Articles | Volume 13, issue 10
19 Oct 2009
19 Oct 2009
Hydrological model performance and parameter estimation in the wavelet-domain
B. Schaefli and E. Zehe
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Uncertainty analysisKey challenges facing the application of the conductivity mass balance method: a case study of the Mississippi River basinCoupled machine learning and the limits of acceptability approach applied in parameter identification for a distributed hydrological modelA systematic assessment of uncertainties in large-scale soil loss estimation from different representations of USLE input factors – a case study for Kenya and UgandaTechnical note: Uncertainty in multi-source partitioning using large tracer data setsAssessment of climate change impact and difference on the river runoff in four basins in China under 1.5 and 2.0 °C global warmingA likelihood framework for deterministic hydrological models and the importance of non-stationary autocorrelationTechnical note: Analytical sensitivity analysis and uncertainty estimation of baseflow index calculated by a two-component hydrograph separation method with conductivity as a tracerUnderstanding the water cycle over the upper Tarim Basin: retrospecting the estimated discharge bias to atmospheric variables and model structureThe effect of input data resolution and complexity on the uncertainty of hydrological predictions in a humid vegetated watershedParameter uncertainty analysis for an operational hydrological model using residual-based and limits of acceptability approachesTechnical note: Pitfalls in using log-transformed flows within the KGE criterionImprovement of model evaluation by incorporating prediction and measurement uncertaintyTransferability of climate simulation uncertainty to hydrological impactsIntercomparison of different uncertainty sources in hydrological climate change projections for an alpine catchment (upper Clutha River, New Zealand)Mapping (dis)agreement in hydrologic projectionsConsistency assessment of rating curve data in various locations using Bidirectional Reach (BReach)The critical role of uncertainty in projections of hydrological extremesResidual uncertainty estimation using instance-based learning with applications to hydrologic forecastingCharacterizing and reducing equifinality by constraining a distributed catchment model with regional signatures, local observations, and process understandingEffects of uncertainty in soil properties on simulated hydrological states and fluxes at different spatio-temporal scalesExtending flood forecasting lead time in a large watershed by coupling WRF QPF with a distributed hydrological modelQuantifying uncertainty on sediment loads using bootstrap confidence intervalsEvent-scale power law recession analysis: quantifying methodological uncertaintyDisentangling timing and amplitude errors in streamflow simulationsReliability of lumped hydrological modeling in a semi-arid mountainous catchment facing water-use changesUsing dry and wet year hydroclimatic extremes to guide future hydrologic projectionsUncertainty contributions to low-flow projections in AustriaAccounting for dependencies in regionalized signatures for predictions in ungauged catchmentsClimate change and its impacts on river discharge in two climate regions in ChinaUncertainty in hydrological signaturesClimate model uncertainty versus conceptual geological uncertainty in hydrological modelingEstimation of predictive hydrologic uncertainty using the quantile regression and UNEEC methods and their comparison on contrasting catchmentsTransferring global uncertainty estimates from gauged to ungauged catchmentsSpatial sensitivity analysis of snow cover data in a distributed rainfall-runoff modelUncertainty reduction and parameter estimation of a distributed hydrological model with ground and remote-sensing dataThe skill of seasonal ensemble low-flow forecasts in the Moselle River for three different hydrological modelsFlow pathways and nutrient transport mechanisms drive hydrochemical sensitivity to climate change across catchments with different geology and topographyThe importance of hydrological uncertainty assessment methods in climate change impact studiesRegional water balance modelling using flow-duration curves with observational uncertaintiesClimate change impacts on the hydrologic regime of a Canadian river: comparing uncertainties arising from climate natural variability and lumped hydrological model structuresFrom maps to movies: high-resolution time-varying sensitivity analysis for spatially distributed watershed modelsBridging the gap between GLUE and formal statistical approaches: approximate Bayesian computationConsidering rating curve uncertainty in water level predictionsTechnical Note: Method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed modelsThe impact of forest regeneration on streamflow in 12 mesoscale humid tropical catchmentsAn ensemble approach to assess hydrological models' contribution to uncertainties in the analysis of climate change impact on water resourcesLocal sensitivity analysis for compositional data with application to soil texture in hydrologic modellingAdaptive correction of deterministic models to produce probabilistic forecastsBayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff modelsHydrological education and training needs in sub-Saharan Africa: requirements, constraints and progress
Hang Lyu, Chenxi Xia, Jinghan Zhang, and Bo Li
Hydrol. Earth Syst. Sci., 24, 6075–6090,Short summary
Baseflow separation plays a critical role in science-based management of water resources. This study addressed key challenges hindering the application of the generally accepted conductivity mass balance (CMB). Monitoring data for over 200 stream sites of the Mississippi River basin were collected to answer the following questions. What are the characteristics of a watershed that determine the method suitability? What length of monitoring data is needed? How can the parameters be more accurate?
