To address the objective of our study, simulations were done with the ENWATBAL model to calculate the daily water balance for a dry (2011), an average (2016) and wet (2015) year of rainfall for a soil in a Pullman (fine, mixed, thermic, Torrertic Paleustoll) and an Amarillo (fine-loamy, mixed, thermic, Aridic Paleustalf) series. For these simulations we used as input hourly measured weather variables for a location near Lubbock, Texas. A brief description of the model, including theory, inputs and soil geometry follow.

The ENWATBAL (ENergy and WATer BALance) model is a one-dimensional and mechanistic representation of a soil, where processes are based on principles of the conservation of mass and energy. The simulation model, ENWATBAL, used in our analysis is described in detail by [36] [37]. We used the version of the simulation model written in compiled BASIC as given by [38]. The ENWATBAL model calculates the energy and water balance of a soil surface by simultaneously solving equations that calculate the fluxes of water and heat in a soil profile. In the model, the upper boundary condition is defined at a screen height of 2 m, i.e., height above the soil surface where weather variables are measured. The lower boundary is the bottom of the profile, where we assume unit hydraulic gradient, i.e., dψ/dx = 1, where ψ is the soil water potential (m) and x is the soil vertical distance (m). The fluxes of water and heat are calculated as follows.

The flux of water is calculated from Darcy’s Law and the equation of continuity:

∂ θ v / ∂ t = ∂ / ∂ x ( K ( θ v ) ( ∂ ψ t o t a l ) / ∂ x ) (1)

where θ_v is the soil volumetric water content (m³/m³), t is time (s), x is the vertical distance in the soil profile (m), K(θ_v) is the unsaturated hydraulic conductivity (m/s) a function of θ_v, and ∂ ψ t o t a l / ∂ x is the total vertical hydraulic potential gradient (m/m). Normally, soil water potential values are expressed in SI units of Pa (MPa and kPa); however, in our case we use the m as the unit of hydraulic head, as it simplifies the unit of the gradient (dψ/dx) to m/m.

The flux of soil heat is calculated from Fourier’s Law and the equation of continuity:

C s ( ∂ T / ∂ t ) = ∂ / ∂ x ( λ ( T ) ∂ T / ∂ x ) (2)

where C_s is soil volumetric heat capacity (J/m³∙˚C), T is the soil temperature (˚C), λ (T) is the soil thermal conductivity (W/m∙˚C) a function of soil temperature T (˚C) and ∂ T / ∂ x is the vertical soil temperature gradient (˚C/m).

The evaporation of water at the soil surface is calculated from the energy balance and the turbulent transport of air above the soil surface, as follows:

R n + L × E + A + G = 0 , (3)

where R_n is the net irradiance, LE is the evaporative flux, A is the sensible heat flux to the air, and G is the soil heat flux. All terms in Equation (3) have units of W/m² and each term of the energy balance is in reference to the soil surface so that during daytime hours, R_n is positive, E is negative, and both A and G are generally negative.

The aerodynamic resistance r_a (s/m) is calculated as:

r a = [ ln ( 2 / Z o ) ] 2 / ( 0.16 × u z ) (4)

where Z_o is the surface roughness (m), and u_z is the measured windspeed (m/s) at a screen height of 2 m above the soil surface. The r_a is corrected (r_c) for stability (S_t) as:

r c = r a × S t (5)

The stability factor (S_t) is calculated as:

S t = 1 / ( 1 − 10 × R i ) (6)

where R_i is Richardson’s number [40], defined by:

R i = [ 9.81 × ( 2 − Z o ) × ( T a − T s ) ] / [ ( T a + 273.16 ) × u z 2 ] (7)

where T_a is the measured air temperature (˚C) at a screen height of 2 m, and T_s is the unknown soil surface temperature (˚C). This method to calculate r_c is given by [41], and used by [42] [43], and others.

