Using surrogate models to quantify uncertainty in simulations of the West African Monsoon

Forecasting the West African monsoon (WAM) on weather and climate timescales suffers from large uncertainties. Particularly the precipitation associated with the WAM has a great socioeconomic impact through effects on agriculture, energy production, water resources and health.  Aside from errors stemming from initial condition uncertainty, forecasts are generally affected by model uncertainties associated with parameter choices in the representation of sub-gridscale processes. To quantify the combined effect of the latter, a comprehensive sensitivity study is conducted by feeding output of a highly-resolved atmospheric model into so-called surrogate models. This technique allows a comprehensive but resource-friendly statistical investigation of the sensitivity of key WAM characteristics to uncertain model parameters.

The ICON (Icosahedral Nonhydrostatic) model, which is operationally used by the German Weather Service (DWD), is used to simulate the WAM in limited-area mode at 13km grid spacing, using ERA-5 re-analyses as boundary data. To separate model parameter related sensitivities from weather noise and to reduce the influence of initial conditions, a sufficiently long simulation time (in this study 4 WAM seasons with 41 days each starting on July 21st) is required. To avoid the immense computational costs of conducting a large matrix of month-long numerical simulations, surrogate models are used to statistically describe the relationship between uncertain model parameters and quantities of interest (QoIs) derived from the simulation output. For this study, we selected the QoIs total precipitation, latitudinal position of the WAM rain belt, location and strength of the Tropical Easterly Jet (TEJ) and the African Easterly Jet (AEJ), location and extent of the Saharan heat low (SHL) as well as location of the Intertropical Discontinuity (ITD).

For each of the chosen six uncertain model parameters probability density functions are assigned based on measurements and previous studies. Maximin Latin hypercube sampling is applied in order to define 60 parameter combinations. Universal kriging as a general case of Gaussian process regression is used to build surrogate models for the QoIs. These then serve to carry out global sensitivity studies in order to identify the parameters that have the greatest influence on the QoIs. The results indicate for which parameters (and thus processes) uncertainties need to be reduced to lower the spread in simulated QoIs. Furthermore, the surrogate model can serve as a basis for parameter identification studies, e. g. by means of maximum likelihood estimation where simulations are compared to observations.

Among the investigated model parameters, the entrainment rate in the convection scheme and the terminal fall velocity of cloud ice show the greatest effects on the QoIs. The former mainly affects the AEJ, the SHL and the ITD, whereas the latter mainly influences the TEJ. Simple isolated relationships between individual model parameters and WAM QoIs, however, rarely exist. Consistent with the complex nature of the WAM system, individual QoIs instead are affected by multiple parameters. On the other hand, individual parameters affect multiple QoIs simultaneously, reflecting the physical relationships between them. This highlights the usefulness of incorporating surrogate models in the analysis of model uncertainty.