Aynom T. Teweldebrhan, Thomas V. Schuler, John F. Burkhart, and Morten Hjorth-Jensen
Hydrol. Earth Syst. Sci., 24, 4641–4658,
Christoph Schürz, Bano Mehdi, Jens Kiesel, Karsten Schulz, and Mathew Herrnegger
Hydrol. Earth Syst. Sci., 24, 4463–4489,Short summary
The USLE is a commonly used model to estimate soil erosion by water. It quantifies soil loss as a product of six inputs representing rainfall erosivity, soil erodibility, slope length and steepness, plant cover, and support practices. Many methods exist to derive these inputs, which can, however, lead to substantial differences in the estimated soil loss. Here, we analyze the effect of different input representations on the estimated soil loss in a large-scale study in Kenya and Uganda.
Alicia Correa, Diego Ochoa-Tocachi, and Christian Birkel
Hydrol. Earth Syst. Sci., 23, 5059–5068,Short summary
The applications and availability of large tracer data sets have vastly increased in recent years leading to research into the contributions of multiple sources to a mixture. We introduce a method based on Taylor series approximation to estimate the uncertainties of such sources' contributions. The method is illustrated with examples of hydrology (14 tracers) and a MATLAB code is provided for reproducibility. This method can be generalized to any number of tracers across a range of disciplines.
Hongmei Xu, Lüliu Liu, Yong Wang, Sheng Wang, Ying Hao, Jingjin Ma, and Tong Jiang
Hydrol. Earth Syst. Sci., 23, 4219–4231,Short summary
1.5 and 2 °C have become targets in the discussion of climate change impacts. However, climate research is also challenged to provide more robust information on the impact of climate change at local and regional scales to assist the development of sound scientific adaptation and mitigation measures. This study assessed the impacts and differences of 1.5 and 2.0 °C global warming on basin-scale river runoff by examining four river basins covering a wide hydroclimatic setting in China.
Lorenz Ammann, Fabrizio Fenicia, and Peter Reichert
Hydrol. Earth Syst. Sci., 23, 2147–2172,Short summary
The uncertainty of hydrological models can be substantial, and its quantification and realistic description are often difficult. We propose a new flexible probabilistic framework to describe and quantify this uncertainty. It is show that the correlation of the errors can be non-stationary, and that accounting for temporal changes in correlation can lead to strongly improved probabilistic predictions. This is a promising avenue for improving uncertainty estimation in hydrological modelling.
Weifei Yang, Changlai Xiao, and Xiujuan Liang
Hydrol. Earth Syst. Sci., 23, 1103–1112,Short summary
This paper analyzed the sensitivity of the baseflow index to the parameters of the conductivity two-component hydrograph separation method. The results indicated that the baseflow index is more sensitive to the conductivity of baseflow and the separation method may be more suitable for the long time series in a small watershed. After considering the mutual offset of the measurement errors of conductivity and streamflow, the uncertainty in baseflow index was reduced by half.
Xudong Zhou, Jan Polcher, Tao Yang, Yukiko Hirabayashi, and Trung Nguyen-Quang
Hydrol. Earth Syst. Sci., 22, 6087–6108,Short summary
Model bias is commonly seen in discharge simulation by hydrological or land surface models. This study tested an approach with the Budyko hypothesis to retrospect the estimated discharge bias to different bias sources including the atmospheric variables and model structure. Results indicate that the bias is most likely caused by the forcing variables, and the forcing bias should firstly be assessed and reduced in order to perform pertinent analysis of the regional water cycle.
