<p>Conveying uncertainty in model predictions is essential, especially when these predictions are used for decision-making. Models are not only expected to achieve the best possible fit to available calibration data but to also capture future observations within realistic uncertainty intervals. Model calibration using Bayesian inference facilitates the tuning of model parameters based on existing observations, while accounting for uncertainties. The model is tested against observed data through the likelihood function which defines the probability of the data being generated by the given model and its parameters. Inference of most plausible parameter values is influenced by the method used to combine likelihood values from different observation data sets. In the classical method of combining likelihood values, referred to here as the <em>AND calibration strategy</em>, it is inherently assumed that the given model is true (error-free), and that observations in different data sets are similarly informative for the inference problem. However, practically every model applied to real-world case studies suffers from model-structural errors that are typically dynamic, i.e., they vary over time. A requirement for the imperfect model to fit all data sets simultaneously will inevitably lead to an underestimation of uncertainty due to a collapse of the resulting posterior parameter distributions. Additionally, biased 'compromise solutions' to the parameter estimation problem result in large prediction errors that impair subsequent conclusions. <br>    <br>We present an alternative <em>AND/OR calibration strategy</em> which provides a formal framework to relax posterior predictive intervals and minimize posterior collapse by incorporating knowledge about similarities and differences between data sets. As a case study, we applied this approach to calibrate a plant phenology model (SPASS) to observations of the silage maize crop grown at five sites in southwestern Germany between 2010 and 2016. We compared model predictions of phenology on using the classical AND calibration strategy with those from two scenarios (OR and ANDOR) in the AND/OR strategy of combining likelihoods from the different data sets. The OR scenario represents an extreme contrast to the AND strategy as all data sets are assumed to be distinct, and the model is allowed to find individual good fits to each period adjusting to the individual type and strength of model error. The ANDOR scenario acts as an intermediate solution between the two extremes by accounting for known similarities and differences between data sets, and hence grouping them according to anticipated type and strength of model error. <br>    <br>We found that the OR scenario led to lower precision but higher accuracy of prediction results as compared to the classical AND calibration. The ANDOR scenario led to higher accuracy as compared to the AND strategy and higher precision as compared to the OR scenario. Our proposed approach has the potential to improve the prediction capability of dynamic models in general, by considering the effect of model error when calibrating to different data sets.</p>

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Probabilistic modelling is one of the most frequently used methods in reservoir simulation to manage uncertainties and assess their impact on reservoir behavior/cumulative production. However, depending on the extent of the uncertainty, 100s of scenarios can be generated leaving engineers unable to meaningfully analyze this data. To remedy this an unsupervised machine learning based workflow was developed to identify unique scenarios which was then paired with an integrated dashboard to enable rapid and deep analysis. A case study was done using data from a Shell operated gas field in the North Sea. Data was first mined from 480 history matched scenarios using python; out of which 20 unique clusters were identified through K-Means clustering of pressure and saturation changes with time in each gridblock. This meant that the team had to look only at 20 scenarios instead of 480 to understand the effect of different inputs on pressure and saturation response. For enhanced analysis, an integrated visualisation dashboard was created to visualize pressure and saturation changes, production profiles and connect them back to input parameters The new methodology enabled the team to integrate different aspects of reservoir modelling from static to dynamic to surface constraints on a single dashboard, making it possible to find patterns in large volumes of data which was previously not possible. For example, a cluster was identified which had high water movement; upon inspection of input parameters it was seen that late life recovery was significantly different in this cluster as compared to others. Being able to visualize different properties of multiple scenarios simultaneously at both group and grid level is a very powerful tool that not only generates insights but significantly reduces analysis time and helps in quality checking property modelling and grid behavior. The developed workflow is quite generic in nature, capable of working with various simulators and can be extended to assessing history match quality in Assisted History Matching (AHM) and multi-scenario modelling. Key parameters impacting different scenarios were identified and the team observed 10x reduction in time and significant reduction in manpower requirements through the new approach

Abstract. Crop models are tools used for predicting year-to-year crop development on field to regional scales. However, robust predictions are hampered by uncertainty in crop model parameters and in the data used for calibration. Bayesian calibration allows for the estimation of model parameters and quantification of uncertainties, with the consideration of prior information. In this study, we used a Bayesian sequential updating (BSU) approach to progressively incorporate additional data at a yearly time-step in order to calibrate a phenology model (SPASS) while analysing changes in parameter uncertainty and prediction quality. We used field measurements of silage maize grown between 2010 and 2016 in the regions of Kraichgau and the Swabian Alb in southwestern Germany. Parameter uncertainty and model prediction errors were expected to progressively be reduced to a final, irreducible value. Parameter uncertainty was reduced as expected with the sequential updates. For two sequences using synthetic data, one in which the model was able to accurately simulate the observations, and the other in which a single cultivar was grown under the same environmental conditions, prediction error was mostly reduced. However, in the true sequences that followed the actual chronological order of cultivation by the farmers in the two regions, prediction error increased when the calibration data were not representative of the validation data. This could be explained by differences in ripening group and temperature conditions during vegetative growth. With implications for manual and automatic data streams and model updating, our study highlights that the success of Bayesian methods for predictions depends on a comprehensive understanding of the inherent structure in the observation data and of the model limitations.