Assessment of the clumped model to estimate olive orchard evapotranspiration using meteorological data and UAV-based thermal infrared imagery

Abstract

A study was performed to evaluate the clumped model in estimating olive orchard evapotranspiration (ET_a) using meteorological data and high-resolution thermal infrared (TIR) imagery obtained from a camera onboard an unmanned aerial vehicle (UAV). An experimental site was established within a superintensive drip-irrigated olive (cv. Arbequina) orchard located in the Pencahue Valley (35.49° S, 71.73°W, and 85 m above sea level), Maule Region, Chile. UAV-based TIR images were collected to obtain the land surface temperature at a very high resolution on 12 clear-sky days during the 2015–2016 growing season. Measurements of the latent heat flux (LE) obtained from an eddy covariance (EC) system were analyzed to assess the clumped model. In addition, submodels to calculate the net radiation (R_n) and soil heat flux (G) were evaluated using a four-way net radiometer and soil heat flux plates with soil thermocouples, respectively. Comparisons indicated that the root mean square error (RMSE) and mean absolute error (MAE) values for LE were 37 and 27 W m⁻², respectively, while those for ET_a were 0.44 and 0.35 mm day⁻¹, respectively. Both UAV-based values for R_n and G were estimated with RMSE < 31 W m⁻² and MAE < 18 W m⁻². The relative RMSE (rRMSE) values were 26% for LE, 24% for ET_a, 5% for R_n, and 11% for G. The results suggest that the clumped model based on UAV-based TIR imagery and meteorological data could produce maps with a very high resolution to estimate the intraorchard spatial variability in olive orchard water requirements.

Appendix

Several equations of the clumped model are presented below. First, the procedure to estimate C^c, C^uc, and C^bs (all dimensionless) are as follows (Brenner and Incoll 1997):

$$ C^{c} = \frac{{R_{{{\text{bs}}}} R_{s} \left( {R_{c} + R_{a} } \right)}}{{R_{s} R_{c} R_{{{\text{bs}}}} + \left( {1 - f_{c} } \right)\left( {R_{s} R_{c} R_{a} } \right) + f\left( {R_{{{\text{bs}}}} R_{s} R_{a} } \right) + f_{c} \left( {R_{{{\text{bs}}}} R_{c} R_{a} } \right)}} $$

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$$ C^{{{\text{uc}}}} = \frac{{R_{{{\text{bs}}}} R_{c} \left( {R_{s} + R_{a} } \right)}}{{R_{s} R_{c} R_{{{\text{bs}}}} + \left( {1 - f_{c} } \right)\left( {R_{s} R_{c} R_{a} } \right) + f_{c} \left( {R_{{{\text{bs}}}} R_{s} R_{a} } \right) + f_{c} \left( {R_{{{\text{bs}}}} R_{c} R_{a} } \right)}} $$

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$$ C^{{{\text{bs}}}} = \frac{{R_{s} R_{c} \left( {R_{{{\text{bs}}}} + R_{a} } \right)}}{{R_{s} R_{c} R_{{{\text{bs}}}} + \left( {1 - f_{c} } \right)\left( {R_{s} R_{c} R_{a} } \right) + f_{c} \left( {R_{{{\text{bs}}}} R_{s} R_{a} } \right) + f_{c} \left( {R_{{{\text{bs}}}} R_{c} R_{a} } \right)}} $$

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while R_c, R_s, R_a and R_bs were computed according to the following equations:

$$ R_{c} = \left( {\Delta + \gamma } \right)r_{a}^{c} + {\gamma r}_{s}^{c} $$

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$$ R_{s} = \left( {\Delta + \gamma } \right)r_{a}^{s} + {\gamma r}_{s}^{s} $$

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$$ R_{a} = \left( {\Delta + \gamma } \right)r_{a}^{a} $$

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$$ R_{{{\text{bs}}}} = \left( {\Delta + \gamma } \right)r_{a}^{{{\text{bs}}}} + {\gamma r}_{s}^{{{\text{bs}}}} $$

