A stochastic framework to assess the performance of flood warning systems based on rainfall‐runoff modeling

Nowadays, Flood Forecasting and Warning Systems (FFWSs) are known as the most inexpensive and efficient non‐structural measures for flood damage mitigation in the world. Benefit to cost of the FFWSs has been reported to be several times of other flood mitigation measures. Beside these advantages, uncertainty in flood predictions is a subject that may affect FFWS's reliability and the benefits of these systems. Determining the reliability of advanced flood warning systems based on the rainfall–runoff models is a challenge in assessment of the FFWS performance which is the subject of this study. In this paper, a stochastic methodology is proposed to provide the uncertainty band of the rainfall–runoff model and to calculate the probability of acceptable forecasts. The proposed method is based on Monte Carlo simulation and multivariate analysis of the predicted time and discharge error data sets. For this purpose, after the calibration of the rainfall–runoff model, the probability distributions of input calibration parameters and uncertainty band of the model are estimated through the Bayesian inference. Then, data sets of the time and discharge errors are calculated using the Monte Carlo simulation, and the probability of acceptable model forecasts is calculated by multivariate analysis of data using copula functions. The proposed approach was applied for a small watershed in Iran as a case study. The results showed using rainfall–runoff modeling based on real‐time precipitation is not enough to attain high performance for FFWSs in small watersheds, and it seems using weather forecasts as the inputs of rainfall–runoff models is essential to increase lead times and the reliability of FFWSs in small watersheds. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation for rainfall-runoff modeled as a partially observed Markov process

Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.     

Dual state–parameter estimation of hydrological models using ensemble Kalman filter

Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.     

On the prediction of persistent processes using the output of deterministic models

A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs.     

Enhancing tidal prediction accuracy in a deterministic model using chaos theory

The classical deterministic approach to tidal prediction is based on barotropic or baroclinic models with prescribed boundary conditions from a global model or measurements. The prediction by the deterministic model is limited by the precision of the prescribed initial and boundary conditions. Improvement to the knowledge of model formulation would only marginally increase the prediction accuracy without the correct driving forces. This study describes an improvement in the forecasting capability of the tidal model by combining the best of a deterministic model and a stochastic model. The latter is overlaid on the numerical model predictions to improve the forecast accuracy. The tidal prediction is carried out using a three-dimensional baroclinic model and, error correction is instigated using a stochastic model based on a local linear approximation. Embedding theorem based on the time lagged embedded vectors is the basis for the stochastic model. The combined model could achieve an efficiency of 80% for 1 day tidal forecast and 73% for a 7 day tidal forecast as compared to the deterministic model estimation.     

Incorporating Natural Changes in Global Climate in Very-Long-Range Forecasting of River Runoff

A method is proposed for incorporating possible global changes in the state of the atmosphere, basing on K. Hasselmann’s theory of stochastic climate models, for assessing the significance of forecasts of variations of annual river runoff depth in the XXI century. The data used includes the results of river runoff simulation at warming, obtained using 21 IPCC climate models along with six IPCC scenarios of greenhouse gas emission, and MEI scenario. The significance index of forecasted runoff variations, i.e., the values of runoff depth increments divided by the standard error of forecasts was mapped. To demonstrate the role of the maps of significance index, which have been constructed taking into account forecast uncertainty because of the natural changes in global climate, those maps were compared with the maps of significance index calculated basing on other sources of errors. At large time scales, the uncertainty of runoff forecasts owing to natural changes in global climate plays the main role in assessing the reliability of forecasts in areas where greenhouse effect is strongest. Estimates of the significance index show that statistically significant changes in the annual runoff depth in the extreme northeast of Eurasia can be expected to occur not earlier than the late XXI century. In other RF regions, as well as in the majority of world areas, the forecasted changes in the annual runoff depth are comparable with the standard errors of the respective estimates or are less than they are.     

Estimating Runoff Using Hydro-Geodetic Approaches

Given the continuous decline in global runoff data availability over the past decades, alternative approaches for runoff determination are gaining importance. When aiming for global scale runoff at a sufficient temporal resolution and with homogeneous accuracy, the choice to use spaceborne sensors is only a logical step. In this respect, we take water storage changes from Gravity Recovery And Climate Explorer (grace) results and water level measurements from satellite altimetry, and present a comprehensive assessment of five different approaches for river runoff estimation: hydrological balance equation, hydro-meteorological balance equation, satellite altimetry with quantile function-based stage–discharge relationships, a rudimentary instantaneous runoff–precipitation relationship, and a runoff–storage relationship that takes time lag into account. As a common property, these approaches do not rely on hydrological modeling; they are either purely data driven or make additional use of atmospheric reanalyses. Further, these methods, except runoff–precipitation ratio, use geodetic observables as one of their inputs and, therefore, they are termed hydro-geodetic approaches. The runoff prediction skill of these approaches is validated against in situ runoff and compared to hydrological model predictions. Our results show that catchment-specific methods (altimetry and runoff–storage relationship) clearly outperform the global methods (hydrological and hydro-meteorological approaches) in the six study regions we considered. The global methods have the potential to provide runoff over all landmasses, which implies gauged and ungauged basins alike, but are still limited due to inconsistencies in the global hydrological and hydro-meteorological datasets that they use.     

