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Robust Water Balance Modeling with Uncertain Discharge and Precipitation Data: Computational Geometry as a New Tool
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Robust vattenbalansmodellering med osäkra vattenförings- och nederbördsdata : beräkningsgeometri som ett nytt verktyg (Swedish)
Abstract [en]

Models are important tools for understanding the hydrological processes that govern water transport in the landscape and for prediction at times and places where no observations are available. The degree of trust placed on models, however, should not exceed the quality of the data they are fed with. The overall aim of this thesis was to tune the modeling process to account for the uncertainty in the data, by identifying robust parameter values using methods from computational geometry. The methods were developed and tested on data from the Choluteca River basin in Honduras.

Quality control of precipitation and discharge data resulted in a rejection of 22% percent of daily raingage data and the complete removal of one out of the seven discharge stations analyzed. The raingage network was not found sufficient to capture the spatial and temporal variability of precipitation in the Choluteca River basin. The temporal variability of discharge was evaluated through a Monte Carlo assessment of the rating-equation parameter values over a moving time window of stage-discharge measurements. Al hydrometric stations showed considerable temporal variability in the stage-discharge relationship, which was largest for low flows, albeit with no common trend. The problem with limited data quality was addressed by identifying robust model parameter values within the set of well-performing (behavioral) parameter-value vectors with computational-geometry methods. The hypothesis that geometrically deep parameter-value vectors within the behavioral set were hydrologically robust was tested, and verified, using two depth functions. Deep parameter-value vectors tended to perform better than shallow ones, were less sensitive to small changes in their values, and were better suited to temporal transfer. Depth functions rank multidimensional data. Methods to visualize the multivariate distribution of behavioral parameters based on the ranked values were developed. It was shown that, by projecting along a common dimension, the multivariate distribution of behavioral parameters for models of varying complexity could be compared using the proposed visualization tools. This has a potential to aid in the selection of an adequate model structure considering the uncertainty in the data.

These methods allowed to quantify observational uncertainties. Geometric methods have only recently begun to be used in hydrology. It was shown that they can be used to identify robust parameter values, and some of their potential uses were highlighted.

Abstract [sv]

Modeller är viktiga verktyg för att förstå de hydrologiska processer som bestämmer vattnets transport i landskapet och för prognoser för tider och platser där det saknas mätdata. Graden av tillit till modeller bör emellertid inte överstiga kvaliteten på de data som de matas med. Det övergripande syftet med denna avhandling var att anpassa modelleringsprocessen så att den tar hänsyn till osäkerheten i data och identifierar robusta parametervärden med hjälp av metoder från beräkningsgeometrin. Metoderna var utvecklade och testades på data från Cholutecaflodens avrinningsområde i Honduras.

Kvalitetskontrollen i nederbörds- och vattenföringsdata resulterade i att 22 % av de dagliga nederbördsobservationerna måste kasseras liksom alla data från en av sju analyserade vattenföringsstationer. Observationsnätet för nederbörd befanns otillräckligt för att fånga upp den rumsliga och tidsmässiga variabiliteten i den övre delen av Cholutecaflodens avrinningsområde. Vattenföringens tidsvariation utvärderades med en Monte Carlo-skattning av värdet på parametrarna i avbördningskurvan i ett rörligt tidsfönster av vattenföringsmätningar. Alla vattenföringsstationer uppvisade stor tidsvariation i avbördningskurvan som var störst för låga flöden, dock inte med någon gemensam trend. Problemet med den måttliga datakvaliteten bedömdes med hjälp av robusta modellparametervärden som identifierades med hjälp av beräkningsgeometriska metoder. Hypotesen att djupa parametervärdesuppsättningar var robusta testades och verifierades genom två djupfunktioner. Geometriskt djupa parametervärdesuppsättningar verkade ge bättre hydrologiska resultat än ytliga, var mindre känsliga för små ändringar i parametervärden och var bättre lämpade för förflyttning i tiden. Metoder utvecklades för att visualisera multivariata fördelningar av välpresterande parametrar baserade på de rangordnade värdena. Genom att projicera längs en gemensam dimension, kunde multivariata fördelningar av välpresterande parametrar hos modeller med varierande komplexitet jämföras med hjälp av det föreslagna visualiseringsverktyget. Det har alltså potentialen att bistå vid valet av en adekvat modellstruktur som tar hänsyn till osäkerheten i data.

