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In this paper, we present a matrix-type adaptive tracking control scheme for a stochastic regression system with multi-threshold quantized observations and observation uncertainty. This observation uncertainty is described by an additive random noise, whose variance could be a polynomial-type rate of increase and tends to infinity. Our method, first, to handle simultaneously parameter uncertainty, quantized observation, and observation uncertainty, incorporates an online stochastic approximation-type parameter identification algorithm. Second, based on the above identification algorithm, we construct a matrix-type adaptive tracking control law by the certainty equivalence principle. In addition, under suitable conditions, the above identification algorithm and matrix-type adaptive tracking control law in the mean square sense can ensure that the estimations of the unknown parameters converge to the true values and achieve asymptotically optimal tracking of the periodic reference signal, respectively. To characterize the effect of observation uncertainty on the convergence speed of the identification algorithm in the mean square sense, a quantitative relationship between observation uncertainty and the convergence speed is proposed. Finally, the effectiveness of the proposed matrix-type adaptive tracking control scheme is verified through a simulation. [ABSTRACT FROM AUTHOR]

Quantifying uncertainties and errors in hydrometric observations is critical to improve our ability to predict streamflow. de Oliveira and Vrugt (2022, https://doi.org/10.1029/2022wr032263) expand on an earlier publication (Vrugt et al., 2005, https://doi.org/10.1029/2004wr003059) to describe a difference‐based variance estimation method that is, used to estimate the aleatory observation uncertainty in streamflow records directly from a time series of such data. The method is then applied to hourly data from 500+ catchments across the contiguous United States. This comment outlines our concerns that the assumptions needed to effectively use difference‐based variance estimation methods are not always met by hourly streamflow records. We illustrate our concerns through the use of a specific test case. We argue that more work is needed to quantify the individual sources of errors and uncertainties in hydrometric observations. Key Points: We review the difference‐based variance estimation approach (de Oliveira & Vrugt, 2022, https://doi.org/10.1029/2022wr032263) to estimate uncertainty in streamflow recordsWe outline our concerns that this method is not always applicable for streamflow records at hourly time stepsMore work is required to explicitly quantify individual error sources in hydrometric monitoring programs [ABSTRACT FROM AUTHOR]

Engineering tests can yield inaccurate data due to instrument errors, human factors, and environmental interference, introducing uncertainty in numerical model updating. This study employs the probability-box (p-box) method for representing observational uncertainty and develops a two-step approximate Bayesian computation (ABC) framework using time-series data. Within the ABC framework, Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps, respectively. A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty, resulting in rapid convergence and accurate parameter estimation with minimal iterations. The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis. The results affirm the efficiency, robustness, and practical applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The extended‐range predictability of three simulated extreme cold events in East Asia in the Community Atmosphere Model (version 4) control experiment, whose atmospheric circulation backgrounds are similar to two recent observational cases, is investigated. The results show that they have a predictability of four pentads. Then, we evaluate the extent of the forecast uncertainty in the 4th pentad caused by the initial atmospheric uncertainties in the Arctic, which are large due to sparse instrumental observations. The initial uncertainty leading to the largest forecast uncertainty is obtained by the conditional nonlinear optimal perturbation method, and referred to as the CNOP‐type initial uncertainty. The forecast of the cold surge in the 4th pentad fails after adding the CNOP‐type initial uncertainty at day 0. In comparison, the forecast uncertainties are much weaker when the initial conditions are perturbed by noises, and the weaker influence may be due to the noises' lack of spatial structure. In terms of how the CNOP‐type initial uncertainty develops, a baroclinic structure is seen in the uncertainties on the first 2 days, followed by a propagating Rossby wave feature from the 2nd pentad to the 4th pentad. Meanwhile, synoptic transient eddy feedback also plays an essential role. The results suggest that the CNOP‐type initial uncertainty has potential to identify sensitive areas for targeted observations; plus, it could serve as a member of ensemble initial perturbations, since it indicates the largest uncertainty growth. Plain Language Summary: Although the notable global warming trend continues, extreme cold events in East Asia remain a common feature during the winter season and cause huge socio‐economic impacts. The atmospheric initial conditions are crucial for the prediction over East Asia. However, they have large uncertainties in the Arctic due to the sparse coverage of conventional data. Utilizing the conditional nonlinear optimal perturbation method, what extent the initial uncertainty in the Arctic can influence the prediction of cold surges is investigated. The results demonstrate that initial Arctic uncertainty can lead to the prediction of cold events in fourth pentad failure. Such initial uncertainty may provide potential application in the identification of sensitive areas for targeted observations. Key Points: The predictability of three simulated extreme cold events in East Asia by CAM4 reaches four pentadsThe conditional nonlinear optimal perturbation‐type initial uncertainty in the Arctic can lead to an extreme cold event appearing as a normal or warm event in the 4th pentadThe forecast uncertainty caused by the noise in the Arctic is weak in the 4th pentad [ABSTRACT FROM AUTHOR]

