## 2 Materials and Methods
### Wheat and Barley Crop Data  
Yield data for wheat and barley crops were obtained on an annual scale, for every province of the study area, from 2001 to 2020. Provincial and regional yield data for the Spanish regions CL and CM were obtained from the Statistical Yearbook of the Ministry of Agriculture [46], which provides provincial and regional grain yields (kg/ha) of wheat and barley in rainfed systems for the period 1904-2020. The crop yield data for the NW, NS and BY regions of Germany were obtained from the German Federal Statistical Office [60], which provides winter wheat and barley grain yields for administrative districts and federal states from 1999 to 2022.  
It was assumed that there was no need to eliminate the trend in the crop yield series because the increase in yields due to technological improvements mainly occurred in the 20 th century [24; 61], prior to the study period.  
The gross primary production (GPP) and leaf area index (LAI) were also used, as they are two important indicators of vegetation growth and biomass and, therefore, have become essential for studying vegetation and climate change interactions [62; 63]. The GPP describes the amount of carbon dioxide fixed by plants through photosynthesis, a key component of the terrestrial carbon cycle [64]. The LAI quantifies leaf area in an ecosystem and is therefore a fundamental variable in processes such as respiration, rainfall interception and photosynthesis [63]. Thus, both variables were obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS). The product MCD15A2H was used to obtain the annual LAI, and the products MOD17A2H and MYD17A2H were used to obtain the annual GPP. The MCD15A2H product version 6 derived from the MODIS Terra/Aqua combined product has a temporal resolution of eight days and a spatial resolution of 500 m [65]. The MOD17A2H and MYD17A2H version 6 products are derived from the MODIS sensorsonboard NASA's Terra and Aqua satellites, respectively, with a temporal resolution of eight days and a spatial resolution of 500 m [66; 67].  
In this study, only the months of the phenological cycle of wheat and barley characteristic of each region for each year were considered. For this purpose, the sowing and harvesting months for wheat and barley crops in the regions of Spain were extracted from the sowing, harvesting and marketing calendar [68], which provides data at the provincial and regional scales. For the choice of dates, those corresponding to semihard and soft wheat (_Triticum aestivum_) and malting barley (two races, _Hordeum distichum_) were considered since they are predominant in CL and CM [46]. In addition, the calendar provides for each month of the year a percentage of sowing and harvesting occurrence. Thus, the months with the highest percentage of sowing and harvesting were selected to establish the beginning and end of the phenological cycle. Due to the high degree of similarity between the provincial and regional phenological cycles in each study region, the regional phenological cycle of each crop was considered for both scales. Thus, the phenological cycle of barley in CL and CM is from November to July, and the phenological cycle of wheat is from October to July in CL and from November to July in CM.  
In the federal states of Germany, the sowing and harvesting months of wheat and barley crops were extracted from the phenological database of Germany's national weather service [69]. It provides the dates of the sowing, emergence, earning, grain filling, milky ripening and harvesting phases, but in this work, only the dates of the sowing and harvesting phases were considered. For the choice of dates, an average of the available dates in the study period was made, and the resulting month was selected. In addition, as in the Spanish regions, the regional phenological cycle of each crop was considered for each region under study and its provinces. Thus, in BY, NS and NW, the phenological cycle of barley is from September to July, and that of wheat is from October to August.