使用定制多重网格求解器改进气象局天气和气候预报
Improving Met Office Weather and Climate Forecasts with Bespoke Multigrid Solvers
AI总结：
针对气象局数值模型中大型稀疏线性方程组求解的计算瓶颈，开发了定制多重网格求解器，将线性系统求解时间减半，使全球预报速度提高10%-15%，并实现单精度稳定收敛，每年节约约30万英镑成本。
摘要：
气象局气候和天气预报能力的核心是一个复杂的数值模型，该模型求解大规模大气流动的方程。由于该模型使用半隐式时间步进，因此需要反复求解一个包含数亿个未知数的大型稀疏线性方程组。这是业务预报的计算瓶颈之一，高效的数值算法对于确保最佳性能至关重要。我们开发并实现了一种定制多重网格求解器来应对这一挑战。与之前使用的 BiCGStab 方法相比，我们的求解器将求解线性系统的时间减少了一半。这带来了整体模型性能的显著提升：全球预报的制作速度提高了 10%-15%。多重网格还避免了单精度下迭代方案的收敛停滞。通过更好地利用计算资源，我们的工作为气象局带来了每年约 30 万英镑的成本节约。
英文摘要：
At the heart of the Met Office climate and weather forecasting capabilities lies a sophisticated numerical model which solves the equations of large-scale atmospheric flow. Since this model uses semi-implicit time-stepping, it requires the repeated solution of a large sparse system of linear equations with hundreds of millions of unknowns. This is one of the computational bottlenecks of operational forecasts and efficient numerical algorithms are crucial to ensure optimal performance. We developed and implemented a bespoke multigrid solver to address this challenge. Our solver reduces the time for solving the linear system by a factor two, compared to the previously used BiCGStab method. This leads to significant improvements of overall model performance: global forecasts can be produced 10%-15% faster. Multigrid also avoids stagnating convergence of the iterative scheme in single precision. By allowing better utilisation of computational resources, our work has led to estimated annual cost savings of GBP 300k for the Met Office.
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