The central and western Tibetan Plateau (CWTP) is characterized by harsh environment and strong interactions among the spheres of earth as well as significant changes in climate and water cycles over the past four decades. The lack of precipitation observations is a bottleneck for the study of land surface processes in this region. Over the past six years, we have designed and established two observation transects across the south-north and the west-east in this region to obtain hourly rainfall data during the warm season (May–September). The south-north transect extends from Yadong Valley on the southern slope of the Himalayas to Shuanghu County in the hinterland of the plateau, with a total of 31 stations; the west-east transect extends from Shiquanhe in the west to Naqu in the central TP, with a total of 22 stations. The observation dataset has been applied to clarify the spatiotemporal characteristics of precipitation in the CWTP, to evaluate the quality of typical gridded precipitation products, to support the development of regional climate models, and to reveal the processes of summertime lake-air interactions. The observation dataset has been released in the National Tibetan Plateau Data Center. [ABSTRACT FROM AUTHOR]

Data assimilation combines observations with numerical model data, to provide a best estimate of a real system. Errors due to unresolved scales arise when there is a spatio-temporal scale mismatch between the processes resolved by the observations and model. We present theory on error, uncertainty and bias due to unresolved scales for situations where observations contain information on smaller scales than can be represented by the numerical model. The Schmidt-Kalman filter, which accounts for the uncertainties in the unrepresented processes, is investigated and compared with an optimal Kalman filter that treats all scales, and a suboptimal Kalman filter that accounts for the large-scales only. The equation governing true analysis uncertainty is reformulated to include representation uncertainty for each filter. We apply the filters to a random walk model with one variable for large-scale processes and one variable for small-scale processes. Our new results show that the Schmidt-Kalman filter has the largest benefit over a suboptimal filter in regimes of high representation uncertainty and low instrument uncertainty but performs worse than the optimal filter. Furthermore, we review existing theory showing that errors due to unresolved scales often result in representation error bias. We derive a novel bias-correcting form of the Schmidt-Kalman filter and apply it to the random walk model with biased observations. We show that the bias-correcting Schmidt-Kalman filter successfully compensates for representation error biases. Indeed, it is more important to treat an observation bias than an unbiased error due to unresolved scales.

In numerical weather prediction (NWP), observations and models are quantitatively compared for the purposes of data assimilation and forecast verification. The spatial and temporal scales represented by the observation and model may differ and this results in a scale mismatch error which may be biased and correlated. The aim of this paper is to investigate the structure of representation error in convection‐permitting NWP models for four meteorological variables: temperature, specific humidity, zonal and meridional wind. We use high‐resolution data from the experimental Met Office London Model (approximately 300 m grid‐length) to simulate perfect observations and lower‐resolution model data. The scale mismatch error and its bias, variance and correlation are calculated from the perfect observation and low‐resolution model equivalents. Our new results show that the scale mismatch bias is significant in the boundary layer for temperature and specific humidity, whereas the variance is significant in the boundary layer for all analysed variables. Contrary to previous studies using low‐resolution (km‐scale) data, horizontal correlations are shown to be insignificant. However, all variables exhibit considerable vertical representation error correlation throughout the boundary layer. Our results suggest that significant biases and vertical correlations exist that should be accounted for to give maximum observation impact in data assimilation and for fairness in model verification and validation. [ABSTRACT FROM AUTHOR]

