Total Predictive Uncertainty Research Articles

A benchmark on uncertainty quantification for deep learning prognostics

Reliable uncertainty quantification on RUL prediction is crucial for informative decision-making in predictive maintenance. In this context, we assess some of the latest developments in the field of uncertainty quantification for deep learning prognostics. This includes the state-of-the-art variational inference algorithms for Bayesian neural networks (BNN) as well as popular alternatives such as Monte Carlo Dropout (MCD), deep ensembles (DE), and heteroscedastic neural networks (HNN). All the inference techniques share the same inception architecture as functional model. The performance of the methods is evaluated on a subset of the large NASA N-CMAPSS dataset for aircraft engines. The assessment includes RUL prediction accuracy, the quality of predictive uncertainty, and the possibility of breaking down the total predictive uncertainty into its aleatoric and epistemic parts. Although all methods are close in terms of accuracy, we find differences in the way they estimate uncertainty. Thus, DE and MCD generally provide more conservative predictive uncertainty than BNN. Surprisingly, HNN achieve strong results without the added complexity of BNN. None of these methods exhibited strong robustness to out-of-distribution cases, with BNN and HNN methods particularly susceptible to low accuracy and overconfidence. BNN techniques presented anomalous miscalibration issues at the later stages of the system lifetime.

Estimating and Modeling Pinus contorta Transpiration in a Montane Meadow Using Sap-Flow Measurements

This study quantifies the transpiration of encroached lodgepole pine (Pinus contorta var. murryana (Grev. & Balf.) Engelm.) in a montane meadow using pre-restoration sap-flow measurements. Lodgepole pine transpiration and its response to environmental variables were examined in Rock Creek Meadow (RCM), Southern Cascade Range, CA, USA. Sap-flow data from lodgepole pines were scaled to the meadow using tree survey data and then validated with MODIS evapotranspiration estimates for the 2019 and 2020 growing seasons. A modified Jarvis–Stewart model calibrated to 2020 sap-flow data analyzed lodgepole pine transpiration’s correlation with solar radiation, air temperature, vapor pressure deficit, and soil volumetric water content. Model validation utilized 2021 growing season sap-flow data. Calibration and validation employed a Markov Chain Monte Carlo (MCMC) approach through the DREAM(ZS) algorithm with a generalized likelihood (GL) function, enabling parameter and total uncertainty assessment. The model’s scaling was compared with simple scaling estimates. Average lodgepole pine transpiration at RCM ranged between 220.6 ± 25.3 and 393.4 ± 45.7 mm for the campaign (mid-July 2019 to mid-August 2020) and 100.2 ± 11.5 to 178.8 ± 20.7 mm for the 2020 partial growing season (April to mid-August), akin to MODIS ET. The model aligned well with observed normalized sap-velocity during the 2020 growing season (RMSE = 0.087). However, sap-velocity, on average, was underpredicted by the model (PBIAS = −6.579%). Model validation mirrored calibration in performance metrics (RMSE = 0.1233; PBIAS = −2.873%). The 95% total predictive uncertainty confidence intervals generated by GL-DREAM(ZS) enveloped close to the theoretically expected 95% of total observations for the calibration (94.5%) and validation (81.8%) periods. The performance of the GL-DREAM(ZS) approach and uncertainty assessment in this study shows promise for future MJS model applications, and the model-derived 2020 transpiration estimates highlight the MJS model utility for scaling sap-flow measurements from individual trees to stands of trees.

DEUCE v1.0: a neural network for probabilistic precipitation nowcasting with aleatoric and epistemic uncertainties

