H11G-01 INVITED 08:05h
Environmental modeling and the propagation of error
Environmental modelling, by definition, requires the development of models to represent the spatially and temporally complex processes that occur in the natural and modified environment. The complexity of the environment relative to the data available for the development of such models necessitates simplifications and assumptions whether the model be data-based empirical, conceptual or physically-based; lumped or distributed. Whilst much effort has been placed on the development of uncertainty estimation techniques to provide quantification of the errors and unknowns associated with environmental models, often key uncertainties remain to be considered explicitly. In this presentation, the explicit propagation of errors and uncertainties is advocated and demonstrated with a number of case studies. The role and propagation of uncertainty and error associated with rainfall-runoff modelling is first considered. Explicit propagation of errors associated with input forcing data and the choice of model structure in a range of applications is demonstrated. Similar examples of error propagation are then demonstrated with regard to sediment fingerprinting, remote sensing of soil moisture and saturation, and infrastructure degradation. These case studies demonstrate a clear need for error propagation techniques to be employed across the range of environmental modelling techniques.
H11G-02 INVITED 08:25h
The Effect of Uncertainty in Spatial Rainfall on Predictions of Storm Runoff
Hydrological response is the result of numerous complex interactions among hydrological inputs (e.g., rain and radiation) and landscape properties (e.g., vegetation, topography, and soil properties) through a number of hydrological processes at the land surface. In many practical problems, the dominant controls on catchment response and on catchment-to-catchment variability are due to spatial rainfall variability. This variability is usually poorly quantified, leading to significant uncertainty in a key driver of hydrological models. I explore two approaches which have been used to explore the significance of rainfall variability to predicted storm runoff: (i) resolving spatial rainfall in detail by measurement and then synthetically discarding the spatial detail in inputs to catchments models; (ii) quantifying the variability statistically and examining its significance in an analytical framework. Results are illustrated using data from the MARVEX project.
H11G-03 08:45h
An attempt to quantify uncertainty in observed river flows: effect on parameterisation and performance evaluation of rainfall-runoff models
Rainfall-runoff models are usually optimized and tested on the basis of (so called) "observed" river flow data. However, strictly speaking river flows are never observed. It is well known that what is observed is usually the river stage, that is subsequently converted in a river flow value by means of a rating curve. Therefore, the "observed" river flow is affected by uncertainty, that can be induced by many different causes. As a matter of fact, the river stage measure is affected by errors, as well as the estimated rating curve. For instance there are approximations in the gauging instruments, as well as in the extrapolation of the rating curve outside the range of the observations that were used for its estimation. This study is aimed at analysing the uncertainty that may affect "observed" river flow data. An attempt is made to quantify the different sources of errors, and to propagate them through the river flow estimation procedure, therefore retrieving an estimation of the total uncertainty in the observed variables. A simulation study is also performed by using synthetic data affected by known sources of uncertainty, in order to assess the potential effect of erroneous observations on rainfall-runoff model parameterization. The effect of errors in the observed variables on total uncertainty in the simulation of river flow data will be also investigated.
http://www.costruzioni-idrauliche.ing.unibo.it/people/alberto
H11G-04 09:00h
The influence of rating curve uncertainty on flood inundation predictions
The uncertainty of rating curves is well explored and understood in current literature. However, most estimations and methods are usually accompanied by a warning not to extrapolate the rating curve beyond a certain range. This is very often impossible for flooding events. Nevertheless, the uncertainty in using these rating curves for flood inundation models is usually ignored. In this paper we investigate the effect of uncertainty of rating curves on flood inundation predictions. The rating curve has been interpolated with two different equations, which are commonly used. The first method is based on a polynomial representation and the second method interpolates data points with the help of the Manning equation. A set of rating curves which represent the system equally well has been derived via the Generalized Likelihood Uncertainty Estimation (GLUE) and the Multicomponent Mapping (Mx) methodology. The multiple rating curves have been used as upstream boundary of the one dimensional unsteady flow routing model HEC-RAS. The manning roughness as well as the model input have been considered as uncertain and varied within a Monte Carlo framework. The model has been evaluated on inundation information retrieved from three different remote sensing sources.
