Improved numerical solvers for coupled chemistry-climate model simulations

2020 ◽  
Author(s):  
Emre Esenturk
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Numerical Solutions ◽  
Iterative Algorithms ◽  
Box Model ◽  
Stiff Systems ◽  
Atmospheric Conditions ◽  
Model Simulations ◽  
Climate Model Simulations ◽  
The Uk

<p>A key and expensive part of coupled atmospheric chemistry-climate model simulations is the integration of gas phase chemistry, which involves dozens of species and hundreds of reactions. These species and reactions form a highly-coupled network of Differential Equations (DEs). There exists orders of magnitude variability in the lifetimes of the different species present in the atmosphere and so solving these DEs to obtain robust numerical solutions poses a “stiff problem”. With newer models having more species and increased complexity it is now becoming increasingly important to have chemistry solving schemes that reduce time but maintain accuracy.</p><p>A sound way to handle stiff systems is by using implicit DE solvers but the computational costs for such solvers are high due to internal iterative algorithms (e.g., Newton-Raphson (NR) methods). Here we propose an approach for implicit DE solvers that improves their convergence speed and robustness with relatively small modification in the code. We achieve this by using Quasi-Newton (QN) methods. We test our approach with numerical experiments on the UK Chemistry and Aerosol (UKCA) model, part of the UK Met Office Unified Model suite, run in both an idealized box-model environment and under realistic 3D atmospheric conditions. The box model tests reveal that the proposed method reduces the time spent in the solver routines significantly, with each QN call costing 27% of a call to the full NR routine. A series of experiments over a range of chemical environments was conducted with the box-model to find the optimal iteration steps to call the QN routine which result in the greatest reduction in the total number of NR iterations whilst minimising the chance of causing instabilities and maintaining solver accuracy. The 3D simulations show that our method for the chemistry solver, speeds up the chemistry routines by around 13%, resulting in a net improvement in overall run-time of the full model by approximately 3% with negligible loss in the accuracy (relative error of order 10<sup>-7</sup>) . The QN method also improves the robustness of the solver by significantly reducing (40% ) the number of grid cells which fail to converge hence avoiding unnecessary timestep adjustments. </p>

scholarly journals Quasi-Newton Methods for Atmospheric Chemistry Simulations: Implementation in UKCA UM Vn10.8

2018 ◽  
Author(s):  
Emre Esenturk ◽  
Luke Abraham ◽  
Scott Archer-Nicholls ◽  
Christina Mitsakou ◽  
Paul Griffiths ◽  
...  
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Numerical Solutions ◽  
Iterative Algorithms ◽  
Box Model ◽  
Stiff Systems ◽  
Atmospheric Conditions ◽  
Newton Raphson ◽  
The Uk ◽  
Quasi Newton

Abstract. A key and expensive part of coupled atmospheric chemistry-climate model simulations is the integration of gas phase chemistry, which involves dozens of species and hundreds of reactions. These species and reactions form a highly-coupled network of Differential Equations (DEs). There exists orders of magnitude variability in the lifetimes of the different species present in the atmosphere and so solving these DEs to obtain robust numerical solutions poses a "stiff problem". With newer models having more species and increased complexity it is now becoming increasingly important to have chemistry solving schemes that reduce time but maintain accuracy. While a sound way to handle stiff systems is by using implicit DE solvers, the computational costs for such solvers are high due to internal iterative algorithms (e.g., Newton-Raphson methods). Here we propose an approach for implicit DE solvers that improves their convergence speed and robustness with relatively small modification in the code. We achieve this by blending the existing Newton-Raphson (NR) method with Quasi-Newton (QN) methods, whereby the QN routine is called only on selected iterations of the solver. We test our approach with numerical experiments on the UK Chemistry and Aerosol (UKCA) model, part of the UK Met Office Unified Model suite, run in both an idealized box-model environment and under realistic 3D atmospheric conditions. The box model tests reveal that the proposed method reduces the time spent in the solver routines significantly, with each QN call costing 27 % of a call to the full NR routine. A series of experiments over a range of chemical environments was conducted with the box-model to find the optimal iteration steps to call the QN routine which result in the greatest reduction in the total number of NR iterations whilst minimising the chance of causing instabilities and maintaining solver accuracy. The 3D simulations show that our moderate modification, by means of using a blended method on the chemistry solver, speeds up the chemistry routines by around 13 %, resulting in a net improvement in overall run-time of the full model by approximately 3 % with negligible loss in the accuracy. The blended QN method also improves the robustness of the solver, reducing the number of grid cells which fail to converge after 50 iterations. The differences in chemical concentrations between the control run and that using the blended QN method are negligible for longer lived species, such as ozone, and below the threshold for solver convergence almost everywhere for shorter lived species such as the hydroxyl radical.

scholarly journals Quasi-Newton methods for atmospheric chemistry simulations: implementation in UKCA UM vn10.8