Linh Hoang, Rajith Mukundan, Karen E. B. Moore, Emmet M. Owens, and Tammo S. Steenhuis
Hydrol. Earth Syst. Sci., 22, 5947–5965,Short summary
The paper analyzes the effect of two input data (DEMs and the combination of soil and land use data) with different resolution and complexity on the uncertainty of model outputs (the predictions of streamflow and saturated areas) and parameter uncertainty using SWAT-HS. Results showed that DEM resolution has significant effect on the spatial pattern of saturated areas and using complex soil and land use data may not necessarily improve model performance or reduce model uncertainty.
Aynom T. Teweldebrhan, John F. Burkhart, and Thomas V. Schuler
Hydrol. Earth Syst. Sci., 22, 5021–5039,
Léonard Santos, Guillaume Thirel, and Charles Perrin
Hydrol. Earth Syst. Sci., 22, 4583–4591,Short summary
The Kling and Gupta efficiency (KGE) is a score used in hydrology to evaluate flow simulation compared to observations. In order to force the evaluation on the low flows, some authors used the log-transformed flow to calculate the KGE. In this technical note, we show that this transformation should be avoided because it produced numerical flaws that lead to difficulties in the score value interpretation.
Lei Chen, Shuang Li, Yucen Zhong, and Zhenyao Shen
Hydrol. Earth Syst. Sci., 22, 4145–4154,Short summary
In this study, the cumulative distribution function approach (CDFA) and the Monte Carlo approach (MCA) were used to develop two new approaches for model evaluation within an uncertainty framework. These proposed methods could be extended to watershed models to provide a substitution for traditional model evaluations within an uncertainty framework.
Hui-Min Wang, Jie Chen, Alex J. Cannon, Chong-Yu Xu, and Hua Chen
Hydrol. Earth Syst. Sci., 22, 3739–3759,Short summary
Facing a growing number of climate models, many selection methods were proposed to select subsets in the field of climate simulation, but the transferability of their performances to hydrological impacts remains doubtful. We investigate the transferability of climate simulation uncertainty to hydrological impacts using two selection methods, and conclude that envelope-based selection of about 10 climate simulations based on properly chosen climate variables is suggested for impact studies.
Andreas M. Jobst, Daniel G. Kingston, Nicolas J. Cullen, and Josef Schmid
Hydrol. Earth Syst. Sci., 22, 3125–3142,
Lieke A. Melsen, Nans Addor, Naoki Mizukami, Andrew J. Newman, Paul J. J. F. Torfs, Martyn P. Clark, Remko Uijlenhoet, and Adriaan J. Teuling
Hydrol. Earth Syst. Sci., 22, 1775–1791,Short summary
Long-term hydrological predictions are important for water management planning, but are also prone to uncertainty. This study investigates three sources of uncertainty for long-term hydrological predictions in the US: climate models, hydrological models, and hydrological model parameters. Mapping the results revealed spatial patterns in the three sources of uncertainty: different sources of uncertainty dominate in different regions.
Katrien Van Eerdenbrugh, Stijn Van Hoey, Gemma Coxon, Jim Freer, and Niko E. C. Verhoest
Hydrol. Earth Syst. Sci., 21, 5315–5337,Short summary
Consistency in stage–discharge data is investigated using a methodology called Bidirectional Reach (BReach). Various measurement stations in the UK, New Zealand and Belgium are selected based on their historical ratings information and their characteristics related to data consistency. When applying a BReach analysis on them, the methodology provides results that appear consistent with the available knowledge and thus facilitates a reliable assessment of (in)consistency in stage–discharge data.
Hadush K. Meresa and Renata J. Romanowicz
Hydrol. Earth Syst. Sci., 21, 4245–4258,Short summary
Evaluation of the uncertainty in projections of future hydrological extremes in the mountainous catchment was performed. The uncertainty of the estimate of 1-in-100-year return maximum flow based on the 1971–2100 time series exceeds 200 % of its median value with the largest influence of the climate model uncertainty, while the uncertainty of the 1-in-100-year return minimum flow is of the same order (i.e. exceeds 200 %) but it is mainly influenced by the hydrological model parameter uncertainty.
