Regional modeling of daily precipitation fields across the Great Lakes region (Canada) using the CFSR reanalysis

Abstract

High densities of local-scale daily precipitation series across relatively large domains are of special interest for a wide range of applications (e.g., hydrological modeling, agriculture). The focus of the present study is to post-process gridded precipitation from a single reanalysis to correct bias and scale mismatch with observations, and to extend the same post-processing at sites without historical data. A Stochastic Model Output Statistical approach combined with meta-Gaussian spatiotemporal random fields, calibrated at sites, is employed to post-process the Climate Forecast System Reanalysis (CFSR) precipitation. The post-processed data, characterized by local parameters, is then mapped across the Great Lakes region (Canada) using two different approaches: (1) kriging, and (2) Vector Generalized Additive Model (VGAM) with spatial covariates. The kriging enables the interpolation of these parameters, while the spatial VGAM helps to spatially post-process CFSR precipitation using a single model. The k-fold cross-validation procedure is employed to assess the ability of the two approaches to predict selected characteristics and climate indices. The kriging and spatial VGAM approaches modeled effectively the distribution of the precipitation process to similar extents (e.g., mean daily precipitation, variability and the number of wet days). The kriging approach produces slightly better estimates of climate indices than the spatial VGAM models. Both approaches demonstrate significant improvement of the metric estimation compared to those of CFSR without post-processing.

RMSE and relative bias estimates

Let $\mathbf {m}_{s} = \{ m_{1,s}, m_{2,s}, \ldots , m_{100,s}\}$, $m_{s}^{(obs)}$, and $m_{s}^{(cfsr)}$ be, respectively, the vector of climate characteristics (e.g., mean) or ETCCDI indices (e.g., mean of the annual CDW), estimated across the 100 post-processed daily precipitation series at the site s, the observed and the CFSR estimates of the same quantity. The RMSE between the observed and post-treated series presented in this study corresponds to:

$$\begin{aligned} \text {RMSE}(obs, pst)^{(n)}&= {} \sqrt{\frac{1}{S} \sum _{i=1}^{S} \left( m_{i}^{(obs)} - m_{n,i}\right) ^{2}},\\ \text {RMSE}(obs, pst)&= {} \frac{1}{N}\sum _{n=1}^{N}\text {RMSE}(obs, pst)^{(n)} \end{aligned}$$

where S is the total number of sites across the domain, and $m_{n,i}$ the characteristic or index for the simulations n (from 1 to N) at the site i. The pst subscript refers to the post-processed values. Similarly, the relative bias expresses as:

$$\begin{aligned} \text {Rbias}(obs, pst)^{(n)}&= \frac{1}{S} \sum _{i=1}^{S} \left( \frac{m_{n,i} - m_{i}^{(obs)}}{m_{i}^{(obs)}} \right) , \\ \text {Rbias}(obs, pst)&= \frac{1}{N} \sum _{n=1}^{N} \text {Rbias}(obs, pst)^{(n)} \end{aligned}$$

The lower and upper limits of the 95% confidence interval for ${\text {RMSE}}(obs, pst)$ was estimated as, respectively, the $2.5{\mathrm{th}}$ and $97.5{\mathrm{th}}$ quantile obtained from the $\{ {\text {RMSE}}(obs, pst)^{(n)} \} _{n \in [1,N]}$ distribution. The same approach was used to provide the 95% confidence interval for ${\text {Rbias}}(obs, pst)$.

Finally, the RMSE and Rbias between observed and CFSR estimates were classically assessed with the followings:

$$\begin{aligned} \text {RMSE}(obs, cfsr)&= {} \sqrt{\frac{1}{S} \sum _{i=1}^{S} \left( m_{i}^{(obs)} - m_{i}^{(cfsr)} \right) ^{2}} \\ \text {Rbias}(obs, cfsr)&= {} \frac{1}{S} \sum _{i=1}^{S} \left( \frac{m_{i}^{(cfsr)} - m_{i}^{(obs)}}{m_{i}^{(obs)}} \right) \end{aligned}$$