Quantile-Based Hydrological Modelling

Predictive uncertainty in hydrological modelling is quantified by using post-processing or Bayesian-based methods. The former methods are not straightforward and the latter ones are not distribution-free (i.e., assumptions on the probability distribution of the hydrological model’s output are necessary). To alleviate possible limitations related to these specific attributes, in this work we propose the calibration of the hydrological model by using the quantile loss function. By following this methodological approach, one can directly simulate pre-specified quantiles of the predictive distribution of streamflow. As a proof of concept, we apply our method in the frameworks of three hydrological models to 511 river basins in the contiguous US. We illustrate the predictive quantiles and show how an honest assessment of the predictive performance of the hydrological models can be made by using proper scoring rules. We believe that our method can help towards advancing the field of hydrological uncertainty.

Mathematical modelling of solute transport in a heterogeneous aquifer

<p>This study provides a contribution to the understanding of parsimony and predictive uncertainty in the context of groundwater solute transport modelling. The study is unique because the modelling was undertaken using tracer test data from a heterogeneous artificial aquifer whose structure was known to a very high level of detail. The aquifer structure was based on a ‘real life’ Canterbury Plains alluvial aquifer (in New Zealand). Parsimonious principles were applied by starting with a simple analytical model that assumed homogeneity then progressively adding heterogeneity using numerical models with varying degrees of parameterisation complexity. The results show that increased complexity did not necessarily make the model better at replicating the tracer test data. For example, the outputs from a numerical model that represented heterogeneity using a zone based approach based on the recorded distribution of all 2,907 blocks that comprised the artificial aquifer was little different to a simple numerical model that adopted a homogenous distribution and included a single value of dispersion. Parameterisation of numerical models using ‘pilot points’ provided the most complex representation of heterogeneity and resulted in the best replication of the tracer test data. However, increasing model complexity had its disadvantages such as decreasing parameterisation uniqueness. The contribution to predictive uncertainty from model parameters and observations was assessed using a linear approach based on Bayes theorem. This approach has been applied to other groundwater modelling studies, but not to solute transport modelling within Canterbury Plains alluvial aquifers or to an artificial aquifer. A unique finding was the reduction in predictive uncertainty along the groundwater flow path. This finding correlated well with the numerical model outputs which showed closer fits to the observation data near the end of the aquifer compared to those near the top of the aquifer where the tracer was injected. Physical solute transport processes were identified and described as part of the modelling. These included the increase in dispersivity with travel distance and the spatial distribution of the aquifer hydraulic properties. Analytical modelling was a useful tool in identifying physical processes, aquifer characteristics and the variation in aquifer hydraulic properties both spatially and with depth. An important finding was the value of undertaking multiple modelling approaches. This is because each approach has its own advantages and disadvantageous and by comparing the results of different approaches, the true facts about the aquifer system are made clearer.</p>

Mathematical modelling of solute transport in a heterogeneous aquifer

<p>This study provides a contribution to the understanding of parsimony and predictive uncertainty in the context of groundwater solute transport modelling. The study is unique because the modelling was undertaken using tracer test data from a heterogeneous artificial aquifer whose structure was known to a very high level of detail. The aquifer structure was based on a ‘real life’ Canterbury Plains alluvial aquifer (in New Zealand). Parsimonious principles were applied by starting with a simple analytical model that assumed homogeneity then progressively adding heterogeneity using numerical models with varying degrees of parameterisation complexity. The results show that increased complexity did not necessarily make the model better at replicating the tracer test data. For example, the outputs from a numerical model that represented heterogeneity using a zone based approach based on the recorded distribution of all 2,907 blocks that comprised the artificial aquifer was little different to a simple numerical model that adopted a homogenous distribution and included a single value of dispersion. Parameterisation of numerical models using ‘pilot points’ provided the most complex representation of heterogeneity and resulted in the best replication of the tracer test data. However, increasing model complexity had its disadvantages such as decreasing parameterisation uniqueness. The contribution to predictive uncertainty from model parameters and observations was assessed using a linear approach based on Bayes theorem. This approach has been applied to other groundwater modelling studies, but not to solute transport modelling within Canterbury Plains alluvial aquifers or to an artificial aquifer. A unique finding was the reduction in predictive uncertainty along the groundwater flow path. This finding correlated well with the numerical model outputs which showed closer fits to the observation data near the end of the aquifer compared to those near the top of the aquifer where the tracer was injected. Physical solute transport processes were identified and described as part of the modelling. These included the increase in dispersivity with travel distance and the spatial distribution of the aquifer hydraulic properties. Analytical modelling was a useful tool in identifying physical processes, aquifer characteristics and the variation in aquifer hydraulic properties both spatially and with depth. An important finding was the value of undertaking multiple modelling approaches. This is because each approach has its own advantages and disadvantageous and by comparing the results of different approaches, the true facts about the aquifer system are made clearer.</p>

Incorporating the field border effect to reduce the predicted uncertainty of pollen dispersal model in Asia

The presence of the field border (FB), such as roadways or unplanted areas, between two fields is common in Asian farming system. This study evaluated the effect of the FB on the cross-pollination (CP) and predicted the CP rate in the field considering and not considering FB. Three experiments including 0, 6.75, and 7.5 m width of the FB respectively were conducted to investigate the effect of distance and the FB on the CP rate. The dispersal models combined kernel and observation model by calculating the parameter of observation model from the output of kernel. These models were employed to predict the CP rate at different distances. The Bayesian method was used to estimate parameters and provided a good prediction with uncertainty. The highest average CP rates in the field with and without FB were 74.29% and 36.12%, respectively. It was found that two dispersal models with the FB effect displayed a higher ability to predict average CP rates. The correlation coefficients between actual CP rates and CP rates predicted by the dispersal model combined zero-inflated Poisson observation model with compound exponential kernel and modified Cauchy kernel were 0.834 and 0.833, respectively. Furthermore, the predictive uncertainty was reducing using the dispersal models with the FB effect.

Statistical Distortion of Supervised Learning Predictions in Optical Microscopy Induced by Image Compression

The growth of data throughput in optical microscopy has triggered the extensive use of supervised learning (SL) models on compressed datasets for automated analysis. Investigating the effects of image compression on SL predictions is therefore pivotal to assess their reliability, especially for clinical use.We quantify the statistical distortions induced by compression through the comparison of predictions on compressed data to the raw predictive uncertainty, numerically estimated from the raw noise statistics measured via sensor calibration. Predictions on cell segmentation parameters are altered by up to 15% and more than 10 standard deviations after 16-to-8 bits pixel depth reduction and 10:1 JPEG compression. JPEG formats with higher compression ratios show significantly larger distortions. Interestingly, a recent metrologically accurate algorithm, offering up to 10:1 compression ratio, provides a prediction spread equivalent to that stemming from raw noise. The method described here allows to set a lower bound to the predictive uncertainty of a SL task and can be generalized to determine the statistical distortions originated from a variety of processing pipelines in AI-assisted fields.