The latent heat transfer (L × E) in Equation (3) is calculated from:

L × E = L × [ ( χ s − χ a ) / r c ] (8)

where L is the latent heat of vaporization (J/kg), χ_s is the absolute humidity at the soil surface (kg/m³) and χ_a is measured absolute humidity of the air temperature (kg/m³) at a screen height of 2 m. The sensible heat flux (A) between the soil surface and air above it is calculated from:

A = [ ( T s − T a ) / r c ] × C a (9)

where T_s is unknown soil surface temperature (˚C), T_a is the measured air temperature (˚C), and C_a is the volumetric heat capacity of the air (J/m³∙˚C). The last term of the energy balance in Equation (3), the soil heat flux (G) is calculated from:

G = − λ ( T ) × ( ∂ T / ∂ x ) (10)

where λ (T) is the soil thermal conductivity (W/m∙˚C) a function of the soil temperature (T) in ˚C, and ∂ T / ∂ x is the vertical soil temperature gradient (˚C/m).

In ENWATBAL the evaporative flux is solved from a combination of the surface energy balance and an aerodynamic model of the turbulent air above the soil surface. The unknown value of the surface energy balance is the soil surface temperature (T_s) in Equations (7) and (9) and this value is found by iteration until the surface energy balance of zero is numerically met. At each time step (Δt), ENWATBAL, begins by finding, from the previous values of the soil water content and temperature of each soil layer, the corresponding soil hydraulic potentials and the water and conductivity values. These are the so-called soil hydraulic properties that include the soil-water pressure potential (ψ) release curve, i.e., ψ(θ_v), and the unsaturated soil hydraulic conductivity, i.e., K(θ_v). The ψ(θ_v) is measured using well established laboratory procedures [44] and K(θ_v) is calculated using measured values of the saturated hydraulic conductivity (K_sat) and ψ(θ_v) with the methods of [45] and [46]. Thereafter, the interlayers fluxes for heat and water are calculated, except for the values at the soil surface, which as previously mentioned are calculated from Equation (3), the energy balance equation. Once the surface temperature (T_s) is known the evaporation of water from the soil surface is calculated. The soil heat flux, G (Equation (10)) is also calculated from the known value of T_s. The soil thermal conductivity is calculated from method given by [47], which is based on soil texture. When it rains, the evaporation rate at the soil surface is modified by the infiltration of rain and detention capacity, i.e., the depth to store water on the soil surface. For additional details the reader is referred to [36] [37] and to [38].

The inputs to the model are categorized as time-dependent variables, constants, soil hydraulic functions, and initial values. The time-dependent inputs are the weather variables, and in our simulations, we used hourly values of solar irradiance, air and dewpoint temperature, and wind-speed all measured at a screen height of 2 m. In our simulations we used hourly weather data for a dry year (2011) with 190 mm of rain, an average year (2016) with 449 mm of rain and a wet year (2015) with 669 mm of rain. The values used were derived from sub-daily meteorological data from the West Texas Mesonet [48] weather station at Abernathy, Texas, which is located ~30 km north of Lubbock, Texas.

Constant input values are the screen height of the meteorological measurements of 2 m, the roughness parameter (Z_o) in Equation (4) of 0.01 m, the saturated hydraulic conductivity (K_sat) and porosity (f) shown in Table 1. These values are given for the two depths of the Pullman and the Amarillo soil series [32].

Soil functions used as input are the soil hydraulic properties, i.e., soil-water retention curve and unsaturated hydraulic conductivity, the soil thermal conductivity and the relationship between albedo and the surface soil water content. In our simulations we used the albedo vs. soil water content function given by [36]. The soil geometry, soil hydraulic properties and initial values used as input are described next.

*Porosity (f) was calculated as f = 1 – (ρ_b/ρ_p), assuming a soil particle density (ρ_p) of 2.65 Mg/m³.

In the model, the soil profile is divided into layers of different thickness and for each layer an initial value, i.e., at time = 0, of soil temperature (T, ˚C) and soil water content (θ_v, m³/m³) is assigned. The thickness of the first soil layer is important as the evaporative fluxes of water and heat at the soil surface is calculated from the midpoint value of this soil layer. An example of the geometry and initial conditions of the soil profile for an Amarillo soil with assumed values of T and θ_v is shown in Table 2. The assigned thickness of the first soil layer was 5 mm, as suggested by [37], which showed that this value was adequate to correctly calculate soil water evaporation. The soil profile was divided into 24 layers for a soil depth of 2.1 m. Further, the profile was divided into two horizons. The first horizon A was 0.45 m in depth and the second horizon B was 1.65 m. Each horizon was characterized with specific soil hydraulic properties, i.e., soil water potential (ψ) and unsaturated hydraulic conductivity (K), both as a function of soil volumetric water content (θ_v). In our simulations we used the values given by [32] for a Pullman and for an Amarillo soil series, shown in Figure 3 for the soil water potential and in Figure 4 for the unsaturated hydraulic conductivity.