Omar Wani, Joost V. L. Beckers, Albrecht H. Weerts, and Dimitri P. Solomatine
Hydrol. Earth Syst. Sci., 21, 4021–4036,Short summary
We generate uncertainty intervals for hydrologic model predictions using a simple instance-based learning scheme. Errors made by the model in some specific hydrometeorological conditions in the past are used to predict the probability distribution of its errors during forecasting. We test it for two different case studies in England. We find that this technique, even though conceptually simple and easy to implement, performs as well as some other sophisticated uncertainty estimation methods.
Christa Kelleher, Brian McGlynn, and Thorsten Wagener
Hydrol. Earth Syst. Sci., 21, 3325–3352,Short summary
Models are tools for understanding how watersheds function and may respond to land cover and climate change. Before we can use models towards these purposes, we need to ensure that a model adequately represents watershed-wide observations. In this paper, we propose a new way to evaluate whether model simulations match observations, using a variety of information sources. We show how this information can reduce uncertainty in inputs to models, reducing uncertainty in hydrologic predictions.
Gabriele Baroni, Matthias Zink, Rohini Kumar, Luis Samaniego, and Sabine Attinger
Hydrol. Earth Syst. Sci., 21, 2301–2320,Short summary
Three methods are used to characterize the uncertainty in soil properties. The effect on simulated states and fluxes is quantified using a distributed hydrological model. Different impacts are identified as function of the perturbation method, of the model outputs and of the spatio-temporal resolution. The study underlines the importance of a proper characterization of the uncertainty in soil properties for a correct assessment of their role and further improvements in the model application.
Ji Li, Yangbo Chen, Huanyu Wang, Jianming Qin, Jie Li, and Sen Chiao
Hydrol. Earth Syst. Sci., 21, 1279–1294,Short summary
Quantitative precipitation forecast produced by the WRF model has a similar pattern to that estimated by rain gauges in a southern China large watershed, hydrological model parameters should be optimized with QPF produced by WRF, and simulating floods by coupling the WRF QPF with a distributed hydrological model provides a good reference for large watershed flood warning and could benefit the flood management communities due to its longer lead time.
Johanna I. F. Slaets, Hans-Peter Piepho, Petra Schmitter, Thomas Hilger, and Georg Cadisch
Hydrol. Earth Syst. Sci., 21, 571–588,Short summary
Determining measures of uncertainty on loads is not trivial, as a load is a product of concentration and discharge per time point, summed up over time. A bootstrap approach enables the calculation of confidence intervals on constituent loads. Ignoring the uncertainty on the discharge will typically underestimate the width of 95 % confidence intervals by around 10 %. Furthermore, confidence intervals are asymmetric, with the largest uncertainty on the upper limit.
David N. Dralle, Nathaniel J. Karst, Kyriakos Charalampous, Andrew Veenstra, and Sally E. Thompson
Hydrol. Earth Syst. Sci., 21, 65–81,Short summary
The streamflow recession is the period following rainfall during which flow declines. This paper examines a common method of recession analysis and identifies sensitivity of the technique's results to necessary, yet subjective, methodological choices. The results have implications for hydrology, sediment and solute transport, and geomorphology, as well as for testing numerous hydrologic theories which predict the mathematical form of the recession.
Simon Paul Seibert, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 20, 3745–3763,Short summary
While the assessment of "vertical" (magnitude) errors of streamflow simulations is standard practice, "horizontal" (timing) errors are rarely considered. To assess their role, we propose a method to quantify both errors simultaneously which closely resembles visual hydrograph comparison. Our results reveal differences in time–magnitude error statistics for different flow conditions. The proposed method thus offers novel perspectives for model diagnostics and evaluation.
Paul Hublart, Denis Ruelland, Inaki García de Cortázar-Atauri, Simon Gascoin, Stef Lhermitte, and Antonio Ibacache
Hydrol. Earth Syst. Sci., 20, 3691–3717,Short summary
Our paper explores the reliability of conceptual catchment models in the dry Andes. First, we show that explicitly accounting for irrigation water use improves streamflow predictions during dry years. Second, we show that sublimation losses can be easily incorporated into temperature-based melt models without increasing model complexity too much. Our work also highlights areas requiring additional research, including the need for a better conceptualization of runoff generation processes.
