[Paper Review] Parameter sensitivity analysis of a sea ice melt pond parametrisation and its emulation using neural networks

Simon Driscoll, Alberto Carrassi+4 more|arXiv (Cornell University)|Apr 11, 2023

Arctic and Antarctic ice dynamicsEarth and Planetary Sciences3 citations

TL;DR

This study investigates parameter sensitivity in a sea ice melt pond parametrization (MPP) within the Icepack model using Sobol sensitivity analysis, revealing high sensitivity to uncertain parameters. It proposes and validates a data-driven neural network emulator that accurately replaces the physics-based MPP, achieving comparable long-term behavior with reduced input complexity, demonstrating a promising path toward improved, interpretable, and efficient subgrid-scale parametrizations in climate models.

ABSTRACT

Accurate simulation of sea ice is critical for predictions of future Arctic sea ice loss, looming climate change impacts, and more. A key feature in Arctic sea ice is the formation of melt ponds. Each year melt ponds develop on the surface of the ice and primarily via affecting the albedo, they have an enormous effect on the energy budget and climate of the Arctic. As melt ponds are subgrid scale and their evolution occurs due to a number of competing, poorly understood factors, their representation in models is parametrised. Sobol sensitivity analysis, a form of variance based global sensitivity analysis is performed on an advanced melt pond parametrisation (MPP), in Icepack, a state-of-the-art thermodynamic column sea ice model. Results show that the model is very sensitive to changing its uncertain MPP parameter values, and that these have varying influences over model predictions both spatially and temporally. Such extreme sensitivity to parameters makes MPPs a potential source of prediction error in sea-ice model, given that the (often many) parameters in MPPs are usually poorly known. Machine learning (ML) techniques have shown great potential in learning and replacing subgrid scale processes in models. Given the complexity of melt pond physics and the need for accurate parameter values in MPPs, we propose an alternative data-driven MPPs that would prioritise the accuracy of albedo predictions. In particular, we constructed MPPs based either on linear regression or on nonlinear neural networks, and investigate if they could substitute the original physics-based MPP in Icepack. Our results shown that linear regression are insufficient as emulators, whilst neural networks can learn and emulate the MPP in Icepack very reliably. Icepack with the MPPs based on neural networks only slightly deviates from the original Icepack and overall offers the same long term model behaviour.

Motivation & Objective

• To assess the sensitivity of sea ice model output to uncertain parameters in a melt pond parametrization (MPP) using global variance-based sensitivity analysis.
• To evaluate whether machine learning, particularly neural networks, can effectively emulate the physics-based MPP in the Icepack model.
• To identify a minimal, yet accurate, set of input variables for a data-driven MPP emulator through feature selection.
• To explore the feasibility of replacing traditional physics-based MPPs with data-driven emulators that improve computational efficiency and interpretability.

Proposed method

• Conducted Sobol sensitivity analysis on the level-ice MPP in Icepack to quantify parameter influence on model output across time and space.
• Trained linear regression and nonlinear neural network models to emulate the MPP’s input-output behavior using synthetic training data generated from the physics-based MPP.
• Performed feature selection using mutual information to identify the most informative input variables, reducing the dimensionality of the emulator input.
• Validated the emulators in online mode by integrating them into the full Icepack model to assess long-term simulation fidelity.
• Compared the performance of the neural network emulator against the original MPP and linear regression emulator in terms of model output accuracy and computational efficiency.
• Explored the potential of using observational data in future work, anticipating challenges in data sparsity and noise, and proposed using combined data assimilation and ML techniques.

Figure 1: Schematic overview of the Icepack model. Panel a: the columnar model set-up, with 4 tiles representing land, open water, slab ice (without snow) and a full ice-thickness distribution (ITD). Panel b: the most important vertical processes represented in Icepack when using the ITD. Courtesy o

Experimental results

Research questions

• RQ1 How sensitive is the Icepack model to variations in the parameters of its melt pond parametrization (MPP)?
• RQ2 Can a machine learning model, specifically a neural network, accurately emulate the behavior of a physics-based MPP in a sea ice model?
• RQ3 Which input variables are most critical for a data-driven MPP emulator to maintain high predictive accuracy?
• RQ4 Can a simplified emulator, using fewer input variables than the original MPP, achieve comparable performance to the full physics-based MPP?
• RQ5 To what extent can a data-driven MPP emulator improve computational efficiency and interpretability compared to traditional parametrizations?

Key findings

• The Icepack model exhibits high and spatially inhomogeneous sensitivity to parameters in the melt pond parametrization, indicating that small parameter uncertainties can lead to large prediction errors.
• Linear regression models were insufficient to emulate the MPP in online mode, failing to reproduce the original Icepack behavior, highlighting the limitations of linear approximations for complex, nonlinear processes.
• Neural network emulators successfully replaced the physics-based MPP in Icepack, showing only slight deviations from the original model and preserving long-term model behavior.
• Feature selection based on mutual information identified a reduced set of input variables—such as previous timestep pond area fraction, pond height, refrozen lid height, near-surface and air temperatures, and snow melt rate—as sufficient for high-performance emulation.
• The resulting smaller neural network emulator achieved good performance with fewer inputs than the original MPP, offering improved computational efficiency and greater physical interpretability.
• The study demonstrates a viable, data-driven pathway toward replacing traditional, over-parametrized MPPs with more accurate, efficient, and interpretable emulators in climate models.

Figure 2: Probability distribution functions we sample from using the SALib library for sensitivity analysis, for the 5 parameters invoked in the level-ice melt pond parametrisation with the mushy thermodynamics scheme (triangular and uniform). Red lines indicate default parameter values in the mode