Impact of the calibration period on the conceptual rainfall-runoff model parameter estimates

Geophysical Research Abstract

Approximating optimal transport with linear programs

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation algorithms for optimal transport.Comment: To appear in SOSA 201

Neizvesnosti u analizi velikih voda metodom parcijalnih serija

In hydrologic practice, flood frequency analysis is usually based on fitting a theoretical distribution to observed data series. Flood frequency analysis in hydrologic practice is essentially based on fitting of a theoretical probability distribution to observed flood data, meaning that the results of the flood frequency analysis is always associated with some amount of uncertainty. For flood frequency analysis that is based on series of annual maximum floods, uncertainties have been investigated in detail and can be readily found in literature on hydrologic statistics. On the other hand, that is not the case with uncertainties in flood frequency analysis based on partial duration series (or peaks over threshold method). The paper describes briefly the peaks over threshold method, and then discusses uncertainties in its application. Uncertainties in quantile estimates and in probability estimates for fixed flood value are considered. Factors affecting these uncertainties are described, including sample size, shape parameters of distributions for exceedances, and parameter estimation method. Several examples showing uncertainties in flood series on Serbian rivers are presented.U hidrološkoj praksi statistička analiza velikih voda zasniva se prevashodno na prilagođivanju teorijske raspodele verovatnoće osmotrenim podacima, što znači da su rezultati analize velikih voda uvek povezani sa određenim neizvesnostima. Neizvesnosti u statističkoj analizi velikih voda koja se zasniva na nizovima godišnjih maksimuma protoka su detaljno izučene i opisane su u stručnoj literaturi iz hidrološke statistike. S druge strane, to nije slučaj sa analizom velikih voda koja se zasniva na metodi pikova, odnosno na parcijalnim serijama. U ovom radu prikazana je ukratko metoda parcijalnih serija, a zatim su razmatrane neizvesnosti u primeni ove metode. Opisani su faktori koji utiču na neizvesnosti, uključujući uticaje dužine niza, vrednosti parametara i vrste metode za ocenu parametara

Analiza rizika od poplava pomoću prekidnih slučajnih procesa

Probabilističko opisivanje veli¬kih voda ima važnu ulogu u hidrotehničkim i vodoprivrednim studijama i projektima koji se bave rizikom od poplava. Osnovni alat za ovaj zadatak je statistička analiza velikih voda, kojom se za određeni protok velike vode vezuje njegova verovatnoća pojave. U tim analizama postoje neizve¬snosti koje najvećim delom potiču od nedovoljnih raspoloživih podataka osmatranja i nepoznavanja raspodele verovatnoće velikih voda. Ove neizvesnosti se ne mogu izbeći, ali je njihovo poznavanje veoma značajno kako bi se omogućilo da se sagledaju ograničenja projektovanih rešenja ili da se, uzimanjem neizvesnosti u obzir, dođe do boljih rešenja. Fokus disertacije su neizvesnosti u oceni velikih voda metodom prekoračenja preko praga (POT metoda), koja je zasnovana na prekidnim slučajnim procesima i predstavlja alter¬nativu standardnom postupku statističke analize godišnjih maksimuma protoka. Iako se ova metoda povremeno nalazila u fokusu istraživača, do sada nije postojalo si¬stematsko razmatranje njene efikasnosti sa gledišta neizvesnosti. Rezultati retkih prethodnih istraživanja nisu bili opšteg karaktera i bili su ograničeni na pojedine slučajeve metode POT. U okviru ove disertacije sistematizovana su dosa¬dašnja saznanja u određi¬vanju neizvesnosti velikih voda metodom POT i izvr¬šeno je vrednovanje odre¬đe¬nih pretpostavki u postupcima proračuna. Obuh¬va¬ćeni su svi relevantni modeli par¬ci¬jalnih serija i postavljen je jedinstven originalni mate¬matički okvir za izvođenje izraza za pokazatelje neizvesnosti u oceni kvantila i verovatnoće velikih voda (pristrasnost, standardna greška, interval poverenja kvantila velikih voda). Metodologija je ilustrovana na većem broju primera uz diskusiju o primenljivosti i efi¬kasnosti pojedinih modela. Disertacija dakle predlaže zaokruženu metodolo¬gi¬ju za celovitu probabilističku analizu velikih voda pomoću metode POT.Probabilistic characterisation of floods is an important task in water resources management studies and projects addressing flood risks. Main tool for this task is the flood frequency analysis, by which a probability of occurrence is attributed to a ceratin flood flow. A range of uncertainties is inherent in the flood frequency analysis, mostly stemming from limited observational data and lack of knowledge on parent probability distributions. These uncertainties cannot be avoided, but knowing their rainges is very important so that they could be considered in the planning and design process. The focus of the dissertation are the uncertainties in flood frequency assessment by the peaks over threshold (POT) method (or partial duration series method), which is founded in the intermittent stochastic processes and represents an alternative to the standard flood frequency analysis of annual maximum floods. Although the POT method has been occasionally in the focus of hydrologic research, there has been no systematic consideration of its efficiency in terms of uncertainties. Results of rare previous studies were not generalized and were limited to particular cases of the POT method. Within this dissertation, the existing knowledge on uncertainties in floods estimated by the POT method has been systematized and certain assumptions in the calculation procedures have been evaluated. All pertinent POT models used in practice are analysed and the consistent and original mathematical framework for deriving analytical expressions for uncertainty measures (bias, standard errors and confidence intervals of flood quantiles) in the flood frequency estimation is developed. The entire methodology is illustrated with a number of examples, with discussion on the applicability and efficiency of particular POT models. The dissertation therefore proposes the methodology for a complete probabilistic analysis of floods based on the POT method

