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The MADIA gridded dataset provides the dekadal series of the main agro-meteorological variables derived from ERA5 hourly surface data, across Italy for the period 1981-2021, and their respective 1981-2010 and 1991-2020 climate normals, also including absolute minimum and maximum and the main quantiles. Temporal and spatial resolutions are 10-day and 0.25 degrees respectively and the dataset is annotated with standard metadata. The dataset was obtained by: (1) estimating the daily time series of minimum, average and maximum air temperature, minimum and maximum air relative humidity, wind speed, surface solar radiation downwards, precipitation and reference evapotranspiration according to the FAO Penman-Monteith method; (2) summarising them to 10-day series as accumulated values for precipitation and evapotranspiration and mean values for the other variables. The MADIA dataset is provided in both NetCDF and csv format. A complementary vector file is provided which reports for every cell the fractions covered of the total area of each administrative unit considered to derive statistics for Italy on the European Nomenclature of Territorial Units for Statistics levels (NUTS 2 and 3). Other potential dataset reuses are the estimation of bioclimatic indices and statistical downscaling of climate scenarios.