On rough convergence of complex uncertain sequences

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. The main purpose of this paper is to introduce rough convergence of complex uncertain sequences and study some convergence concepts namely rough convergence in measure, rough convergence in mean, rough convergence in distribution of complex uncertain sequences. Lastly some relationship between them have been investigated.

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J 12. Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J 14. We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J 6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 R Sat, as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed J n values.

Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures

Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation.

Expected Recurrence of Extreme Winds in Northwestern Sahara and Associated Uncertainties

Estimating the probability of the occurrence of hazardous winds is crucial for their impact in human activities; however, this is inherently affected by the shortage of observations. This becomes critical in poorly sampled regions, such as the northwestern Sahara, where this work is focused. The selection of any single methodological variant contributes with additional uncertainty. To gain robustness in the estimates, we expand the uncertainty space by applying a large body of methodologies. The methodological uncertainty is constrained afterward by keeping only the reliable experiments. In doing so, we considerably narrow the uncertainty associated with the wind return levels. The analysis suggest that not necessarily all methodologies are equally robust. The highest 10-min speed (wind gust) for a return period of 50 years is about 45 ms−1 (56 ms−1). The intensity of the expected extreme winds is closely related to orography. The study is based on wind and wind gust observations that were collected and quality controlled for the specific purposes herein. We also make use of a 12-year high-resolution regional simulation to provide simulation-based wind return level maps that endorse the observation-based results. Such an exhaustive methodological sensitivity analysis with a long high-resolution simulation over this region was lacking in the literature.

MESMER-M: an Earth System Model emulator for spatially resolved monthly temperatures

The degree of trust placed in climate model projections is commensurate to how well their uncertainty can be quantified, particularly at timescales relevant to climate policy makers. On interannual to decadal timescales, model uncertainty due to internal variability dominates and is imperative to understanding near-term and seasonal climate events, but hard to quantify owing to the computational constraints on producing large ensembles. To this extent, emulators are valuable tools for approximating climate model runs, allowing for exploration of the model uncertainty space surrounding select climate variables at a significantly reduced computational cost. Most emulators, however, operate at annual to seasonal timescales, leaving out monthly information that may be essential to assessing climate impacts. This study extends the framework of an existing spatially resolved, annual-scale Earth System Model (ESM) emulator (MESMER, Beusch et al. 2020) by a monthly downscaling module (MESMER-M), thus providing local monthly temperatures from local yearly temperatures. We first linearly represent the mean response of the monthly temperature cycle to yearly temperatures using a simple harmonic model, thus maintaining month to month correlations and capturing changes in intra-annual variability. We then construct a month-specific local variability module which generates spatio-temporally correlated residuals with month and yearly temperature dependent skewness incorporated within. The performance of the resulting emulator is demonstrated on 38 different ESMs from the 6th phase of the Coupled Model Intercomparison Project (CMIP6). The emulator is furthermore benchmarked using a simple Gradient Boosting Regressor based, physical model trained on biophysical information. We find that while regional-scale, biophysical feedbacks may induce non-uniformities in the yearly to monthly temperature downscaling relationship, statistical emulation of regional effects shows comparable skill to approaches with physical representation. Thus, MESMER-M is able to generate ESM-like, large initial-condition ensembles of spatially explicit monthly temperature fields, thereby providing monthly temperature probability distributions which are of critical value to impact assessments.

Uncertain Independent Increment Processes are Contour Processes

Uncertain processes are used to model dynamic indeterminate systems associated with human uncertainty, and uncertain independent increment processes are a type of uncertain processes with independent uncertain increments. This paper mainly verifies a basic property about the sample paths of uncertain independent increment processes, which states that uncertain independent increment processes defined on a continuous uncertainty space are contour processes, a type of uncertain processes with a spectrum of sample paths as the skeletons. Based on this property, the extreme values and the time integral of an uncertain independent increment process are investigated, and their inverse uncertainty distributions are obtained.

From emission scenarios to spatially resolved projections with a chain of computationally efficient emulators: MAGICC (v7.5.1) – MESMER (v0.8.1) coupling

Producing targeted climate information at the local scale, including major sources of climate change projection uncertainty for diverse emissions scenarios, is essential to support climate change mitigation and adaptation efforts. Here, we present the first chain of computationally efficient Earth System Model (ESM) emulators allowing to rapidly translate greenhouse gas emission pathways into spatially resolved annual-mean temperature anomaly field time series, accounting for both forced climate response and natural variability uncertainty at the local scale. By combining the global-mean, emissions-driven emulator MAGICC with the spatially resolved emulator MESMER, ESM-specific as well as constrained probabilistic emulated ensembles can be derived. This emulation chain can hence build on and extend large multi-ESM ensembles such as the ones produced within the 6th phase of the Coupled Model Intercomparison Project (CMIP6). The main extensions are threefold. (i) A more thorough sampling of the forced climate response and the natural variability uncertainty is possible with millions of emulated realizations being readily created. (ii) The same uncertainty space can be sampled for any emission pathway, which is not the case in CMIP6, where some of the most societally relevant strong mitigation scenarios have been run by only a small number of ESMs. (iii) Other lines of evidence to constrain future projections, including observational constraints, can be introduced, which helps to refine projected future ranges beyond the multi-ESM ensemble's estimates. In addition to presenting results from the coupled MAGICC-MESMER emulator chain, we carry out an extensive validation of MESMER, which is trained on and applied to multiple emission pathways for the first time in this study. The newly developed MAGICC-MESMER coupled emulator will allow unprecedented assessments of the implications of manifold emissions pathways at regional scale.

Scenario reduction methodologies under uncertainties for reservoir development purposes: distance-based clustering and metaheuristic algorithm

The simulation process under uncertainty needs numerous reservoir models that can be very time-consuming. Hence, selecting representative models (RMs) that show the uncertainty space of the full ensemble is required. In this work, we compare two scenario reduction techniques: (1) Distance-based Clustering with Simple Matching Coefficient (DCSMC) applied before the simulation process using reservoir static data, and (2) metaheuristic algorithm (RMFinder technique) applied after the simulation process using reservoir dynamic data. We use these two methods as samples to investigate the effect of static and dynamic data usage on the accuracy and rate of the scenario reduction process focusing field development purposes. In this work, a synthetic benchmark case named UNISIM-II-D considering the flow unit modelling is used. The results showed both scenario reduction methods are reliable in selecting the RMs from a specific production strategy. However, the obtained RMs from a defined strategy using the DCSMC method can be applied to other strategies preserving the representativeness of the models, while the role of the strategy types to select the RMs using the metaheuristic method is substantial so that each strategy has its own set of RMs. Due to the field development workflow in which the metaheuristic algorithm is used, the number of required flow simulation models and the computational time are greater than the workflow in which the DCSMC method is applied. Hence, it can be concluded that static reservoir data usage on the scenario reduction process can be more reliable during the field development phase.