For all three years, dry, average and wet, the annual evaporation of water was higher in the Amarillo soil series compared to the Pullman and this difference decreased with increasing rainfall (Table 3). For example, on the dry year the evaporation of water from the Amarillo soil was 222 mm vs. 125 mm from the Pullman, i.e., 40% less. Similarly, on the wet year the water evaporation in the Amarillo soil was 700 mm compared to 529 mm on the Pullman soil, i.e., a difference of 20%. Another noteworthy difference in the total evaporation of water between the two-soil series is that in the Amarillo series all rainfall was lost to evaporation. Further, in the Amarillo soil series stored water in the soil profile also contributed to the total annual evaporative loss. On an annual basis, no stored soil water in the Pullman series contributed to the evaporative loss of water.

A major difference between the two-soil series was the capability of the Pullman soils to store rainfall in the profile. For example, in the dry year, 64 mm of rain was stored in the soil profile, which is 34% of the total rainfall. In the average year, 109 mm of the rain (24% of rainfall) and in the wet year 140 mm of rain (21% of total rainfall) was stored in the soil. The implications of this storage of rainfall for dryland crop production in the semiarid Texas High Plains are important. From these results we can conclude that regardless of rainfall amount, soils in the Pullman series have an increased ability to store rainfall. Further, this storage could be enhanced using conservation-bench and level-bench terraces, contour and blocked furrows and minimum tillage practices as suggested by [54]. Soils in the Pullman series are mainly in the northern region of the THP and cover about 1.5 × 10⁶ ha. Furthermore, these results suggest that the storage of rainfall in soils of the Amarillo series will be challenging and will require incorporation of best management practices, such as surface residue and minimum tillage to maximize rainfall storage [55] [56].

A difficulty in using surface residues to conserve water is that in many cases this practice results in decreasing water that may be stored in the soil as the water used to establish the residue exceeds the amount of water stored in the soil [52] [57] [58] [59]. However, there are other benefits associated with the surface residue such as increasing infiltration [57] and promoting biophysical and chemical soil properties to enhance soil health [60] [61]. Currently, this is an important topic of research to determine appropriate types of residue to use for dryland production in the THP and particularly in areas where the predominant soil series is the Amarillo.

The calculated differences in the evaporative losses between the two-soil series and for the same environmental conditions are due to their respective soil hydraulic properties (Figure 3 and Figure 4). For example, in the Amarillo soil series, in the surface 0.4 m layer, the soil water content between 0.20 to 0.50 m³/m³ is held over a relatively narrow range of pressure potential (0 to 10 kPa); whereas, for the Pullman soil series and for the same range of soil water content the pressure potential varies from 0 to 100 kPa, i.e., an order of magnitude larger, and this is due to the higher clay content on the surface layer. Further, soils in Pullman series in the upper soil layer (0.3 m) have a porosity of 55% compared to 47% for the Amarillo soil, indicating a higher storage capacity. These physical properties affect infiltration and water storage capacity [57] [58].

Results of the remaining components of the water balance, i.e., infiltration, drainage and runoff are shown in Table 3. The calculated infiltration of rainfall indicated no differences between the two-soil series and for any of the three rainfall scenarios. In our simulations and for the calculation of drainage we assumed unit hydraulic gradient, i.e., dψ/dx = 1, at the lower boundary of the soil profile, which was at a depth of about 2 m from the soil surface. This assumption netted 11 mm of annual drainage in the Amarillo soil and no drainage in the Pullman soil series. Finally, the last component of the annual water balance was runoff and results indicated no runoff for the Amarillo soil series and runoff amounts of 14 mm for the Pullman soil series for an average rainfall and 5 mm for the wet year. The calculation of water runoff from a soil surface is affected by many variables, e.g., rainfall amount and rate, antecedent soil water content, particularly in the surface 0.2 m, and detention capacity. A detailed analysis with different rainfall intensities, initial soil water contents and detention capacities and their effect on infiltration and runoff was beyond the scope of this paper and is the subject of a forthcoming article.