Analiza rizika od poplava pomoću prekidnih slučajnih procesa

Probabilističko opisivanje veli¬kih voda ima važnu ulogu u hidrotehničkim i vodoprivrednim studijama i projektima koji se bave rizikom od poplava. Osnovni alat za ovaj zadatak je statistička analiza velikih voda, kojom se za određeni protok velike vode vezuje njegova verovatnoća pojave. U tim analizama postoje neizve¬snosti koje najvećim delom potiču od nedovoljnih raspoloživih podataka osmatranja i nepoznavanja raspodele verovatnoće velikih voda. Ove neizvesnosti se ne mogu izbeći, ali je njihovo poznavanje veoma značajno kako bi se omogućilo da se sagledaju ograničenja projektovanih rešenja ili da se, uzimanjem neizvesnosti u obzir, dođe do boljih rešenja. Fokus disertacije su neizvesnosti u oceni velikih voda metodom prekoračenja preko praga (POT metoda), koja je zasnovana na prekidnim slučajnim procesima i predstavlja alter¬nativu standardnom postupku statističke analize godišnjih maksimuma protoka. Iako se ova metoda povremeno nalazila u fokusu istraživača, do sada nije postojalo si¬stematsko razmatranje njene efikasnosti sa gledišta neizvesnosti. Rezultati retkih prethodnih istraživanja nisu bili opšteg karaktera i bili su ograničeni na pojedine slučajeve metode POT. U okviru ove disertacije sistematizovana su dosa¬dašnja saznanja u određi¬vanju neizvesnosti velikih voda metodom POT i izvr¬šeno je vrednovanje odre¬đe¬nih pretpostavki u postupcima proračuna. Obuh¬va¬ćeni su svi relevantni modeli par¬ci¬jalnih serija i postavljen je jedinstven originalni mate¬matički okvir za izvođenje izraza za pokazatelje neizvesnosti u oceni kvantila i verovatnoće velikih voda (pristrasnost, standardna greška, interval poverenja kvantila velikih voda). Metodologija je ilustrovana na većem broju primera uz diskusiju o primenljivosti i efi¬kasnosti pojedinih modela. Disertacija dakle predlaže zaokruženu metodolo¬gi¬ju za celovitu probabilističku analizu velikih voda pomoću metode POT.Probabilistic characterisation of floods is an important task in water resources management studies and projects addressing flood risks. Main tool for this task is the flood frequency analysis, by which a probability of occurrence is attributed to a ceratin flood flow. A range of uncertainties is inherent in the flood frequency analysis, mostly stemming from limited observational data and lack of knowledge on parent probability distributions. These uncertainties cannot be avoided, but knowing their rainges is very important so that they could be considered in the planning and design process. The focus of the dissertation are the uncertainties in flood frequency assessment by the peaks over threshold (POT) method (or partial duration series method), which is founded in the intermittent stochastic processes and represents an alternative to the standard flood frequency analysis of annual maximum floods. Although the POT method has been occasionally in the focus of hydrologic research, there has been no systematic consideration of its efficiency in terms of uncertainties. Results of rare previous studies were not generalized and were limited to particular cases of the POT method. Within this dissertation, the existing knowledge on uncertainties in floods estimated by the POT method has been systematized and certain assumptions in the calculation procedures have been evaluated. All pertinent POT models used in practice are analysed and the consistent and original mathematical framework for deriving analytical expressions for uncertainty measures (bias, standard errors and confidence intervals of flood quantiles) in the flood frequency estimation is developed. The entire methodology is illustrated with a number of examples, with discussion on the applicability and efficiency of particular POT models. The dissertation therefore proposes the methodology for a complete probabilistic analysis of floods based on the POT method

