Stewart W. Franks

IAHS decade on predictions in ungauged basins (PUB), 2003-2012: Shaping an exciting future for the hydrological sciences

Abstract Drainage basins in many parts of the world are ungauged or poorly gauged, and in some cases existing measurement networks are declining. The problem is compounded by the impacts of human-induced changes to the land surface and climate, occurring at the local, regional and global scales. Predictions of ungauged or poorly gauged basins under these conditions are highly uncertain. The IAHS Decade on Predictions in Ungauged Basins, or PUB, is a new initiative launched by the International Association of Hydrological Sciences (IAHS), aimed at formulating and implementing appropriate science programmes to engage and energize the scientific community, in a coordinated manner, towards achieving major advances in the capacity to make predictions in ungauged basins. The PUB scientific programme focuses on the estimation of predictive uncertainty, and its subsequent reduction, as its central theme. A general hydrological prediction system contains three components: (a) a model that describes the key processes of interest, (b) a set of parameters that represent those landscape properties that govern critical processes, and (c) appropriate meteorological inputs (where needed) that drive the basin response. Each of these three components of the prediction system, is either not known at all, or at best known imperfectly, due to the inherent multi-scale space—time heterogeneity of the hydrological system, especially in ungauged basins. PUB will therefore include a set of targeted scientific programmes that attempt to make inferences about climatic inputs, parameters and model structures from available but inadequate data and process knowledge, at the basin of interest and/or from other similar basins, with robust measures of the uncertainties involved, and their impacts on predictive uncertainty. Through generation of improved understanding, and methods for the efficient quantification of the underlying multi-scale heterogeneity of the basin and its response, PUB will inexorably lead to new, innovative methods for hydrological predictions in ungauged basins in different parts of the world, combined with significant reductions of predictive uncertainty. In this way, PUB will demonstrate the value of data, as well as provide the information needed to make predictions in ungauged basins, and assist in capacity building in the use of new technologies. This paper presents a summary of the science and implementation plan of PUB, with a call to the hydrological community to participate actively in the realization of these goals.

Bayesian analysis of input uncertainty in hydrological modeling: 2. Application

The Bayesian total error analysis (BATEA) methodology directly addresses both input and output errors in hydrological modeling, requiring the modeler to make explicit, rather than implicit, assumptions about the likely extent of data uncertainty. This study considers a BATEA assessment of two North American catchments: (1) French Broad River and (2) Potomac basins. It assesses the performance of the conceptual Variable Infiltration Capacity (VIC) model with and without accounting for input (precipitation) uncertainty. The results show the considerable effects of precipitation errors on the predicted hydrographs (especially the prediction limits) and on the calibrated parameters. In addition, the performance of BATEA in the presence of severe model errors is analyzed. While BATEA allows a very direct treatment of input uncertainty and yields some limited insight into model errors, it requires the specification of valid error models, which are currently poorly understood and require further work. Moreover, it leads to computationally challenging highly dimensional problems. For some types of models, including the VIC implemented using robust numerical methods, the computational cost of BATEA can be reduced using Newton-type methods.

Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory

Parameter estimation in rainfall-runoff models is affected by uncertainties in the measured input/output data (typically, rainfall and runoff, respectively), as well as model error. Despite advances in data collection and model construction, we expect input uncertainty to be particularly significant (because of the high spatial and temporal variability of precipitation) and to remain considerable in the foreseeable future. Ignoring this uncertainty compromises hydrological modeling, potentially yielding biased and misleading results. This paper develops a Bayesian total error analysis methodology for hydrological models that allows (indeed, requires) the modeler to directly and transparently incorporate, test, and refine existing understanding of all sources of data uncertainty in a specific application, including both rainfall and runoff uncertainties. The methodology employs additional (latent) variables to filter out the input corruption given the model hypothesis and the observed data. In this study, the input uncertainty is assumed to be multiplicative Gaussian and independent for each storm, but the general framework allows alternative uncertainty models. Several ways of incorporating vague prior knowledge of input corruption are discussed, contrasting Gaussian and inverse gamma assumptions; the latter method avoids degeneracies in the objective function. Although the general methodology is computationally intensive because of the additional latent variables, a range of modern numerical methods, particularly Monte Carlo analysis combined with fast Newton-type optimization methods and Hessian-based covariance analysis, can be employed to obtain practical solutions.

Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis

The lack of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall-runoff (CRR) models remains a key challenge in hydrology. The Bayesian total error analysis (BATEA) methodology provides a comprehensive framework to hypothesize, infer, and evaluate probability models describing input, output, and model structural error. This paper assesses the ability of BATEA and standard calibration approaches (standard least squares (SLS) and weighted least squares (WLS)) to address two key requirements of uncertainty assessment: (1) reliable quantification of predictive uncertainty and (2) reliable estimation of parameter uncertainty. The case study presents a challenging calibration of the lumped GR4J model to a catchment with ephemeral responses and large rainfall gradients. Postcalibration diagnostics, including checks of predictive distributions using quantile-quantile analysis, suggest that while still far from perfect, BATEA satisfied its assumed probability models better than SLS and WLS. In addition, WLS/SLS parameter estimates were highly dependent on the selected rain gauge and calibration period. This will obscure potential relationships between CRR parameters and catchment attributes and prevent the development of meaningful regional relationships. Conversely, BATEA provided consistent, albeit more uncertain, parameter estimates and thus overcomes one of the obstacles to parameter regionalization. However, significant departures from the calibration assumptions remained even in BATEA, e.g., systematic overestimation of predictive uncertainty, especially in validation. This is likely due to the inferred rainfall errors compensating for simplified treatment of model structural error.

Multi-decadal variability of flood risk

Recent research has highlighted the persistence of multi-decadal epochs of enhanced/reduced flood risk across New South Wales (NSW), Australia. Recent climatological studies have also revealed multi-decadal variability in the modulation of the magnitude of El Nin椀/Southern Oscillation (ENSO) impacts. In this paper, the variability of flood risk across NSW is analysed with respect to the observed modulation of ENSO event magnitude. This is achieved through the use of a simple index of regional flood risk. The results indicate that cold ENSO events (La Nin和) are the dominant drivers of elevated flood risk. An analysis of multidecadal modulation of flood risk is achieved using the interdecadal Pacific Oscillation (IPO) index. The analysis reveals that IPO modulation of ENSO events leads to multi-decadal epochs of elevated flood risk, however this modulation appears to affect not only the magnitude of individual ENSO events, but also the frequency of their occurrence. This dual modulation of ENSO processes has the effect of reducing and elevating flood risk on multi-decadal timescales. These results have marked implications for achieving robust flood frequency analysis as well as providing a strong example of the role of natural climate variability.

On constraining the predictions of a distributed model: The incorporation of fuzzy estimates of saturated areas into the calibration process

Distributed hydrological models are generally overparameterized, resulting in the possibility of multiple parameterizations from many areas of the parameter space providing acceptable fits to observed data. In this study, TOPMODEL parameterizations are conditioned on discharges, and then further conditioned on estimates of saturated areas derived from ERS-I synthetic aperture radar (SAR) images combined with the In (α/tan β) topographic index, and compared to ground truth saturation measurements made in one small subcatchment. The uncertainty associated with the catchment-wide predictions of saturated area is explicitly incorporated into the conditioning through the weighting of estimates within a fuzzy set framework. The predictive uncertainty associated with the parameterizations is then assessed using the generalized likelihood uncertainty estimation (GLUE) methodology. It is shown that despite the uncertainty in the predictions of saturated area the methodology can reject many previously acceptable parameterizations with the consequence of a marked reduction in the acceptable range of a catchment average transmissivity parameter and of improved predictions of some discharge events.

