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SEBAL - Dca.ufcg.edu.br

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4. The aerodynamic resistance to heat transport (r ah ) is computed in model F12 as is u * instep 3. A series of iterations is required to determine the value for r ah for each period thatconsiders the impacts of instability (i.e., buoyancy) on r ah and H. Assuming neutralatmospheric conditions, an initial r ah is computed using Equation (26). z 1 is the height justabove the zero plane displacement (d ≅ 0.67 × height of vegetation) for the surface orcrop canopy and z 2 is some distance above the zero plane displacement, but below theheight of the surface boundary layer. Based on experienced analysis, values of 0.1 meterfor z 1 and 2.0 meters for z 2 are assigned. Steps 3 and 4 are completed by running modelF12 to compute initial values of u * and r ah . The file for z om from model F11 is input alongwith u 200 , which was calculated above with equation (29). Save the output files and themodel 5 .5. To compute the sensible heat flux (H) from Equation (25), the near surfacetemperature difference (dT) for each pixel needs to be defined. This is given asdT = T z1 – T z2 . The air temperature at each pixel is unknown, along with explicit valuesfor T z1 and T z2 . Therefore, only the difference dT is utilized. <strong>SEBAL</strong> computes dT foreach pixel by assuming a linear relationship between dT and T s :dT = b + aT s (32)where; b and a are the correlation coefficients. To define these coefficients, <strong>SEBAL</strong>uses the two “anchor” pixels where a value for H can be reliably estimated. Values for Hand dT at these “anchor” pixels are computed in a spreadsheet format as explained inAppendix 8 and in the following steps. The linearity of the dT vs. T s function is a majorpresumption of <strong>SEBAL</strong>. However, research by Bastiaanssen and others and by theUniversity of Idaho at Kimberly, indicate that this assumption appears to fit a large rangeof conditions.a) At the “cold” pixel, we define the sensible heat flux as H cold = R n – G - λET coldfrom Equation (23). Experience in Idaho shows that the most “cold” (wet)agricultural fields have an ET rate about 5% larger than the reference ET (ET r ).Hence, ET cold is assumed to be 1.05 × ET r (which was calculated earlier in the<strong>SEBAL</strong> process, Appendix 3). H cold is now calculated in the spreadsheet as:H cold = R n – G – 1.05λET r . dT cold is computed in the spreadsheet using theinverse of Equation (25):dT cold = H cold × r ah_cold / (ρ cold × c p ) (33)5 Note that because dT is defined as ∆T between z 1 and z 2 , the estimate of T air as T air = T s + dT is not areal, representation of air temperature. This is because the T at z 1 is generally somewhat less than T s . Inaddition, T s is a radiometrically derived surface temperature, whereas T at z 1 is an aerodynamicallyrepresentative temperature.30

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