When Does Vapor Pressure Deficit Drive or Reduce Evapotranspiration?

Abstract Increasing vapor pressure deficit (VPD) increases atmospheric demand for water. While increased evapotranspiration (ET) in response to increased atmospheric demand seems intuitive, plants are capable of reducing ET in response to increased VPD by closing their stomata. We examine which effect dominates the response to increasing VPD: atmospheric demand and increases in ET or plant response (stomata closure) and decreases in ET. We use Penman‐Monteith, combined with semiempirical optimal stomatal regulation theory and underlying water use efficiency, to develop a theoretical framework for assessing ET response to VPD. The theory suggests that depending on the environment and plant characteristics, ET response to increasing VPD can vary from strongly decreasing to increasing, highlighting the diversity of plant water regulation strategies. The ET response varies due to (1) climate, with tropical and temperate climates more likely to exhibit a positive ET response to increasing VPD than boreal and arctic climates; (2) photosynthesis strategy, with C3 plants more likely to exhibit a positive ET response than C4 plants; and (3) plant type, with crops more likely to exhibit a positive ET response, and shrubs and gymniosperm trees more likely to exhibit a negative ET response. These results, derived from previous literature connecting plant parameters to plant and climate characteristics, highlight the utility of our simplified framework for understanding complex land‐atmosphere systems in terms of idealized scenarios in which ET responds to VPD only. This response is otherwise challenging to assess in an environment where many processes coevolve together.


Introduction
The manuscript analyzes the partial derivative of ET with respect to VPD. This assumes that all other quantities remain fixed, including the plant parameters g 1 and uWUE (and by extension, λ). In reality, these parameters may vary with environmental conditions, and specifically soil moisture. However because soil moisture only enters the partial derivative directly through these plant terms, if the plant parameters are weak functions of soil moisture then the theory can be directly applied to a broader range of conceptual VPD scenarios, including observed compound events between high VPD and low soil moisture Zhou et al. (2019). To help the reader assess the soil moisture dependence of uWUE (and partially by extension λ and g 1 ), we provide here figures showing the distribution X -2 : of uWUE with SWC for each of 66 FLUXNET sites from the FLUXNET-2015 database.
The functional relationship between uWUE and SWC varies, with a mix of sites showing strong and weak SWC-dependence. For all sites the ratio of signal to noise is very low, an unfortunate consequence of taking a ratio of two highly uncertain eddy-covariance derived fluxes. In general we find this analysis inconclusive.
The paper does not rely on assumptions about uWUE's functional relationship with soil moisture so we do not include the figures in the body of the manuscript. But given that constant uWUE and g 1 assumptions can make our theory more useful to the reader we provide the figures for their interpretation, and motivation for future research.
Additionally, we include a figure showing the joint distribution between saturation vapor pressure and relative humidity calculated from the FLUXNET-2015 data. Relative humidity and saturation vapor pressure are much more independent than saturation vapor pressure and VPD, and we use an assumption that relative humidity and saturation vapor pressure can be approximated as independent in order to evaluate ∂ET ∂V P D . Please note that at a given site, the relationship may be more or less independent depending on the hydroclimate. We filter and quality control the FLUXNET-2015 data using a similar procedure as Zhou et al. (2015): • Only measured or highest ("good") quality gapfilled data, according to quality control flags, are used.
• To isolate the growing season, we only use days in which the average Gross Primary Productivity (GPP) exceeds 10% of the observed 95th percentile of GPP for a given site.
GPP is calculated using the nighttime respiration partitioning method.
• We remove days with rain and the day following to avoid issues with rain interception and sensor saturation at high relative humidity (Medlyn et al. (2017)).
• For SWC measurements, we use the shallowest observed layer available at each site.
Additionally, as in Lin et al. (2018), we restrict data to the daytime, which is identified when downwelling shortwave radiation is greater than 50 W m −2 and sensible heat flux is greater than 5 W m −2 . To reduce the chance of sensor saturation at high relative humidity, we remove all time steps for which VPD is less than .01 kPa, and to reduce errors at low windspeeds we remove all periods with wind magnitudes less than 0.5 m s −1 . Timesteps with negative observed GPP or ET are also removed, and we aggregate half hourly data to hourly averages to reduce noise Lin et al. (2018). After these quality control procedures, 400,983 upscaled hourly observations remain. Kurbatova, J., Li, C., Varlagin, A., Xiao, X., & Vygodskaya, N. (2008, jul