Water stress

To calculate Water stress Risk, we use the variable [Copernicus Climate Data Store (CDS)]:

• monthly soil moisture in upper soil portion (mrsos): soil moisture in the upper layer (first 7 cm), expressed in kg m⁻². This indicator is a direct measure of water quantity available for plant roots and therefore an excellent proxy for agricultural and ecological water stress. Unlike other risks based on absolute thresholds, water stress is highly dependent on local climate. Therefore, a given month's risk level is defined by comparing its soil moisture value with the historical statistical distribution (percentiles) of values for that same calendar month. A month is considered 'in stress' if it is significantly drier than its historical norm. To define annual risk level, we count the number of months when soil moisture drops below certain historical thresholds:
• $N_{\text{extreme}}$: Number of months when soil moisture is in the driest 10% of history (value ≤ 10th percentile).
• $N_{\text{very high}}$: Number of months when moisture is between the 10th and 20th driest percentile.
• $N_{\text{high}}$: Number of months when moisture is between the 20th and 30th driest percentile. This approach allows assessment of soil moisture deficit duration and severity during the year.

The methodology used for Water Stress Risk assessment is a state-of-the-art approach, fully supported by climate and agronomy science, as it:

• Uses a direct physical variable (mrsos - soil moisture) that is closer to actual impact on vegetation compared to purely meteorological indicators like rain.
• Defines 'stress' not with absolute thresholds, but through statistical anomaly (percentiles) relative to local climatology, making it applicable to any ecosystem.
• Assesses annual risk considering both intensity (how dry is a month) and duration (how many months are in stress).

The use of Soil Moisture as a key indicator for agricultural and ecological drought is standard practice. Major international reports and monitoring systems are based on it.

• Special Report on Climate Change, Desertification, Land Degradation, Sustainable Land Management, Food Security, and Greenhouse gas fluxes in Terrestrial Ecosystems (SRCCL) This IPCC report dedicates entire sections to how climate change affects soil moisture, identifying it as the crucial variable connecting meteorological drought (lack of rain) to agricultural drought (lack of water for plants) and land degradation.

Our approach of using historical percentiles to define stress thresholds is the basis of widely used standardized indices.

• Multivariate Standardized Drought Index: A parametric multi-index model This work uses the Standardized Soil Moisture Index (SSI). SSI is calculated by considering the historical series of soil moisture values for a given month, calculating the probability distribution and transforming the current value into a standardized anomaly. Using percentiles (10th, 20th, 30th) is the non-parametric way to do this.

Counting the number of months exceeding stress thresholds is standard practice for assessing drought severity and duration during the year, used by major drought observatories.

• The European and Global Drought Observatories These operational monitoring systems are not based on a single 'dry day', but assess drought evolution over time. Their classification maps are the result of synthesizing several indicators, where persistence of anomaly conditions (just like our count of months $N_{\text{high}}$, $N_{\text{very high}}$, $N_{\text{extreme}}$) is a critical factor for raising alert level. Our risk matrix, which assigns higher risk to prolonged stress ($N_{\text{high}} \geq 3$) or intense stress ($N_{\text{extreme}} > 0$), reflects exactly the operational logic of these bodies.

In conclusion, our methodology is a synthesis of best scientific and operational practices. It uses a direct and relevant physical variable (soil moisture), evaluates it with a robust and standardized statistical method (percentile-based anomalies), and classifies annual risk considering both intensity and duration of stress, in full coherence with major world drought monitoring systems.