.196 0.134 0.101 0.279
UVz [%] 1.181 0.754 0.588 0.401 0.304 0.838
The esul s o he calcula ion o unce ain ies o ese oi s o age capaci y pe o med by using andom
sequences o a i icial discha ge se ies gene a ed by LTAR gene a o we e p ocessed in Table. 3.
Table 3. Unce ain ies o Rese oi S o age Capaci y, Calcula ion in he Random Sequences o A i icial Discha ge
Se ies - LTAR Gene a o .
α 0.2 0.3 0.4 0.5 0.6 0.7
Op [m3 s-1] 0.306 0.459 0.612 0.765 0.918 1.071
μ(Vz) [m3] 1 904 002 5 150 868 8 497 199 15 720 905 32 631 340 59 591 484
uVz= σ(Vz) [m3] 10 069 11 522 13 268 56 030 181 391 181 391
UVz [m3] 30 206 34 567 39 805 168 090 544 173 544 172
uVz = σ(Vz) [%] 0.529 0.224 0.156 0.356 0.556 0.304
UVz [%] 1.586 0.671 0.468 1.069 1.668 0.913
The esul s o he calcula ion o unce ain ies o ese oi s o age capaci y pe o med by using andom
sequences o a i icial discha ge se ies gene a ed by LTMA gene a o we e p ocessed in Table 4.
1100 D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
Table 3. Unce ain ies o Rese oi S o age Capaci y, Calcula ion in he Random Sequences o A i icial Discha ge
Se ies - LTMA Gene a o .
α 0.2 0.3 0.4 0.5 0.6 0.7
Op [m3 s-1] 0.306 0.459 0.612 0.765 0.918 1.071
μ(Vz) [m3] 2 565 124 6 186 623 12 630 862 23 997 166 37 998 040 71 329 584
uVz= σ(Vz) [m3] 9 237 9 241 64 044 72 420 134 711 281 753
UVz [m3] 27 711 27 723 192 133 217 261 404 134 845 259
uVz = σ(Vz) [%] 0.360 0.149 0.507 0.302 0.355 0.395
UVz [%] 1.080 0.448 1.521 0.905 1.064 1.185
4. Summa y and Conclusion
The heo e ical desc ip ion o he gene a ion o andom sequences o sampling hou ly wa e s ages and posi ion
(Q,h) poin s o s age - discha ge a ing cu e, including hei in eg a ion in o he eal discha ge se ies and ela ed
ese oi s o age capaci y calcula ions we e desc ibed in o de ails in a icle Ma on e al. (2011) and in he
Doc o al Thesis (Ma on, 2011).
In he pape he e is ou lined he p ocedu e o inco po a ion o measu emen unce ain ies o sampling wa e
s ages and posi ion (Q,h) poin s o s age - discha ge a ing cu e in o he se ies o a e age mon hly discha ges.
Nowadays, his piece o in o ma ion is no speci ied in he common p ac ice and e en he in e als in which he
unce ain y o he a e age mon hly discha ges can mo e is no known. The a icle shows how hese unce ain ies
can be g asped and inco po a ed in o ollow-up wa e managemen calcula ions. No only in o he ese oi s o age
capaci y calcula ion de e mined om eal discha ge se ies, bu also hei inco po a ion in o he gene a ing o
a i icial discha ge se ies. These ones se e as an ex ended hyd ological ounda ion in he design o assessmen o
he ese oi s o age capaci y wi h a high demand on i s hyd ological eliabili y. The esul s p esen ed in he pape
show ha unce ain ies o mon hly discha ges in he hyd ome ic gauging s a ion S a ka/Bo o nice a e a iable
mon h by mon h and mo e in an in e al o s anda d unce ain y uQm om ±0,34% o ±0,925%, ex ended
unce ain y om UQm = ±1.02% o UQm = ±2,775%. The alue o a e age s anda d unce ain y uQm de e mined
om mon hly alues o e he yea uQm = ± 0.549%, which co esponds o he expanded unce ain y
UQm = ± 1.647%.
The UNCE-V so wa e allows o in eg a e he unce ain y in o he calcula ions ei he as absolu e alues by
s anda d de ia ions σ(Qm), o as ela i e alues by he coe icien o a ia ion C (Qm). So wa e is able o in eg a e
he unce ain ies also as a cons an alue o he whole pe iod o solu ions, o as a iable alues o each mon h. In
ou case measu emen unce ain ies we e in eg a ed in o he eal and a i icial discha ge se ies o a e age mon hly
discha ges a iably, sepa a ely o each mon h. I means ha each mon h co esponded one alue o he ela i e
unce ain y e e ed o in Table 1.