Abstract. Precipitation nowcasting (forecasting locally for 0–6 h) serves both public security and industries, facilitating the mitigation of losses incurred due to, e.g., flash floods and is usually done by predicting weather radar echoes, which provide better performance than numerical weather prediction (NWP) at that scale. Probabilistic nowcasts are especially useful as they provide a desirable framework for operational decision-making. Many extrapolation-based statistical nowcasting methods exist, but they all suffer from a limited ability to capture the nonlinear growth and decay of precipitation, leading to a recent paradigm shift towards deep-learning methods which are more capable of representing these patterns. Despite its potential advantages, the application of deep learning in probabilistic nowcasting has only recently started to be explored. Here we develop a novel probabilistic precipitation nowcasting method, based on Bayesian neural networks with variational inference and the U-Net architecture, named DEUCE. The method estimates the total predictive uncertainty in the precipitation by combining estimates of the epistemic (knowledge-related and reducible) and heteroscedastic aleatoric (data-dependent and irreducible) uncertainties, using them to produce an ensemble of development scenarios for the following 60 min. DEUCE is trained and verified using Finnish Meteorological Institute radar composites compared to established classical models. Our model is found to produce both skillful and reliable probabilistic nowcasts based on various evaluation criteria. It improves the receiver operating characteristic (ROC) area under the curve scores 1 %–5 % over STEPS and LINDA-P baselines and comes close to the best-performer STEPS on a continuous ranked probability score (CRPS) metric. The reliability of DEUCE is demonstrated with, e.g., having the lowest expected calibration error at 20 and 25 dBZ reflectivity thresholds and coming second at 35 dBZ. On the other hand, the deterministic performance of ensemble means is found to be worse than that of extrapolation and LINDA-D baselines. Last, the composition of the predictive uncertainty is analyzed and described, with the conclusion that aleatoric uncertainty is more significant and informative than epistemic uncertainty in the DEUCE model.

Smoothed Online Combinatorial Optimization Using Imperfect Predictions

Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive rounds. We study smoothed online combinatorial optimization problems when an imperfect predictive model is available, where the model can forecast the future cost functions with uncertainty. We show that using predictions to plan for a finite time horizon leads to regret dependent on the total predictive uncertainty and an additional switching cost. This observation suggests choosing a suitable planning window to balance between uncertainty and switching cost, which leads to an online algorithm with guarantees on the upper and lower bounds of the cumulative regret. Empirically, our algorithm shows a significant improvement in cumulative regret compared to other baselines in synthetic online distributed streaming problems.

Quantitative assessment of rock lithology from gamma-ray and mud logging data

The data on vertical variations of the rock lithological content along the geological profiles of boreholes are essential for interwell correlation, geological or hydrodynamic modeling, optimization of drilling process, etc. There are direct (investigation of core samples) and indirect (processing and interpretation of well-logging data) methods applied in petroleum engineering to determine rock lithology. Both approaches have several limitations (such as low quality of logging data in case of washouts, low frequency of sampling of drill cuttings, limited number of wells drilled with coring, etc.) calling for alternative approaches to determine rock lithological content along the borehole. One of the alternative solutions could be application of mud logging (drilling and mud gas data) due to the strong physical background of interrelations between drilling and mud gas data on one side and rock lithology on the other. Literature review shows that many of existing machine learning-based solutions assume application of mud logging data mainly for rock typing (qualitative assessment of rock lithology). Concurrently, many applied problems require quantitative data on rock lithology (volumetric concentrations of rock lithological components). To fill this gap, we assessed the capabilities of mud logging data for quantitative characterization of rock lithology. We proposed a new algorithm for the task at hand relying on special data processing and machine learning algorithms. As an input data we used drilling, mud gas, and gamma-ray data. The results of the developed algorithm application for three industrial wells confirmed the effectiveness of the developed algorithm. During our research we compared the performance of XGBoost algorithm and 1-D convolutional neural network. Obtained results allow concluding that the obtained regression models and developed algorithm exhibit good generalization ability providing the average total prediction uncertainty on unseen well of less than 0.15 c.u.

Applications of Bayesian Neural Networks in Outlier Detection.

Anomaly detection is crucial in a variety of domains, such as fraud detection, disease diagnosis, and equipment defect detection. With the development of deep learning, anomaly detection with Bayesian neural networks (BNNs) becomes a novel research topic in recent years. This article aims to propose a widely applicable method of outlier detection (a category of anomaly detection) using BNNs based on uncertainty measurement. There are three kinds of uncertainties generated in the prediction of BNNs: epistemic uncertainty, aleatoric uncertainty, and (model) misspecification uncertainty. Although the approaches in previous studies are adopted to measure epistemic and aleatoric uncertainty, a new method of utilizing loss functions to quantify misspecification uncertainty is proposed in this article. Then, these three uncertainty sources are merged together by specific combination models to construct total prediction uncertainty. In this study, the key idea is that the observations with high total prediction uncertainty should correspond to outliers in the data. The method of this research is applied to the experiments on Modified National Institute of Standards and Technology (MNIST) dataset and Taxi dataset, respectively. From the results, if the network is appropriately constructed and well-trained and model parameters are carefully tuned, most anomalous images in MNIST dataset and all the abnormal traffic periods in Taxi dataset can be nicely detected. In addition, the performance of this method is compared with the BNN anomaly detection methods proposed before and the classical Local Outlier Factor and Density-Based Spatial Clustering of Applications with Noise methods. This study links the classification of uncertainties in essence with anomaly detection and takes the lead to consider combining different uncertainty sources to reform detection outcomes instead of using only single uncertainty each time.

