Measured Soil Water Evaporation As a Function of the Square Root of Time and of Reference ET.

Soil water evaporation (E) occurs in two stages: the constant rate stage (Stage 1, S1), where water supply is unlimited and E is at the maximum rate determined by available energy and atmospheric demand; and the falling rate stage (Stage 2, S2), where the E rate is controlled by soil water supply and soil hydraulic characteristics.  The amount of S1 E has been estimated as a function of potential evaporation, or as a set amount based on soil textural class.  At the end of S1, S2 E has been estimated as a function of the square root of time (SQRTT), and of the square root of reference evapotranspiration (ETo) (SQRTETo).  An expected plot for cumulative S1 and S2 in the SQRTT model would be two connected linear segments with different slopes. An expected plot for the SQRTETo model would be a curvilinear cumulative S1 followed by a linear cumulative S2.  Both S2 slopes would remain constant for the remainder of the measurement period. 

 On a daily time step, estimates of S1 and S2 E lose accuracy because, in reality, E has both diurnal and daily fluctuations, and the transition from S1 to S2 could occur at any time during the 24-h period.  The objective of this research was to compare measured cumulative E of two soil textural classes using the SQRTT and SQRTETo models on an hourly time step to  determine how clearly a change from S1 to S2 was indicated by a change in the linear relationships between cumulative E and the two models.

Experiments were conducted at the Soil-Plant-Environment Research facility at USDA Agricultural Research Service in Bushland, TX using weighing lysimeters.  Lysimeter mass was measured hourly using deck (platform) scales.  Water application amounts ranged from 10 to 50 mm, and were applied to uniformly cover the soil surface.

The relationships were analyzed for a clay loam and sandy loam.  On an hourly time step for both soils, the SQRTT model initially produced a “stair step” cumulative S1 E due to a decline, but not a cessation, in nighttime E compared with daytime E during the first several nights as time progressed.  The second linear slope began 59 hours following the irrigation for the clay loam and 33 hours for the sandy loam.  The cumulative S1 E was 20.6 mm for the clay loam and 13.5 mm for the sandy loam, The SQRTETo model produced a cumulative S1 E that first was curvilinear then linear in slope, followed by a linear cumulative S2 slope. The second linear slope began 52 hours following the irrigation for the clay loam and 47 hours for the sandy loam. The cumulative S1 E was 18.9 mm for the clay loam, and 14.4 mm for the sandy loam.

Both models produced reasonable estimates of S1 evaporation with the change from S1 to S2 E occurring at various times during the 24-h period following water application.  The relationship between cumulative E and SQRTETo was more linear because it reflected the declines in E rates during the night due to declines in ETo.  These declines were not shown in the SQRTT model in which changes were driven by the progression of time.