Conditioning of Flow Projections under Climate Change on Hydrologic Signatures within the GLUE Framework

Climate change impact on water resources is generally quantified in terms of relative changes in characteristicflows (e.g. annual runoff, median annual flows, etc.) over a future period compared to the baseline one. Thesechanges are estimated under the assumed emission scenarios and with one or more modelling chains (combinationsof the Global and Regional Climate Models, and a hydrological model). Since different modelling chains yielddifferent projections, estimates of these relative changes are uncertain. High prediction uncertainty is reflected in awide 90 per cent prediction uncertainty band (90PPU) or in a distribution that resembles the uniform distribution.Therefore, research in robustness of the modelling chains has been conducted. The goal of the research is toappoint higher probabilities to the projections obtained by the more robust chains, and in that way reduce theuncertainty in flow projections under climate change.In this research, the hydrologic projections are conditioned on the hydrologic signatures within the GLUEframework. Namely, a relative change obtained with a modelling chain is assigned a likelihood depending on theperformance of the chain in terms of the hydrologic signatures over the baseline period. High flow projections (2ndpercentile of the daily flows) are conditioned on the high-segment of the flow duration curve (FDC), projectionsof the median flows are conditioned on the FDC mid-segment slope, and the projections of the low flows areconditioned on the FDC low-segment. The projections of total annual runoff are conditioned on the entire FDC.The likelihoods are quantified in terms of Nash-Sutcliffe efficiency coefficient (NSE) evaluated from the FDCs ofthe flows simulated by the modelling chains and the observed FDC.The methodology presented is applied to develop flow projections in the Kolubara River catchment in Ser-bia over the mid 21st century (2041-2070). Hydrologic projections are obtained by the HBV-light hydrologicmodel with input from five climate models (combinations of the Global and Regional Climate Models), all rununder A1B emission scenario. The outputs of the climate models are bias-corrected to reproduce distributions ofthe precipitation depths and temperatures observed in the baseline period (1961-1990). The best twenty parametersets out 25,000 sampled ones are kept in the analysis, resulting in 100 modelling chains.The GLUE conditioning did not significantly affect the median values of the projections, but only thewidth of the prediction bands. All modelling chains perform equally well in terms of the entire FDC and itsmid-segment. Therefore, the GLUE-conditioned projections of annual runoff volume and median flows are similarto the unconditioned ones (i.e. GLUE conditioning yields slightly narrower 90PPUs). Model efficiency in the highflow domain differs between the modelling chains: however, the GLUE conditioning leads to somewhat narrower90PPU. Only few modelling chains performed well in the low flow domain, therefore the width of the 90PPU wasconsiderably reduced by conditioning (from 61.5% to 36.8%)Geophysical Research Abstract