Unce ain ies o ese oi s o age capaci y de e mined om eal and a i icial discha ge se ies ha e been
changing wi h inc easing imp o ed ou low Op. In e ms o absolu e alues o he unce ain y i is possible o see
he inc ease o unce ain y wi h he co esponding inc ease o imp o ed ou low Op and ese oi s o age capaci y
Vz. E en i he e a e some cases ha occu in he esul s when he alues o absolu e unce ain y o ese oi
s o age capaci y do no change wi h he inc easing alue o imp o ed ou low Op. This phenomenon is caused by
he me hod o he ese oi s o age capaci y calcula ion, which esul s om basic equa ion o ese oi in he
summa i e o m. I can be gene ally s a ed ha he a e age ela i e s anda d and ela i e ex ended unce ain y o
he ese oi s o age capaci y a ies on he alues uVz = ±0.263% and UVz = ±0.789 % a he s o age capaci y
de e mined om eal discha ge se ies. The s anda d unce ain y in he ese oi s o age capaci y de e mined om
a i icial discha ge se ies o gene a o LTAR was uVz = ± 0.483% and he expanded unce ain y was
U Vz = ± 1.449% o he gene a o LTMA was s anda d unce ain y uVz = ± 0.391% and he expanded unce ain y
was UVz = ± 1.174%.
The abo e-men ioned esul s should be accep ed. The ques ion is how o p esen he esul s o unce ain ies o
he ese oi s o age capaci y o a he wha way o he implemen a ion o unce ain ies is gene ally accep able.
1101
D. Ma on e al. / P ocedia Enginee ing 70 ( 2014 ) 1094 – 1101
F om he esul s i is ob ious ha he impac o unce ain ies o membe s o eal and a i icial discha ge se ies on
he alues o ese oi s o age capaci y is no insigni ican . So how he indi idual inpu se ies a e implemen ed
in o he solu ion by Mon e Ca lo me hod no only by means o one alue, bu he ange o andomly gene a ed
inpu se ies, also he calcula ed s o age olume is desc ibed by he ange o s o age olumes whose ange o sca e
is signi ican . Cu en ly, he used hyd ological eliabili y o solu ions (assu ance o imp o ed ou low om he
ese oi ) in he Czech s anda ds is ecommended o conside he alues om 95% o 99.5% (acco ding o he
impo ance o he wa e use o he socie y). I is ob ious ha he ou lined p ocedu e will s ongly de o m ac ually
achie ed hyd ological eliabili y o he solu ion. The abo e-men ioned p oblem could be a oided by he ac ha
om he spec um o s o age capaci ies only he highes s o age capaci y will be conside ed which co esponds o
he unce ain y UVz ha will be conside ed as alue μ(Vz) + UVz. Ob iously, mo e accu a e solu ion is an
in oduc ion o unce ain ies o he p ima y inpu s di ec ly in o he solu ion wi h using he di e en ypes o wa e
managemen solu ion s o age ese oi unc ion when conside ing he hyd ological eliabili y less han 100% and
dealing wi h i by ou lined wo king p ocess.
The desc ibed me hod o he unce ain y inco po a ion in o he de e mina ion o alues o he a e age mon hly
discha ges as well as i s ollow-up implemen a ion in o he ela ed calcula ions o he ese oi s o age capaci y is
uni e sal. I can be used a a ious hyd ome ic gauging s a ion and di e en ypes o measu ing ins umen s
which measu ing o wa e s ages and discha ges is ealized wi h. Cu en ly, he men ioned p ocedu e o de i ing
he unce ain y o a e age mon hly discha ge is based on he use o mo e algo i hms and he calcula ion is ime
consuming. The au ho s y o au oma ize he whole p ocess o he calcula ion mo e so ha he calcula ions could
be mo e e ec i e and applicable o o he hyd ome ic gauging s a ion wi h a ying wa e bea ing and he leng h
measu emen .
Acknowledgemen s
This pape was suppo ed by he p ojec “CZ.1.07/2.3.00/30.0039 Excellen young esea che s a B no
Uni e si y o Technology” o B no Uni e si y o Technology and i was he esul o speci ic esea ch p ojec
“FAST-S-12-19 Wa e supply and hyd opowe unc ion o ese oi sys em unde condi ion o unce ain y inpu
hyd ological da a”.
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