Stephen Oni, Martyn Futter, Jose Ledesma, Claudia Teutschbein, Jim Buttle, and Hjalmar Laudon
Hydrol. Earth Syst. Sci., 20, 2811–2825,Short summary
This paper presents an important framework to improve hydrologic projections in cold regions. Hydrologic modelling/projections are often based on model calibration to long-term data. Here we used dry and wet years as a proxy to quantify uncertainty in projecting hydrologic extremes. We showed that projections based on long-term data could underestimate runoff by up to 35% in boreal regions. We believe the hydrologic modelling community will benefit from new insights derived from this study.
Juraj Parajka, Alfred Paul Blaschke, Günter Blöschl, Klaus Haslinger, Gerold Hepp, Gregor Laaha, Wolfgang Schöner, Helene Trautvetter, Alberto Viglione, and Matthias Zessner
Hydrol. Earth Syst. Sci., 20, 2085–2101,Short summary
Streamflow estimation during low-flow conditions is important for estimation of environmental flows, effluent water quality, hydropower operations, etc. However, it is not clear how the uncertainties in assumptions used in the projections translate into uncertainty of estimated future low flows. The objective of the study is to explore the relative role of hydrologic model calibration and climate scenarios in the uncertainty of low-flow projections in Austria.
Susana Almeida, Nataliya Le Vine, Neil McIntyre, Thorsten Wagener, and Wouter Buytaert
Hydrol. Earth Syst. Sci., 20, 887–901,Short summary
The absence of flow data to calibrate hydrologic models may reduce the ability of such models to reliably inform water resources management. To address this limitation, it is common to condition hydrological model parameters on regionalized signatures. In this study, we justify the inclusion of larger sets of signatures in the regionalization procedure if their error correlations are formally accounted for and thus enable a more complete use of all available information.
H. Xu and Y. Luo
Hydrol. Earth Syst. Sci., 19, 4609–4618,Short summary
This study quantified the climate impact on river discharge in the River Huangfuchuan in semi-arid northern China and the River Xiangxi in humid southern China. Climate projections showed trends toward warmer and wetter conditions, particularly for the River Huangfuchuan. The main projected hydrologic impact was a more pronounced increase in annual discharge in both catchments. Peak flows are projected to appear earlier than usual in the River Huangfuchuan and later than usual in River Xiangxi.
I. K. Westerberg and H. K. McMillan
Hydrol. Earth Syst. Sci., 19, 3951–3968,Short summary
This study investigated the effect of uncertainties in data and calculation methods on hydrological signatures. We present a widely applicable method to evaluate signature uncertainty and show results for two example catchments. The uncertainties were often large (i.e. typical intervals of ±10–40% relative uncertainty) and highly variable between signatures. It is therefore important to consider uncertainty when signatures are used for hydrological and ecohydrological analyses and modelling.
T. O. Sonnenborg, D. Seifert, and J. C. Refsgaard
Hydrol. Earth Syst. Sci., 19, 3891–3901,Short summary
The impacts of climate model uncertainty and geological model uncertainty on hydraulic head, stream flow, travel time and capture zones are evaluated. Six versions of a physically based and distributed hydrological model, each containing a unique interpretation of the geological structure of the model area, are forced by 11 climate model projections. Geology is the dominating uncertainty source for travel time and capture zones, while climate dominates for hydraulic heads and steam flow.
N. Dogulu, P. López López, D. P. Solomatine, A. H. Weerts, and D. L. Shrestha
Hydrol. Earth Syst. Sci., 19, 3181–3201,
F. Bourgin, V. Andréassian, C. Perrin, and L. Oudin
Hydrol. Earth Syst. Sci., 19, 2535–2546,
T. Berezowski, J. Nossent, J. Chormański, and O. Batelaan
Hydrol. Earth Syst. Sci., 19, 1887–1904,
F. Silvestro, S. Gabellani, R. Rudari, F. Delogu, P. Laiolo, and G. Boni
Hydrol. Earth Syst. Sci., 19, 1727–1751,
M. C. Demirel, M. J. Booij, and A. Y. Hoekstra
Hydrol. Earth Syst. Sci., 19, 275–291,Short summary
This paper investigates the skill of 90-day low-flow forecasts using three models. From the results, it appears that all models are prone to over-predict runoff during low-flow periods using ensemble seasonal meteorological forcing. The largest range for 90-day low-flow forecasts is found for the GR4J model. Overall, the uncertainty from ensemble P forecasts has a larger effect on seasonal low-flow forecasts than the uncertainty from ensemble PET forecasts and initial model conditions.