Issues in generating stochastic observables for hydrological models

This paper provides a historical review and critique of stochastic generating models for hydrological observables, from early generation of monthly discharge series, through flood frequency estimation by continuous simulation, to current weather generators. There are a number of issues that arise in such models, from uncertainties in the observational data on which such models must be based, to the potential persistence effects in hydroclimatic systems, the proper representation of tail behaviour in the underlying distributions, and the interpretation of future scenarios.     

Uncertainties in real‐time flood forecasting with neural networks

Although artificial neural networks (ANNs) have been applied in rainfall runoff modelling for many years, there are still many important issues unsolved that have prevented this powerful non‐linear tool from wide applications in operational flood forecasting activities. This paper describes three ANN configurations and it is found that a dedicated ANN for each lead‐time step has the best performance and a multiple output form has the worst result. The most popular form with multiple inputs and single output has the average performance. In comparison with a linear transfer function (TF) model, it is found that ANN models are uncompetitive against the TF model in short‐range predictions and should not be used in operational flood forecasting owing to their complicated calibration process. For longer range predictions, ANN models have an improved chance to perform better than the TF model; however, this is highly dependent on the training data arrangement and there are undesirable uncertainties involved, as demonstrated by bootstrap analysis in the study. To tackle the uncertainty issue, two novel approaches are proposed: distance analysis and response analysis. Instead of discarding the training data after the model's calibration, the data should be retained as an integral part of the model during its prediction stage and the uncertainty for each prediction could be judged in real time by measuring the distances against the training data. The response analysis is based on an extension of the traditional unit hydrograph concept and has a very useful potential to reveal the hydrological characteristics of ANN models, hence improving user confidence in using them in real time. Copyright © 2006 John Wiley & Sons, Ltd.     

A data based mechanistic approach to nonlinear flood routing and adaptive flood level forecasting

Operational flood forecasting requires accurate forecasts with a suitable lead time, in order to be able to issue appropriate warnings and take appropriate emergency actions. Recent improvements in both flood plain characterization and computational capabilities have made the use of distributed flood inundation models more common. However, problems remain with the application of such models. There are still uncertainties associated with the identifiability of parameters; with the computational burden of calculating distributed estimates of predictive uncertainty; and with the adaptive use of such models for operational, real-time flood inundation forecasting. Moreover, the application of distributed models is complex, costly and requires high degrees of skill. This paper presents an alternative to distributed inundation models for real-time flood forecasting that provides fast and accurate, medium to short-term forecasts. The Data Based Mechanistic (DBM) methodology exploits a State Dependent Parameter (SDP) modelling approach to derive a nonlinear dependence between the water levels measured at gauging stations along the river. The transformation of water levels depends on the relative geometry of the channel cross-sections, without the need to apply rating curve transformations to the discharge. The relationship obtained is used to transform water levels as an input to a linear, on-line, real-time and adaptive stochastic DBM model. The approach provides an estimate of the prediction uncertainties, including allowing for heterescadasticity of the multi-step-ahead forecasting errors. The approach is illustrated using an 80 km reach of the River Severn, in the UK.     

Sensitivity of acoustic propagation to uncertainties in the marine environment as characterized by various rapid environmental assessment methods

Accurate sonar performance prediction modelling depends on a good knowledge of the local environment, including bathymetry, oceanography and seabed properties. The function of rapid environmental assessment (REA) is to obtain relevant environmental data in a tactically relevant time frame, with REA methods categorized by the nature and immediacy of their application, from historical databases through remotely sensed data to in situ acquisition. However, each REA approach is subject to its own set of uncertainties, which are in turn transferred to uncertainty in sonar performance prediction. An approach to quantify and manage this uncertainty has been developed through the definition of sensitivity metrics and Monte Carlo simulations of acoustic propagation using multiple realizations of the marine environment. This approach can be simplified by using a linearized two-point sensitivity measure based on the statistics of the environmental parameters used by acoustic propagation models. The statistical properties of the environmental parameters may be obtained from compilations of historical data, forecast conditions or in situ measurements. During a field trial off the coast of Nova Scotia, a set of environmental data, including oceanographic and geoacoustic parameters, were collected together with acoustic transmission loss data. At the same time, several numerical models to forecast the oceanographic conditions were run for the area, including 5- and 1-day forecasts as well as nowcasts. Data from the model runs are compared to each other and to in situ environmental sampling, and estimates of the environmental uncertainties are calculated. The forecast and in situ data are used with historical geoacoustic databases and geoacoustic parameters collected using REA techniques, respectively, to perform acoustic transmission loss predictions, which are then compared to measured transmission loss. The progression of uncertainties in the marine environment, within and between different REA categories, and the consequences on acoustic propagation are examined.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

A data-based regional scale autoregressive rainfall-runoff model: a study from the Odra River

