Combining the FAO-56 method and the complementary principle to partition the evapotranspiration of typical plantations and grasslands in the Chinese Loess Plateau

Quantifying the evapotranspiration (ET) water consumption characteristics of typical vegetation [Robinia pseudoacacia (single vegetation), mixed plantations of Robinia pseudoacacia and Platycladus orientalis (double-mixed vegetation), and natural grassland (multiple-mixed vegetation)] in the Chinese Loess Plateau has both theoretical and practical significance. However, the proportionality and inverse hypotheses of ET, namely, the FAO-56 method and generalized complementary relationship (GCR), have limitations when used individually to estimate ET, evaporation (E), and transpiration (T). This study explores the feasibility of scaling water stress coefficient (Ks) using calibration-free or parameterized GCR for different vegetation types and quantities. The single crop coefficient (Kc) curves and basal crop coefficient adjustment (Kcb-a/Kcb-p) curves of typical vegetation were defined and validated to partition ET without soil moisture usage. The results revealed that both curves exhibited polynomial functional response relationships to the week ordinal (WO) of the growing season within a complete hydrological cycle (with 0.60 < R2 < 0.78 at the 0.01 significance level). By expressing the soil evaporation coefficient (Ke) as a function of Ks, Kc, and Kcb, the calibration-free combined method (combining the GCR and the FAO-56 method – GCR/FAO-56) demonstrated superior simulation performance for E, T, and ET across different vegetation types with an average Nash–Sutcliff Efficiency of 0.71 during the validation period compared to that of the parameterized method, with the highest sensitivity in E simulation. The simulated E, T, and ET values closely matched the actual values and maintained the order of Robinia pseudoacacia > mixed plantation > natural grassland during the growing season. The average biases for E, T, and ET during the validation period were 18.5, 7.0, and 25.5 mm, respectively, in Robinia pseudoacacia; 10.8, 11.1, and 19.7 mm in mixed plantation; and 2.7, 7.0, and 19.6 mm in natural grassland. The overall T/ET ratios for both plantations exceeded 51.07%, with mixed plantation being higher, surpassing 70% in dry years and exhibiting minimal variation in T (44.4 mm) across hydrological years. However, T/ET ratios in natural grassland were < 0.5, indicating that E was the primary form of water consumption. Average relative biases of the simulated and actual T/ET values were only 1.76%, 2.53%, and 1.87% for Robinia pseudoacacia, mixed plantation, and natural grassland, respectively. Furthermore, the accuracy of the calibration-free combined method increased with the number of vegetation species during the validation period. This study extended and discussed the feasibility in typical vegetation of combining the positive and negative correlation principles of evapotranspiration and further provided a possibility for how to partition ET with a fewer dataset [Rn, u, Tavg, RH or Td, P, LAI] without soil moisture, and also provided scientific suggestions for future vegetation restoration as well as water resources management.