2018 ◽  
Vol 11 (8) ◽  
pp. 3089-3108 ◽  
Author(s):  
Emre Esentürk ◽  
Nathan Luke Abraham ◽  
Scott Archer-Nicholls ◽  
Christina Mitsakou ◽  
Paul Griffiths ◽  
...  
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Numerical Solutions ◽  
Iterative Algorithms ◽  
Box Model ◽  
Stiff Systems ◽  
Atmospheric Conditions ◽  
Newton Raphson ◽  
The Uk ◽  
Quasi Newton

Abstract. A key and expensive part of coupled atmospheric chemistry–climate model simulations is the integration of gas-phase chemistry, which involves dozens of species and hundreds of reactions. These species and reactions form a highly coupled network of differential equations (DEs). There exist orders of magnitude variability in the lifetimes of the different species present in the atmosphere, and so solving these DEs to obtain robust numerical solutions poses a stiff problem. With newer models having more species and increased complexity, it is now becoming increasingly important to have chemistry solving schemes that reduce time but maintain accuracy. While a sound way to handle stiff systems is by using implicit DE solvers, the computational costs for such solvers are high due to internal iterative algorithms (e.g. Newton–Raphson methods). Here, we propose an approach for implicit DE solvers that improves their convergence speed and robustness with relatively small modification in the code. We achieve this by blending the existing Newton–Raphson (NR) method with quasi-Newton (QN) methods, whereby the QN routine is called only on selected iterations of the solver. We test our approach with numerical experiments on the UK Chemistry and Aerosol (UKCA) model, part of the UK Met Office Unified Model suite, run in both an idealised box-model environment and under realistic 3-D atmospheric conditions. The box-model tests reveal that the proposed method reduces the time spent in the solver routines significantly, with each QN call costing 27 % of a call to the full NR routine. A series of experiments over a range of chemical environments was conducted with the box model to find the optimal iteration steps to call the QN routine which result in the greatest reduction in the total number of NR iterations whilst minimising the chance of causing instabilities and maintaining solver accuracy. The 3-D simulations show that our moderate modification, by means of using a blended method for the chemistry solver, speeds up the chemistry routines by around 13 %, resulting in a net improvement in overall runtime of the full model by approximately 3 % with negligible loss in the accuracy. The blended QN method also improves the robustness of the solver, reducing the number of grid cells which fail to converge after 50 iterations by 40 %. The relative differences in chemical concentrations between the control run and that using the blended QN method are of order  ∼  10−7 for longer-lived species, such as ozone, and below the threshold for solver convergence (10−4) almost everywhere for shorter-lived species such as the hydroxyl radical.

scholarly journals Climate change increases the probability of heavy rains like those of storm Desmond in the UK – an event attribution study in near-real time

2015 ◽  
Vol 12 (12) ◽  
pp. 13197-13216 ◽  
Author(s):  
G. J. van Oldenborgh ◽  
F. E. L. Otto ◽  
K. Haustein ◽  
H. Cullen
Keyword(s):  
Climate Change ◽  
Climate Model ◽  
Extreme Event ◽  
Initial Assessment ◽  
Model Simulations ◽  
Event Attribution ◽  
Climate Model Simulations ◽  
Using Data ◽  
The Uk ◽  
Precipitation Events

Abstract. On 4–6 December 2015, the storm "Desmond" caused very heavy rainfall in northern England and Scotland, which led to widespread flooding. Here we provide an initial assessment of the influence of anthropogenic climate change on the likelihood of one-day precipitation events averaged over an area encompassing northern England and southern Scotland using data and methods available immediately after the event occurred. The analysis is based on three independent methods of extreme event attribution: historical observed trends, coupled climate model simulations and a large ensemble of regional model simulations. All three methods agree that the effect of climate change is positive, making precipitation events like this about 40 % more likely, with a provisional 2.5–97.5 % confidence interval of 5–80 %.

scholarly journals Anthropogenic forcing and response yield observed positive trend in Earth’s energy imbalance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shiv Priyam Raghuraman ◽  
David Paynter ◽  
V. Ramaswamy
Keyword(s):  
Radiative Forcing ◽  
Climate Model ◽  
Solar Spectrum ◽  
Internal Variability ◽  
Satellite Observations ◽  
Positive Trend ◽  
Energy Imbalance ◽  
Model Simulations ◽  
Heat Uptake ◽  
Climate Model Simulations

AbstractThe observed trend in Earth’s energy imbalance (TEEI), a measure of the acceleration of heat uptake by the planet, is a fundamental indicator of perturbations to climate. Satellite observations (2001–2020) reveal a significant positive globally-averaged TEEI of 0.38 ± 0.24 Wm−2decade−1, but the contributing drivers have yet to be understood. Using climate model simulations, we show that it is exceptionally unlikely (<1% probability) that this trend can be explained by internal variability. Instead, TEEI is achieved only upon accounting for the increase in anthropogenic radiative forcing and the associated climate response. TEEI is driven by a large decrease in reflected solar radiation and a small increase in emitted infrared radiation. This is because recent changes in forcing and feedbacks are additive in the solar spectrum, while being nearly offset by each other in the infrared. We conclude that the satellite record provides clear evidence of a human-influenced climate system.

Sign in / Sign up

Export Citation Format

Share Document