AbstractThis study aims to estimate climatological cloudburst frequencies from daily precipitation sums for a dense network of 161 historical Danish stations covering the period 1914–2010, in order to reveal any systematic regional differences. We define a cloudburst day for a given station as a day when the maximum 1‐h precipitation sum exceeds a predefined threshold; we use the thresholds 15, 20 and 25 mm, corresponding to a cloudburst frequency around 0.42, 0.16 and 0.06 year−1, respectively. Supplementing the historical data, we use hourly data from a modern network and relate the daily probability of cloudburst occurrence to the corresponding daily precipitation using binary regression. This allows an estimation of the cloudburst frequency from a series of daily sums. To validate the methods, we use 33 stations that have been operating for 30 years or longer. For these stations, we demonstrate significant skill by comparing observed and estimated cloudburst frequencies with a jackknife procedure. By applying the model to the 161 historical series, we estimate climatological cloudburst frequencies throughout Denmark. We find large systematic regional variations across Denmark and these variations are much larger, but with a similar regional pattern, than obtained by previous work. We suggest applying the approach to the historical daily precipitation series that exist across the world.