INLA-SPDE Spatial Model Outperforms Kriging for Predicting Extreme Rainfall Across Japan

Japan's geography creates a near-perfect laboratory for extreme precipitation research. The archipelago spans diverse climate zones, from subtropical Okinawa to subarctic Hokkaido, with mountain ranges that intercept moisture-laden air and complex coastlines that amplify storm systems. Heavy rain and flooding are regular features of the landscape, and climate change is intensifying both the frequency and severity of extreme precipitation events. For engineers designing flood defenses, drainage systems, and rural infrastructure, the ability to estimate the probability of extreme rainfall at locations where no weather station exists is a practical necessity, not just an academic interest.

The challenge is that Japan's network of 752 meteorological observation stations is not evenly distributed. Coverage concentrates around urban areas. Large portions of the country - particularly mountainous and rural regions that may be most vulnerable to flooding - have sparse measurement records. Spatial interpolation methods, which estimate conditions at unobserved locations from data at observed ones, are essential for filling these gaps. But the methods available differ substantially in how well they handle extreme values.

Three Methods, Four Climate Zones

Associate Professor Jihui Yuan, Emeritus Professor Kazuo Emura, and Professor Craig Farnham from Osaka Metropolitan University's Graduate School of Human Life and Ecology, along with Visiting Researcher Zhichao Jiao from Yantai University, conducted a systematic comparison of spatial prediction methods using 40 years of hourly precipitation data from all 752 stations, covering the period 1981 to 2020.

The team first divided Japan into four areas based on climate characteristics, then fitted a Generalized Extreme Value distribution at each station using the Markov Chain Monte Carlo (MCMC) method. This produced estimates of precipitation return values - the rainfall amounts expected to be exceeded once every 2, 5, 10, 25, 50, or 100 years - at each measurement location. The key challenge was then extending those estimates to unobserved locations using spatial interpolation.

The study compared three approaches. Standard ordinary kriging (OK) interpolates values based on spatial correlation structure. Kriging with external drift (KED) incorporates additional predictor variables - in this case, annual precipitation, distance from coast, and population density. The third method, Integrated Nested Laplace Approximation combined with Stochastic Partial Differential Equation (INLA-SPDE), takes a fully probabilistic approach to spatial prediction that accounts for uncertainty more formally than kriging-based methods.

A known limitation of standard kriging is that it tends to underestimate extreme values - precisely the values that matter most for disaster preparedness planning. This happens because kriging methods smooth predictions toward the mean, which reduces estimated extremes in areas where observed values are already high.

INLA-SPDE Performs Better Where It Counts

Evaluated using Leave-One-Out Cross-Validation - a technique that tests each station's predicted value against its actual observed value by temporarily excluding it from the model - INLA-SPDE, particularly a version that incorporated annual precipitation as a covariate, showed higher prediction stability than kriging approaches, especially at long return periods. With a smaller standard deviation for 50-year and 100-year return value estimates, it produced more consistent predictions across the network.

The spatial analysis also revealed a pattern with practical implications: the high-risk precipitation zone in Japan is expanding northward. Areas that historically sat outside the most intense rainfall regions are increasingly falling within them as climate conditions shift. This expansion would not be visible from urban station networks alone and requires the kind of spatial modeling that can characterize conditions in rural and mountainous areas where observation coverage is thin.

What Comes Next

Professor Yuan identified two clear directions for follow-on work. Incorporating dynamic meteorological factors such as typhoon tracks into the model would move it closer to capturing how extreme events actually develop rather than treating them purely as statistical distributions. Extending the framework to spatiotemporal models would allow the team to study how high-risk zones move and evolve over time rather than producing only a static snapshot.

The study's limitations are methodological. The analysis treats each station's extreme value estimate as fixed input rather than propagating uncertainty from the station-level fitting through to the spatial prediction step. The covariates used - annual precipitation, coastal distance, and population - are reasonable first choices but may not capture all the geographic factors that influence extreme rainfall in Japan's complex terrain.

The findings were published in the Journal of Hydrology: Regional Studies.