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Temporal persistence in unforced climate variability makes detection of trends in surface temperature difficult. Part of the challenge is methodological since standard techniques assume a separation of time scales between trend and noise. In this work we present a novel Bayesian approach to trend detection under the assumption of long-range dependent natural variability, and we use estimates of historical forcing to test if the method correctly discriminates trends from low-frequency natural variability. As an application we analyze 2$^\circ \times $2$^\circ$ gridded data from the GISS Surface Temperature Analysis. In the time period from 1900 to 2015 we find positive trends for 99% of the grid points. For 84\% of the grid points we are confident that the trend is positive, meaning that the 95% credibility interval for the temperature trend contained only positive values. This number increased to 89% when we used estimates of historical forcing to specify the noise model. For the time period from 1900 to 1985 the corresponding ratios were 42% and 52%. Our findings demonstrate that positive trends since 1900 are now detectable locally over most of Earth's surface.

Warming Trends and Long-Range Dependent Climate Variability Since Year 1900: A Bayesian Approach