The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each point in space and time rather than a single output value, thus producing a probabilistic weather forecast. This enables the calculation of both uncertainty and skill metrics for the neural network predictions, and overcomes the common difficulty of inferring uncertainty from these predictions. This approach is data-driven and the neural network is trained on the WeatherBench dataset (processed ERA5 data) to forecast geopotential and temperature 3 and 5 days ahead. Data exploration leads to the identification of the most important input variables. In order to increase computational efficiency, several neural networks are trained on small subsets of these variables. The outputs are then combined through a stacked neural network, the first time such a technique has been applied to weather data. Our approach is found to be more accurate than some coarse numerical weather prediction models and as accurate as more complex alternative neural networks, with the added benefit of providing key probabilistic information necessary for making informed weather forecasts.
The trustworthiness of neural networks is often challenged because they lack the ability to express uncertainty and explain their skill. This can be problematic given the increasing use of neural networks in high stakes decision-making such as in climate change applications. We address both issues by successfully implementing a Bayesian Neural Network (BNN), where parameters are distributions rather than deterministic, and applying novel implementations of explainable AI (XAI) techniques. The uncertainty analysis from the BNN provides a comprehensive overview of the prediction more suited to practitioners' needs than predictions from a classical neural network. Using a BNN means we can calculate the entropy (i.e. uncertainty) of the predictions and determine if the probability of an outcome is statistically significant. To enhance trustworthiness, we also spatially apply the two XAI techniques of Layer-wise Relevance Propagation (LRP) and SHapley Additive exPlanation (SHAP) values. These XAI methods reveal the extent to which the BNN is suitable and/or trustworthy. Using two techniques gives a more holistic view of BNN skill and its uncertainty, as LRP considers neural network parameters, whereas SHAP considers changes to outputs. We verify these techniques using comparison with intuition from physical theory. The differences in explanation identify potential areas where new physical theory guided studies are needed.
The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure related parameters in both the hydrodynamic and morphodynamic solvers. This uncertainty can be addressed through the application of adjoint methods. These have the notable advantage that the number and/or dimension of the uncertain parameters has almost no effect on the computational cost associated with calculating the model sensitivities. Here, we develop the first freely available and fully flexible adjoint hydro-morphodynamic model framework. This flexibility is achieved through using the pyadjoint library, which allows us to assess the uncertainty of any parameter with respect to any output functional, without further code implementation. The model is developed within the coastal ocean model Thetis constructed using the finite element code-generation library Firedrake. We present examples of how this framework can perform sensitivity analysis, inversion and calibration for a range of uncertain parameters based on the final bedlevel. These results are verified using so-called dual-twin experiments, where the `correct' parameter value is used in the generation of synthetic model test data, but is unknown to the model in subsequent testing. Moreover, we show that inversion and calibration with experimental data using our framework produces physically sensible optimum parameters and that these parameters always lead to more accurate results. In particular, we demonstrate how our adjoint framework can be applied to a tsunami-like event to invert for the tsunami wave from sediment deposits.
This manuscript is a non-peer reviewed EarthArXiv preprint that has been submitted for publication in COMPUTERS & GEOSCIENCES. 1. Introduction Data from 2010 shows that almost 400 million people lived in areas less than 5m above average sea level (CIESIN, 2013) and this population keeps growing. As sea levels rise and with the potential for storms to increase in strength and frequency due to a changing climate, the coastal zone is becoming an ever more critical location for the application of advanced modelling techniques. A particularly important example is the development and application of improved morphodynamic models to simulate sediment transport accurately. The effects of climate change will cause hydrodynamic changes leading to increased erosion rates, increasing flooding and erosion risk in coastal zones. The coupled and non-linear nature of this problem makes it especially challenging, since models must solve both hydrodynamic and sediment trsnsport processes together with their two-way coupled interactions. Furthermore, there are two types of sediment transport processes that should be resolved: suspended sediment in the fluid and bedload transport propagating along the bed itself. Over the last 40 years, increasingly complex morphodynamic models have been developed to predict sediment transport in fluvial and coastal zones. These models can be one-dimensional (1D), two-dimensional (2D) or threedimensional (3D), and are discussed in detail in Amoudry (2008), Amoudry and Souza (2011) and Papanicolaou et al. (2008), which we draw upon for a brief review here. 1D models generally use finite difference methods to solve a simple system of equations and are the cheapest computationally. However, they cannot capture velocity in the crossstream and vertical directions. 2D (or 2DH) models adopt the shallow water approximation and can use finite difference (e.g. XBeach-Roelvink et al., 2015), finite volume (e.g. Mike 21-Warren and Bach, 1992), or finite element based methods to solve a more complex system of equations. They capture velocity in both the streamwise and cross-stream directions on planview geometries in the horizontal. 3D models are similar to 2D, but solve an even more complex full system of equations using finite difference (e.g. ROMS-Warner et al., 2008), finite volume (e.g. Fast3d-Landsberg et al., 1998) or finite element based methods. They are thus potentially more accurate, but considerably more computationally expensive. More sophisticated models offer 2D and 3D options, such as Telemac-Mascaret (Hervouet, 1999) and Delft3d (Deltares, 2014), which use finite element/volume and finite difference based methods, respectively. In choosing a model, one must balance the simplicity and computational efficiency of a 2D model against the potential accuracy of a 3D one.
Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.
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