Examples of the daily evaporation of water from a bare soil and calculated with the ENWATBAL model for the entire simulation period for the Pullman soil series for both the wet and dry year are shown in Figure 5 and in Figure 6 for the Amarillo soil series. The daily evaporation of water is plotted as a negative number to indicate a loss; whereas, the corresponding daily rainfall is shown as a positive number to indicate again. The corresponding cumulative rainfall and cumulative evaporation for the dry year for both soil series is plotted in Figure 7(a) and for the wet year, the cumulative values are plotted in Figure 7(c). The net gain or loss of water, i.e., rainfall-evaporation, resulting in water stored in the profile for both soil series is plotted in Figure 7(b) for the dry year and in Figure 7(d) for the wet year. To further highlight the dynamic nature of the process of daily evaporation from a bare soil we selected 70 days, from day of year (DOY) 100 to DOY 170, for the wet year and for the Pullman soil series (Figure 8). The corresponding daily rainfall for the 70-day period is shown as a histogram (Figure 8). On the other extreme as an example and to illustrate the evaporation of water from a bare soil under very dry conditions we selected a 30-day period, from DOY 160 to DOY 190, for both soil series and these results

are shown in Figure 9. No rainfall occurred during this time period on the dry year. Also shown is the daily evaporation for both soil series in the wet year with 152 mm of rain (Figure 9).

As expected, the high peaks of evaporative water loss from the soil surface occur immediately after a rainfall and the magnitude, rate and duration, is a function of the prevailing environmental conditions. For example, in the Pullman soil series and in the dry year (Figure 5) the largest loss of water to evaporation (5.1 mm/d) occurred on DOY 79 following a 27 mm rain the day before. Thereafter, the daily evaporation did not exceed 4 mm/d as the summer months were extremely dry, with about 12 mm of rain from DOY 122 to DOY 244, and a corresponding 22 mm of cumulative evaporation. In the wet year, the daily

evaporative loss was close to 10 mm/d on three days of the summer (DOY 126, 129 and 136) and over this 10-day period the total rainfall was 83 mm (Figure 5). The total rainfall during the summer months (May to August) was 390 mm. The dry year is an example of a catastrophic year where all dryland crops would fail, and the wet year is an example of timely rain events in the spring. However, too much rainfall during the fall interferes with harvest and many of these storms are accompanied by severe weather, i.e., high windspeed and hail that may damage crops. The same pattern of daily water evaporation calculated for the Pullman soil series (Figure 5) was also calculated for the Amarillo soil series (Figure 6) for both the dry and wet year. In the dry year and during the summer months (DOY 122 to DOY 244) there was 12 mm of rainfall with 20 mm of evaporation and in the wet year the summer rainfall was 386 mm with 394 mm lost to evaporation (Figure 6).

These results can be used to illustrate the effect of surface residue, minimum tillage and self-mulching on modifying the rate of water evaporation. Indeed, surface residues retard the rate of evaporative losses and extend the total amount of time that would be required to evaporate the same amount of water, when compared to a bare surface [58] [59]. Regardless, the total amount, i.e., the integral, of water evaporated from a bare soil surface compared to surface with residue is the same and it is the rate of evaporation that differs. Further, clayey soils such as the Pullman series have an inherent characteristic that they tend to self-mulch [62]. The net result of minimum tillage [54] is to reduce soil water evaporation compared to conventional practices. The combination of surface residue and minimum tillage can in effect increase the water use efficiency of a crop, i.e., crop water use per unit water transpired, without additional input of water [52]. Our results suggest that storage of rainfall in combination with management of minimum tillage and surface residue could be achieved in the Pullman soil series in years of average or wetter rainfall. However, this would be a more difficult task to achieve in the Amarillo soil series and they would be categorized as a soil series with a higher risk for crop production.

