Quantile-based neural network reconstruction of temperature and precipitation over Norway

In recent years, machine learning has been used increasingly for climatological applications. It has been applied to traditional geostatistical problems, such as objective analysis, including reconstructing the value of an atmospheric variable at an unobserved location given observations at nearby locations. These approaches provide new possibilities for combining information from irregular observation networks and may offer advantages over classical interpolation methods, particularly in capturing nonlinear relationships.

In this study, we apply a neural network model to estimate hourly temperature and precipitation at a given location based on nearby observations. The aim is to estimate both the expected value and the associated uncertainty. The neural network is based on an approach originally developed for post-processing numerical weather prediction output, which provides probabilistic forecasts in the form of quantile functions. These quantile functions are represented as linear combinations of Bernstein basis polynomials, with coefficients predicted by the network. This representation allows for a flexible and consistent description of the predictive distribution while ensuring that the estimated quantiles are consistent with the observed data.

We present results comparing the probabilistic predictions from the neural network with those obtained using traditional geostatistical methods such as kriging. The spatial filtering properties of the two methods are investigated using both synthetic Gaussian random fields and real observational data as input, allowing us to assess their performance under controlled as well as realistic conditions.

Furthermore, we evaluate the reconstruction method on a dense observation network that includes crowdsourced data, providing insight into its performance in data-rich and heterogeneous observational settings.