Estimating areal precipitation and quantifying the associated uncertainties are important for both hydrological research and water resource management. However, many, if not all, precipitation products provide only the precipitation at reasonable spatial scales without uncertainty attached. In this paper, we promote a double smoothing technique to derive the precipitation amounts at small grid size based on gauge observations and then propose a bootstrap method to quantify the rainfall model estimation uncertainty (the uncertainty of rainfall estimation by a given model; here our model is double smoothing) by the traditional bootstrap for parameter uncertainty and the rainfall product uncertainty in term of prediction. As the residuals by the direct use of smoothing approach are heterogeneous, making the direct use of bootstrapping method invalid, we use an empirical transformation to stabilise the residuals. Furthermore, by using bootstrapping method, we can easily upscale the precipitation and the associate uncertainty to any required scales. The product is easy to use in research and practice. We demonstrate our methods by applying it to Murray Darling Basin in the eastern Australia.
- Nonparametric kernel smoothing
- Rainfall product
- Uncertainty estimation