The cumulative plots of rainfall and of evaporation of water as a function of DOY, for both soil series on the dry year (Figure 7(a)) and the wet year (Figure 7(c)) show the evolution of water into or out, i.e., storage, in the soil profile. The storage of water for both soil series is shown in Figure 7(b) for the dry year and in Figure 7(d) for the wet year. In the dry year, the Amarillo soil shows a negative value throughout the year and a positive value for the Pullman soil (Figure 7(b)). In the wet year, the differences in storage capacity for the Pullman are in sharp contrast compared to the Amarillo soil (Figure 7(d)). The storage of water in the Pullman series is positive throughout the year, gradually increasing from +25 mm on DOY 30, to about +150 mm on DOY 130, and thereafter fluctuates ± 25 mm, ending with a value of +140 mm. The pattern in the Amarillo soil series is very different and begins with a –25 mm on DOY 120 and increasing to close to +75 mm on DOY 140 and thereafter decreases to −25 mm on DOY 260, ending with a value of close to −25 mm. These differences in storage capacity of the two-soil series are directly related to their respective soil hydraulic properties (Figure 3 and Figure 4). These simulated results illustrate that the Pullman soils are better suited to store rainfall for subsequent crop water use. However, site-specific use of crop residues and minimum tillage can be used on both soil series to maximize infiltration and to reduce runoff [57] [58] [59].

The daily evaporation and rainfall for a period of 70 days, from DOY 100 to DOY 170, for the Pullman soil in the wet year, is shown in Figure 8. The cumulative evaporation for this 70-day period was 214 mm with 372 mm of rain. Note that there were eight rain events of >20 mm and of these, three events were >40 mm on DOY 134, 164 and 170. This is the type of wet period were the rainfall rate exceeds the infiltration capacity, leading to runoff. However, only 5 mm of runoff (Table 3) were calculated. Details regarding runoff as a function of fall rates will be subject of a separate article.

Examples of daily water evaporation from DOY 160 to DOY 190 for the wet and dry year for the Pullman and Amarillo soil series are shown in Figure 9. In the wet year, there was a rain event of 41 mm on DOY 164 and of 50 mm on DOY 170 and the total rainfall was 152 mm, and no rain occurred in the dry year. The daily water evaporation from the Amarillo was ≥ than from the Pullman on both the dry and wet year. The dry year, is an example of the perils of extreme arid conditions due to no rainfall, showing the low daily values of water evaporation. This example of a dry cycle is not unusual in the THP and under these circumstances there are no viable options to assure a successful dryland crop. In the wet year, the cumulative daily evaporation was 141 mm in the Amarillo and 107 mm in the Pullman series, and in the dry year the cumulative evaporation was 3 mm for the Amarillo vs. 1 mm in the Pullman series. The self-mulching property of the Pullman soil is evident following the pattern of evaporation on DOY 171, where the evaporation rate dropped from 9 to 2 mm/d on DOY 180. Similarly, for the Amarillo series the daily evaporation rate decreased from 9 to 4 mm/d over the same time period, indicating that a higher rate of evaporation was maintained resulting in less water stored in the soil. Further, in the dry year, the daily pattern of soil water evaporation for the Amarillo series shows a gradual decline, from 0.12 mm/d to 0.08 mm/d; however, the daily pattern for the Pullman soil series fluctuates, i.e., increasing and decreasing the day after; albeit, these fluctuations are >0.05 mm/d. These variations between the two-soil series are due to the differences in soil hydraulic properties (Figure 3 and Figure 4) of the surface layers. Further, this is an example of the self-mulching capacity of the Pullman soil due to its higher clay content on the surface horizon of 41 % clay compared to 21% in the Amarillo soil series (Table 1). A difficulty in managing crops under dryland conditions and on the decision to plant a cover crop for residue management is the uncertainty of forecasting rainfall [63]. This by far is the largest impediment to assure a successful dryland crop every year.

As previously noted, the storage of rainfall in the soil is a function of many soil properties and characteristics of the rain event (intensity and duration). Of particular interest is the detention of water on the soil surface to allow more time for the water to infiltrate in the soil. This practice via the use of furrow dikes [64] has been shown to be successful to harvest rainfall across the landscape [65]. Simulation of the effects of different detention capacities on rainfalls of different rates and amount is a subject of a forthcoming article.