H11G-05 09:15h
Bayesian analysis of data and model error in rainfall-runoff hydrological models
A major unresolved issue in the identification and use of conceptual hydrologic models is realistic description of uncertainty in the data and model structure. In particular, hydrologic parameters often cannot be measured directly and must be inferred (calibrated) from observed forcing/response data (typically, rainfall and runoff). However, rainfall varies significantly in space and time, yet is often estimated from sparse gauge networks. Recent work showed that current calibration methods (e.g., standard least squares, multi-objective calibration, generalized likelihood uncertainty estimation) ignore forcing uncertainty and assume that the rainfall is known exactly. Consequently, they can yield strongly biased and misleading parameter estimates. This deficiency confounds attempts to reliably test model hypotheses, to generalize results across catchments (the regionalization problem) and to quantify predictive uncertainty when the hydrologic model is extrapolated. This paper continues the development of a Bayesian total error analysis (BATEA) methodology for the calibration and identification of hydrologic models, which explicitly incorporates the uncertainty in both the forcing and response data, and allows systematic model comparison based on residual model errors and formal Bayesian hypothesis testing (e.g., using Bayes factors). BATEA is based on explicit stochastic models for both forcing and response uncertainty, whereas current techniques focus solely on response errors. Hence, unlike existing methods, the BATEA parameter equations directly reflect the modeler's confidence in all the data. We compare several approaches to approximating the parameter distributions: a) full Markov Chain Monte Carlo methods and b) simplified approaches based on linear approximations. Studies using synthetic and real data from the US and Australia show that BATEA systematically reduces the parameter bias, leads to more meaningful model fits and allows model comparison taking into account forcing uncertainty. The full MCMC approach also yields estimates of the true forcing (conditioned on the model assumptions), which can be used to improve data collection. We expect the ability to meaningfully disaggregate sources of uncertainty to be of significant benefit in hydrology and environmental modeling in general.
H11G-06 09:30h
Uncertainty Quantification of Satellite Precipitation Estimation and Monte Carlo Assessment of the Error Propagation into Hydrologic Response
A general framework to quantify the error associated with satellite-based precipitation estimates, at various spatial and temporal scales is presented. In addition, the impact of using such precipitation data as input to a hydrologic rainfall-runoff model is examined. The uncertainty in the satellite-based precipitation estimates, as a function of the space (A), time (T), sampling frequency (Dt), and spatio-temporal average of precipitation estimates (R), using two years of high resolution PERSIANN-CCS* precipitation data over Southwest U.S, is determined. Parameter sensitivity analysis is conducted at 5o x 5o latitude-longitude grids for 16 selected areas. The eventual goal of this latter step is to obtain a generalization of the error function. The influence of spatio-temporal precipitation errors on hydrologic response is examined using a Monte Carlo approach. By this approach, an ensemble of precipitation data is generated, as forcing to the hydrologic model, and the resulting uncertainty in the forecasted streamflow is estimated. The applicability and usefulness of this procedure is demonstrated in the case of the Leaf River Basin, located north of Collins, Mississippi. It is shown that the current strategy offers a more realistic uncertainty assessment of precipitation estimates and the correspondingly streamflow forecasts. *Hong, Y., K. Hsu, S. Sorooshian, and X. Gao, 2004: Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network--Cloud Classification System, Journal of Applied Meteorology, in press.
H11G-07 09:45h
Estimating Model Parameter Uncertainty Using A Distribution Oriented Approach and a Similarity Measure
We use two very recently introduced in hydrology measures of performance: the Distributions Oriented (DO) approach and a set theory-based similarity metric - the Hausdorff Norm (HN) to evaluate the performance of two extensively used distributed rainfall-runoff models: Topmodel and PRMS. The distribution oriented approach considers the bivariate distribution of model outputs and observations and the corresponding marginal distributions. The Hausdorff norm allows for the inclusion, within the same framework or measure, both the spatial and temporal scales as a single multi-dimensional array. The performance evaluation is carried out over different time and spatial scales. The models are run over two nested catchments located in different climatic environments - one relatively wet, the Blue River in Oklahoma, and other semi-arid - the Sycamore Creek in Arizona. The levels and quality of input information are very dissimilar. To drive the models radar precipitation is used for the Blue River while the products generated at the University of Washington and gage measurements are used for Sycamore Creek. Both catchments have nested gages and the models are run to simulate 10 years of daily runoff at those points with different levels of discretization/resolution. Both measures: the DO and the HN, are used for parameter estimation using the multiple objective framework developed at the University of Arizona -that allows for the inclusion of trade-off uncertainties of the objective functions, and are compared against each other and against traditional scalar measures of performance as Nash Sutcliffe efficiency, bias, and general duration curves. In the Sycamore Creek a PRMS parameterization of the channel transmission losses is also considered for evaluation because of the important role played by those losses in the shape of the hydrographs.