Data assimilation combines observations with numerical model data, to provide a best estimate of a real system. Errors due to unresolved scales arise when there is a spatio-temporal scale mismatch between the processes resolved by the observations and model. We present theory on error, uncertainty and bias due to unresolved scales for situations where observations contain information on smaller scales than can be represented by the numerical model. The Schmidt-Kalman filter, which accounts for the uncertainties in the unrepresented processes, is investigated and compared with an optimal Kalman filter that treats all scales, and a suboptimal Kalman filter that accounts for the large-scales only. The equation governing true analysis uncertainty is reformulated to include representation uncertainty for each filter. We apply the filters to a random walk model with one variable for large-scale processes and one variable for small-scale processes. Our new results show that the Schmidt-Kalman filter has the largest benefit over a suboptimal filter in regimes of high representation uncertainty and low instrument uncertainty but performs worse than the optimal filter. Furthermore, we review existing theory showing that errors due to unresolved scales often result in representation error bias. We derive a novel bias-correcting form of the Schmidt-Kalman filter and apply it to the random walk model with biased observations. We show that the bias-correcting Schmidt-Kalman filter successfully compensates for representation error biases. Indeed, it is more important to treat an observation bias than an unbiased error due to unresolved scales. [ABSTRACT FROM AUTHOR]

Direct discharge measurements during flood events can be challenging from a technical as well as from a safety point of view. Therefore, flood discharges are often estimated by extrapolating a rating curve. Extrapolations far outside the range of the directly measured discharges are common, although the associated errors can be large. In this article, a novel method to determine suitable stage measurement locations and derive rating curves using a hydraulic scale model is presented. A hydraulic scale model for a natural gauging station site is produced with a computer numerical control technique, making a detailed representation of the prototype topography and bathymetry. The site is characterized by a complex geometry, and the results of the scale model study reveal that the current location of stage measurement is not suitable for determining the rating curve for high flows. The scale model is used to identify potential locations for future stage measurements, and a flood rating curve is constructed based on field measurements for low flows and scale model data for high flows. The study shows how hydraulic scale modelling can be used to provide more reliable rating curves for large discharges and evaluate new or existing gauging stations located at sites with challenging measurement conditions. [ABSTRACT FROM AUTHOR]

Lane-changing of surrounding vehicles is a risky situation because vehicle accidents can be easily caused by driver's unawareness of the surrounding vehicle. Much research has conducted on lane-change recognition (LCR) to avoid these vehicle accidents by warning drivers. LCR is a technology to estimate lane-changing behaviors of surrounding vehicles from observation data: position, velocity, and lane information. Since these observation data change continuously during lanechanging, most research for LCR has used time series data based on hidden Markov model (HMM). A challenging point of LCR is that HMM could make false positives in LCR when the observation data include uncertainties such as sensor noise and object detection error. Previous research has tried to process observation data by using Bayesian filter. However, the approach cannot remove all data uncertainties. This paper proposes a method for using observation uncertainty through an adaptive HMM for LCR. In the method, HMM models are modified in real time based on data covariance to filter data with high uncertainty. For evaluation of the algorithm, it was tested through 71 lane-changing cases in real driving situations. The results show that the proposed method enhanced the recognition accuracy by 25.3 % (63.3 % → 88.7 %) than a previous LCR method. [ABSTRACT FROM AUTHOR]