This paper aims to compare the performances of multivariate autoregressive (MAR) techniques and univariate autoregressive (AR) methods applied to regional scale rainfall-runoff modelling. We focus on the case study from the upper and middle reaches of the Odra River with its main tributaries in SW Poland. The rivers drain both the mountains (the Sudetes) and the lowland (Nizina Śląska). The region is exposed to extreme hydrologic and meteorological events, especially rain-induced and snow-melt floods. For the analysis, four hydrologic and meteorological variables are chosen, i.e., discharge (17 locations), precipitation (7 locations), thickness of snow cover (7 locations) and groundwater level (1 location). The time period is November 1971–December 1981 and the temporal resolution of the time series is of 1 day. Both MAR and AR models of the same orders are fitted to various subsets of the data and subsequently forecasts of discharge are derived. In order to evaluate the predictions the stepwise procedure is applied to make the validation independent of the specific sample path of the stochastic process. It is shown that the model forecasts peak discharges even 2–4 days in advance in the case of both rain-induced and snow-melt peak flows. Furthermore, the accuracy of discharge predictions increases if one analyses the combined data on discharge, precipitation, snow cover, and groundwater level instead of the pure discharge multivariate time series. MAR-based discharge forecasts based on multivariate data on discharges are more accurate than AR-based univariate predictions for a year with a flood, however, this relation is reverse in the case of the free-of-flooding year. In contrast, independently of the occurrence of floods within a year, MAR-based discharge forecasts based on discharges, precipitation, snow cover, and groundwater level are more precise than AR-based predictions.     

Improving runoff prediction using agronomical information in a cropped,loess covered catchment

Predicting runoff hot spots and hot‐moments within a headwater crop‐catchment is of the utmost importance to reduce adverse effects on aquatic ecosystems by adapting land use management to control runoff. Reliable predictions of runoff patterns during a crop growing season remain challenging. This is mainly due to the large spatial and temporal variations of topsoil hydraulic properties controlled by complex interactions between weather, growing vegetation, and cropping operations. This interaction can significantly modify runoff patterns and few process‐based models can integrate this evolution of topsoil properties during a crop growing season at the catchment scale. Therefore, the purpose of this study was to better constrain the event‐based hydrological model Limburg Soil Erosion Model by incorporating temporal constraints for input topsoil properties during a crop growing season (LISEM). The results of the temporal constraint strategy (TCS) were compared with a classical event per event calibration strategy (EES) using multi‐scale runoff information (from plot to catchment). The EES and TCS approaches were applied in a loess catchment of 47 ha located 30 km northeast of Strasbourg (Alsace, France). A slight decrease of the Nash–Sutcliffe efficiency criterion on runoff discharge for TCS compared to EES was counterbalanced by a clear improvement of the spatial runoff patterns within the catchment. This study showed that limited agronomical and climatic information added during the calibration step improved the spatial runoff predictions of an event‐based model. Reliable prediction of runoff source, connectivity, and dynamics can then be derived and discussed with stakeholders to identify runoff hot spots and hot‐moments for subsequent land use and crop management modifications.     

Effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data

This paper investigates the effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu-White model. To handle uncertainty in the rock-physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock-physics models and we consider the parameters of the rock-physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock-physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock-physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock-physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock-physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation.     

The issue of global warming and changes in the runoff of Russian rivers

Maps of a series of characteristics were calculated and constructed for RF territory, including mean values of changes in runoff depths (evaluated by the main climate models of the Intergovernmental Panel on Climate Change) due to greenhouse effect estimated for 2040–2070; root-mean-square deviations from these values; relative errors of the estimates; mean values of changes in the runoff depth for different scenarios of greenhouse gas emissions; absolute and relative deviations of these values from their means for scenarios and integration of models. Chronological forecasts of possible changes in the mean runoff values for the rivers of Volga, Northern Dvina, Pechora, Ob, Yenisei, Lena, Yana, Indigirka, Kolyma, and Amur up to 2100 are calculated, and the root-mean-square errors of these characteristics are evaluated for the maximum number of uncertainties in the forecast. The greenhouse effect is shown to be less significant, other factors being the same, for rivers with small drainage basins and rivers with small modulus of flow.     

Evaluating sources of uncertainty in Australian runoff projections

Generating estimates of the future impacts of climate change on human and natural systems is confounded by cascading uncertainties which propagate through the impact assessment. Here, a simple stochastic rainfall–runoff model representing 238 river basins on the Australian continent was used to assess the sensitivity of the risk of runoff changes to various sources of uncertainty. Uncertainties included global mean temperature change, greenhouse gas stabilisation targets, catchment sensitivities to climatic change, and the seasonality of runoff, rainfall, and evaporation. Model simulations provided estimates of the first-order risk of climate change to Australian catchments, with several regions having high likelihoods of experiencing significant reductions in future runoff. Climate uncertainty (at global and regional scales) was identified as the dominant driving force in hydrological risk assessments. Uncertainties in catchment sensitivities to climatic changes also influenced risk, provided they were sufficiently large, whereas structural assumptions of the model were generally negligible. Collectively, these results indicate that rigorous assessment of climate risk to water resources over relatively long time-scales is largely a function of adequately exploring the uncertainty space of future climate changes.