# Towards the Prototype Probabilistic Earth-System Model for Climate Prediction

### Stochastic Earth System Modeling : Key Results

**Stochastic representation of sub-grid uncertainty for dynamical core development (Subramanian et al., 2018, sub judice)**

- While representing resolved scales is an inherently well-defined procedure, development of new parameterisations is inherently imprecise and uncertain and currently represented by stochastic approaches in many operational weather models.
- Because of the nonlinearity of the climate, this stochasticity will inevitably percolate into the dynamical core, and therefore determine a lower bound to the numerical accuracy with which dynamical cores should be formulated.
- We describe a low-cost stochastic scheme, which can be bolted onto any existing deterministic dynamical core and could be used to adjust accuracy in future dynamical-core development work.
- The overall key point of the study is that there is no point trying to develop dynamical cores that are more precise than the level of uncertainty provided by our stochastic scheme.

**Impact of stochastic perturbations on tropical precipitation distribution (Watson et al., 2017, In Prep.)**

- Climate models tend to have too little variability in the tropics.
- The standard deterministic configuration of the EC-Earth model at 80km grid spacing has too few heavy rainfall events in the tropics (shown by the green curve for northern South America).
- Adding a stochastic parameterisation greatly increases the frequency of heavy rainfall events (red curve).
- The stochastic scheme is more effective at this than the much more expensive option of decreasing the grid spacing to 16km (blue curve).

** Impact of stochastic perturbations on ENSO variability in a climate model (CESM; Christensen et al., 2017, J. Clim.)**

- The stochastic parametrisation scheme SPPT has a significant positive impact on the El Nino-Southern Oscillation in the coupled climate model CCSM4.
- The power spectrum of the Nino 3.4 index in observations (a) shows a broad peak of 2-7 years while in the control model (b) ENSO is too periodic and has too large an amplitude.
- These ENSO characteristics are greatly improved on the inclusion of the stochastic parametrisation scheme ‘SPPT’, such that the model integration (black) more closely represents the observed ENSO (grey). Christensen et al, 2017, J. Climate.

** Impact of stochastic perturbations on MJO variability in a climate model (EC Earth; Davini et al., 2017, GMD; Subramanian et al., 2017, In Prep.)**

- The stochastic parametrisation scheme SPPT has a positive impact on the propagation of the Madden-Julian Oscillation in the Tropics in the EC-Earth climate model.
- The lead-lag correlation of precipitation at each longitude with precipitation in the Indian Ocean in observations (b) shows a strong propagation of precipitation from the west Indian Ocean to central Pacific over a period of 45 days while in the control model (a) the MJO precipitation shows propagation in the Indian Ocean but does not show a strong correlation past the Maritime Continent.
- The MJO propagation past the Maritime Continent is improved with the stochastic parametrisation scheme ‘SPPT’. This is also reflected with improved power in the intraseasonal wind and OLR variability in the Tropics for this simulation (not shown).

** Impact of stochastic parameterization in ocean models on low frequency climate variability (EC Earth; Juricke et al., 2017)**

- Stochastic perturbations to ocean deep convection and eddy timescales, and Turbulent Kinetic Energy tendencies for vertical mixing
- 2m air temperature mean squared skill score for (left) deterministic reference forecast and (right) forecast with stochastic ocean schemes, for start dates 1981-2010 and the averaged forecast months December to February ( months 8-10), referenced to ERA-Interim.
- Highlighted are those areas where the two ensembles are significantly different from 0 according to a 1000 sample bootstrapping. Optimal forecasts would reach a skill of 1, while forecast skill below 0 suggests a model performance worse than a guess based on climatology.

### Imprecise computing for Earth System modeling : Key Results

** Reduced Precision in Weather Forecasting Models (Dueben et al., 2016; Váňa et al., 2017)**

- To save computing power, numerical precision can be reduced significantly in weather and climate models before rounding errors reduce model quality Link to manuscript.
- A precision analysis can help to understand model error and model uncertainty in Earth System models. Link to manuscript
- An explicit representation of model uncertainty via stochastic parametrisation schemes can help to adjust numerical precision to the optimal level. Link to manuscript

** Impact of imprecise computations in a land surface model (Dawson et al., 2017, In Prep.)**

- A hybrid precision land surface model, where tendency terms are evaluated at 16-bit precision but time-stepping is done at single-precision, produces an accurate simulation of soil temperature over lead times of several months.
- This work demonstrates that even when reducing precision throughout a whole model fails, much of the benefit of low precision can be recovered by structuring the simulation as a small high-precision part, and a low precision part.

** Use of FPGA hardware for exploring reduced precision computations (Jeffress et al., 2017, sub judice) **

- Using FPGA resources for resolution rather than precision yields 28.9% forecast improvement and 10x energy reduction
- In the above figure the coarse resolution simulation (blue line) was done at double precision with 8 grid points in the periodic Lorenz-96 model. The medium resolution simulation (green line) was done with 16 grid points at single precision and the fine inexact simulation (red line) was done with 32 grid points at Integer 16-bit precision.