When is evapotranspiration at an urban tree site energy-limited versus water-limited? Evidence from eddy-covariance and soil moisture measurements in Berlin

Urban vegetation helps reduce heat stress through evapotranspiration (ET) and shading. However, we still do not fully understand how atmospheric energy demand and soil water availability influence ET in an urban environment. Specifically, it is unclear when urban ET shifts from being limited by energy to being limited by water. In this study, we examine this transition at an urban tree-dominated site in Berlin, Germany. We use eddy-covariance (EC) flux measurements combined with soil moisture observations at various depths.
We analyze two years (2019-2020) of EC data, which includes latent heat flux, net radiation, and weather variables, as well as soil moisture observations at six depths ranging from 5 cm to 1 m. After applying quality control, turbulence filtering, and selecting condensation-free daytime data, we aggreage the ET data to daily daytime averages. We then relate ET to net radiation, vapor pressure deficit (VPD), and soil moisture. We represent near‑surface soil moisture as the average of the 5-20 cm layers, which reflects the most dynamically active portion of the root zone under the constrained soil conditions typical of this urban environment.
We hypothesize that ET is mainly energy-limited when the soil is wet. However, as the topsoil dries, it becomes water-limited, even when the atmospheric demand is high. Our hypothesis is supported by several exploratory analyses. Scatter plots showing ET against net radiation, classified by soil moisture levels (wet, medium, dry), reveal three consistent trends: (A) in wet conditions, ET rises sharply with radiation, showing an energy-limited state; (B) in dry conditions, the ET-radiation relationship weakens and levels off, indicating water limitation despite high radiation; and (C) in intermediate soil moisture conditions, we see a transitional response. 
Linear regression models demonstrate that the slope of the ET-radiation relationship significantly declines from wet to dry soil states. Adding VPD enhances the performance of the linear regression model (R² ≈ 0.75), highlighting the influence of atmospheric demand. Meanwhile, the interaction terms between soil moisture and radiation remain significantly important. A linear mixed-effects model, which includes year as a random factor, produces similar results, indicating that these patterns hold steady across different years. 
Segmented regression of ET against topsoil moisture identified a statistically significant breakpoint at approximately 8-9% volumetric soil moisture, marking a transition from water-limited conditions at low soil moisture to weak ET sensitivity at higher soil moisture. Below this threshold, ET responds strongly to changes in soil moisture, indicating a water-limited regime. Above the threshold, ET shows little additional sensitivity to soil moisture and is predominantly controlled by energy availability.
 In conclusion, our results provide clear quantitative evidence that urban evapotranspiration alternates between energy-limited and water-limited regimes, with shallow soil moisture exerting a dominant control during dry periods. These findings highlight the vulnerability of urban vegetation to soil drying and have important implications for urban climate adaptation, green infrastructure management, and land-atmosphere modeling under increasing drought frequency.