Calculation of VPD and PET

The VPD was calculated as the difference between the average of the saturated vapor pressure (e_s) at T_x and T_n (i.e., daily average e_s), and the actual vapor pressure of the air, which was approximated as the es at the T_dew

Saturated vapor pressure (kPa) at given temperature T was derived using the following equation:

We calculated PET (mm day⁻¹) using the FAO Penman–Monteith equation for reference evapotranspiration for a well-watered grass of 0.12 m height, with fixed surface resistance of 70 s m⁻¹ and albedo of 0.23 for green crop surfaces¹⁷:

where m is the slope of the saturation vapor pressure curve at the mean daily temperature (kPa K⁻¹) calculated as m=4098*esTa*Ta+237.3−2; g is the psychrometric constant (kPa K⁻¹); U is the wind speed (m s⁻¹); and R_n is the net irradiance (MJ m⁻² day⁻¹).

R_s is the incoming solar shortwave radiation, and R_n is the net shortwave radiation

where R_so is the clear day R_s, which was approximated as:

In this expression, Lat is the latitude (in decimal degrees) and DOY is the day of the year. Because daily R_s and U measurements were not available for the NWS-COOP stations, we used climatological averages derived from the gridded Prediction of Worldwide Energy Resources (POWER) dataset⁵³ (0.5° resolution), extracted from grid points at each station location.

For the psychrometric constant (g), we used the following formula:

where P is the average atmospheric pressure (kPa) calculated as:

where Pb is the static pressure (101.3 kPa); Tb is the standard temperature (293 K), Lb is the standard temperature lapse rate (−0.0065 K m⁻¹); h is the elevation above sea level (m); g₀ is the mean gravitational acceleration (9.80665 m s⁻²); M is the molar mass of Earth’s air (0.0289644 kg mol⁻¹); and R is the universal gas constant (8.31446 J mol⁻¹ K⁻¹). Elevation above sea level was extracted from data collected by the Shuttle Radar Topography Mission⁵⁴.

In addition to PET and VPD, we calculated the specific humidity of the air (SH; g kg⁻¹) using the following equation:

All variables were aggregated by year, so they represented the average for the JJA period at each station, given that preliminary analysis using daily values gave similar results with a small standard deviation.