Dessa metoder möjliggjorde kvantifiering av observationsosäkerheter. Geometriska metoder har helt nyligen börjat användas inom hydrologin. I studien demonstrerades att de kan användas för att identifiera robusta parametervärdesuppsättningar och några av metodernas potentiella användningsområden belystes.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. , p. 95
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1010
Keywords [en]
Alpha shape, Convex hull, Depth function, Discharge, Hydrological models, Honduras, Model calibration, Parameter-value estimation, Precipitation, Rating curve, Robust, Robustness, Uncertainty estimation, Water resources.
Keywords [sv]
Alfaform, avbördningskurva, djupfunktion, Honduras, hydrologiska modeller, konvext hölje, modellkalibrering, nederbörd, osäkerhetsskattning, parametervärdesskattning, robust, robusthet, vattenföring, vattenresurser
National Category
Oceanography, Hydrology and Water Resources
Research subject
Hydrology
Identifiers
URN: urn:nbn:se:uu:diva-190686ISBN: 978-91-554-8575-7 (print)OAI: oai:DiVA.org:uu-190686DiVA, id: diva2:584843
Public defence
2013-02-22, Axel Hambergsalen, Earth Sciences Department, Villavägen 16, Uppsala, 13:00 (English)
Opponent
Supervisors
Funder
Sida - Swedish International Development Cooperation Agency, 75007349 and SWE-2005-296Available from: 2013-02-01 Created: 2013-01-08 Last updated: 2018-01-11Bibliographically approved
List of papers
1. Precipitation data in a mountainous catchment in Honduras: quality assessment and spatiotemporal characteristics
Open this publication in new window or tab >>Precipitation data in a mountainous catchment in Honduras: quality assessment and spatiotemporal characteristics
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2010 (English)In: Journal of Theoretical and Applied Climatology, ISSN 0177-798X, E-ISSN 1434-4483, Vol. 101, no 3-4, p. 381-396Article in journal (Refereed) Published
Abstract [en]

An accurate description of temporal and spatial precipitation variability in Central America is important for local farming, water supply and flood management. Data quality problems and lack of consistent precipitation data impede hydrometeorological analysis in the 7,500 km(2) Choluteca River basin in central Honduras, encompassing the capital Tegucigalpa. We used precipitation data from 60 daily and 13 monthly stations in 1913-2006 from five local authorities and NOAA's Global Historical Climatology Network. Quality control routines were developed to tackle the specific data quality problems. The quality-controlled data were characterised spatially and temporally, and compared with regional and larger-scale studies. Two gap-filling methods for daily data and three interpolation methods for monthly and mean annual precipitation were compared. The coefficient-of-correlation-weighting method provided the best results for gap-filling and the universal kriging method for spatial interpolation. In-homogeneity in the time series was the main quality problem, and 22% of the daily precipitation data were too poor to be used. Spatial autocorrelation for monthly precipitation was low during the dry season, and correlation increased markedly when data were temporally aggregated from a daily time scale to 4-5 days. The analysis manifested the high spatial and temporal variability caused by the diverse precipitation-generating mechanisms and the need for an improved monitoring network.

National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:uu:diva-135001 (URN)10.1007/s00704-009-0222-x (DOI)000280578900012 ()
Available from: 2010-12-06 Created: 2010-12-03 Last updated: 2017-12-11Bibliographically approved
2. Temporal variability in stage-discharge relationships
Open this publication in new window or tab >>Temporal variability in stage-discharge relationships
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2012 (English)In: Journal of Hydrology, ISSN 0022-1694, E-ISSN 1879-2707, Vol. 446, p. 90-102Article in journal (Refereed) Published
Abstract [en]

