One-step approach for estimating maize actual water use: Part I. Modeling a variable surface resistance

Abstract

In a global scenario of climate change, water scarcity and population growth, it is imperative to optimize crop water management. One way is by calibrating a physically based crop evapotranspiration (ET) model, in the so-called one-step approach; as opposed to the two-step approach that uses reference evapotranspiration and crop coefficients. The Penman–Monteith (Symposium of the society for experimental biology, the state and movement of water in living organisms, Academic Press, Inc., New York; Monteith, Symposium of the society for experimental biology, the state and movement of water in living organisms, Academic Press, Inc., New York, 1965) ET model uses a bulk surface resistance (r_s) term. This variable describes the resistance (stomatal, leaf, and canopy) to crop water transpiration and water evaporation from the soil surface. If the crop is not transpiring at a potential rate the r_s resistance depends on the water status of the soil and vegetation. The stomatal resistance is influenced by climate and by water availability. However, this influence is different from crop to crop. The resistance increases when the crop is stressed and when the soil water availability limits ET. In this study, surface resistance was parameterized for grain maize considering a number of plant and environmental variables for water stressed and non-stressed conditions. The independent explanatory variables that facilitated a good calibration of r_s, on a half-hourly basis, were: net radiation, photosynthetic active radiation, aerodynamic resistance, crop height, and leaf area index. The application of the obtained “r_s” model (based on the variables mentioned above) resulted in maize ET (mm 30-min⁻¹) estimation error of less than 1 ± 10% when evaluated with eddy covariance based ET data. This result is evidence that it is possible to calculate maize ET with a small associated error at very small time scales, for water deprived and advective conditions, using the one-step ET approach.

Appendices

Appendices

Appendix A

Variables used in the Penman–Monteith equation (Monteith 1965).

• 1 Atmospheric pressure (P, in kPa) was calculated as follow: P = 101.3 × [(293 − 0.0065 × z)/293]^5.26; z is the altitude in m (287 m).

• 2 Latent heat of vaporization (λ, in MJ kg⁻¹) was estimated as function of T_a: λ = 2.501 − (2.361 × 10^− 3) × T_a; T_a in °C.

• 3 Specific heat of the air at constant pressure (C_p, 1013 J kg⁻¹ °C⁻¹).

• 4 Psychrometric constant (γ, in kPa °C⁻¹) was calculated as: γ = (c_p × 10^− 6 × P)/(0.622 × λ); c_p, P and λ in the same units shown above.

• 5 Saturation vapor pressure (e_s in kPa) was estimated as: e_s = 0.6108 exp(17.27 × T_a/T_a + 237.3); e_s saturation vapour pressure at the air temperature (kPa), T_a air temperature (°C), exp(..) 2.7183 (base of natural log) raised to the power (..).

• 6 Actual vapor pressure (e_a) was measured (kPa).

• 7 Slope of saturation vapor pressure curve (∆) was estimated as:

  $$\Delta =\frac{{4098\left[ {0.6108\exp \left( {\frac{{17.27{T_{\text{a}}}}}{{{T_{\text{a}}}+237.3}}} \right)} \right]}}{{{{\left( {{T_{\text{a}}}+237.3} \right)}^2}}},$$

  where ∆ is the slope of saturation vapor pressure curve at air temperature T (kPa °C⁻¹), T_a is the air temperature (°C), exp(..) 2.7183 (base of natural logarithm) raised to the power (..).

• 8 ρ_a is the mean air density at constant pressure (kg m^− 3):

  $${\rho _{\text{a}}}=\frac{P}{{1.01\left( {{T_{\text{a}}}+273} \right)R}},$$

  where P is the atmospheric pressure (kPa), T_a is the air temperature (°C), and R is the specific gas constant = 0.287 kJ kg⁻¹ K⁻¹.

• 9 z_m is the height of wind measurements (m), 2 m above the corn height, since u was measured 2 m over the canopy by the 3D sonic anemometer of the EC system.

• 10 d is zero plane displacement height (m): d = 2/3 × h_c.

• 11 The roughness length governing momentum transfer, z_om (m) = 0.123 × h_c.

• 12 z_h is the height of humidity measurements: 2.5 m.

• 13 The roughness length governing transfer of heat and vapor, z_oh (m), can be approximated by: z_oh = 0.1 z_om.

• 14 K is von Karman´s constant, 0.41 (−).

• 15 r_a aerodynamic resistance (s m⁻¹):

  $${r_{\text{a}}}=\frac{{\ln \left( {\frac{{{z_{\text{m}}} - d}}{{{z_{{\text{om}}}}}}} \right)\ln \left( {\frac{{{z_{\text{h}}} - d}}{{{z_{{\text{oh}}}}}}} \right)}}{{{K^2}{u_z}}},$$

  where r_a is the aerodynamic resistance (s m⁻¹), z_m is the height of wind measurements (m), z_h is the height of humidity measurements (m), d is the zero plane displacement height (m), z_om is the roughness length governing momentum transfer (m), z_oh is the roughness length governing transfer of heat and vapor (m), K is the von Karman’s constant, 0.41 (−), u_z is the wind speed at height z (m s⁻¹).

Appendix B

See Table 7.

Table 7 Maize leaf area index (LAI) and canopy height (h_c)

Appendix C

See Tables 8 and 9.

Table 8 Auto correlation among considered variables for 30 min average diurnal data

Table 9 Auto correlation among considered variables for average diurnal values