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where r_a^c = aerodynamic resistance of the olive tree (s m⁻¹) from the leaf surface to the mean surface flow height (z_m); r_a^a = aerodynamic resistance (s m⁻¹) between z_m and z_r; r_a^bs = aerodynamic resistance (s m⁻¹) of the bare soil surface between the rows and z_m; r_a^s = aerodynamic resistance (s m⁻¹) between the soil under the olive tree canopy and z_m; r_s^c = canopy resistance (s m⁻¹); r_s^s = soil surface resistance under the olive tree canopy (s m⁻¹); and r_s^bs = soil surface resistance between the rows (s m⁻¹).Also, the submodels r_b, r_a^a, r_s^a, and r_a^bs were calculated using following equations:

$$ r_{b} = \left( {\frac{\eta }{a}} \right)\left( {\frac{w}{{u_{h} }}} \right)^{0.5} \left( {1 - e^{{{\raise0.7ex\hbox{${ - n}$} \!\mathord{\left/ {\vphantom {{ - n} 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}} } \right)^{ - 1} $$

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$$ u_{h} = \left( {\frac{{u^{*} }}{k}} \right)\ln \left( {\frac{h - d}{{z_{o} }}} \right) $$

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$$ u^{*} = \mathop{\longrightarrow}\limits^[{\ln \left[ {\frac{{z_{r} - d}}{{z_{o} }}} \right]}]{{ku_{r} }} $$

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$$ z_{o} = z^{\prime }_{o} + 0.3h\left( {c_{d} {\text{LAI}}} \right)^{0.5} $$

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where r_b = mean boundary layer resistance (s m⁻¹); a = constant value (Choudhury and Monteith 1988); w = average leaf width (m); u_h = wind speed at the top of the canopy average height (m s⁻¹); n = eddy diffusivity decay coefficient (dimensionless); η = attenuation coefficient for wind speed (dimensionless); k = von Karman’s constant (dimensionless); h = height of the olive canopy (m); d = displacement height (m); z_o = roughness length (m); u* = friction velocity (m s⁻¹); u_r = wind speed at z_r (m s⁻¹); c_d = drag coefficient (dimensionless); z_o = roughness length of the bare soil (m).

Later, r_a^a and r_s^a were estimated using the following expressions:

$$ r_{a}^{a} = \left( {\frac{1}{{ku^{*} }}} \right)\ln \left( {\frac{{z_{r} - d}}{h - d}} \right) + \left( {\frac{h}{{nK_{h} }}} \right)\left( {e^{{n\left( {1 - \frac{{\left( {Z_{0} + d_{p} } \right)}}{h}} \right)}} - 1} \right) $$

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$$ r_{a}^{s} = \left( {\frac{{he^{n} }}{{nK_{h} }}} \right)\left( {e^{{\left( {\frac{{ - nz^{\prime}_{0} }}{h}} \right)}} - e^{{\left( {\frac{{ - n(Z_{0} + d_{p} }}{h}} \right)}} } \right) $$

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$$ K_{h} = {\text{ku*}}\left( {h - d} \right) $$

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where K_h = diffusivity at the top of the canopy (m² s⁻¹); Z₀ is the zero-roughness length of the surface (m); d_p = zero-plane displacement height (m).

Meanwhile, assuming a linear variation between r_a^b and r_a^s_, the aerodynamic resistance between the bare soil surface and z_m (r_a^bs) was calculated according to Brenner and Incoll (1997) and Villagarcía et al. (2007):

$$ r_{a}^{{{\text{bs}}}} = f_{c} \cdot {\text{r}}_{a}^{s} + \left( {1 - f_{c} } \right)r_{a}^{b} $$

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$$ r_{a}^{b} = \frac{{\ln \left( {\frac{{z_{m} }}{{z\prime_{0} }}} \right)^{2} }}{{k^{2} u_{m} }} $$

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where u_m = wind speed at z_m (m s⁻¹).