Quantifying and reducing the uncertainty in multi-source precipitation products using Bayesian total error analysis: A case study in the Danjiangkou Reservoir region in China

Quantifying and reducing the errors and uncertainties in high-resolution gridded precipitation products are essential for hydrological modelling to generate realistic parameter estimates and accurate model predictions. Formal Bayesian inference provides a powerful tool to quantify rainfall uncertainty and other uncertainty factors in hydrological modelling. An efficient way to reduce rainfall uncertainty in hydrological modelling is to merge precipitation estimates from multiple sources prior to their real-world applications. However, it remains a challenging task to optimally determine the weightings of different precipitation estimates based on the predictive ability of a hydrological model, especially from a probabilistic perspective. This study addresses this issue by evaluating and merging six gridded precipitation products using formal Bayesian inference schemes, including the Markov Chain Monte Carlo (MCMC) approach and Bayesian total error analysis (BATEA). MCMC describes the total predictive uncertainty using residual error models. In contrast, BATEA utilizes the storm depth multiplier approach to separately account for rainfall uncertainty in probabilistic uncertainty quantification. A novel signature of model predictability that combines the reliability and precision of probabilistic model predictions is developed to quantify the predictive ability of a hydrological model from precipitation estimates. Using the proposed predictability signature, we examined the benefit of optimally merging multi-source precipitation estimates in improving the accuracy of hydrologic simulations by applying the method to the Danjiangkou Reservoir region (DRR) between 1998 and 2007. The analysis demonstrates that (1) BATEA, compared to MCMC, can provide more realistic estimates of model parameters and tighter predictive intervals of daily streamflow when using rain gauge observations as well as gridded precipitation products; and (2) the proposed predictability signature is efficient for optimally merging precipitation measurements as it can produce tighter uncertainty bands and better streamflow simulations than individual precipitation estimates. This study provides insights into improved quantification and reduction of uncertainty in multi-source precipitation products for hydrological modelling.

Uncertainty quantification in super-resolution guided wave array imaging using a variational Bayesian deep learning approach

Super-resolution guided wave array imaging has shown to be a feasible tool to detect and image sub-wavelength defects. However, research gaps remain in effectively quantifying and understanding the uncertainties in super-resolution imaging. In this study, we present a Bayesian deep learning approach to quantify and interpret various uncertainties in super-resolution guided wave array imaging. Specifically, we implement a Monte Carlo (MC) dropout scheme in the multi-scale deep learning models for approximate Bayesian inference to effectively quantify uncertainties in super-resolution subwavelength defect imaging. Furthermore, we decompose the total predictive uncertainty into distinct uncertainty sources: aleatoric uncertainty inherent in the data and epistemic uncertainty associated with the Bayesian deep learning model. From the experimental study, we observe that the two types of uncertainty (aleatoric and epistemic) in super-resolution guided wave array imaging can be successfully quantified using the multi-scale Bayesian deep learning approach. We further discuss the effectiveness of the Bayesian deep learning approach in small-data cases and compare the super-resolution imaging performance with a non-Bayesian (deterministic) deep learning approach.

