Fixing the water and energy budget imbalances in ECMWF’s Integrated Forecasting System (IFS)

by Tobias Becker* and ECMWF modelling teams**

One of the advantages of having a community of people looking at the behaviour of our models is that it makes us look at old problems in a new light. A good example is the first nextGEMS hackathon in October 2021, at which we found that both of our nextGEMS models, ICON and the Integrated Forecasting System (IFS), do not conserve energy well. The atmospheric energy leakage amounts to 6.6 W m^-2 in ICON and 6.3 W m^-2 in the IFS, at 4 to 5 km resolution with no parametrisation of deep convection. Analysis quickly showed that most of the energy imbalance in the IFS is related to water non-conservation, and that this issue gets worse when spatial resolution is increased and when the parametrisation of deep convection is switched off. Figure 1 shows that the nextGEMS Cycle 1 simulations with the IFS have an artificial source of water in the atmosphere, which is responsible for 4.6% and 10.7% of the total precipitation, in the simulation with deep convection parameterisation at 9 km (the configuration used for ECMWF’s operational high resolution ten-day forecasts) and without deep convection parameterisation at 4 km, respectively.

The water non-conservation of the IFS had been known for a long time, given that the departure point interpolation of the Semi-Lagrangian advection scheme used in the IFS is non-conserving. However, while this issue was acknowledged to be detrimental for the accuracy of climate integrations (Roberts et al., 2018), so far it was thought that it does not affect the quality of numerical weather forecasts which span timescales ranging from a few hours to seasons ahead. Further analysis after the hackathon by the modelling teams at ECMWF has shown that about 50% of this artificial atmospheric water source is created as water vapour. The additional water vapour not only affects the radiation energy budget of the atmosphere, but can also cause energy non-conservation when heat is released through condensation. The other 50% of water is created as cloud liquid, cloud ice, rain or snow. The artificial source of water is related to higher-order interpolation in the semi-Lagrangian advection scheme, causing spurious extrema. For the moist species, spurious minima can result in negative values, which are clipped, leaving the spurious maxima to increase condensate mass.

To address the problem of water non-conservation in the IFS, three adjustments were required: a small bug fix in the IFS code, a switch from cubic to linear horizontal interpolation  in the advection scheme for cloud liquid, cloud ice, rain and snow, and most importantly, the activation of a global tracer mass fixer for all moist species, including water vapour. Activating tracer mass fixers increases the computational cost of running a simulation, but we succeeded to find an accurate yet cost-effective setup that uses a Finite Differences approach rather than a Finite Elements approach to calculate the vertical integrals for the tracer mass fixers. Note that tracer mass fixers assure global mass conservation, so locally tracer non-conservation is still possible but is expected to have been significantly reduced. Figure 1 shows that with these three model changes, global water non-conservation is essentially eliminated (less than 0.1%) in our new nextGEMS simulations (labelled Cycle1.2), while the global energy budget imbalance has reduced to less than 1 W m^-2 (not shown). 

Importantly, global water conservation turns out to be beneficial not only for long integrations, but also for the quality of ECMWF’s medium-range weather forecasts. Preliminary results suggest that the model changes performed to fix the water and energy imbalances improve the skill scores of the medium-range weather forecasts for many variables, but most robustly for precipitation. Figure 2 shows that the mean absolute error against rain gauge measurements is about 2-3% smaller in 9 km forecasts that ensure global water conservation compared to the default 9 km forecasts.

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* Alexander von Humboldt Fellow at ECMWF
** Special thanks to Thomas Rackow, Xabier Pedruzo, Irina Sandu, Richard Forbes, Michail Diamantakis, Peter Bechtold, Inna Polichtchouk and to the participants of the 1st nextGEMS hackathon