J. Crossman, M. N. Futter, P. G. Whitehead, E. Stainsby, H. M. Baulch, L. Jin, S. K. Oni, R. L. Wilby, and P. J. Dillon
Hydrol. Earth Syst. Sci., 18, 5125–5148,Short summary
We projected potential hydrochemical responses in four neighbouring catchments to a range of future climates. The highly variable responses in streamflow and total phosphorus (TP) were governed by geology and flow pathways, where larger catchment responses were proportional to greater soil clay content. This suggests clay content might be used as an indicator of catchment sensitivity to climate change, and highlights the need for catchment-specific management plans.
M. Honti, A. Scheidegger, and C. Stamm
Hydrol. Earth Syst. Sci., 18, 3301–3317,
I. K. Westerberg, L. Gong, K. J. Beven, J. Seibert, A. Semedo, C.-Y. Xu, and S. Halldin
Hydrol. Earth Syst. Sci., 18, 2993–3013,
G. Seiller and F. Anctil
Hydrol. Earth Syst. Sci., 18, 2033–2047,
J. D. Herman, J. B. Kollat, P. M. Reed, and T. Wagener
Hydrol. Earth Syst. Sci., 17, 5109–5125,
M. Sadegh and J. A. Vrugt
Hydrol. Earth Syst. Sci., 17, 4831–4850,
A. E. Sikorska, A. Scheidegger, K. Banasik, and J. Rieckermann
Hydrol. Earth Syst. Sci., 17, 4415–4427,
J. D. Herman, J. B. Kollat, P. M. Reed, and T. Wagener
Hydrol. Earth Syst. Sci., 17, 2893–2903,
H. E. Beck, L. A. Bruijnzeel, A. I. J. M. van Dijk, T. R. McVicar, F. N. Scatena, and J. Schellekens
Hydrol. Earth Syst. Sci., 17, 2613–2635,
J. A. Velázquez, J. Schmid, S. Ricard, M. J. Muerth, B. Gauvin St-Denis, M. Minville, D. Chaumont, D. Caya, R. Ludwig, and R. Turcotte
Hydrol. Earth Syst. Sci., 17, 565–578,
L. Loosvelt, H. Vernieuwe, V. R. N. Pauwels, B. De Baets, and N. E. C. Verhoest
Hydrol. Earth Syst. Sci., 17, 461–478,
P. J. Smith, K. J. Beven, A. H. Weerts, and D. Leedal
Hydrol. Earth Syst. Sci., 16, 2783–2799,
A. E. Sikorska, A. Scheidegger, K. Banasik, and J. Rieckermann
Hydrol. Earth Syst. Sci., 16, 1221–1236,
D. A. Hughes
Hydrol. Earth Syst. Sci., 16, 861–871,
Beven, K. J. and Freer, J.: Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11–29, 2001.
Blöschl, G. and Zehe, E.: Invited commentary – On hydrological predictability, Hydrol. Process., 19, 3923–3929, 2005.
Boyle, D. P.: Multicriteria calibration of hydrological models, Department of Hydrology and Water Resources, University of Arizona, Tucson, 193 pp., 2000.
Contreras-Cristán, A., Gutiérrez-Peña, E., and Walker, S. G.: A Note on Whittle's Likelihood, Commun. Stat.-Simul. C., 35, 857–875, 2006.
Daubechies, I.: Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 357 pp., 1992.
Frei, C. and Schär, C.: Detection probability of trends in rare events: Theory and application to heavy precipitation in the Alpine region, J. Climate, 14, 1568–1584, 2001.
Gabor, D.: Theory of communication, J. IEE, 93, 429–457, 1946.
Gaucherel, C.: Use of wavelet transform for temporal characterisation of remote watersheds, J. Hydrol., 269, 101–121, 2002.
Grossmann, A. and Morlet, J.: Decomposition of Hardy functions into square integrable wavelet constant shape, SIAM J. Math. Anal., 15, 723–736, 1984.