Uncertainty-guided man–machine integrated patient-specific quality assurance

PurposeProviding the confidence level (Uncertainty) of prediction results and guiding patient-specific quality assurance (pQA) can enhance the safety of AI (Artificial intelligence)-based automatic pQA models. However, even state-of-the-art automatic pQA models can only predict the gamma passing rate (GPR) and cannot quantify the prediction uncertainty, limiting the safe clinical translation of these models. This study aims to develop an uncertainty-guided man–machine integrated pQA (UgMi-pQA) method to address this issue. MethodsAn uncertainty-aware dual-task deep learning (UDDL) model, combined with an interwoven training method and Monte Carlo dropout approximation Bayesian inference, to enable simultaneous output of the predicted GPR and corresponding total prediction uncertainty to guide pQA. 1541 pairs of field fluences and GPRs collected from 165 glioma, 50 lung (conventional fractionation), and 20 liver cases were separated for the UDDL model training, validation, calibration, and test in a ratio of 7:1:1:1, respectively. Furthermore, 413 pairs of fluences and GPRs collected from 12 breast, 10 cervix, 9 esophagus, 8 tongue, and 12 lung SBRT cases were gathered for the out-of-distribution (OOD) detection. ResultsClinical accuracy of 100.0% was reached with only 61.7% of the workload. Samples with substantial prediction errors and failed samples with low label GPR (<95%) could be successfully screened out. The capability ranges of two different models were both successfully identified with the prediction uncertainty significantly larger for OOD samples than for in-distribution samples (p < 0.01). ConclusionThis study presents the first work on uncertainty quantification for deep learning automatic pQA tasks. The UgMi-pQA method can balance the efficiency and safety of the automatic pQA models and promote their clinical application.

A new approach for suspended sediment load calculation based on generated flow discharge considering climate change

Abstract Use of general circulation models (GCMs) is common for forecasting of hydrometric and meteorological parameters, but the uncertainty of these models is high. This study developed a new approach for calculation of suspended sediment load (SSL) using historical flow discharge data and SSL data of the Idanak hydrometric station on the Marun River (in the southwest of Iran) from 1968 to 2014. This approach derived sediment rating relation by observed data and determined trend of flow discharge time series data by Mann-Kendall nonparametric trend (MK) test and Theil-Sen approach (TSA). Then, the SSL was calculated for a future period based on forecasted flow discharge data by TSA. Also, one hundred annual and monthly flow discharge time series data (for the duration of 40 years) were generated by the Markov chain and the Monte Carlo (MC) methods and it calculated 90% of total prediction uncertainty bounds for flow discharge time series data by Latin Hypercube Sampling (LHS) on Monte Carlo (MC). It is observed that flow discharge and SSL will increase in summer and will reduce in spring. Also, the annual amount of SSL will reduce from 2,811.15 ton/day to 1,341.25 and 962.05 ton/day in the near and far future, respectively.

Quantifying the Uncertainties in Data-Driven Models for Reservoir Inflow Prediction

Reservoir inflow prediction is subject to high uncertainties in data-driven modelling. In this study, a decomposition scheme is proposed to evaluate the individual and combined contributions of uncertainties from input sets and data-driven models to the total predictive uncertainty. Six variables (i.e., inflow (Q), precipitation (P), relative humidity (H), minimum temperature (Tmin), maximum temperature (Tmax) and precipitation forecast (F)), and three data-driven models (i.e., artificial neural network (ANN), support vector machine (SVM), and adaptive neuro fuzzy inference systems (ANFIS)) are used to produce an ensemble of 10-day inflow forecast for Huanren reservoir in China, and the analysis of variance (ANOVA) method is employed to decompose the uncertainty. The ensemble forecast results show that when the three variables, i.e., Q, P and F, are used only, the predictive accuracy of the data-driven models is very high and the addition of the other three variables, i. e., H, Tmin and Tmax, can slightly improve the predictive accuracy. The decomposition results indicate that the input set is the dominant source of uncertainty, the contribution of the data-driven model is limited and has a strong seasonal variation: larger in winter and summer, smaller in spring and autumn. Most importantly, the interactive contribution of the input set and the data-driven model to the total predictive uncertainty is very high and is more significant than the individual contribution from the model itself, implying that the combined effects of the input set and the data-driven model should be carefully considered in the modelling process.

