Large-scale biospheric drought response intensifies linearly with drought duration

Soil moisture droughts have comprehensive implications for terrestrial ecosystems. Here we study accumulated impacts of the strongest observed droughts on vegetation. The results show that drought duration, the time during which surface soil moisture is below seasonal average, is a key diagnostic variable for predicting drought-integrated changes in (i) gross primary productivity, (ii) evapotranspiration, (iii) vegetation greenness, and (iv) crop yields. Drought-integrated anomalies in these vegetation-related variables scale linearly with drought duration with a slope depending on climate. In arid regions, the slope is steep such that vegetation drought response intensifies with drought duration, whereas in humid regions, it is small such that drought impacts on vegetation are weak even for long droughts. These emergent large-scale linearities are not well captured by stateof-the-art hydrological, land surface and vegetation models. Overall, the linear relationship of drought duration versus vegetation response and crop yield reductions can serve as model benchmark, and support drought impact interpretation and prediction. 5

out of the half-monthly period. In the case of the 8-daily GPP and ET data we infer half-monthly estimates by computing weighted means of the 8-day periods within a half-monthly interval; the weights are thereby determined from the amount of days of each 8-day period that are within the considered half-monthly interval.
All analyses are restricted to time periods when all concerned data products are available.

Datasets
A) Drought forcing datasets A1) Soil Moisture: We employ the gridded surface soil moisture dataset from the European Space Agency's (ESA) Climate Change Initiative (CCI), version 4.4 (http://www.esa-soilmoisture-cci.org, accessed on 2 August 2018). Therefrom, we use the combined product which is derived with observations from active and passive satellites (14). This is a global product which covers the time period 1978-2016.

A2) Precipitation:
Gridded precipitation is obtained from the ERA-Interim reanalysis dataset (15). The data is available between 1979-2015, and the spatial and temporal resolutions are 0.5°x0.5° and 1 day, respectively.

B) Vegetation datasets B1) Gross Primary Productivity (GPP) and evapotranspiration (ET):
We employ GPP and ET data from the FluxCom dataset (16). Therefrom we use the RS product. It is derived by upscaling site-level observations in conjunction with satellite data using multiple machine learning methods. This global product spans between 2001-2015. Its spatial and temporal resolutions are 0.083°x0.083° and 8 days, respectively.

B2) Normalized Differential Vegetation Index (NDVI):
Gridded NDVI data are obtained from the Global Inventory Modeling and Mapping Studies (GIMMS) product, version 3g (17). This product is derived from satellite observations. It is a global dataset which covers the time period 1982-2015. Its spatial and temporal resolutions are 0.083°x0.083° and half-monthly, respectively.

B3) Agricultural yields:
We use information on agricultural yields from the EUROSTAT database which summarizes crop yield statistics for various European countries (http://appsso.eurostat.ec.europa.eu/nui/, accessed on 6 April 2018). In particular we use data on 5 major crops: "cereals (excluding rice)", "wheat (including spelt)", "grain maize and corn-cob-mix", "potatoes (including early potatoes and seed 30 35 40 45 potatoes)", and "sugar beet (excluding seed)". The data are available between 1950-2015, even though only few countries reported data earlier than 1990. In order to isolate climate-induced variations in crop yields from anthropogenic effects (e.g. technical progress), we removed the longterm trend from each crop yield time series; this trend is determined with fitted cubic smoothing splines (as in 36).

C) Irrigation data
Irrigation data is also employed from the EUROSTAT database which provides corresponding statistics for various European countries (http://appsso.eurostat.ec.europa.eu/nui/, accessed on 6 April 2018). The data are available for the years 2005,2007,2010,2013. In order to infer the relative importance of irrigation in each country we compute the ratio of the mean area "irrigated at least once a year : Total (excl kitchen gardens and area under glass)" across the available years, and the mean "utilised agricultural area" as also determined from the available years.

D) Land cover data
The fraction of agricultural area within a grid cell is determined from the MODIS (Moderate Resolution Imaging Spectroradiometer) product MCD12Q1. Thereby, we consider cropland and mosaics between cropland and natural vegetation. This global dataset is invariant in time, and has a spatial resolution of 0.5°x0.5°.    Figure S3, and respective results.