As acute climate change impacts weather and climate variability, there is increased demand for robust climate impact model predictions from which forecasts of the impacts can be derived. The quality of those predictions are limited by the climate drivers for the impact models which are nonlinear and highly variable in nature. One way to estimate the uncertainty of the model drivers is to assess the distribution of ensembles of climate forecasts. To capture the uncertainty in the impact model outputs associated with the distribution of the input climate forecasts, each individual forecast ensemble member has to be propagated through the physical model which can imply high computational costs. It is therefore desirable to train a surrogate model which allows predictions of the uncertainties of the output distribution in ensembles of climate drivers, thus reducing resource demands.This study considers a climate driven disease model, the Liverpool Malaria Model (LMM), which predicts the malaria transmission coefficient R0. Seasonal ensembles forecasts of temperature and precipitation with a 6-month horizon are propagated through the model, predicting the distribution of transmission time series. The input and output data is used to train surrogate models in the form of a Random Forest Quantile Regression (RFQR) model and a Bayesian Long Short-Term Memory (BLSTM) neural network. Comparing the predictive performance, the RFQR better predicts the time series of the individual ensemble member, while the BLSTM offers a direct way to construct a combined distribution for all ensemble members. An important element of the proposed methodology is that accounting for non-normal distributions of climate forecast ensembles can be captured naturally by a Bayesian formulation.