Non-intrusive uncertainty quantification in the simulation of turbulent spray combustion using Polynomial Chaos Expansion: A case study

A major source of input uncertainties in the simulation of turbulent spray combustion is introduced by the need to specify the state of the liquid spray after primary breakup, i.e. a spray boundary condition for the lagrangian transport equations. To further enhance the credibility and predictive capabilities of such simulations, output uncertainties should be reported in addition to the quantities of interest. Therefore, this paper presents results from a comprehensive quantification of uncertainties from the specification of a spray boundary condition and numerical approximation errors. A well characterized lab-scale spray flame is studied by means of an Euler-Lagrange simulation framework using detailed finite rate chemistry. As direct Monte Carlo sampling of the simulation model is prohibitive, non-intrusive Polynomial Chaos expansion (PCE) is used for forward propagation of the uncertainties. Uncertain input parameters are prioritized in a screening study, which allows for a reduction of the parameter space. The computation of probabilistic bounds reveals an extensive uncertainty region around the deterministic reference simulation. In an a posteriori sensitivity analysis, the majority of this variance is traced back to the uncertain spray cone angle of the atomizer. The explicit computation of input uncertainties finally allows for an evaluation of total predictive uncertainty in the case considered.

Evaluating the Temporal Dynamics of Uncertainty Contribution from Satellite Precipitation Input in Rainfall-Runoff Modeling Using the Variance Decomposition Method

Satellite precipitation estimates (SPE), characterized by high spatial-temporal resolution, have been increasingly applied to hydrological modeling. However, the errors and bias inherent in SPE are broadly recognized. Yet, it remains unclear to what extent input uncertainty in hydrological models driven by SPE contributes to the total prediction uncertainty, resulting from difficulties in uncertainty partitioning. This study comprehensively quantified the input uncertainty contribution of three precipitation inputs (Tropical Rainfall Measurement Mission (TRMM) near-real-time 3B42RTv7 product, TRMM post-real-time 3B42v7 product and gauge-based precipitation) in rainfall-runoff simulation, using two hydrological models, the lumped daily Ge´nie Rural (GR) and distributed Coupled Routing and Excess STorage (CREST) models. For this purpose, the variance decomposition method was applied to disaggregate the total streamflow modeling uncertainty into seven components (uncertainties in model input, parameter, structure and their three first-order interaction effects, and residual error). The results showed that the total uncertainty in GR was lowest, moderate and highest when forced by gauge precipitation, 3B42v7 and 3B42RTv7, respectively. While the total uncertainty in CREST driven by 3B42v7 was lowest among the three input data sources. These results highlighted the superiority of post-real-time 3B42v7 in hydrological modeling as compared to real-time 3B42RTv7. All the input uncertainties in CREST driven by 3B42v7, 3B42RTv7 and gauge-based precipitation were lower than those in GR correspondingly. In addition, the input uncertainty was lowest in 3B42v7-driven CREST model while highest in gauge precipitation-driven GR model among the six combination schemes (two models combined with three precipitation inputs abovementioned). The distributed CREST model was capable of making better use of the spatial distribution advantage of SPE especially for the TRMM post-real-time 3B42v7 product. This study provided new insights into the SPE’s hydrological utility in the context of uncertainty, being significant for improving the suitability and adequacy of SPE to hydrological application.

Effects of stream nitrate data frequency on watershed model performance and prediction uncertainty

High-frequency water quality monitoring is increasingly used in examining the nutrient fluxes within catchments. Despite this, no studies have assessed the impact of monitoring frequency on the uncertainty of nitrate estimates obtained from distributed or semi-distributed catchment models. This study aims to evaluate the impacts of two different frequencies of nitrate sampling on the performance of a catchment hydrology model, including the uncertainty in both predictions and calibrated parameters. The investigation uses the HYPE model to simulate streamflow and nitrate concentrations (2010–2015) in the Selke catchment, a heterogeneous mesoscale catchment in central Germany. The Bayesian inference scheme of the DREAM code was employed for calibration and uncertainty analysis, and to explore differences between fortnightly and daily nitrate sampling strategies. The results indicate that: (a) the posterior uncertainty intervals of nitrogen-export process parameters were narrower when the model was calibrated to daily nitrate measurements, while similar maximum likelihood parameter values were obtained regardless of the sampling frequency; (b) the model calibrated using daily nitrate data better represented both daily and fortnightly nitrate measurements relative to that obtained using fortnightly sampling; (c) the daily nitrate dataset produced significantly smaller parametric prediction uncertainty, but only modest reduction in total prediction uncertainty, relative to the fortnightly nitrate dataset; (d) model structural error and measurement errors are the primary sources of total prediction uncertainty, and these combine to inhibit the benefits of high-frequency monitoring. We conclude that the adequacy of sampling frequency is dependent on model structure and measurement errors, such that higher-frequency nitrate monitoring may not markedly reduce the uncertainty of nutrient predictions, depending on other levels and sources of uncertainty.

