Modelling Short‐Scale Variability and Uncertainty During Mineral Resource Estimation Using a Novel Fuzzy Estimation Technique

For mineral resource assessment, techniques based on fuzzy logic are attractive because they are capable of incorporating uncertainty associated with measured variables and can also quantify the uncertainty of the estimated grade, tonnage etc. The fuzzy grade estimation model is independent of the distribution of data, avoiding assumptions and constraints made during advanced geostatistical simulation, e.g., the turning bands method. Initially, fuzzy modelling classifies the data using all the component variables in the data set. We adopt a novel approach by taking into account the spatial irregularity of mineralisation patterns using the Gustafson–Kessel classification algorithm. The uncertainty at the point of estimation was derived through antecedent memberships in the input space (i.e., spatial coordinates) and transformed onto the output space (i.e., grades) through consequent membership at the point of estimation. Rather than probabilistic confidence intervals, this uncertainty was expressed in terms of fuzzy memberships, which indicated the occurrence of mixtures of different mineralogical phases at the point of estimation. Data from different sources (other than grades) could also be utilised during estimation. Application of the proposed technique on a real data set gave results that were comparable to those obtained from a turning bands simulation.     

Response to commentary by J. L. Bamber,W. P. Aspinall and R. M. Cooke (2016)

In a commentary paper, Bamber et al. (Nat Clim Change 3:424–427, 2016) respond to our recent assessment (De Vries and Van de Wal Clim Change 1–14, 2015) of their expert judgment based study on projections of future sea level rise due to the melting of the large ice sheets (Bamber and Aspinall Nat Clim Chang 3:424–427, 2013). In this response we comment on their remarks.     

Extreme storm surge modelling in the North Sea

This study shows that storm surge model performance in the North Sea is mostly unaffected by the application of temporal variations of surface drag due to changes in sea state provided the choice of a suitable constant Charnock parameter in the sea-state-independent case. Including essential meteorological features on smaller scales and minimising interpolation errors by increasing forcing data resolution are shown to be more important for the improvement of model performance particularly at the high tail of the probability distribution. This is found in a modelling study using WAQUA/DCSMv5 by evaluating the influence of a realistic air-sea momentum transfer parameterization and comparing it to the influence of changes in the spatial and temporal resolution of the applied forcing fields in an effort to support the improvement of impact and climate analysis studies. Particular attention is given to the representation of extreme water levels over the past decades based on the example of the Netherlands. For this, WAQUA/DCSMv5 is forced with ERA-Interim reanalysis data. Model results are obtained from a set of different forcing fields, which either (i) include a wave-state-dependent Charnock parameter or (ii) apply a constant Charnock parameter (α _{C h} =?0.032) tuned for young sea states in the North Sea, but differ in their spatial and/or temporal resolution. Increasing forcing field resolution from roughly 79 to 12 km through dynamically downscaling can reduce the modelled low bias, depending on coastal station, by up to 0.25 m for the modelled extreme water levels with a 1-year return period and between 0.1 m and 0.5 m for extreme surge heights.     

Atmospheric blocking and its relation to jet changes in a future climate

The future changes of atmospheric blocking over the Euro-Atlantic sector, diagnosed from an ensemble of 17 global-climate simulations obtained with the ECHAM5/MPI-OM model, are shown to be largely explainable from the change of the 500 hPa mean zonal circulation and its variance. The reduction of the blocking frequency over the Atlantic and the increased frequency of easterly upper-level flow poleward of 60°N are well explained by the changes of mean zonal circulation. In winter and autumn an additional downstream shift of the frequency maximum is simulated. This is also seen in a subset of the CMIP5 models with RCP8.5. To explain this downstream shift requires the inclusion of the changing variance. It is suggested that the increased downstream variance is caused by the stronger, more eastward extending future jet, which promotes Rossby wave breaking and blocking to occur further downstream. The same relation between jet-strength and central-blocking longitude is found in the variability of the current climate.     

On the direction of Rossby wave breaking in blocking

The direction of Rossby wave breaking at the onset of large-scale atmospheric blocking events is shown to relate closely to its position relative to the location of the climatological storm tracks. Using ERA-Interim reanalysis data from October 1989 to March 2009 and a dynamically-based blocking index, Rossby wave breaking is shown to occur preferentially cyclonically to the north, and anticyclonically to the south of the average storm tracks location. Therefore the results support existing theory on the relation between Rossby wave breaking direction and barotropic shear of the background wind. The further away from the storm tracks the breaking occurs, the stronger this preference in breaking direction. Regional differences can also be explained. For the European region on average 70?% of the detected blocking took place after anticyclonic Rossby wave breaking event that occurred on average 6° south of the climatological storm tracks position. Over Western Pacific wave breaking prior to blocking occurs predominantly cyclonically and on average 6° north of the storm tracks. Differences in blocking duration and intensity are found to be within estimated error margins at most longitudes, except for the Atlantic-Europe sector where the blocking events following anticyclonic blocking are also the strongest.     

Impacts of El Niño–southern oscillation on global runoff: Characteristic signatures and potential mechanisms

Runoff signatures, including low flow, high flow, mean flow and flow variability, have important implications on the environment and society, predominantly through drought, flooding and water resources. Yet, the response of runoff signatures has not been previously investigated at the global scale, and the influencing mechanisms are largely unclear. Hence, this study makes a global assessment of runoff signature responses to the El Niño and La Niña phases using daily streamflow observations from 8217 gauging stations during 1960–2015. Based on the Granger causality test, we found that ~15% of the hydrological stations of multiple runoff signatures show a significant causal relationship with El Niño–southern oscillation (ENSO). The quantiles of all runoff signatures were larger during the El Niño phase than during the La Niña phase, implying that the entire flow distribution tends to shift upward during El Niño and downward during La Niña. In addition, El Niño has different effects on low and high flows: it tends to increase the low and mean flow signatures but reduces the high flow and flow variability signatures. In contrast, La Niña generally reduces all runoff signatures. We highlight that the impacts of ENSO on streamflow signatures are manifested by its effects on precipitation (P), potential evaporation (PET) and leaf area index (LAI) through ENSO-induced atmospheric circulation changes. Overall, our study provides a comprehensive picture of runoff signature responses to ENSO, with valuable insights for water resources management and flood and drought disaster mitigation.