This paper investigates a multi-agent asymptotic consensus problem with binary-valued observations and observation uncertainty. This uncertainty is described by an additive random noise, whose variance could follow a polynomial-type rate of increase, and even tend to infinity. A stochastic approximation-type asymptotic consensus algorithm is proposed: firstly, to handle simultaneously quantized observation and observation uncertainty, each agent estimates its neighbors' states through an online estimation algorithm; secondly, based on the estimated states of neighbors and its own state, every agent designs its consensus control in real-time. Under suitable conditions, the above estimation algorithm in the mean square sense can ensure that the estimations of unknown neighbors' states converge to the true values. And the states of the agents can achieve an asymptotic consensus effect by this asymptotic consensus algorithm. In addition, to characterize the impact of observation uncertainty on the consensus speed and the convergence speed, two quantitative relationships between observation uncertainty and these two speeds are given, respectively, which have not been considered before. Finally, two simulations are given to verify the above theoretical results. [ABSTRACT FROM AUTHOR]

Eight short-range, open-terrain SF6 tracer tests in low wind speeds were conducted during Phase 2 of Project Sagebrush using continuous releases. Four tests were made during very unstable conditions in July and August 2016, and four during very stable conditions in October 2016. All tests featured 10-min averaging and 1-Hz sampling of tracer concentrations together with an extensive suite of meteorological measurements. We find that the uncertainty in well-mixed daytime measurements of tracer concentrations, using the absolute value of the relative percentage difference in collocated duplicate samplers, approaches a downwind limit of about 7-8%. Concentration variability in collocated sampling, due to stochastic factors and independent of measurement uncertainty, increases the total observational uncertainty closer to the source from about 20% (daytime) to 40% (very stable conditions). Longer averaging periods moderately reduce the concentration variability. The data indicate that the large increase in concentration variability is linked with the suppression of turbulent mixing, small eddy length scales, and meandering in very stable conditions. These results should be considered when comparing observations with model predictions in evaluations. [ABSTRACT FROM AUTHOR]

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The FRANC project (Forecasting Rainfall exploiting new data Assimilation techniques and Novel observations of Convection) has researched improvements in numerical weather prediction of convective rainfall via the reduction of initial condition uncertainty. This article provides an overview of the project’s achievements. We highlight new radar techniques: correcting for attenuation of the radar return; correction for beams that are over 90% blocked by trees or towers close to the radar; and direct assimilation of radar reflectivity and refractivity. We discuss the treatment of uncertainty in data assimilation: new methods for estimation of observation uncertainties with novel applications to Doppler radar winds, Atmospheric Motion Vectors, and satellite radiances; a new algorithm for implementation of spatially-correlated observation error statistics in operational data assimilation; and innovative treatment of moist processes in the background error covariance model. We present results indicating a link between the spatial predictability of convection and convective regimes, with potential to allow improved forecast interpretation. The research was carried out as a partnership between University researchers and the Met Office (UK). We discuss the benefits of this approach and the impact of our research, which has helped to improve operational forecasts for convective rainfall events.

The accurate prediction and estimation of grain yield for smallholder farms are crucial for agricultural management. In this study, we propose an image-driven data assimilation framework that enables smallholder farmers to estimate crop yield. In the framework, a convolutional neural network was trained using label distribution learning to estimate the probability distribution of rice crop states from images. The mean and variance of the estimated probability were regarded as observed values and variances, which were then assimilated into the ORYZA2000 crop growth model to estimate the final yield. Compared with the accuracy (R2 = 0.410, RMSE = 1.059 t ha−1) of yield estimation by assimilating field sampling observations, the proposed method significantly improved accuracy, with R2 = 0.646 and RMSE = 0.679 t ha−1. The results demonstrated the feasibility of driving a crop growth model using easily available camera images. Additionally, the probability distribution estimation method made it possible to quantify the error for each observation. The method provides a new perspective for quantifying the observation error, thereby indicating a potential research direction for data assimilation. After that, we used numerous simulation cases to determine the most valuable observation combination for final grain yield estimation, the final yield prediction ability at different development stages, and the model performance affected by number of images. Finally, a series of factors that may affect the applicability of the framework was discussed. This study establishes an intelligent data assimilation framework for smallholder farmers that can absorb crop phenotyping data from digital cameras with a low cost and simple implementation. [ABSTRACT FROM AUTHOR]