Generating Coherent Ensemble Forecasts After Hydrological Postprocessing: Adaptations of ECC‐Based Methods

AbstractHydrological ensemble forecasts are frequently miscalibrated, and need to be statistically postprocessed in order to account for the total predictive uncertainty. Very often, this step relies on parametric, univariate techniques that ignore the between‐basins and between‐lead times dependencies. This calls for a procedure referred to as sampling‐reordering, which generates a coherent multivariate ensemble from the marginal postprocessed distributions. The ensemble copula coupling (ECC) approach, which is already popular in the field of meteorological postprocessing, is attractive for hydrological forecasts as it preserves the dependence structure of the raw ensemble assumed as spatially and temporally coherent. However, the existing implementations of ECC have strong limitations when applied to hourly streamflow, due to raw ensembles being frequently nondispersive and to streamflow data being strongly autocorrelated. Based on this diagnosis, this paper investigates several variants of ECC, in particular the addition of a perturbation to the raw ensemble to handle the nondispersive cases, and the smoothing of the temporal trajectories to make them more realistic. The evaluation is conducted on a case study of hydrological forecasting over a set of French basins. The results show that the new variants improve upon the existing ECC implementations, while they remain simple and computationally inexpensive.

Parameter and input data uncertainty estimation for the assessment of water resources in two sub-basins of the Limpopo River Basin

Abstract. The demand for water resources is rapidly growing, placing more strain on access to water and its management. In order to appropriately manage water resources, there is a need to accurately quantify available water resources. Unfortunately, the data required for such assessment are frequently far from sufficient in terms of availability and quality, especially in southern Africa. In this study, the uncertainty related to the estimation of water resources of two sub-basins of the Limpopo River Basin – the Mogalakwena in South Africa and the Shashe shared between Botswana and Zimbabwe – is assessed. Input data (and model parameters) are significant sources of uncertainty that should be quantified. In southern Africa water use data are among the most unreliable sources of model input data because available databases generally consist of only licensed information and actual use is generally unknown. The study assesses how these uncertainties impact the estimation of surface water resources of the sub-basins. Data on farm reservoirs and irrigated areas from various sources were collected and used to run the model. Many farm dams and large irrigation areas are located in the upper parts of the Mogalakwena sub-basin. Results indicate that water use uncertainty is small. Nevertheless, the medium to low flows are clearly impacted. The simulated mean monthly flows at the outlet of the Mogalakwena sub-basin were between 22.62 and 24.68 Mm3 per month when incorporating only the uncertainty related to the main physical runoff generating parameters. The range of total predictive uncertainty of the model increased to between 22.15 and 24.99 Mm3 when water use data such as small farm and large reservoirs and irrigation were included. For the Shashe sub-basin incorporating only uncertainty related to the main runoff parameters resulted in mean monthly flows between 11.66 and 14.54 Mm3. The range of predictive uncertainty changed to between 11.66 and 17.72 Mm3 after the uncertainty in water use information was added.

Quantification of water resources uncertainties in the Luvuvhu sub-basin of the Limpopo river basin

In the absence of historical observed data, models are generally used to describe the different hydrological processes and generate data and information that will inform management and policy decision making. Ideally, any hydrological model should be based on a sound conceptual understanding of the processes in the basin and be backed by quantitative information for the parameterization of the model. However, these data are often inadequate in many sub-basins, necessitating the incorporation of the uncertainty related to the estimation process. This paper reports on the impact of the uncertainty related to the parameterization of the Pitman monthly model and water use data on the estimates of the water resources of the Luvuvhu, a sub-basin of the Limpopo river basin. The study reviews existing information sources associated with the quantification of water balance components and gives an update of water resources of the sub-basin. The flows generated by the model at the outlet of the basin were between 44.03 Mm3 and 45.48 Mm3 per month when incorporating +\\-20% uncertainty to the main physical runoff generating parameters. The total predictive uncertainty of the model increased when water use data such as small farm and large reservoirs and irrigation were included. The dam capacity data was considered at an average of 62% uncertainty mainly as a result of the large differences between the available information in the national water resources database and that digitised from satellite imagery. Water used by irrigated crops was estimated with an average of about 50% uncertainty. The mean simulated monthly flows were between 38.57 Mm3 and 54.83 Mm3 after the water use uncertainty was added. However, it is expected that the uncertainty could be reduced by using higher resolution remote sensing imagery.

