Effects of Spatial Grid Resolution on the Statistical Power of Testing Earthquake Forecast Models

Abstract

<p>The Collaboratory for the Study of Earthquake Predictability (CSEP) is an international effort to independently evaluate earthquake forecasting models and to provide the cyber-infrastructure together with a suite of testing methods. For global forecasts, CSEP defines a grid-based format to describe the expected rate of earthquakes, which is composed of 6.48 million cells for a 0.1º spacing. The spatial performance of the forecast is tested using the Spatial test (S-test), based on joint log-likelihood evaluations. The high-resolution grid combined with sparse and inhomogeneous earthquake distributions leads to many empty cells that may never experience an earthquake, biasing the S-test results. To explore this issue, we conducted a global earthquake forecast experiment. We tested a spatially uniform forecast model, which is non-informative and should be rejected by the S-test. However, it is not rejected by the S-test when the spatial resolution is high enough to allocate each observed earthquake in individual cells, thus raising questions about the test statistical power.</p><p>The number of observed earthquakes used to evaluate global forecasts is usually only a few hundred, in contrast to the millions of spatial cells. Our analysis shows that for such disparity, the statistical power of tests for single-resolution grids also depends on the number of earthquakes available to evaluate a model. With few earthquakes, the S-test does not allow powerful testing.</p><p>We propose to use a multi-resolution grid to generate and test earthquake forecast models, in which the resolution can be set freely based on available data, e.g., by the number of earthquakes per cell. Data-driven multi-resolution grids demonstrate the ability to reject the uniform forecast, contrary to a high-resolution grid. Furthermore, multi-resolution grids offer powerful testing with as minimum as four earthquakes available in the test catalog. Therefore, we propose to use multi-resolution grids in future CSEP global forecast experiments and to further study its application in regional and local experiments, where such sparsity of observations is present.</p>