This study presents a general MonteCarlo-based methodology for the validation of chemical transport model (CTM) concentration re-analyzed fields over a certain domain. A set of re-analyses is evaluated by applying the observation uncertainty ( U) approach (Thunis et al. Atmos Environ 59:476-482 ), developed in the frame of Forum for Air Quality Modelling in Europe (FAIRMODE; ). Modeled results from the chemical transport model (Transport and Chemical Aerosol Model (TCAM)) (Carnevale et al. Sci Total Environ 390:166-176 ) for year 2005 are used as background values. The model simulation domain covers the Po Valley with a 6 × 6 km resolution. Measured data for both assimilation and evaluation are provided by approximately 50 monitoring stations distributed across the Po Valley. The main statistical indicators (i.e., bias, root mean square error, correlation coefficient, standard deviation) as well as different types of diagrams (scatter plots and target plots) have been produced and visualized with the Delta evaluation tool V3.6. The target criteria are fulfilled by 97 % of the sites for the re-analyzed fields and by 61 % for the modeled values, showing how the application of the assimilation technique improves TCAM raw fields. The model underprediction of PM concentration (normalized mean bias (NMB) up to −70 %) is reduced at almost all sites in the re-analysis (NMB in the range −20-+20 %,). The correlation coefficient R is higher for the re-analyzed fields (0.7-1) compared to the raw ones (0.2-0.8). [ABSTRACT FROM AUTHOR]

Highlights: [•] We developed a robust approach for uncertainty assessment of input data. [•] Simulation results were evaluated on measured evapotranspiration. [•] The uncertainty of eddy-covariance measurements was tackled. [•] Empirical and process based models are similarly affected by input uncertainties. [•] Uncertainties of meteorological input and of parameters have a similar importance. [ABSTRACT FROM AUTHOR]

Abstract: Observation uncertainty is nowadays recognized as a serious issue undermining the reliability of hydrological studies. For instance, many recent contributions show that river flow observations are affected by errors that may reach 25% even when state-of-the-art measurement techniques are adopted. Yet, there is still little guidance by the literature on the most appropriate modelling strategies to be adopted under observation uncertainty. We carried out a series of simulation experiments and explored how the selection of appropriate model complexity can help reduce the impact of observation uncertainty. We found that model structure plays a relevant role and, in particular, a description of the relevant physical processes that come into play can effectively contribute to limit the impact of data errors and therefore significantly reduce overall uncertainty. [Copyright &y& Elsevier]

Abstract: A set of statistical indicators fit for air quality model evaluation is selected based on experience and literature: The Root Mean Square Error (RMSE), the bias, the Standard Deviation (SD) and the correlation coefficient (R). Among these the RMSE is proposed as the key one for the description of the model skill. Model Performance Criteria (MPC) to investigate whether model results are ‘good enough’ for a given application are calculated based on the observation uncertainty (U). The basic concept is to allow for model results a similar margin of tolerance (in terms of uncertainty) as for observations. U is pollutant, concentration level and station dependent, therefore the proposed MPC are normalized by U. Some composite diagrams are adapted or introduced to visualize model performance in terms of the proposed MPC and are illustrated in a real modeling application. The Target diagram, used to visualize the RMSE, is adapted with a new normalization on its axis, while complementary diagrams are proposed. In this first application the dependence of U on concentrations level is ignored, and an assumption on the pollutant dependent relative error is made. The advantages of this new approach are finally described. [Copyright &y& Elsevier]

Abstract: This study investigates the uncertainty in the estimation of the design flood induced by errors in flood data. We initially describe and critically discuss the main sources of uncertainty affecting river discharge data, when they are derived using stage-discharge rating curves. Then, different error structures are used to investigate the effects of flood data errors on design flood estimation. Annual maxima values of river discharge observed on the Po River (Italy) at Pontelagoscuro are used as an example. The study demonstrates that observation errors may have a significant impact on the uncertainty of design floods, especially when the rating curve is affected by systematic errors. [Copyright &y& Elsevier]

The article presents a study on habitat supervision. It highlights the detection of trend in source-sink landscapes as well as the change in its demography. It also outlines the application of a stochastic model of territorial species for analyzing the power of sensing negative trends and poor reproductive success.