Gupta, H. V., Beven, K. J., and Wagener, T.: Model Calibration and Uncertainty Estimation, in: Encyclopedia of Hydrological Sciences, edited by: Anderson, M. G., Wiley, Chichester, UK, 2015–2032, 2005.
Hannan, E. J.: The asymptotic theory of linear time-series models, J. Appl. Prob., 10, 130–145, 1973.
Herbst, M. and Casper, M. C.: Towards model evaluation and identification using Self-Organizing Maps, Hydrol. Earth Syst. Sci., 12, 657–667, 2008.
Herren, E. R., Bauder, A., Hoelzle, M., and Maisch, M.: The Swiss Glaciers 1999/2000 and 2001/2002, Glaciological Commission of the Swiss Academy of Sciences, Zürich, Glaciological Report 121/122, 73, 2002.
Hock, R.: Temperature index melt modelling in mountain areas, J. Hydrol., 282, 104–115, 2003.
Holschneider, M.: Wavelets: an analysis tool, Oxford University Press, Oxford, UK, 423 pp., 1998.
Kaiser, G.: A friendly Guide to Wavelets, edited by: Birkhäuser, New York, USA, 300 pp., 1994.
Kavetski, D., Kuczera, G., and Franks, S. W.: Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory, Water Resour. Res., 42, W03407, https://doi.org/10.1029/2005WR004368, 2006a.
Kavetski, D., Kuczera, G., and Franks, S. W.: Calibration of conceptual hydrological models revisited: 1. Overcoming numerical artefacts, J. Hydrol., 320, 173–186, 2006b.
Klok, E. J., Jasper, K., Roelofsma, K. P., Gurtz, J., and Badoux, A.: Distributed hydrological modelling of a heavily glaciated Alpine river basin, Hydrol. Sci. J., 46, 553–570, 2001.
Labat, D.: Recent advances in wavelet analyses: Part 1. A review of concepts, J. Hydrol., 314, 275–288, 2005.
Lafrenière, M. and Sharp, M.: Wavelet analysis of inter-annual variability in the runoff regimes of glacial and nival stream catchments, Bow Lake, Alberta, Hydrol. Process., 17, 1093–1118, 2003.
Lane, S. N.: Assessment of rainfall-runoff models based upon wavelet analysis, Hydrol. Processes, 21, 586–607, 2006.
Leyland, G. B.: Multi-Objective Optimisation Applied to Industrial Energy Problems, Laboratoire d'Energétique Industrielle, Ecole Polytechnique Fédérale de Lausanne, Switzerland, available at: http://library.epfl.ch/theses, 188 pp., 2002.
Maraun, D. and Kurths, J.: Cross wavelet analysis: significance testing and pitfalls, Nonlin. Processes Geophys., 11, 505–514, 2004.
Maraun, D., Kurths, J., and Holschneider, M.: Non-stationary Gaussian Processes in Wavelet Domain: Definitions, Estimation and Significance Testing, Phys. Rev. E, 75, 016707, https://doi.org/10.1103/PhysRevE.75.016707, 2007.
Montanari, A. and Toth, E.: Calibration of hydrological models in the spectral domain: an opportunity for ungauged basins?, Water Resour. Res., 43, W05434, https://doi.org/10.1029/2006WR005184, 2007.
Moulines, E., Roueff, F., and Taqqu, M. S.: A wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series, Ann. Stat., 36, 1925–1956, 2008.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models. Part I, a discussion of principles, J. Hydrol., 10, 282–290, 1970.
Nicótina, L., Alessi Celegon, E., Rinaldo, A., and Marani, M.: On the impact of rainfall patterns on the hydrologic response, Water Resour. Res., 44, W12401, https://doi.org/10.1029/2007WR006654, 2008.
Priestley, M.: Spectral Analysis and Time Series, Academic Press, London, UK, 884 pp., 1981.
Rango, A. and Martinec, J.: Revisiting the degree-day method for snowmelt computations, Water Resour. Bull., 31, 657–669, 1995.
Reusser, D. E., Blume, T., Schaefli, B., and Zehe, E.: Analysing the temporal dynamics of model performance for hydrological models, Hydrol. Earth Syst. Sci. Discuss., 5, 3169–3211, 2008.