Insights on the impact of systematic model errors on data assimilation performance in changing catchments

Abstract The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation.

Can integrative catchment management mitigate future water quality issues caused by climate change and socio-economic development?

Abstract. The design and evaluation of solutions for integrated surface water quality management requires an integrated modelling approach. Integrated models have to be comprehensive enough to cover the aspects relevant for management decisions, allowing for mapping of larger-scale processes such as climate change to the regional and local contexts. Besides this, models have to be sufficiently simple and fast to apply proper methods of uncertainty analysis, covering model structure deficits and error propagation through the chain of sub-models. Here, we present a new integrated catchment model satisfying both conditions. The conceptual iWaQa model was developed to support the integrated management of small streams. It can be used to predict traditional water quality parameters, such as nutrients and a wide set of organic micropollutants (plant and material protection products), by considering all major pollutant pathways in urban and agricultural environments. Due to its simplicity, the model allows for a full, propagative analysis of predictive uncertainty, including certain structural and input errors. The usefulness of the model is demonstrated by predicting future surface water quality in a small catchment with mixed land use in the Swiss Plateau. We consider climate change, population growth or decline, socio-economic development, and the implementation of management strategies to tackle urban and agricultural point and non-point sources of pollution. Our results indicate that input and model structure uncertainties are the most influential factors for certain water quality parameters. In these cases model uncertainty is already high for present conditions. Nevertheless, accounting for today's uncertainty makes management fairly robust to the foreseen range of potential changes in the next decades. The assessment of total predictive uncertainty allows for selecting management strategies that show small sensitivity to poorly known boundary conditions. The identification of important sources of uncertainty helps to guide future monitoring efforts and pinpoints key indicators, whose evolution should be closely followed to adapt management. The possible impact of climate change is clearly demonstrated by water quality substantially changing depending on single climate model chains. However, when all climate trajectories are combined, the human land use and management decisions have a larger influence on water quality against a time horizon of 2050 in the study.

Methods used for quantifying the prediction uncertainty of artificial neural network based hydrologic models

Application of artificial neural network (ANN) models has been reported to solve variety of water resources and environmental related problems including prediction, forecasting and classification, over the last two decades. Though numerous research studies have witnessed the improved estimate of ANN models, the practical applications are sometimes limited. The black box nature of ANN models and their parameters hardly convey the physical meaning of catchment characteristics, which result in lack of transparency. In addition, it is perceived that the point prediction provided by ANN models does not explain any information about the prediction uncertainty, which reduce the reliability. Thus, there is an increasing consensus among researchers for developing methods to quantify the uncertainty of ANN models, and a comprehensive evaluation of uncertainty methods applied in ANN models is an emerging field that calls for further improvements. In this paper, methods used for quantifying the prediction uncertainty of ANN based hydrologic models are reviewed based on the research articles published from the year 2002 to 2015, which focused on modeling streamflow forecast/prediction. While the flood forecasting along with uncertainty quantification has been frequently reported in applications other than ANN in the literature, the uncertainty quantification in ANN model is a recent progress in the field, emerged from the year 2002. Based on the review, it is found that methods for best way of incorporating various aspects of uncertainty in ANN modeling require further investigation. Though model inputs, parameters and structure uncertainty are mainly considered as the source of uncertainty, information of their mutual interaction is still lacking while estimating the total prediction uncertainty. The network topology including number of layers, nodes, activation function and training algorithm has often been optimized for the model accuracy, however not in terms of model uncertainty. Finally, the effective use of various uncertainty evaluation indices should be encouraged for the meaningful quantification of uncertainty. This review article also discusses the effectiveness and drawbacks of each method and suggests recommendations for further improvement.