Statistička analiza velikih voda Dunava i Save na području Beograda

The paper presents a methodology for analysis of the coincident annual maximum floods of the Danube and Sava Rivers at their confluence in Belgrade, as a part of the flood control project aimed to provide boundary conditions for the hydraulic modelling of the confluence sector. The Danube and Sava confluence is under back-water effect from the Iron Gate Reservoir. Estimating the probability of coincidence of floods at the Danube and Sava confluence is crucial for the efficient protection of Belgrade against floods because the Sava floods can have a significant contribution to the Danube floods. Due to the Iron Gate backwater effect, stream-flow measurements are not performed systematically near the Danube and Sava confluence at Belgrade. Flood assessment has therefore to be based on the data recorded at upstream gauging stations. Particularly, the only useful flood flows measurement data on the Danube upstream of Belgrade are available at the Bogojevo gauging station, which is located upstream of the confluence of the Tisa River with the Danube. This situation imposed that the design floods of the Danube immediately upstream of the Sava confluence should be estimated by considering coincident floods of the Danube at Bogojevo and of the Tisa River at Senta. The methodological approach in this paper has therefore included the establishment of a trivariate distribution of annual maximum floods of the Danube, the Tisa and the Sava rivers, based on the observed data. The identified trivariate distribution is then used in Monte Carlo experiments to simulate annual maxima of the Danube upstream of Tisa and of the Tisa, which were combined into the flood flows of the Danube upstream of Belgrade. This simulated flood series and the simulated Sava floods are then used for the assessment of the coincidence probability at the Danube and Sava confluence.U radu je prikazan postupak analize koincidencije maksimalnih godišnjih protoka na Dunavu i Savi u zoni Beograda, koja je specifična po tome što se nalazi pod usporom akumulacije Đerdap. Za efikasnu zaštitu od velikih voda u zonama ušća dve reke od ključnog značaja je procena verovatnoće koincidencije velikih voda obe reke, s obzirom da velike vode pritoke mogu uticati na velike vode glavne reke. U zoni Beograda posle uspostavljanja akumulacije Đerdap ne postoje sistematska merenja protoka, pa se računski protoci velikih voda i njihova koincidencija moraju proceniti na osnovu protoka na uzvodnim stanicama. Metodološki postupak sastojao se od analize godišnje koincidencije velikih voda Dunava, Tise i Save na osnovu raspoloživih podataka, pri čemu je određena trodimenzionalna raspodela velikih voda na ove tri reke kojom se uzima u obzir korelacija između pojave velikih voda na njima. Monte Karlo simulacijama iz dobijene trodimenzionalne raspodele formirana je raspodela velikih voda na Dunavu uzvodno od Beograda i određena koincidencija godišnjih maksimuma Dunava i Save kod Beograda

Mogućnosti za primenu modela HEC-HMS za kontinualne hidrološke simulacije

To examine the applicability of the HEC-HMS software for continuous runoff simulations, efficiencies of three different HEC-HMC models are assessed. The first and the second models are lumped ones, based on deficit and constant loss model and (more complex) Soil Moisture Accounting (SMA) loss model, respectively, whereas the third model is the semi-distributed version of the first one. In this way, the impact of the increase model structural complexity and parameter spatial disaggregation on model's ability to reproduce observed flows can be estimated. The models are calibrated against flows observed at the Beli Brod stream gauge. Model efficiencies are quantified in terms of relative bias, correlation coefficients and Nash-Sutcliffe efficiency coefficients for both, flows and the logarithms of flows. Also, model performance is estimated by visual comparison between simulated and observed hydrographs. The results indicate certain HEC-HMS's disadvantages and limitations to the application for continuous runoff simulations.U ovom radu su analizirane mogućnosti paketa hidroloških modela HEC-HMS za kontinualne hidrološke simulacije poredenjem rezultata tri različito postavljena modela sa osmotrenim hidrogramima. Modeli su formirani za sliv reke Kolubare do hidrološke stanice Beli Brod. Slaganje simuliranih i osmotrenih hidrograma kvantifikovano je preko nekoliko pokazatelja kvaliteta modela. Rezultati u ovom radu ukazuju na neke nedostatke i ograničenja HEC-HMS-a u primeni za kontinualne hidrološke simulacije

Ekonomsko vrednovanje mera za zaštitu od poplava na slivu reke Tamnave

radu se razmatraju mere zaštite od poplava na slivu reke Tamnave i njihovo ekonomsko vrednovanje pomoću razvijenog modela šteta fine rezolucije. Štete od poplava su procenjene za tri moguća scenarija zaštite (sive, zelene i sivo-zelene mere), kao i za referentno stanje zaštite iz 2014. godine. Smanjenje gubitaka tj. šteta u odnosu na referentno stanje smatra se koristima od određenog scenarija zaštite. Razvijeni model šteta se zasniva na kartama ugroženosti i detaljnim podacima o najvažnijim receptorima rizika. Rezultati su pokazali da planirane retenzije kao aktivne zelene mere zaštite značajno smanjuju štete od poplava. Planirano nadvišenje postojećih nasipa primenjeno bez retenzija donosi manje koristi u smislu izbegnite štete, dok u kombinaciji sa retenzijama praktično ne donosi nikakve koristi. Pokazano je da su predložena metodologija i mikro model šteta primenljivi za razmatranje efekata različitih vrsta mera u savremenom pristupu zaštite od poplava u kome se akcenat stavlja na zelene mere i prirodi bliska rešenja