Schaefli, B., Hingray, B., and Musy, A.: Improved calibration of hydrological models: use of a multi-objective evolutionary algorithm for parameter and model structure uncertainty estimation, Hydrology: Science and Practice for the 21st Century, London, UK, 362–371, 2004.
Schaefli, B.: Quantification of modelling uncertainties in climate change impact studies on water resources: Application to a glacier-fed hydropower production system in the Swiss Alps, Ecole Polytechnique Fédérale de Lausanne, Switzerland, vailable at: http://library.epfl.ch/theses, 209 pp., 2005.
Schaefli, B., Hingray, B., Niggli, M., and Musy, A.: A conceptual glacio-hydrological model for high mountainous catchments, Hydrol. Earth Syst. Sci., 9, 95–109, 2005.
Schaefli, B., Balin Talamba, D., and Musy, A.: Quantifying hydrological modeling errors through a mixture of normal distributions, J. Hydrol., 332, 303–315, 2006.
Schaefli, B. and Gupta, H.: Do Nash values have value?, Hydrol. Process., 21, 2075–2080, 2007.
Schaefli, B., Maraun, D., and Holschneider, M.: What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology, Adv. Water Resour., 30(12), 2511–2525, https://doi.org/10.1016/j.advwatres.2007.06.004, 2008
Schaefli, B. and Zehe, E.: Hydrological model performance and parameter estimation in the wavelet-domain, Hydrol. Earth Syst. Sci. Disc., 6, 2451–2498, 2009.
Schmidli, J. and Frei, C.: Trends of heavy precipitation and wet and dry spells in Swizterland during the 20th century, Intern. J. Climatol., 25, 753–771, 2005.
Schreiber, T. and Schmitz, A.: Surrogate time series, Physica D, 142, 346–382, 2000.
Shumway, R. H. and Stoffer, D. S.: Time Series Analysis and Its Applications, With R Examples, 2nd edn., Springer, New York, USA, 576 pp., 2006.
Si, B. C. and Zeleke, T. B.: Wavelet coherency analysis to relate saturated hydraulic properties to soil physical properties, Water Resour. Res., 41, W11424, https://doi.org/10.1029/2005WR004118, 2005.
Torrence, C. and Compo, G. P.: A practical guide to wavelet analysis, B. Am. Meteorol. Soc., 79, 61–78, 1998.
Velasco, C.: Gaussian semiparametric estimation of non-stationary time series, J. Time Ser. Anal., 20, 87–127, 1999.
Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A shuffled complex evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic models, Water Resour. Res., 39, 1201, https://doi.org/10.1029/2002WR001642, 2003.
Wagener, T., Boyle, D. P., Lees, M. J., Wheater, H. S., Gupta, H. V., and Sorooshian, S.: A framework for development and application of hydrological models, Hydrol. Earth Syst. Sci., 5, 13–26, 2001.
Weisstein, E. W.: Metric, From MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/Metric.html, last access: 19 March 2009, 2009.
Whittle, P.: Estimation and information in stationary time series, Ark. Mat., 2, 423–434, 1953.
Willis, I.: Hydrology of glacierized basins, in: Encyclopedia of Hydrological Sciences, edited by: Anderson, M. G., Wiley, Chichester, UK, 2601–2631, 2005.
Winsemius, H., Schaefli, B., Montanari, A., and Savenije, H. H. G.: On the calibration of hydrological models in ungauged basins: a framework for integrating hard and soft hydrological information, Water Resour. Res., https://doi.org/10.1029/2009WR007706, in press, 2009.
Yao, Q. and Brockwell, P. J.: Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series, J. Time Ser. Anal., 27, 857–875, 2006.
Yilmaz, K. K., Gupta, H. V., and Wagener, T.: A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, https://doi.org/10.1029/2007WR006716, 2008.
Zehe, E., Becker, R., Bardossy, A., and Plate, E.: Uncertainty of simulated catchment runoff response in the presence of threshold processes: Role of initial soil moisture and precipitation, J. Hydrol., 315, 183–202, 2005.
Zehe, E., Elsenbeer, H., Lindenmaier, F., Schulz, K., and Blöschl, G.: Patterns of predictability in hydrological threshold systems, Water Resour. Res., 43, W07434, https://doi.org/10.1029/2006WR005589, 2007.