On the sensitivity of soil-vegetation-atmosphere transfer (SVAT) schemes: equifinality and the problem of robust calibration

Current ‘physically based’ soil-vegetation-atmosphere transfer (SVAT) schemes use increasingly complex descriptions of the physical mechanisms governing evapotranspiration fluxes, thereby requiring the specification of a large number of parameters controlling the vertical fluxes over a single homogeneous area. Recent attention towards the incorporation of sub-grid scale spatial variability in SVAT parameterisations promises to increase the number of parameters for these models. In this paper, it is demonstrated that a simple patch scale SVAT model still permits too many degrees of freedom in terms of fitting the model predictions to calibration or validation data; it is shown that good model fits may be achieved in many areas of the parameter space. Using a Monte Carlo framework, a sensitivity analysis is performed for simulations of data sets from FIFE and Amazonian sites. This is employed to evaluate the role of each parameter for each forcing dataset, and to identify the controlling and redundant parameters and processes. The results suggest that equifinality of parameter sets in calibration to field data must be expected, that there will be a consequent uncertainty in predictive capability and that more emphasis will be required on identifying the critical controls on evapotranspiration in extending predictions from patch to landscape scale in different environments.

Long-term behaviour of ENSO: interactions with the PDO over the past 400 years inferred from paleoclimate records

This study uses proxy climate records derived from paleoclimate data to investigate the long-term behaviour of the Pacific Decadal Oscillation (PDO) and the El Nino Southern Oscillation (ENSO). During the past 400 years, climate shifts associated with changes in the PDO are shown to have occurred with a similar frequency to those documented in the 20th Century. Importantly, phase changes in the PDO have a propensity to coincide with changes in the relative frequency of ENSO events, where the positive phase of the PDO is associated with an enhanced frequency of El Nino events, while the negative phase is shown to be more favourable for the development of La Nina events.

Flood frequency analysis: Evidence and implications of secular climate variability, New South Wales

[1] One of the assumptions of flood frequency analysis is that annual maximum flood peaks are independently and identically distributed. Recent work has shown there exist persistent climate modes that modulate regional climates over multiyear timescales around the globe. Such persistence raises the question whether annual maximum floods are indeed independently and identically distributed. This study revisits this assumption. Noting that a significant shift in Pacific and Indian Ocean sea surface temperatures and other atmospheric variables occurred in the mid-1940s, 41 flood records in New South Wales, Australia, were stratified into pre-1945 and post-1945 records. It was found that the two-parameter lognormal distribution adequately fitted the stratified samples, and in many cases the stratified distributions were significantly different. In fact, the ratio of the post-1945 to the pre-1945 20-year flood exceeded one for 37 of the 41 sites. The evidence that the flood probability model is climate dependent for the case study region is strong. This has implications for flood risk assessment requiring inter alia the need to distinguish between short- and long-term flood risk. In the presence of long-term climate persistence, traditional flood frequency analysis can at best only provide estimates of long-term or unconditional flood risk. The estimation of short-term flood risks will require improved mechanistic understanding of multidecadal climate variability and the development of stochastic models that explicitly recognize such secular variations.

Bayesian estimation of uncertainty in land surface-atmosphere flux predictions

This study addresses the assessment of uncertainty associated with predictions of land surface-atmosphere fluxes using Bayesian Monte Carlo simulation within the generalized likelihood uncertainty estimation (GLUE) methodology. Even a simple soil vegetation-atmosphere transfer (SVAT) scheme is shown to lead to multiple acceptable parameterizations when calibration data are limited to timescales of typical intensive field campaigns. The GLUE methodology assigns a likelihood weight to each acceptable simulation. As more data become available, these likelihood weights may be updated by using Bayes equation. Application of the GLUE methodology can be shown to reveal deficiencies in model structure and the benefit of additional calibration data. The method is demonstrated with data sets taken from FIFE sites in Kansas, and ABRACOS data from the Amazon. Estimates of uncertainty are propagated for each data set revealing significant predictive uncertainty. The value of additional periods of data is then evaluated through comparing updated uncertainty estimates with previous estimates using the Shannon entropy measure.