Although discharge estimations are central for water management and hydropower, there are few studies on the variability and uncertainty of their basis; deriving discharge from stage heights through the use of a rating curve that depends on riverbed geometry. A large fraction of the world's river-discharge stations are presumably located in alluvial channels where riverbed characteristics may change over time because of erosion and sedimentation. This study was conducted to analyse and quantify the dynamic relationship between stage and discharge and to determine to what degree currently used methods are able to account for such variability. The study was carried out for six hydrometric stations in the upper Choluteca River basin, Honduras, where a set of unusually frequent stage-discharge data are available. The temporal variability and the uncertainty of the rating curve and its parameters were analysed through a Monte Carlo (MC) analysis on a moving window of data using the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Acceptable ranges for the values of the rating-curve parameters were determined from riverbed surveys at the six stations, and the sampling space was constrained according to those ranges, using three-dimensional alpha shapes. Temporal variability was analysed in three ways: (i) with annually updated rating curves (simulating Honduran practices), (ii) a rating curve for each time window, and (iii) a smoothed, continuous dynamic rating curve derived from the MC analysis. The temporal variability of the rating parameters translated into a high rating-curve variability. The variability could turn out as increasing or decreasing trends and/or cyclic behaviour. There was a tendency at all stations to a seasonal variability. The discharge at a given stage could vary by a factor of two or more. The quotient in discharge volumes estimated from dynamic and static rating curves varied between 0.5 and 1.5. The difference between discharge volumes derived from static and dynamic curves was largest for sub-daily ratings but stayed large also for monthly and yearly totals. The relative uncertainty was largest for low flows but it was considerable also for intermediate and large flows. The standard procedure of adjusting rating curves when calculated and observed discharge differ by more than 5% would have required continuously updated rating curves at the studied locations. We believe that these findings can be applicable to many other discharge stations around the globe.

Keywords
Rating curve, Discharge, Uncertainty, Temporal variability, Alluvial river
National Category
Oceanography, Hydrology and Water Resources
Identifiers
urn:nbn:se:uu:diva-177587 (URN)10.1016/j.jhydrol.2012.04.031 (DOI)000305365300009 ()
Available from: 2012-07-16 Created: 2012-07-16 Last updated: 2018-06-01Bibliographically approved
3. Exploring the hydrological robustness of model-parameter values with alpha shapes
Open this publication in new window or tab >>Exploring the hydrological robustness of model-parameter values with alpha shapes
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2013 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 49, no 10, p. 6700-6715Article in journal (Refereed) Published
Abstract [en]

Estimation of parameter values in hydrological models has gradually moved from subjective, trial-and-error methods into objective estimation methods. Translation of nature's complexity to bit operations is an uncertain process as a result of data errors, epistemic gaps, computational deficiencies, and other limitations, and relies on calibration to fit model output to observed data. The robustness of the calibrated parameter values to these types of uncertainties is therefore an important concern. In this study, we investigated how the hydrological robustness of the model-parameter values varied within the geometric structure of the behavioral (well-performing) parameter space with a depth function based on α shapes and an in-depth posterior performance analysis of the simulations in relation to the observed discharge uncertainty. The α shape depth is a nonconvex measure that may provide an accurate and tight delimitation of the geometric structure of the behavioral space for both unimodal and multimodal parameter-value distributions. WASMOD, a parsimonious rainfall-runoff model, was applied to six Honduran and one UK catchment, with differing data quality and hydrological characteristics. Model evaluation was done with two performance measures, the Nash-Sutcliffe efficiency and one based on flow-duration curves. Deep parameter vectors were in general found to be more hydrologically robust than shallow ones in the analyses we performed; model-performance values increased with depth, deviations to the observed data for the high-flow aspects of the hydrograph generally decreased with increasing depth, deep parameter vectors generally transferred in time with maintained high performance values, and the model had a low sensitivity to small changes in the parameter values. The tight delimitation of the behavioral space provided by the α shapes depth function showed a potential to improve the efficiency of calibration techniques that require further exploration. For computational reasons only a three-parameter model could be used, which limited the applicability of this depth measure and the conclusions drawn in this paper, especially concerning hydrological robustness at low flows.

Keywords
robustness, parameter estimation, alpha shape
National Category
Ocean and River Engineering
Identifiers
urn:nbn:se:uu:diva-190679 (URN)10.1002/wrcr.20533 (DOI)000327432500040 ()
Available from: 2013-01-08 Created: 2013-01-08 Last updated: 2017-12-06Bibliographically approved
4. Robust parameters and assessment of structural uncertainty in hydrological models using a depth function
Open this publication in new window or tab >>Robust parameters and assessment of structural uncertainty in hydrological models using a depth function
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(English)Manuscript (preprint) (Other academic)
National Category
Natural Sciences Oceanography, Hydrology and Water Resources
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-190684 (URN)
Available from: 2013-01-08 Created: 2013-01-08 Last updated: 2018-01-11

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Output format
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