Adjoint-based sensitivity analysis for a numerical storm surge model

Warder, Simon C.; Horsburgh, Kevin; Piggott, Matthew D.

doi:10.1016/j.ocemod.2021.101766

Cited by 16 publications

(11 citation statements)

References 33 publications

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“…The adjoint method has already been used successfully with the hydrodynamic component of Thetis (e.g. Warder et al, 2021), but we expand upon this here by using the adjoint method with a coupled model which requires extending the pyadjoint code to ensure that the coupling is correctly captured. In particular, the coupling between the components of the hydro-morphodynamic model relies on a split mechanism, which extracts the velocity and elevation from the hydrodynamic component so that both can be passed to the morphodynamic component.…”

Section: Adjoint Methodsmentioning

confidence: 99%

“…Although the adjoint method has previously been used with the hydrodynamic component of Thetis, e.g. in Warder et al (2021), this work is the first time pyadjoint is used in a coupled model. A further advantage of this hydro-morphodynamic model is that it is more accurate than industry-standard models such as Telemac-Mascaret, as shown in Clare et al (2021a), partly because of the relatively novel use of a discontinuous Galerkin based finite element discretisation.…”

Section: Introductionmentioning

confidence: 99%

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Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

Clare¹,

Kramer²,

Cotter³

et al. 2021

Preprint

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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.

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Section: Adjoint Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

Clare¹,

Kramer²,

Cotter³

et al. 2021

Preprint

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show abstract

“…One approach to tuning the parameters of idealised axisymmetric storms would be to minimise the cost functions of adjoint models for storm surges at tide gauges (e.g. Wilson et al 2013;Warder et al 2021). For storm surges and waves, which demand an accurate simulation of extreme wind speeds and extreme low pressures, such a probabilistic approach to synthesising mid-latitude storms is likely to be more insightful than full NWP ensemble simulations from high-resolution climate models (which currently lack the resolution to generate extreme wind speeds and low pressures).…”

Section: Discussionmentioning

confidence: 99%

“Grey swan” storm surges pose a greater coastal flood hazard than climate change

et al. 2021

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In this paper, we show that over the next few decades, the natural variability of mid-latitude storm systems is likely to be a more important driver of coastal extreme sea levels than either mean sea level rise or climatically induced changes to storminess. Due to their episodic nature, the variability of local sea level response, and our short observational record, understanding the natural variability of storm surges is at least as important as understanding projected long-term mean sea level changes due to global warming. Using the December 2013 North Atlantic Storm Xaver as a baseline, we used a meteorological forecast modification tool to create “grey swan” events, whilst maintaining key physical properties of the storm system. Here we define “grey swan” to mean an event which is expected on the grounds of natural variability but is not within the observational record. For each of these synthesised storm events, we simulated storm tides and waves in the North Sea using hydrodynamic models that are routinely used in operational forecasting systems. The grey swan storms produced storm surges that were consistently higher than those experienced during the December 2013 event at all analysed tide gauge locations along the UK east coast. The additional storm surge elevations obtained in our simulations are comparable to high-end projected mean sea level rises for the year 2100 for the European coastline. Our results indicate strongly that mid-latitude storms, capable of generating more extreme storm surges and waves than ever observed, are likely due to natural variability. We confirmed previous observations that more extreme storm surges in semi-enclosed basins can be caused by slowing down the speed of movement of the storm, and we provide a novel explanation in terms of slower storm propagation allowing the dynamical response to approach equilibrium. We did not find any significant changes to maximum wave heights at the coast, with changes largely confined to deeper water. Many other regions of the world experience storm surges driven by mid-latitude weather systems. Our approach could therefore be adopted more widely to identify physically plausible, low probability, potentially catastrophic coastal flood events and to assist with major incident planning.

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“…For more detail on Thetis adjoint and its applications, see previous studies e.g. Warder et al (2019Warder et al ( , 2021, Goss et al (2020).…”

Section: Two-dimensional Adjoint-capable Shallow Water Modelmentioning

confidence: 99%

“…Intuition might suggest that the optimal experiment design would likely consist of parameter regions of similar area, or containing similar volumes of observation data. However, a recent study on storm surge sensitivity to bottom friction coefficient in the North Sea (Warder et al, 2021) found that, due to the dynamics of surge propagation along the east coast of the UK, several tide gauge locations in the region exhibit similar spatial patterns of sensitivity to the bottom friction coefficient in the North Sea. This suggests that the tide gauges in the North Sea provide redundant information, which may explain why the optimal experiment design assigns a single friction parameter to the entire North Sea.…”

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confidence: 99%

Optimal experiment design for bottom friction parameter estimation

Warder¹,

Piggott²

2021

Preprint

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It is common practice within numerical coastal ocean modelling to perform model calibration with respect to a bottom friction parameter. While many modelling studies employ a spatially uniform coefficient, within the parameter estimation literature the coefficient is typically taken to be spatially (or even temporally) varying. A parameter estimation experiment requires an appropriate set of observations, and also the selection of an appropriate parameter space which captures the spatial variability of the bottom friction parameter. In regions such as the Bristol Channel, which is used as a case study within this work, observation data is relatively abundant; here we use observations of M2 and S2 harmonic amplitudes and phases at 20 locations within the Channel. However, as is typical within friction parameter estimation problems, there is no obvious constraint on the spatial variation of the friction coefficient. Here, we define the parameter estimation 'experiment design' as the mapping from a small number of friction parameters onto the model domain. We propose a robust method for the appropriate selection of a low-dimensional experiment design, utilising an optimal experiment design (OED) technique via construction of the Fisher Information Matrix.The objective is to identify the experiment design resulting in the tightest possible constraints on the unknown parameters, given the available observation data. We construct the Fisher Information Matrix via the use of an adjoint shallow water numerical model, Thetis, and perform a variant of D-optimal design to find the optimal experiment design from within two a priori choices of design space. These are based on splitting the model domain either by simple slices across the channel, or by the type of sediment found on the sea bed. We first validate the OED framework by utilising a Bayesian inference algorithm to perform parameter estimation using a selection of experiment designs, which confirms that the OED framework offers a good estimate of the true parameter uncertainty resulting from the use of a given experiment design. An exploration of the full space of experiment designs shows that up to three Manning's n coefficient values can be estimated from the observation data to within an uncertainty of approximately 0.001 s m −1/3 , but that the experiment design is highly influential in achieving this threshold, thus demonstrating the value of our approach as a preliminary step in a parameter estimation study. We also investigate the sensitivity of the achievable parameter uncertainty to the availability of observation data and its measurement uncertainty, providing insights useful to the design of future observation surveys. Finally, we further demonstrate our OED framework with an application to a model of the northwest European continental shelf.

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Adjoint-based sensitivity analysis for a numerical storm surge model

Cited by 16 publications

References 33 publications

Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

“Grey swan” storm surges pose a greater coastal flood hazard than climate change

Optimal experiment design for bottom friction parameter estimation

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